NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

On the Use of Coupled Wind, 

Wave, and Current Fields in the 

Simulation of Loads on BottomSupported Offshore Wind 

Turbines during Hurricanes

March 2012 — September 2015

Eungsoo Kim and Lance Manuel 

University of Texas at Austin

Austin, Texas

Milan Curcic and Shuyi S. Chen

University of Miami 

Coral Gables, Florida

Caleb Phillips and Paul Veers 

National Renewable Energy Laboratory

Golden, Colorado

NREL Technical Monitor: Paul Veers

Technical Report

NREL/TP-5000-65283

June 2016
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

On the Use of Coupled Wind, 

Wave, and Current Fields in 

the Simulation of Loads on 

Bottom-Supported Offshore 

Wind Turbines during 

Hurricanes

March 2012 — September 2015

Eungsoo Kim and Lance Manuel 

University of Texas at Austin

Austin, Texas

Milan Curcic and Shuyi S. Chen 

University of Miami 

Coral Gables, Florida

Caleb Phillips and Paul Veers 

National Renewable Energy Laboratory

Golden, Colorado

NREL Technical Monitor: Paul Veers

Technical Report

NREL/TP-5000-65283

June 2016
This publication was reproduced from the best available copy

submitted by the subcontractor and received little editorial review at NREL.

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Cover Photos by Dennis Schroeder: (left to right) NREL 26173, NREL 18302, NREL 19758, NREL 29642, NREL 19795.

NREL prints on paper that contains recycled content. 
Acknowledgments

The authors wish to acknowledge the assistance received from project collaborators including 

Mr. John Michalakes, previously a staff member at the National Renewable Energy Laboratory 

where he initiated the project summarized in this report, and now at the National Oceanic and 

Atmospheric Administration. John’s leadership was essential in formulating the team and setting 

the direction for this work. We also acknowledge substantial assistance from Dr. Mark Donelan, 

of the University of Miami’s Rosenstiel School of Marine and Atmospheric Science. Mark was a 

tireless and insightful collaborator on the wave dynamics simulation and helped interpret the 

results for use in the loads simulation. 

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-

08GO28308 with the National Renewable Energy Laboratory. Funding for the work was 

provided by the DOE Office of Energy Efficiency and Renewable Energy, Wind and Water 

Power Technologies Office. 

1

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1 Overview

In the United States, potential offshore wind plant sites have been identified along the Atlantic 

seaboard and in the Gulf of Mexico. It is imperative that we define external conditions associated 

with hurricanes and severe winter storms and consider load cases for which wind turbines may 

need to be designed. We selected two hurricanes, Ike (2008) and Sandy (2012), and investigated 

the effect these tropical storms would have on bottom-supported offshore wind turbines that 

were hypothetically in or close to their path as they made landfall. For realistic turbine loads 

assessment, it is important that the coupled influences of the changing wind, wave, and current 

fields are simulated throughout the evolution of the hurricanes. We employed a coupled model—

specifically, the University of Miami Coupled Model (UMCM)—that integrates atmospheric, 

wave, and ocean components to produce needed wind, wave, and current data. The wind data are 

used to generate appropriate vertical wind profiles and full wind velocity fields including 

turbulence; the current field over the water column is obtained by interpolated discrete output 

current data; and short-crested irregular second-order waves are simulated using output 

directional wave spectra from the coupled model. 

We studied two monopile-supported offshore wind turbines sited in 20 meters of water in the 

Gulf of Mexico to estimate loads during Hurricane Ike, and a jacket space-frame platformsupported offshore wind turbine sited in 50 meters of water in the mid-Atlantic region to 

estimate loads during Hurricane Sandy. In this report we discuss in detail how the simulated 

hurricane wind, wave, and current output data are used in turbine loads studies. In addition,

important characteristics of the external conditions are studied, including the relative importance 

of swell versus wind seas, aerodynamic versus hydrodynamic forces, current velocity effects, 

yaw control options for the turbine, hydrodynamic drag versus inertia forces, and soil-structure 

interaction effects. A detailed framework is presented that explains how coupled inputs can be 

included in turbine loads studies during a hurricane. This framework can aid in future efforts 

aimed at developing offshore wind turbine design criteria and load cases related to hurricanes. 

The UMCM was created by the University of Miami for this project and was essential in

producing simultaneous wind and wave conditions during all aspects of the hurricane, especially 

as it approached and passed through areas of potential offshore wind plant development. 

Appendix A includes a description of the scope and nature of the UMCM and details the 

modeling capabilities that it possesses. Some example outputs provide a visualization of the 

kinds of data that are generated. The results for each of the two selected hurricanes (Ike and 

Sandy) are also detailed. The University of Miami team used extensive buoy data from both 

storms to validate the UMCM capabilities, some extracts of which are shown here. More 

documentation of model validation can be found in the References section. 

Appendix B describes how users can access this extensive data set of wind and wave conditions 

for both Hurricane Ike and Hurricane Sandy at user-specified potential development sites. The 

data have been housed at the National Renewable Energy Laboratory for future use, and software 

hooks have been created to enable users to extract time series of interest from the more than two

Tera-byte data set. Examples time series from the Hurricane Ike and Hurricane Sandy data are 

plotted to illustrate the types of the data that can be extracted.

2

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2 Modeling Hurricane Ike’s Influence on a Monopile-Supported Offshore Wind Turbine

2.1 Problem description

Over a 5-day period in the evolution of Hurricane Ike (2008) prior to landfall, the response of a monopile-supported

5-MW offshore wind turbine is evaluated in a step-wise procedure. As sites for the turbines to be analyzed, we select

locations 60 km to the right and left of the track of Ike, points A and B, respectively, as shown in Fig. 2.1, where the

water depth is 20 meters.

−100 −95 −90 −85 −80 −75 −70

15

20

25

30

35

Longitude

Latitude

Hurricane Ike Track

B

A

A : 60km right of track

B : 60km left of track

15:00 UTC 2008−09−12

Figure 2.1. Track of Hurricane Ike and selected locations of two sites, one to

the left and the other to the right of the track where the water depth is 20 m.

Based on output from UMCM, coupled wind and wave fields at the two selected locations are simulated and

we evaluate the turbine response on a 5-MW offshore wind turbine over a period of the storm’s evolution when it

is close to landfall. We present the theoretical background and formulation for directional second-order nonlinear

irregular wave modeling and outline a procedure for numerical simulation of the sea surface elevation and associated

wave kinematics. We also present characteristics of the hurricane wind fields and show how a spectral method

is adopted to simulate these hurricane turbulent wind fields. Finally, we investigate how yaw and pitch controls

influence the response of the selected offshore wind turbine during a hurricane.

3

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2.2 Hurricane Waves

In this study, hurricane-generated wave kinematics are simulated based on directional wave spectra resulting from

the UMCM output; the model was initialized at 12:00 UTC on September 9, 2008. A wave spectrum from the

UMCM output consists of 36 directional bins and 37 frequency bins covering a range from 0.03 Hz to 2 Hz, over

which the discrete frequencies are logarithmically spaced. As an illustration of the development of wave inputs for

turbine loads analysis, we present in Fig. 2.2 normalized directional wave spectra with significant wave height (Hs)

obtained from UMCM that apply to the two selected site A and B; these spectra are for 80 to 120 hours after the

start of the simulation (with updates shown every 10 hours). Red and blue arrows in these spectra represent the mean

wind and wave direction, respectively. Also, in these wave spectra, N describe waves propagating toward north, etc.,

and the dashed circles and the solid circle (inner to outer) correspond to wave frequencies of 0.1, 0.2, 0.3, and 0.4

Hz. In these wave spectra plots, we see that directional spreading of wave energy is significant and that the wave

spectrum, before passing the sites, has two well-separated peaks. Although the wave energy at high frequencies is

closely linked to the wind field and the mean wave direction is dominated by the low-frequency wave component;

this low-frequency wave component is classified as swell which contributes significantly to the total wave energy at

the two sites.

2.2.1 Wave simulation theory

It is common practice to model the irregular sea surface elevation process as a Gaussian random process using

linear Airy wave theory. However, to generate realistic hurricane wave fields, it is essential to account for both

wave directionality and nonlinearity. In this study, directionality and nonlinearity of the waves are accounted for by

employing directional irregular second-order wave formulations proposed by Sharma and Dean [1] for finite water

depths. This second-order wave modeling formulation is an extension of the theory developed by Longuet-Higgins

et al. [2] for waters of infinite depth to apply to waters of arbitrary finite depth. A nonlinear boundary value problem

is solved up to second order by a perturbation approach accounting for contributions from linear components from

arbitrary frequencies and directions. The second-order wave system is one that is forced by the linear system and all

information on second-order amplitudes and phases is related to the characteristics of the first-order spectrum.

2.2.1.1 Boundary value problem formulation

If the effects of viscosity and turbulence can be regarded as small, incompressible flows can be described well by a

velocity potential. In other words, the velocity components u, v, and w, can be defined in terms of the gradients of the

velocity potential, φ, given in terms of the three Cartesian directions, x, y, and z.

(u,v,w) = 

∂φ

∂x

,

∂φ

∂y

,

∂φ

∂z



(2.1)

The mass conservation equation for an incompressible fluid is

∂u

∂x

+

∂v

∂y

+

∂w

∂z

= 0 (2.2)

which can be combined with Eq. 2.1 to yield

∇

2

φ =

∂

2φ

∂x

2

+

∂

2φ

∂y

2

+

∂

2φ

∂z

2

= 0 (2.3)

where −h ≤ z ≤ η and −∞ ≤ x,y ≤ ∞

Sharma and Dean proposed a second-order velocity potential function that satisfies the appropriate boundary

conditions for the problem.

4

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H N

s

= 1.5 m

0 0.5 1

H N

s

= 1.6 m

0 0.5 1

H N

s

= 3.2 m

0 0.5 1

H N

s

= 3.6 m

0 0.5 1

H N

s

= 5.0 m

0 0.5 1

H N

s

= 7.2 m

0 0.5 1

H N

s

= 4.5 m

0 0.5 1

H N

s

= 8.3 m

0 0.5 1

H N

s

= 4.3 m

0 0.5 1

H N

s

= 4.8 m

0 0.5 1

h = 80

h = 90

h = 100

h = 110

h = 120

Site B Site A



	











Figure 2.2. Wave spectra for Sites A and B from over a 40-hour period during Hurricane Ike; N describe

waves propagating toward north, etc., and the dashed circles and the solid circle (inner to outer) correspond

to wave frequencies of 0.1, 0.2, 0.3, and 0.4 Hz. (blue arrow: wave direction; red arrow: wind direction).

5

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• Bottom Boundary Condition (BBC)

At the bottom boundary, the velocity normal to the boundary is equal to zero. For this case of a horizontal

boundary at depth, h, we have:

∂φ

∂z









z=−h

= 0 (2.4)

• Kinematic Free Surface Boundary Condition (KFSBC)

A water particle on the free surface remains on the free surface and the vertical velocity at the free surface is

equal to the total rate of change of the sea surface elevation:

∂η

∂t

+

∂φ

∂x

∂η

∂x

+

∂φ

∂y

∂η

∂y

=

∂φ

∂z

(2.5)

where z = η.

• Dynamic Free Surface Boundary Conditions (DFSBC)

The pressure, p, follows from Bernoulli’s equation:

p

ρ

+gz+

∂φ

∂t

+

1

2

∇φ · ∇φ = −Q(t) (2.6)

where Q(t) is an arbitrary function of time. Instead of including the variation with time of Q in the velocity potential,

φ, let Q be a constant. At the free surface, z = η, the pressure is equal to the atmospheric pressure, patm and if we

choose Q = −patm/ρ in Eq.2.6, we can rewrite the equation as follows [3]:

⇒ gη +

∂φ

∂t

+

1

2

∇φ · ∇φ = 0 (2.7)

• Combined Free Surface Boundary Condition (CFSBC)

We can write an alternative form of Eqs. 2.5 and 2.7 above, by eliminating the unknown free surface elevation

η. This then involves only φ and its derivatives:

−

∂

2φ

∂t

2

−g

∂φ

∂z

−(

∂

∂t

+

1

2

∇φ · ∇)|∇φ|

2 = 0 (2.8)

where z = η

2.2.1.2 Solution of the boundary value problem

A perturbation approach is adopted for solution of the boundary value problem formulated in the previous section.

This approach assumes that all variables can be expanded as a convergent power series of a small parameter, such

as the wave steepness. Also, it is assumed that the combined free surface boundary condition (CFSBC) can be

expanded in a convergent Maclaurin series about the mean water level, z = 0, in terms of the small parameter.

The velocity potential, φ, and sea surface elevation, η, may be represented in the following manner using wave

steepness, ε, as the perturbation parameter:

φ(x,y,z,t) = φ

(1)

(x,y,z,t) +φ

(2)

(x,y,z,t) +... (2.9)

η(x,y,t) = η

(1)

(x,y,t) +η

(2)

(x,y,t) +... (2.10)

where η

(i)

and φ

(i)

(where i=1,2) is proportional to ε

i or O(εi

). By substituting the perturbation expansions for

φ and η into the Laplace equation (Eq. 2.3) and the bottom boundary condition (Eq. 2.4), we obtain two separate

boundary conditions as follows:

6

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∇

2

φ

(1) = 0; ∇2

φ

(2) = 0 (2.11)

∂φ

(1)

∂z











z=−h

= 0; ∂φ

(2)

∂z











z=−h

= 0 (2.12)

We also have:

∂

2φ(1)

∂t

2

+g

∂φ

(1)

∂z

= 0 (2.13)

∂

2φ(2)

∂t

2

+g

∂φ

(2)

∂z

= −

∂

∂t







∇φ

(2)







2

−η

(1)

∂

∂t

"

∂

2φ(1)

∂t

2

+g

∂φ

(1)

∂z

#

(2.14)

η

(1) = −

1

g

∂φ

(1)

∂t

(2.15)

η

(2) = −

1

g

 

∂φ

(2)

∂t

+

1

2

|∇φ

(1)

|

2

!

−

1

g

η

(1)

∂

2φ(1)

∂z∂t

(2.16)

where z = 0.

• First-Order Solution

We select a first-order velocity potential, φ

(1) of the following form which satisfies 2.11, 2.12, and 2.13:

φ

(1)

(~x,z,t) = (−1)

N

∑

i=1

M

∑

m=1

g

ωi

aim

cosh[|~ki|(h+z)]

cosh(|

~ki

|h)

·sin(ωi

t −~kim ·~x+εim)

(2.17)

⇒ φ

(1)

(~x,z,t) = Re[

N

∑

i=1

M

∑

m=1

ι

g

ωi

Aim

cosh[|

~ki

|(h+z)]

cosh(|

~kim|h)

· exp(ιωit)

· exp(−ι(

~kim ·~x)]

(2.18)

where Aim = aim exp(−ιεim); ~x = (x,y) is a point on the horizontal x-y plane; ωi

is the angular frequency; ~kiis the

wave number which is related to the frequency, ωi, through the linear dispersion relation, ω

2

i = g|

~ki

|tanh(|

~ki

|h)

(where h is the water depth); ι =

√

−1 and~kim =



|

~ki

|cosθm,|

~ki

|sinθm



; N and M are the total number of frequencies and the total number of wave directions considered, respectively. Also, aim refers to the component spectral

amplitudes, which are calculated as follows:

E



a

2

im

2



= S(ωi

,θm)∆ω∆θ (2.19)

where, E [•] is the expected value of •.

By substituting Eq. 2.17 into Eq. 2.15, we obtain the first-order component of the surface wave elevation, η

(1)

,

as follows:

7

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η

(1)

(~x,t) =

N

∑

i=1

M

∑

m=1

aimcos(ωit −~kim ·~x+εim) (2.20)

⇒ η

(1)

(~x,t) = Re[

N

∑

i=1

M

∑

m=1

Aim · exp(ιωi

t)

· exp(−ι(~kim ·~x)]

(2.21)

• Second-Order Solution

Second-order waves are obtained as a result of sum and difference interactions between pairs of frequencies and

the phases of the second-order contributions are determined by the sum and difference interactions of the phases of

the first-order component phases, which are random. The second-order velocity potential which satisfies Eqs. 2.11,

2.12, and 2.14 is given as follows:

φ

(2)

(~x,z,t) = (−1)·

N

∑

i, j=1

M

∑

m,n=1

aimajn ·B

±

i jmn ·sin((ωi ±ωj)t

−(

~kim ·~x±~kjn ·~x) + (εim ±ε jn))

(2.22)

⇒ φ

(2)

(~x,z,t) = Re[

N

∑

i, j=1

M

∑

m,n=1

ιAimAjn ·B

±

i jmn · exp(ι(ωi ±ωj)t)

· exp(−ι(

~kim ·~x±~kjn ·~x))

(2.23)

By employing the first-order potential, φ

(1)

, the first-order surface elevation. η

(1)

, and the second-order potential, φ

(2)

, in Eq. 2.16, we obtain a second-order correction to the linear sea surface elevation as follows:

η

(2)

(~x,t) =

N

∑

i, j=1

M

∑

m,n=1

aimajn ·K

±

i jmn · cos((ωi ±ωj)t

−(~kim ·~x±~kjn ·~x) + (εim ±ε jn))

(2.24)

⇒ η

(2)

(~x,t) = Re[

N

∑

i, j=1

M

∑

m,n=1

AimAjn ·K

±

i jmn · exp(ι(ωi ±ωj)t)

· exp(−ι(~kim ·~x±~kjn ·~x))

(2.25)

Quadratic transfer functions (QTF), K

±

i jmn and B

±

i jmn, derived by Sharma and Dean [1] are given as follows:

K

±

i jmn =

1

4

"

D

±

i jmn −(kikjcos(θm −θn)∓RiRj)

p

RiRj

+ (Ri +Rj)

#

(2.26)

B

±

i jmn =

1

4

cos[k

±

i jmn

(h+z)]

cos[k

±

i jmn(h)]

D

±

i jmn

ωi ±ωj

(2.27)

8

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where

Ri = |

~ki

|tanh(|

~ki

|h) (2.28)

D

±

i jmn =

(

√

Ri ±

p

Rj)[pRj(ki

2 −Ri

2

)±

√

Ri(kj

2 −Rj

2

)]

[(√Ri ±

p

Rj)

2 −k

±

i jmntanh(k

±

i jmnh)]

+

[2(

√

Ri ±

p

Rj)

2

][kikjcos(θm −θn)∓RiRj]

[(√Ri ±

p

Rj)

2 −k

±

i jmntanh(k

±

i jmnh)]

(2.29)

In the above, k

+

i jmn and k

−

i jmn are given as follows :

k

+

i jmn =

q

ki

2 +kj2 +2kikjcos(θm −θn)

k

−

i jmn =

q

ki

2 +kj2 −2kikjcos(θm −θn)

(2.30)

For infinite water depth, the equations proposed by Sharma and Dean [1] reduce to those derived by LonguetHiggins et al. [2] for deep water. Also, for~ki =~kj and N = 1, the formulas for the velocity potential and surface

elevation reduce to the familiar Stokes second-order equations [4].

• Validity of Second-Order Wave Theory

While the second-order irregular wave modeling outlined above is a more accurate representation of irregular

seas in shallow waters compared to the linear irregular wave model, it obviously does not model the complete nonlinear characteristics of ocean waves and is not valid for all cases. The physical parameter that determines the range of

validity is the wave steepness. When the wave steepness exceeds a certain value, the second-order model is no longer

valid and a higher-order model is then required. In fact, when waves become too steep, they can break and no model

based on solution of Laplace’s equation (given in terms of velocity potential) is valid.

2.2.2 Second-order wave kinematics

Second-order wave kinematics are evaluated using the wave velocity potentials presented in Sec. 2.2.1.2. It is assumed that the considered fluid is incompressible, inviscid, and irrotational.

2.2.2.1 Water particle velocity

The velocity field of the irrotational fluid can be expressed as follows:

~u = ∇φ (2.31)

~u

(1) = (u

(1)

x ,u

(1)

y ,u

(1)

z ) = ∇φ

(1) =

 

∂φ

(1)

∂x

,

∂φ

(1)

∂y

,

∂φ

(1)

∂z

!

(2.32)

~u

(2) = (u

(2)

x ,u

(2)

y ,u

(2)

z ) = ∇φ

(2) =

 

∂φ

(2)

∂x

,

∂φ

(2)

∂y

,

∂φ

(2)

∂z

!

(2.33)

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2.2.2.2 Water particle acceleration

The acceleration of a water particle can be evaluated by the material or substantial derivative of the velocity vector,

~u:

D

Dt

~u =

∂~u

∂t

|{z}

Term1

+~u · ∇~u

| {z }

Term2

(2.34)

where Term 1 and Term 2 are the local acceleration at a fixed point and the convective acceleration, respectively.

We are only interested in the acceleration at a fixed point, which is evaluated as follows:

~a

(1) = (a

(1)

x ,a

(1)

y ,a

(1)

z ) = ∂~u

(1)

∂t

=

 

∂u

(1)

x

∂t

,

∂u

(1)

y

∂t

,

∂u

(1)

z

∂t

!

(2.35)

~a

(2) = (a

(2)

x ,a

(2)

y ,a

(2)

z ) = ∂~u

(2)

∂t

=

 

∂u

(2)

x

∂t

,

∂u

(2)

y

∂t

,

∂u

(2)

z

∂t

!

(2.36)

2.2.2.3 Dynamic pressure

To obtain the first- and second-order pressure, we substitute the perturbation expansions of the velocity potential into

Bernoulli’s equation (Eq. 2.6) and separate terms of the same order:

p

ρ

+gz+

∂

∂t

(φ

(1) +φ(2) +...) + 1

2

∇(φ

(1) +φ(2) +...)· ∇(φ(1) +φ(2) +...) = −Q (2.37)

p

ρ

= −gz−Q+

"

∂φ

(1)

∂t

#

| {z }

O(ε)

+

"

∂φ

(2)

∂t

+

1

2

∇φ

(1)

· ∇φ

(1)

#

| {z }

O(ε

2)

+O(ε

3

) +... (2.38)

Thus, the first- and second-order dynamic pressures, p

(1)

d

and p

(2)

d

, are obtained as follows [5] [6]:

p

(1)

d = −ρ

∂φ

(1)

∂t

(2.39)

p

(2)

d = −ρ

"

∂φ

(2)

∂t

+

1

2

∇φ

(1)

· ∇φ

(1)

#

= −ρ

"

∂φ

(2)

∂t

#

| {z }

Term1

−ρ



1

2

~u

(1)

·~u

(1)



| {z }

Term2

(2.40)

where Term 1 and Term 2 are the second-order potential term and the quadratic interaction term, respectively.

The second-order dynamic pressure in this study is evaluated by only including the contribution of the second-order

potential term, Term 1.

2.2.3 Numerical simulation of second-order waves

In this section, the criteria and algorithms used to numerically simulate irregular second-order wave are presented.

First, we discuss the issue of validity of the second-order wave theory that was briefly raised in Sec. 2.2.1.2.

10

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2.2.3.1 Limitation of Second-Order Wave Theory and Cut-Off Frequency

The solution of the second-order boundary value problem is derived based on a perturbation approach, which uses

wave steepness, ε ≪ 1 as an expansion parameter. For a regular wave, Dean and Dalrymple [7] defined ε = ka/2,

where k and a are the wavenumber and wave amplitude, respectively. According to them, the second-order wave

theory is valid if two criteria are fulfilled:

• Convergence: First, the ratio of the second-order term to the first order term in Eq. 2.9 must be much smaller

than unity:

ε

2φ(2)

εφ

(1)

=

kaφ

(2)

2φ

(1) ≪ 1 (2.41)

⇒

3

8

kacosh(2kh)

cosh(kh)sinh3(kh)

≪ 1 (2.42)

• No bump in the trough: Second, the physical properties of the wave profile require that there is no bump in

the trough. This is indicated by a negative second derivative of the wave trough, which leads to the criterion:

ka <

sinh3(kh)

cosh(kh)[2+cosh(2kh)] (2.43)

In addition to the above two criteria, the breaking criterion for the wave steepness must be fulfilled. For arbitrary water depth, the Miche breaking criterion is as follows [8]:

H

L

=

2a

2π/k

< 0.142tanh(kh) (2.44)

⇒ ka < 0.142π tanh(kh) (2.45)

Figure 2.3 illustrates the different limiting criteria expressed for ka as a function of kh. The shaded region in

Fig. 2.3 represents wave steepness conditions for which second-order wave theory is valid. According to the figure,

we note (except when kh → 0) that:

• when kh < 0.62π, the maximum wave steepness is restricted by the “no bump in the trough” criterion in

Eq. 2.43.

• when kh > 0.62π, the maximum wave steepness is restricted by the breaking wave criterion in Eq. 2.45.

In the regular wave case, the validity of the second-order wave theory can be controlled by simply limiting

the considered maximum wavenumber in order to satisfy the three criteria (see Eqs. 2.42, 2.43, and 2.45). However, because these criteria were derived for regular waves, they may not be directly extended for use with irregular

wave. The following three criteria can be used to arrive at the maximum wave frequency for valid application of the

second-order wave theory:

• Hu and Zhao [9]: Based on results from numerical simulations, Hu and Zhao [9] suggested that the secondorder wave model presented here is valid as long as Hs/Lz

is less than approximately 0.08, where Hsis the

significant wave height and Lzis the wavelength corresponding to the zero-crossing frequency, ωz =

p

γ2/γ0,

where γn is given by

γn =

Z

ω

n

S(ω)dω (2.46)

• Stansberg [10]: Stansberg [10] proposed a useful criterion to establish the highest frequency for which

second-order wave theory may be considered valid. It is given in terms of a cut-off wavenumber as follows:

kcut =

2

E(amax)[1+1/2(kpE(amax))] (2.47)

11

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0

0.1

0.2

0.3

0.4

0.5

kh

ka

Convergence

No bump

Breaking wave

࣊ ࣊૛૟ Ǥ ૙࣊૚ Ǥ૙

kh 

shallow Intermediate depth deep

Figure 2.3. Different limiting criteria for wave steepness, ka, as a

function of normalized water depth, kh, for second-order waves

where kcut is related to the limiting (cut-off) frequency, ωcut , through the linear dispersion relation and kp is the

wavenumber corresponding to the spectral peak period, Tp; E(amax) is the expected value of the extreme wave

amplitude of a Gaussian wave record, which follows a Rayleigh distribution. The denominator in Eq. 2.47 is a

simplified second-order correction for a non-Gaussian wave field. According to extreme value theory, E(amax)

is given as follows:

E(amax) = Hs

4

[

p

2ln(Nz) + p

γem

2ln(Nz)

] (2.48)

Nz =

tmax

Tz

(2.49)

where γem = 0.577... is the Euler-Mascheroni constant; Nz

is the number of zero-upcrossing wave cycles and

tmax is the duration of the simulation.

• DNV-RP-C205 [11]: DNV-RP-C205 [11] guidelines provide a simpler criterion for the application of secondorder wave theory by defining a limiting cut-off frequency as follows:

ωcut =

r

2g

Hs

(2.50)

For irregular waves, the validity of the use of second-order wave theory is significantly affected by the spectral

or statistical properties of the considered irregular waves such as the peak wave period (Tp), the significant wave

height (Hs), and the duration of the simulations (tmax), which influence the limiting criteria. During a numerical

simulation of the second-order wave kinematics, therefore, the maximum wave frequency arbitrarily assigned without considering the spectral properties of the irregular waves may result in the generation of physically incorrect

12

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second-order wave kinematics. In this study, the criterion proposed by Stansberg [10] is employed to simulate the

second-order sea surface elevation and associated wave kinematics.

2.2.3.2 Sampling Theorem and Additional Requirement of Cut-Off Frequency, ωcut

In digital simulation of the sea surface elevation and associated kinematics, we replace continuous time, t, by a

discrete time array, tp = p∆t, where ∆t = tmax/Nt, such that p = 1,2,...,Nt. By virtue of the periodicity of Fourier

series, we have

∆ω =

2π

tmax

(2.51)

Consideration of the Nyquist frequency provides a prescription for the nominal sampling interval required to

avoid aliasing. This may be stated simply as follows:

• The sampling frequency, ωs = 2π/∆t, should be at least twice the highest frequency contained in the signal.

In mathematical terms, we have:

ωs ≥ 2ωcut (2.52)

If ωcut = Nω∆ω, we must then satisfy the following inequality:



ωs =

2π

∆t

=

2π

tmax/Nt



≥



2ωcut = 2Nω∆ω = 2Nω

2π

tmax 

(2.53)

⇒ Nt ≥ 2Nω (2.54)

In the numerical simulation of second-order wave kinematics, the largest frequency of wave components generated by the second-order wave-wave interaction is 2Nω∆ω, which is associated with the sum-frequency interaction.

Therefore, to satisfy the sampling theorem for second-order wave simulation, we must ensure that:

Nt ≥ 4Nω (2.55)

This simply means that the cut-off frequency, ωcut , evaluated by the criterion presented in Sec. 2.2.3.1 must

satisfy:

h

Nt =

tmax

∆t

i

≥



4Nω = 4

ωcut

∆ω

= 4

ωcut

2π/tmax 

(2.56)

⇒ ωcut ≤

π

2∆t

(2.57)

2.2.3.3 Singularity of Quadratic Transfer Function (QTF)

Formulations for the first- and second-order wave kinematics shown in previous sections are determined from the

solution of the boundary value problem (see Eqs. 2.3 - 2.8). When we implement these formulations to numerically

simulate wave kinematics, some problems arise that stem from the physically correct or weakly-correct assumptions

considered in solution of the boundary value problem. One of the issues has to do with the singularity of the firstand second-order wave kinematics transfer functions. This singularity problem is also seen in QTFs proposed by

other researchers (Longuet-Higgins [2]; Marthinsen and Winterstein [12]; Nwogu [13]) presented below.

QTF proposed by Longuet-Higgins [2]

B

±

i j =

g

2

ωiωj

(ωi ±ωj)(~ki

· ~kj ∓ |~ki||~kj|)

(ωi ±ωj)

2 −g|

~ki ±~kj

|

(2.58)

13

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QTF used by Marthinsen and Winterstein [12]

B

±

i j = (1−δi, j)

g

2

ωiωj

g

2

|~ki||k~

j

|

2ωiωj

−

1

4

(ω

2

i +ω

2

j ±ωiωj) + g

2

4

ωi

|~kj|

2±ωj

|~ki|

2

ωiωj(ωi±ωj)

(ωi ±ωj)−g

|~ki|±|k~

j

|

ωi±ωj

tanh[(|~ki| ± |~kj|)h]

(2.59)

where δi, j = 1 if i = j and zero otherwise. This is introduced to avoid the singularity of B

±

i j.

QTF proposed by Nwogu [13]

K

±

i j =

ωiωj(k

±

i jh)

2

cos(θi −θj)[1−(α +1/3)(k

±

i jh)

2

]

2λk

′

i

k

′

j

h

3

+

ω

±

i j [1−α(k

±

i jh)

2

][ωik

′

j

h(|

~ki

|h± |~kj|hcos(θi −θj))

2λk

′

i

k

′

j

h

3

+

ωjk

′

i

h(|~ki|hcos(θi −θj)± |~kj|h)]

2λk

′

i

k

′

j

h

3

(2.60)

λ = (ω

±

i j)

2

[1−α(k

±

i jh)

2

]−g(k

±

i j)

2

h[1−(α +1/3)(k

±

i jh)

2

] (2.61)

k

′

i = |~ki

|[1−(α +1/3)(|~ki

|h)

2

(2.62)

where α = (zα/h)

2/2+ (zα/h) and zα ≈ −0.53h from shallow water depths up to the deep water depth limit.

• Singularity at ω = 0

When ωiin Eq. 2.17 approaches zero, the denominator of the equation approaches zero. Although the numerator also approaches zero, we may have computational difficulties and special treatment may be required during

numerical simulation of the kinematics depending on the software tool used. To avoid discontinuity or singularity

problems at zero frequency, one can simply set the kinematics equal to zero there and not attempt evaluation.

QTFs of the second-order wave elevation and the velocity potential, i.e., K

±

i jmn and B

±

i jmn, also have similar

singularity issues at zero frequency. As shown in Eq. 2.26, the denominator of the first term in the expression for

K

±

i jmn is p

RiRj, which approaches zero when either ωi or ωj approaches zero.

In the numerator of the expression for B

±

i jmn in Eq. 2.27, the term, D

±

i jmn, appears that is defined in Eq. 2.29. The

numerator in both the first and second terms in the expression for D

±

i jmn approaches zero when either ωi or ωj goes to

zero. In this case, there is no need for any special treatment during numerical simulation because the denominator of

B

±

i

jmn is not zero unless ωi = ωj = 0.

Based on the possibility of singularities in the first- and second-order transfer functions, we assume that the

formulations presented in Sec. 2.2.1.2 are not used to evaluate first- and second-order wave kinematics when ωi = 0

or ωj = 0. This assumption is physically acceptable because we are assuming that a zero-frequency regular wave

does not have any wave energy and that the zero-energy wave component does not interact with any other wave

components.

• Singularity at diagonal components of K

−

i jmn and B

−

i jmn

Another singularity to be considered during numerical simulation results from the discontinuity in the diagonal

component of K

−

i jmn and B

−

i jmn. When ωi = ωj

, the denominator terms for D

−

i jmn are equal to zero, which makes K

−

i jmn

and B

−

i jmn singular along the diagonal components. Physically, the interaction between two wave components propagating in opposite directions with same magnitude results in total energy loss. This can be explained by studying

Fig. 2.4, which shows how two wave components interact. As shown in the figure, two free wave components,~ki

14

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and~kj

, generate new bounded wave components,~ki +~kj and~ki −~kj, by sum and difference interactions, respectively. Therefore, unlike difference-interaction QTFs for second-order wave (hydrodynamic) forces, in the case of

kinematics, all diagonal components of K

−

i jmn and B

−

i jmn should be set to zero; this only means that total energy loss

results from the interaction of two wave components with the same magnitude and opposite propagation directions,

i.e.,~ki −~ki.





(a) Sum interaction.





(b) Difference interaction.

Figure 2.4. Sum and difference interaction of wavenumber vectors

2.2.3.4 Inverse Fast Fourier Transform

Agarwal and Manuel [14] discuss the numerical simulation of uni-directional second-order waves in detail. It involves a single sum of component harmonics that can be efficiently computed using the Inverse Fast Fourier Transform (IFFT). On the other hand, simulation of directional irregular second-order waves involves a double sum, which

can be computationally expensive. The procedure presented by Agarwal and Manuel [14] made it possible to rewrite

the double summation as a single summation by appropriately re-assembling and rewriting indices (or coefficients)

of terms involved. Once the indices for an equivalent single summation are assembled, a one-dimensional IFFT

procedure, similar to that for linear waves, can be used to carry out the nonlinear (second-order) wave simulations

efficiently. We extend this same procedure to the numerical simulation of irregular directional second-order waves. A

flowchart for calculation of directional second-order wave kinematics and resulting hydrodynamic loads is presented

in Fig. 2.5. This calculation procedure is incorporated into the open-source software, FAST, for coupled aero-servohydro-elastic analysis of offshore wind turbines.

2.3 Hurricane Winds

UMCM provides mean wind field data corresponding to 10 meters above the mean surface level generated at a

1.3 km grid resolution. This large-scale mean wind field data must be down-scaled using a scale-bridging procedure

to provide the needed wind field at about a 10 m resolution around the rotor to allow meaningful aerodynamic load

computations. In this study, the turbulent wind fields are simulated using a spectral method based on characteristics

of the surface wind field obtained from UMCM; these characteristics consist of the sustained 1-minute surface wind

speeds, U1min, the mean wind direction, the surface drag coefficient, CD, and the surface stress, τ.

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Wave Spectrum

S(ωi,θm)

Random amplitude and Phase

aim ∼ Rayleigh

E[a

2

im] = 2S(ωi

,θm)∆ω∆θ

εim ∼ Uniform[0, 2π]

2-D Fourier coefficient

(r = x or y or z)

X

±

i j =

M

∑

m=1

M

∑

n=1

X

(2)±

i jmn

U

±

r,i j =

M

∑

m=1

M

∑

n=1

U

(2)±

r,i jmn and U ̇ ±r,i j =

M

∑

m=1

M

∑

n=1

U ̇

(2)±

r,i jmn

P

±

i j =

M

∑

m=1

M

∑

n=1

P

(2)±

i jmn

X

(2)±

i jmn , U

(2)±

r,i jmn, U ̇

(2)±

r,i jmn, and P

(2)±

i jmn ⇒ Appendix C

Fourier coefficient

(r = x or y or z)

Xi =

M

∑

m=1

X

(1)

im

c Ur,i =

M

∑

m=1

U

(1)

r,im and U ̇

r,i =

M

∑

m=1

U ̇

(1)

r,im

Pi =

M

∑

m=1

P

(1)

im

X

(1)

im , U

(1)

r,im, U ̇

(1)

r,im, and P

(1)

im ⇒ Appendix C

Assemble 1-D Fourier coefficient

Y

±

k = ∑∑

|i±j|=k



X

±

i j 

Z

±

r,k = ∑∑

|i±j|=k



U

±

r,i j

and Z ̇±

r,k = ∑∑

|i±j|=k



U ̇ ±

r,i j

P

±

k = ∑∑

|i±j|=k



P

±

i j 

Time series

η

(2)

(t) ← R



IFFT Y

±

k



u

(2)

r (z,t) ← R

h

IFFT Z

±

r,k

i

u ̇

(2)

r (z,t) ← R

h

IFFT Z ̇±

r,k

i

p

(2)

(z,t) ← R



IFFT P

±

k



Time series

η

(1)

(t) ← R[IFFT (Xi)]

u

(1)

r (z,t) ← R[IFFT (Ur,i)]

u ̇

(1)

r (z,t) ← R



IFFT U ̇

r,i



p

(1)

(z,t) ← R[IFFT (Pi)]

Add First- and Second-Order component

η(t) = η

(1)

(t) + η

(2)

(t)

u(z,t) = u

(1)

(z,t) + u

(2)

(z

∗

,t)

u ̇(z,t) = u ̇

(1)

(z,t) + u ̇

(2)

(z

∗

,t)

p(z,t) = p

(1)

(z,t) + p

(2)

(z

∗

,t)

z

∗ = min(0,z)

First-Order Second-Order

Figure 2.5. Flowchart for the numerical simulation of second-order directional waves

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2.3.1 Mean wind field

We are interested in simulations of 1-hour duration for turbine response statistics; for this, we desire information on

the 1-hour mean wind speed at hub height of the turbine. This requires conversion from 1-minute to 1-hour averaging in time as well as adjustment of 10 m winds to elevations corresponding to the rotor swept area of the turbine. In

a World Meteorological Organization (WMO) report by Harper et al. [15], conversion factors are recommended for

relating the WMO standard 10-minute average wind speed to 1-minute, 2-minute, and 3-minute “sustained” winds

in tropical cyclone conditions. The report indicates that an at-sea conversion factor between the 1-minute sustained

wind speed and the 10-minute average wind speed should be 0.93, rather than the traditional value of 0.88, which is

shown to be associated more with an off-land exposure. Accordingly, this conversion factor of 0.93 is used to estimate the 10-minute mean wind speed from the 1-minute sustained wind speed. Since there is not enough published

data to obtain an estimate of the 1-hour mean wind speed from the 1-minute or the 10-minute wind speed, we assume

that the 1-hour mean wind speed (needed for this study) is the same as the 10-minute wind speed, without applying

any additional conversion factor. Bryan and Rotunno [16] showed that the grid size used in hurricane wind field

simulation can significantly affect the wind speed averaged over the grid. Although the mean wind velocity fields

from UMCM are generated for a coarse 1.3 km grid resolution, we interpolate these mean wind fields over a finer

grid (10 m × 10 m) over the wind turbine rotor swept area, which is used for the dynamic analysis of the selected

offshore wind turbine in this study.

Among various approaches adopted to describe the variation of wind speed with elevation in the atmospheric

boundary layer, Panofsky and Dutton [17] proposed a form for the vertical wind speed profile that includes a stability

term, Ψm, from planetary boundary layer theory, as follows:

U10min(z) = u∗

κ

[ln(

z

z0

)−Ψm] (2.63)

where u∗ is the friction velocity, equal to pτ/ρa ( where τ = wind stress on the ocean surface and ρa = air density),

κ is the von Kármán constant, and z0 is the surface roughness length. Powell et al. [18] showed that logarithmic

mean wind profiles apply in tropical cyclones at least in the lowest 200 m and then the profile levels off slightly with

a peak near 500 m. Also, Hsu [19] has shown that, during a hurricane, the effect of stability in Eq. 2.63 is negligible.

Accordingly, in this study, we use the familiar logarithmic law wind profile to estimate surface mean wind speeds

during a hurricane:

U10min(z) = u∗

κ

ln(

z

z0

) (2.64)

The friction velocity, u∗, and the surface roughness length, z0, in Eq. 2.64 were derived based on mean wind field

parameters from UMCM as shown in Fig. 2.6. Because the wind stress, τ, from UMCM takes into account the

influence of wave height, the surface mean wind speeds evaluated by Eq. 2.64 and the wave heights are coupled

through τ. Vertical wind profiles are evaluated with respect to the mean surface level (MSL); variations in the MSL

due to storm surge are not considered.

2.3.2 Turbulent wind field

The turbulence intensity is an important controlling parameter for simulating turbulent wind fields; it is dependent

on the atmospheric stability and the surface roughness length. Ishizaki [20] evaluated the turbulent intensity of hurricane winds as a function of mean wind speed up to 30 m/s and found that it generally reduces with an increase in

mean wind speed. On the other hand, studies by Ochi [21] showed that, for hurricane winds over 40 m/s, turbulence

intensity increases slightly with increase in mean wind speed; the increase in sea surface roughness with wind speed

may be one of the factors that contributes to this increase in turbulent intensity. Due to the lack of measurement data

of hurricane turbulent wind fields over water, in this study, the relationship in IEC 61400-1 [22] between turbulence

intensity and wind speed (for a selected wind turbine class) is employed.

The modified Kaimal model, defined in the IEC wind turbine design standard (IEC 61400-1) [22], assumes

neutral atmospheric stability. The model is widely used in turbine loads studies and is presented here as the basis for

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80 90 100 110 120

0

20

40

60

U1min(z=10m) (m/s)

80 90 100 110 120

1

1.5

2

2.5

x 10−3

Cd

80 90 100 110 120

0

2

4

6

hour

τ (N/m

2

)

(a) UMCM (WRF) output.

80 90 100 110 120

0

20

40

60

U1min(z=10m) (m/s)

80 90 100 110 120

0

1

2

3

x 10−3

z

0 (mm)

80 90 100 110 120

0

1

2

hour

u

* (m/s)

(b) Derived values.

Figure 2.6. Various mean wind field parameters from UMCM (U1min, Cd, and τ) and derived wind properties (z0 and u∗); where U1min =1-minute mean wind speed, Cd =drag coefficient, τ =wind stress, z0 =surface roughness length, and u∗ = friction velocity (note:

the blue dashed line corresponds to Site B and the red solid line corresponds to Site A).

18

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turbulence modeling and, later, it is combined with a steady wind profile to define the neutrally stable boundary layer

or neutral boundary layer(NBL). The power spectral density functions for any of the three turbulence components, K

= u

′

, v

′

, or w

′

, are given as follows:

SK(f) = 4σ

2

KLK/Uhub

(1+6 f LK/Uhub)

5

3

(2.65)

where SK(f) (in (m/s)2/Hz) is the one-sided power spectrum for turbulence component, K; σK is the standard deviation of turbulence component, K; f refers to the frequency of interest in Hertz (Hz); Uhub is the mean hub-height

mean wind speed; and LK is an integral length scale parameter that can be computed as follows:

Lu

′ = 8.10ΛU

Lv

′ = 2.70ΛU

Lw′ = 0.66ΛU (2.66)

where ΛU is a longitudinal turbulence scale parameter taken to be 42 m corresponding to a wind turbine with hub

height 90 m above the mean water level [22]. The required turbulence standard deviations may be computed as

follows:

σu

′ = Ire f(0.75Uhub +5.6 m/s)

σv

′ = 0.8σu′

σw′ = 0.5σu

′ (2.67)

where Ire f is the expected value of the turbulence intensity at a hub-height mean wind speed of 15 m/s. For turbulence category B (medium turbulence characteristics) in wind turbine design, Ire f = 14%. The cross-power spectral

density function corresponding to locations, i and j, (for any turbulence component) is defined as follows:

Si j(f) = Cohi j(f)

q

Sii(f)Sj j(f) (2.68)

where Cohi j(f) is the coherence function. For turbulence component, K, we have:

K = u

′

,v

′

,w

′

: Coh(K)

i j (r, f) = exp



−12s

f r

Uhub 2

+



0.12 r

LK

2



 (2.69)

in which r is the separation (distance) between points i and j.

2.4 Turbine Response

2.4.1 Turbine Model

A 5-MW wind turbine model developed at NREL and representative of utility-scale offshore wind turbines being

manufactured today is considered. The turbine is a variable-speed, collective pitch-controlled machine with a maximum rotor speed of 12.1 rpm; its rated wind speed is 11.5 m/s. It is assumed to have a hub height of 90 meters

(above the mean sea level) and a rotor diameter of 126 meters. The turbine is assumed to be sited in 20 meters of water; it has a monopile support structure of 6-meter diameter, which is assumed to be rigidly connected at the seafloor.

Fundamental frequencies for the tower fore-aft and side-to-side bending modes are around 0.32 Hz and 0.31 Hz,

respectively. This turbine model with monopile foundation has been the subject of several simulation studies (see, for

example, Agarwal and Manuel [23], [24]).

19

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
$NCFG

0CEGNNG

5GTXKEG

2NCVHQTO

4QVQT

&KCOGVGT


O

5QKN

5GC$GF

5GC.GXGN (41068+'9 5+&'8+'9

/QPQRKNG

6QYGT

9CVGT&GRVJ


O

*WD

*GKIJV


O

Figure 2.7. Selected 5-MW offshore wind turbine with a monopile support structure

20

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
2.4.2 Swell versus Wind Seas

As shown in Fig. 2.2, the hurricane directional waves are composed of swell at low frequencies and locally generated

waves above approximately three times the spectral peak frequency. There is, however, no tendency for the spectrum

to become bimodal in either frequency or direction. Rather, the spectra are directionally skewed, with a smooth directional transition from low frequency to high frequency [25]. Following Holthuijsen [26], wind sea waves are more

irregular and short-crested, respond quickly to wind variations, and are characterized by a rather broad spectrum.

On the other hand, swell consists of rather regular long-crested waves whose evolution is not as strongly affected by

the wind, and its spectrum is narrower. Still, the distinction between wind sea and swell is often not obvious. Under

changing winds (in both magnitude and direction) wave systems can overlap in parts of the frequency-direction domain giving rise to a rather continuous spectrum in which the presence of two or more distinct systems is not clearly

discernible. Portilla et al. [27] introduced several schemes to separate a swell from a locally generated wave, which

include a wind sea and swell identification scheme that uses the directional wave spectrum and available wind data

(on the mean wind direction, ψ, and the mean wind speed, Uo). If a directional wave spectrum and this wind information are available, a straightforward step to identify wind sea and swell components is to apply a definition for

wind seas based on wave age [28]. The wind sea and swell identification scheme that we use is described in Fig. 2.8.

According to this separation scheme, wave components that (1) propagate in wave direction, θ, between ψ − π/2

and ψ + π/2 and (2) travel at a wave phase velocity, cp, slower than Uo cos(θm − ψ) are classified as being part of

a wind sea. In Fig. 2.9, the directional wave spectrum for a location on the left side of the track of Hurricane Ike

(i.e., Site B), as obtained from the UMCM at 100 hours after the start of the simulation, is separated into wind sea

and swell by the wave age criterion proposed by Komen et al. [28]; in this figure, the wave spectrum is normalized

by a maximum wave spectrum value.

	



 

	



Ψ



  Ψ

ω	


















 

  
		 

Figure 2.8. Wind sea and swell separation procedure using wave age criterion

Using the procedure outlined, directional wave spectra from 80 to 120 hours are separated into wind sea and

swell. In Fig. 2.10, wave variances (σ

2

η

) and mean wave frequencies (fm) of wind sea and swell are evaluated after

the separation. Before the hurricane passes the selected sites, the swell components significantly contribute to the

overall wave energy. Note that the mean wave frequency of the swell component is significantly below 0.3 Hz (which

is the resonant frequency associated with the first tower bending mode for the wind turbine used in this study); this

suggests that the contribution of swell to total turbine response may not be significant.

The variation of the mean wave frequency and wave direction for swell and wind seas are presented in Fig. 2.11.

21

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1 0.5 0

0

0.5

1

f(Hz)

Hs = 5.0 m

mean wind

direction

Wind

Swell

E N W S E

0

0.1

0.2

0.3

0.4

0

0.2

0.4

0.6

0.8

1

Figure 2.9. Wind sea and swell separation, normalized by the wave spectrum maximum value (blue line: swell spectrum; red line: wind sea spectrum).

22

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0

200

400

600

d (km)

0

3

6

σ

2η(m

2

)

80 85 90 95 100 105 110 115 120

0

0.2

0.4

f

m(Hz)

hour

(a) Site B.

0

200

400

600

d (km)

0

3

6

σ

2η(m

2

)

80 85 90 95 100 105 110 115 120

0

0.2

0.4

f

m(Hz)

hour

(b) Site A.

Figure 2.10. Variation with time in the distance between the site and hurricane eye (d), wave variance (σ

2

η

), and

mean wave frequency (fm) (black dashed line: wind sea + swell; blue solid line: swell; red solid line: wind sea) 23

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While the mean wave frequency and wave direction corresponding to wind seas are significantly changed with the

hurricane movement because these wind seas are greatly affected by local wind direction and speed changes, the

variation in mean wave frequency and wave direction corresponding to swell is relatively insignificant because the

evolution of swell is not as strongly affected by the local wind.

N

at 120hrs at 120hrs

at 80hrs

at 80hrs

(a) Site B.

N

at 120hrs

at 120hrs

at 80hrs

at 80hrs

(b) Site A.

Figure 2.11. Variation of the mean wave frequency and wave direction every 10 hours; N indicates

waves propagating toward north, etc., and the dashed and solid circles (inner to outer) correspond to

wave frequencies of 0.1, 0.2, 0.3, and 0.4 Hz (blue dots and line: swell sea; red dots and line: wind sea).

After the hurricane waves are separated into wind sea and swell by the procedure described in Fig. 2.8, the variances of the tower bending moment resulting from the wind sea and swell are compared in Fig. 2.12. Only the effect

of wave loads is included in evaluating the turbine response. Although the contribution from swell components to

the overall wave energy is comparable with and even sometimes higher than that from wind seas, the contribution

of swell to the fore-aft tower bending moment (FATBM) at the base is relatively very small when compared with

its contribution to the side-to-side tower bending moment (SSTBM). Two possible factors can explain the small

FATBM contribution from swell; these are: (1) the significantly lower mean wave frequency of the swell component

is less than 0.3 Hz which is near the resonant frequency associated with first tower bending mode; and (2) the relatively strong misalignment between the mean wind direction (in the direction of bending of FATBM) and the mean

direction of the swell sea. This second factor also helps explain the higher contribution of swell to SSTBM than to

FATBM. On the other hand, because of the relatively slight misalignment between the wind sea and the mean wind

direction, a larger portion of the wind sea energy contributes to FATBM and this leads to higher FATBM response

corresponding to wind seas rather than to SSTBM response. Still, for most of the time covered by the simulation, the

contribution from the wind sea to the SSTBM response is higher than from swell due to the significantly lower mean

wave frequency of the swell component. Overall, it is found that the FATBM response is significantly higher than the

SSTBM response.

2.4.3 Effect of feathered blades

During the hurricane, the blades of the wind turbine are pitched to feather to minimize turbine loads. The effect of

feathering blades on the turbine response is evaluated using turbulent wind velocity fields with a mean longitudinal

wind velocity of about 27 m/s at 90 m above MSL. Two difference turbine states are studied: (1) Case 1: the turbine

maintains yaw control and can track the changing wind direction perfectly, and (2) Case 2: the turbine experiences

24

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80 90 100 110 120

0

2

4

6

σ

2η(m

2

)

80 90 100 110 120

0

100

200

300

400

hour

σ

2FATBM(MN

2−m

2

)

(a) FATBM-Site B.

80 90 100 110 120

0

2

4

6

σ

2η(m

2

)

80 90 100 110 120

0

100

200

300

400

hour

σ

2FATBM(MN

2−m

2

)

(b) FATBM-Site A.

80 90 100 110 120

0

2

4

6

σ

2η(m

2

)

80 90 100 110 120

0

30

60

90

120

150

hour

σ

2SSTBM(MN

2−m

2

)

(c) SSTBM-Site B.

80 90 100 110 120

0

2

4

6

σ

2η(m

2

)

80 90 100 110 120

0

30

60

90

120

150

hour

σ

2SSTBM(MN

2−m

2

)

(d) SSTBM-Site A.

Figure 2.12. Variation in the tower response (bending moment) variance with time indicating contributions

from wind sea and swell (black dash line: wind sea + swell; blue solid line: swell; red solid line: wind sea)

25

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Top view

Top view (A-A section)

	






	



 parallel to rotor plane



	


	





	









	



	





 	











Case 1

Case 2



∥

∥



Figure 2.13. Schematic sketch of a parked wind turbine and definition of loads on blades

some yaw misalignment or yaw error. In this study, a single yaw misalignment or yaw error case of 90 degrees is

evaluated; note that this may not provide the worst-case scenario for turbine loads. Figure 2.13 shows a schematic

sketch of a parked wind turbine which is considered in this study; one of blades of the turbine is oriented at a 0◦

azimuth angle (i.e., in the 12 o’clock position) and is designated as Blade 1. The figure also shows the top view of a

cross section of Blade 1 with wind flow directions indicated for both cases. Tangential forces, FT and normal forces,

FN, are defined in the figure for Blade 1. The dominant longitudinal wind and the cross (lateral) wind directions in

both cases are aligned with the x and y directions, respectively, of the turbine base coordinate system as shown in the

figure.

Table 2.1 shows 1-hour maximum bending moments at the root of Blade 1 for two different pitch angle cases.

As can be seen, when cross winds are not included, both out-of-plane and in-plane bending moments at the blade

root are decreased when the blades are pitched to feather; the in-plane bending moment is decreased from 1,215

kN-m to 563 kN-m and the out-of-plane bending moment is decreased from 8,053 kN-m to 453 kN-m. However,

when cross winds are included, while the out-of-plane bending moment is decreased from 8,278 kN-m to 1,065 kNm by feathering the blades, the in-plane bending moment is increased from 1,688 kN-m to 2,788 kN-m. Also, upon

including the cross wind, in-plane and out-of-plane bending moments are both significantly increased, especially

when the blades are feathered. Feathering the blades increases the contribution of the cross wind on blade root

moments.

Table 2.1. One-hour maximum bending moment at blade root with and without the cross wind velocity contribution for a blade at a 0◦ azimuth angle.

in-plane bending moment (kN-m) out-of-plane bending moment (kN-m)

pitch angle (β) = 0

◦ pitch angle (β) = 90◦ pitch angle (β) = 0◦ pitch angle (β) = 90◦

without cross wind 1,215 563 8,053 453

with cross wind 1,688 2,788 8,278 1,065

Figure 2.14 shows the effect of yaw misalignment on bending moments at the blade root. The blade root inplane bending moments are much more significantly influenced by yaw error than the out-of-plane bending moments. As shown in Fig. 2.13, the dominant wind in Case 2 is aligned with the rotor plane, and it increases the

26

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0 100 200 300 400 500 600

10

20

30

40

50

time (sec)

u(m/s)

0 100 200 300 400 500 600

−20

−10

0

10

20

time (sec)

v(m/s)

(a)

0 200 400 600

−8

−6

−4

−2

0

2

4

RootMOoP(x10

3kN−m)

0 200 400 600

−8

−6

−4

−2

0

2

4

time (sec)

RootMIP(x10

3kN−m)

(b)

Figure 2.14. (a) Turbulent wind velocity time series and (b) associated blade root bending moments (blue line: Case 1; red line: Case 2)

maximum in-plane bending moment as well as the mean in-plane bending moment.

Figure 2.15 shows the variation in aerodynamic forces at several sections along Blade 1 for the two different

yaw-control cases. At most blade sections and for both cases, the tangential forces, FT , corresponding to bending

moments in the rotor plane are significantly larger than the normal forces, FN, corresponding to the moments orthogonal to the rotor plane. It is also seen that Case 2 leads to larger tangential forces than Case 1.

2.4.4 Effect of turbine control

We now investigate how yaw and pitch controls influence the response of the selected offshore wind turbine during a

hurricane. A wind turbine’s control and safety systems play a vital role in regulating aerodynamic loads by adjusting

the blade pitch angle with changing wind speed and the nacelle yaw angle with changing wind direction. In this

study, using simulated wind and wave fields, we evaluate: (1) the effect of different nacelle yaw angles relative to the

wind direction (i.e., different amounts of yaw error or misalignment); (2) the effect of different blade pitch angles;

(3) the effect of different turbine parking strategies—e.g., parked (at standstill) or in an idling state; and (4) load

maxima at different blade azimuthal configurations while the turbine is in a standstill state.

2.4.4.1 Effect of yaw misalignment

First, the effect of yaw misalignment on turbine response is studied; seven different yaw misalignments (θyaw =

-90, -60, -30, 0, 30, 60, and 90 degrees) are considered. The 0-degree yaw misalignment corresponds to a case with

enough backup power for active yawing so as to have no yaw error; the others could represent cases with insufficient

yaw system backup power that, then, lead to varying degrees of yaw misalignment or error. We assume that the

wind turbine is in an idling state and that all the blades are feathered, or turned to a 90-degree pitch angle. From

Fig. 2.16 for an idling turbine at Site A, it can be seen that while the contribution from hydrodynamic loading to

the tower response is only very slightly influenced by the amount of yaw misalignment, the aerodynamic loading

contribution is significantly influenced by it. Peak tower bending moment values occur for a yaw misalignment of

27

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0 3 6 9 12 15 18

0

10

20

30

Section #

Maximum F

N(kN)

0 3 6 9 12 15 18

0

10

20

30

Section #

Maximum F

T(kN)

Figure 2.15. Maximum normal force (FN) and tangential force (FT ) on blade (circles: Case 1; triangles: Case 2)

-90 -60 -30 0 30 60 90

0

20

40

60

80

100

120

140

θ

yaw

(degree)

Mx(MN-m)

only aero

only hydro

aero+hydro

-90 -60 -30 0 30 60 90

0

20

40

60

80

100

120

140

θ

yaw

(degree)

My(MN-m)

only aero

only hydro

aero+hydro

Figure 2.16. Maximum tower bending moment at mudline (at 100 hrs) for an idling turbine at Site A.

28

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0 10 20 30 40 50 60 70 80 90 100

0

50

100

150

pitch angle(degree)

Mx(MN-m)

only aero

aero+hydro

0 10 20 30 40 50 60 70 80 90 100

0

50

100

150

pitch angle(degree)

My(MN-m)

only aero

aero+hydro

Figure 2.17. Effect of pitch angle on tower bending moment (at 100 hours) for an idling turbine at Site A.

80 90 100 110 120

0

10

20

30

40

50

60

70

80

hour

Mx(MN-m)

azimuth=0o

azimuth=90o

azimuth=180o

80 90 100 110 120

0

10

20

30

40

50

60

70

80

hour

My(MN-m)

azimuth=0o

azimuth=90o

azimuth=180o

090

180



(a) wind alone.

80 90 100 110 120

0

10

20

30

40

50

60

70

80

hour

Mx(MN-m)

azimuth=0o

azimuth=90o

azimuth=180o

80 90 100 110 120

0

10

20

30

40

50

60

70

80

hour

My(MN-m)

azimuth=0o

azimuth=90o

azimuth=180o

090

180



(b) wind and waves.

Figure 2.18. Effect of blade azimuthal position on tower bending moment for a parked-standstill turbine at Site A during Hurricane Ike.

29

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about 30 degrees; when the misalignment changes from 0 to 30 degrees, the tower bending loads are seen to increase

by as much as a factor of 4.

2.4.4.2 Effect of blade pitch angle

We discuss next the sensitivity of the tower response to the blade pitch angle. In this sensitivity study, all the blades

are locked at a set pitch angle selected to be between 20 and 90 degrees. We assume that the wind turbine is in an

idling state and that the rotor is yawed to be in alignment with the mean wind direction. From Fig. 2.17, as expected,

we see that a 90-degree pitch angle results in the lowest tower response maxima and that, when the pitch angle is

reduced from 30 to 20 degrees, an extremely large increase in the maximum tower bending moment results. Clearly,

blade pitch control is important during the hurricane.

80 90 100 110 120

0

20

40

60

hour

Mx(MN-m)

Idling

stand-still

80 90 100 110 120

0

20

40

60

hour

My(MN-m)

Idling

stand-still

(a) only wind.

80 90 100 110 120

0

20

40

60

hour

Mx(MN-m)

Idling

stand-still

80 90 100 110 120

0

20

40

60

hour

My(MN-m)

Idling

stand-still

(b) wind + wave.

Figure 2.19. Effect of turbine parking strategy on tower loads for a

turbine at Site A (with no yaw misalignment) during Hurricane Ike.

30

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
2.4.4.3 Effect of blade azimuthal configuration

Next, for the wind turbine assumed to be in a parked-standstill state, we evaluate the tower response at three different

blade azimuthal configurations. In the first case, one of blades of the turbine is oriented at a 0◦azimuth angle (i.e., in

the 12 o’clock position); this blade is designated as Blade 1. In the second and third cases, the azimuth counterclockwise angles of Blade 1 are 90 and 180 degrees, respectively. We assume that the wind turbine is in a parked-standstill

state, that the rotor and nacelle are yawed so as to be aligned with the mean wind direction, and that all three blades

are feathered. From Fig. 2.18, it can be seen that while My (the tower base fore-aft moment), in this case with zero

yaw error, is not significantly different for different blade azimuthal configurations, Mx (the tower base side-to-side

moment) is seen to vary by a considerably larger amount; this range can be as much as 25% of the value, say, at

the zero-degree azimuthal configuration. In general, though not at all times during the simulation, the largest and

smallest tower loads are observed at the 0 and 180 degree azimuthal configurations, respectively.

2.4.4.4 Effect of alternative turbine parking strategies: standstill versus idling

At very high wind speeds, it is expected that an offshore wind turbine will be parked and held either at a standstill

state or allowed to rotate in an idling state. We now discuss the effect that such alternative turbine parking strategies

have on turbine loads. We assume that the turbine rotor is yawed so as to be aligned with the mean wind direction

and that all three blades are feathered; also, for the parked-standstill case, one of the blades is assumed to be at a

zero-degree azimuthal position. From Fig. 2.19, we can see that My (the tower base fore-aft moment), in this case

with zero yaw error, is not significantly different for the two different turbine parking strategies. In contrast, Mx (the

tower base side-to-side moment) is seen to be noticeably different and the parked-standstill case leads to larger loads

than the idling case.

2.5 Result and Discussion

We have carried out in-depth studies of the response of a monopile-supported 5-MW offshore wind turbine during

Hurricane Ike. The intensity and track of Hurricane Ike are numerically simulated by a fully coupled atmosphericwave-ocean model, UMCM. Based on directional wave spectra resulting from the UMCM output, hurricanegenerated wave kinematics are simulated using directional irregular second-order waves. We have presented the

wave modeling approach adopted as well as a numerical procedure for simulating the directional nonlinear waves.

A mean wind field is defined and turbulent wind fields are stochastically simulated using a Fourier-based spectral

procedure; both are based on characteristics of the surface wind field obtained from the UMCM output obtained over

a duration of 120 hours.

Because hurricane directional waves are composed of two wave components, swell and wind sea which have

different characteristics, their characteristics are evaluated after separating swell and wind sea components from

directional wave spectra resulting from the UMCM output based on the wave age criterion. Although the swell

component significantly contributes to overall wave energy, the mean wave frequency of this swell component is

significantly lower than resonant frequencies associated with tower bending. Also, while mean wave frequencies

and wave directions corresponding to wind seas are significantly changed with hurricane movement because these

wind seas are greatly affected by the local wind direction and speed change; in contrast, the variation of mean wave

frequencies and wave directions corresponding to swell is relatively insignificant because the evolution is not as

strongly affected by the local wind.

At selected locations, we evaluated the effect on turbine load maxima, during the simulation of Hurricane

Ike, of: (i) different nacelle yaw angles relative to the mean wind direction (i.e., different amounts of yaw error

or misalignment); (ii) different blade pitch angles; and (iii) different turbine parking strategies (i.e., considering a

turbine in either a standstill or idling state). In addition, we studied loads for different blade azimuthal positions.

Based on the numerical studies presented, we can make the following general conclusions:

31

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
• While the contribution from hydrodynamic loading to the tower response is only very slightly influenced by

the amount of yaw misalignment, the aerodynamic loading contribution is significantly influenced by it; peak

tower bending moment values occur for a yaw misalignment of about 30 degrees. The significantly lower

turbine loads in the case of zero yaw misalignment highlights the importance of a reliable yaw backup power

system, which is strongly recommended since a grid failure during a hurricane could result in loss of the

needed yaw control.

• Blade pitch control is important during the hurricane; as expected, a 90-degree pitch angle results in the lowest

tower response maxima and in a systematic study, it was found that when the pitch angle is reduced from 30 to

20 degrees, a significant increase in the maximum tower bending moment results.

• While the tower base fore-aft moment in a case with zero yaw error does not vary greatly for different blade

azimuthal positions, the tower base side-to-side moment is seen to vary by a considerably larger amount; this

range can be as much as 25% of the value, say, at the zero-degree azimuthal position. In general, though not at

all times during the hurricane, largest and smallest tower load maxima occurred for rotor configurations where

one blade is in the 0 and 180 degree azimuthal position, respectively.

• While the tower base fore-aft moment in a case with zero yaw error is not significantly different for the different turbine parking strategies considered, the tower base side-to-side moment is seen to be noticeably different

and the parked-standstill case leads to systematically larger loads than the idling case during the hurricane.

32

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3 Modeling Hurricane Sandy’s Influence on a Jacket-Supported Offshore Wind Turbine

3.1 Problem Description

For evaluating the response of an offshore wind turbine (OWT) during the evolution of Hurricane Sandy (2012),

we consider ten mid-Atlantic sites identified for potential wind energy development. These selected sites shown

in Figure 3.1 were in or close to the path of Hurricane Sandy. Some general information on the selected sites is

presented in Table 3.1. The water depth at some of these sites is greater than 30 m. Depending on the water depth

range, in our analyses, we considered at many as three fixed water depths (20 m, 45 m, and 50 m) possible at any

site. Because a monopile support structure becomes progressively uneconomical as the water depth increases beyond

25-30m [29], other types of support structures such as jackets or tripods might be better candidates at those water

depths. To illustrate the detailed procedure related to the response evaluations of an offshore wind turbine with a

jacket support structure, we consider only a single site where the water depth is 50 m.

−86 −82 −78 −74 −70 −66

24

28

32

36

40

44

Longitude

Latitude

1

2

3

4

5

6

7

8

9

10

Hurricane Sandy track

Figure 3.1. The locations of ten selected offshore wind plant sites and the simulated track of Hurricane Sandy.

As was the case for Hurricane Ike discussed in Chapter 2, coupled wind and wave fields at the locations of

interest are simulated based on the UMCM output. Figure 3.4 shows the variation with time of the wind and wave

directions; the red circle indicates the location of the hurricane eye at the specified time. In the figure, the red and

blue arrows represent the wind and wave directions, respectively, at the ten selected sites (locally) while the green

arrows depict the full-field wind direction over the entire simulation domain. As shown in this figure, the wind and

wave directions and the misalignments between the two at each site change noticeably as the hurricane moves along

its track.

33

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(a) At 10:00 UTC on October 28, 2012 (t0).

−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(b) At t0 + 10 hours.

Figure 3.2. Variation with time during Hurricane Sandy of the full-field wind direction (green arrows), local wind direction (blue arrows), and local wave direction (red arrows) at the locations of the ten selected sites (at t0 and t0 + 10 hours).

34

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(a) At t0 + 20 hours.

−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(b) At t0 + 30 hours.

Figure 3.3. Variation with time during Hurricane Sandy of the full-field wind direction (green arrows), local wind direction (blue arrows), and local wave direction

(red arrows) at the locations of the ten selected sites (at t0 + 20 and t0 + 30 hours).

35

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(a) At t0 + 40 hours.

−80 −78 −76 −74 −72 −70 −68 −66

30

32

34

36

38

40

42

44

Longitude

Latitude

(b) At t0 + 50 hours.

Figure 3.4. Variation with time during Hurricane Sandy of the full-field wind direction (green arrows), local wind direction (blue arrows), and local wave direction

(red arrows)at the locations of the ten selected sites (at t0 + 40 and t0 + 50 hour ) .

36

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Table 3.1. General information on ten potential offshore wind plant

sites selected for analysis in this study (source: www.4coffshore.com).

Wind Energy Area (ID) Water Depth Range Distance from shore

1 Maryland WEA South (US4O) 11-36 m 24.4 km

2 Massachusetts WEA (US0V) 31-62 m 38.7 km

3 New Jersey (US4S) 14-32 m 30.1 km

4 New York RFI (US4J) 18-42 m 40.8 km

5 North Carolina(US4E) 15-44 m 41.5 km

6 Rhode Island & MA (US3C) 26-49 m 31.5 km

7 Virginia (US3H) 18-33 m 54.2 km

8 North Carolina(US4E) 15-44 m 41.5 km

9 Cape Wind, MA (US03) 1-18 m 14.2 km

10 Apex Offshore Wind, NC (US99) 26-29 m 32.2 km

In this chapter, we present detailed response results only for an offshore wind turbine at Site No. 1. Figure 3.5

shows the location of Site No. 1 along with the track of Hurricane Sandy as extracted from a best track database and

estimated by the UMCM simulation; the larger red star indicates the location of Site No. 1 while the smaller blue

stars indicate locations of the other nine sites. The figure serves to display the evolution of track of the hurricane over

a 60-hour period beginning at 00:00 UTC on October 28, 2012 (0 hour).

3.2 Hurricane-Induced Waves

Irregular hurricane-generated waves are numerically simulated using second-order wave theory and the methodology

presented in Chapter 2. Table 3.2 summarizes information on wave spectra from UMWM output and on ocean

currents from HYCOM output obtained following the UMCM simulation of Hurricane Sandy. As shown in the table,

wave spectra for Hurricane Sandy are continuously generated for separate 1-min periods. However, to simulate

1-hour sea surface elevation process and associated wave kinematics in the time domain for subsequent turbine

load calculation, we need to employ a wave spectrum that represents the entire 1-hour period. Figure 3.6a shows

the wave spectrum 40 hours after 10:00 UTC on October 28, 2012 at the 50-meter water depth location within

Site No. 1. Figures 3.6b, 3.6c, and 3.6d show, respectively, computed wave spectra 1, 10, and 60 minutes later.

Differences between the wave spectra over the entire hour are not significant; hence, in this study, we simply assume

that the UMWM wave spectrum from the first minute each hour is representative of the spectrum over the entire

hour. Of course, as the hurricane progresses, these wave spectra are updated each hour to generate the changing sea

surface elevation and wave kinematics.

Table 3.2. Wave and current information from UMWM and HYCOM.

Physics Output Resolution Data

model files spatial temporal used

Current current_xx.nc every 2 m depth 10 min vcx, vcy, vcz

(HYCOM) (at each site)

Wave umwmspc_xx.nc at each site 1 min F(~k), k, θ

(UMWM) U(z = 10 m)

Figures 3.7 and 3.8 show the variation with time of the frequency-dependent wave spectrum, S(fn), and the

direction-dependent wave spreading function, D(θm), defined as follows:

S(fn) =

M

∑

m=1

S(fn,θm)∆θm;σ

2

η =

N

∑

n=1

S(fn)∆fn (3.1)

37

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40hrs

Site 1

30hrs

20hrs

10hrs

50hrs

60hrs

Figure 3.5. Location of Site No. 1 and the simulated track of Hurricane Sandy

evaluated based on UMCM output (compared to a best track database).

38

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D(θm) =

N

∑

n=1

S(fn,θm)∆fn;σ

2

η =

M

∑

m=1

D(θm)∆θm (3.2)

where σ

2

η

is the variance of the sea surface elevation process. From Figs. 3.7 and 3.8, it can be seen that at around 46

hours, both the wave spectrum and the directional spreading change quite abruptly as the hurricane’s eye passes the

site. During that hour, our assumption that the first minute’s wave spectrum is representative of the entire hour would

not be an acceptable one.

3.3 Hurricane-Induced Wind Field

Table 3.3 summarizes information on the wind field from WRF output obtained following the UMCM simulation of

Hurricane Sandy. In the table, a geometric height, z (elevation above the mean sea level), corresponding to the three

output wind velocity components, Ux(z), Uy(z), and Uz(z), are evaluated as follows, using an initial geopotential,

PHB, and a perturbation geopotential, PH [30]:

geometric height: z =

PH +PHB

9.81

(3.3)

While turbulent wind fields for Hurricane Ike in Chapter 2 were simulated using mean wind field data sampled every hour and only at a location 10 meters above the mean sea surface level (with an assumed vertical wind

shear), we demonstrate how the WRF output can allow us to make use of available wind field data provided every 10

minutes and at several elevations to stochastically simulate turbulent wind fields for Hurricane Sandy.

Table 3.3. Wind field information from WRF output for Hurricane Sandy.

Physics Output Resolution Data

model files spatial temporal used

Wind wrf_xx.nc 12×12 km 10 min u

∗

(tp)

(WRF) 4×4 km Ux(z,tp), Uy(z,tp), Uz(z,tp)

1.3×1.3 km PHB(z,tp), PH(z,tp)

Figure 3.9 presents the overall procedure to simulate turbulent wind fields using WRF output for Hurricane

Sandy. In order to simulate an hour-long fully turbulent wind field including the vertical wind shear, as a the

first step, we compute six values of the 10-min sampled total wind speed, U(z,tp), the horizontal wind direction,

θhor(z,tp), and the vertical wind direction, θver(z,tp), using WRF output Ux(z,tp), Uy(z,tp), and Uz(z,tp) (where

p = 1,2,...6 during the hour). This is done as follows:

U(z,tp) = p

[Ux(z,tp)]2 + [Uy(z,tp)]2 + [Uz(z,tp)]2(3.4)

θhor(z,tp) = atan2



Uy(z,tp)

Ux(z,tp)



(3.5)

θver(z,tp) = atan2



Uz(z,tp)

√

(Ux(z,tp))2+(Uy(z,tp))2



(3.6)

atan2(y,x) =







arctan y

x

x > 0

arctan y

x +π y ≥ 0,x < 0

arctan y

x −π y < 0,x < 0

+π/2 y > 0,x = 0

−π/2 y < 0,x = 0

undefined y = 0,x = 0

(3.7)

39

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The time-varying non-turbulent wind velocity at time, tn, i.e., U(z,tn), and the wind directions, θhor(z,tn) and

θver(z,tn) at intervals equal to ∆t may be found by applying the simple interpolation function, Interp, using computed values of U(z,tp), θhor(z,tp), and θver(z,tp).

U(z,tn) = Interp(n∆t,tp,U(z,tp)) (3.8)

θhor(z,tn) = Interp(n∆t,tp,θhor(z,tp)) (3.9)

θver(z,tn) = Interp(n∆t,tp,θver(z,tp)) (3.10)

where tn = n∆t and n = 1,2,...3600/∆t, corresponding to a wind velocity field output every second for one hour.

The zero-mean turbulent wind fields for Hurricane Sandy, i.e., u

′

(z,tn), v

′

(z,tn), and w

′

(z,tn) are simulated using

the original form of the Kaimal turbulence power spectral density functions (Kaimal et al. [31]); needed quantities

such as the one-hour mean wind speed, Um(z), and friction velocity, u

∗

m, are evaluated as follows using the six 10-

minute interval WRF output variables, U(z,tp) and u

∗

(tp), in each hour:

Um(z) = 1

6 ∑

6

p=1U(z,tp) (3.11)

u

∗

m =

1

6 ∑

6

p=1

u

∗

(tp) (3.12)

Effectively, then, u

∗

m, arising from the WRF output, scales the turbulence intensity during each hour of the simulation

of the hurricane.

Finally, the “total” wind velocity field is computed by adding the time-varying non-turbulent wind field to the

zero-mean turbulent wind field as follows:

u(z,tn) = U(z,tn)+ u

′

(z,tn) (3.13)

v(z,tn) = U(z,tn)+ v

′

(z,tn) (3.14)

w(z,tn) = U(z,tn)+ w

′

(z,tn) (3.15)

Next, the wind velocities evaluated in Eqs. 3.13-3.15 are rotated relative to a fixed inertial reference frame

coordinate system (defined at the wind turbine) by employing two transformation matrices, [Thor] and [Tver]. Thus,

we have:





ux

uy

uz



 = [Thor][Tver]





u

v

w



 (3.16)

where

[Thor] =





cosθhor −sinθhor 0

sinθhor cosθhor 0

0 0 1



 (3.17)

[Tver] =





cosθver 0 −sinθver

0 1 0

sinθver 0 cosθver



 (3.18)

and θhor and θver are defined in Eqs. 3.9 and 3.10 for every time instant if interest, tn.

The overall simulation procedure leading to full 4-D wind fields, presented in Fig. 3.9, is integrated into the

open-source aeroelastic simulation program, FAST [32], by making use of the UserWind module there.

40

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3.3.1 Mean Wind Field during Hurricane Sandy

The mean vertical wind profile for Hurricane Ike was estimated using the classical log law that was presented in

Eq. 2.64. Such a logarithmic profile, which is commonly used to describe vertical wind shear, does not account for

atmospheric stability effects. In contrast, because the WRF output provides wind field data at several elevations, we

can directly use these data to obtain the mean wind shear for full wind field simulation during Hurricane Sandy. The

WRF output for Hurricane Sandy provides mean wind field data at 6 different elevations up to 200 meters above the

bottom surface; Fig. 3.10 shows the variation with time of the horizontal mean wind speed and the vertical mean

wind speed. The vertical wind direction, θver(z,tp), is less than 2 degrees during the simulation. Even though the

WRF output includes a vertical wind velocity component, U(z,tp), the magnitude of this component is very small as

can be confirmed from Fig. 3.10.

In Fig. 3.11, the surface wind shear extracted from the WRF output is compared with the wind shear estimated

by the classical log law (Eq. 2.64) which does not account for stability effects. The computed wind shear profile

presented in Fig. 3.11 corresponds to a time, 40 hours after 00:00 UTC on October 28, 2012 and it applies to a 50-m

water depth location at Site No. 1; this profile more closely resembles stable atmospheric boundary layer conditions

with greater wind shear than in the log-law profile.

3.3.2 Turbulent Wind Field during Hurricane Sandy

In the present study, the Veers method [33], based on Fourier techniques, is utilized to generate a turbulent wind field

(over the swept area of the offshore wind turbine rotor) that is comprised of three orthogonal zero-mean velocity

components. To this turbulent wind field, the time-varying mean wind field, discussed previously, is added to yield

the full wind field over the rotor that is needed for loads analyses. The required inputs for the Veers method are

target turbulence power spectral density (PSD) functions and coherence functions; physical parameters in these target

functions depend on the WRF output that changes every hour.

3.3.2.1 Turbulence Power Spectral Density Functions

A power spectral density function describes the contribution to the variance of a stochastic process as a function of

frequency; it has, for example, dimensions of [variable units]2 per Hertz (Hz). Intuitively, then, the PSD function

describes the frequency content of the stochastic process. In this study, the original Kaimal turbulence power spectra

(Kaimal et al. [31]) are used as the basis for simulating the three orthogonal components of turbulence:

Su(f) = 105u

2

∗

z/Ure f



1+33 f z/Ure f  5

3

(3.19)

Sv(f) =

17u

2

∗

z/Ure f



1+9.5 f z/Ure f  5

3

(3.20)

Sw(f) =

2u

2

∗

z/Ure f

1+5.3



f z/Ure f  5

3

(3.21)

where Su(f), Sv(f), and Sw(f) (in (m/s)2/Hz) are one-sided power spectra for the longitudinal, transverse, and vertical wind velocity components, respectively. Also, f refers to the frequency of interest in Hertz (Hz), u∗ is the friction

velocity (in m/s), z is the elevation (in meters), and Ure f is a reference wind velocity (in m/s). For Hurricane Sandy,

Ure f and u∗, needed to define the Kaimal power spectra are taken as Um(z) and u

∗

m as given by Eqs. 3.11 and 3.12,

respectively. It should be noted that the modified Kaimal power spectra as specified in the IEC wind turbine design standard [22] are defined differently from the ones described above in Eqs. 3.19-3.21. One benefit of using the

original Kaimal power spectra in Eqs. 3.19-3.21 instead of the IEC Kaimal spectra is that the parameters involved

41

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depend only on physical quantities and they do not require any additional assumptions. With the IEC Kaimal spectra,

a pre-determined longitudinal turbulence scale parameter, ΛU , and reference turbulence intensity, Ire f , have to be

assigned.

3.3.2.2 Turbulence Coherence Functions

The coherence function for any single turbulence component is a frequency-dependent measure of the correlation of

that component at two spatially separated points. In this study, this coherence function is modeled as follows [34] :

Cohε(j,k, f,Ujk ) = exp"−f



c

2

y

(yj −yk)

2 +c2

z

(zj −zk)

2

1/2

0.5



Ure f(zj) +Ure f(zk)



#

(3.22)

where Cohε(j,k, f,Ujk) is a dimensionless coherence function for each turbulence component of interest, ε (i.e., u,

v, or w), at locations, (yj,zj) and (yk,zk), expressed as a function of frequency, f ; also, cy and cz are coherence decay

parameters (dimensions: L

−1

) for lateral (y) and vertical (z) separations, respectively; for k = 1, cy = 10 and cz = 3 ,

for k = 2, cy = 6.5 and cz = 3 and for k = 3, cy = 3.0 and cz = 0.5 [35]. Again, Ure f , needed to define the coherence

functions is taken as Um(z) as given by Eq. 3.11. The coherence functions together with the PSD functions are used

to assemble the full-field frequency-dependent cross-power spectral density (CPSD) function matrix over the entire

simulation domain covering the turbine’s rotor; the Veers method provides a means to use this CPSD matrix to

generate time series of the wind velocity over the rotor-swept area. Note that even though no coherence is considered

between the orthogonal turbulence components, they are intrinsically correlated with each other in time through u

∗

m

resulting from the WRF model output.

3.4 Offshore Wind Turbine Response during Hurricane Sandy

An uncoupled modeling scheme is used to analyze the response of an offshore wind turbine with a jacket support

structure as illustrated in Fig. 3.12. While in a coupled modeling approach, aerodynamic and hydrodynamic load

effects are evaluated in a single computation step or software tool, an uncoupled modeling approach uses two separate software tools or computational steps to evaluate the aerodynamic and hydrodynamic load effects. The rotor

aerodynamic forces are first evaluated in FAST, using a baseline wind turbine assumed fixed rigidly at the base.

Aerodynamic loads evaluated at the nacelle (top of the tower) are applied as point loads in Abaqus [36] to a structural model of the tower and jacket support structure, which is also subjected to hydrodynamic forces resulting from

waves and currents.

Unlike monopile-type support structures that have rotational symmetry due to their cylindrical sections, the

orientation of its jacket support structure beneath affects the overall response of a wind turbine due to lack of rotational symmetry. Hence, as shown in Fig. 3.13, a combination of three separate considerations should be made in

order to evaluate the response of the wind turbine with a jacket support structure during a hurricane. These threes

considerations are:

(1) Support structure orientation, θ1 (defined with regard to the wind direction),

(2) Wind and wave misalignment, θ2,

(3) Yaw misalignment, θ3.

To simplify the analyses in this study, we assume that the support structure orientation, θ1, and the yaw misalignment, θ3, are each equal to zero. Thus, only wind-wave misalignment varies during the evolution or movement

of the hurricane in our analyses. As mentioned earlier, we will present response evaluations of 1-hour duration, beginning at 00:00 UTC on October 28, 2012 (the start of the UMCM simulations). These response computations are

repeated every 10 hours, beginning 10 hours after the start of the simulations and ending 60 hours after the start. The

response computations are only for a Site No. 1, depicted in Fig. 3.5.

42

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3.4.1 Turbine Model

All the investigations in this study are for a 5-MW offshore wind turbine with a jacket support structure as shown

in Fig. 3.14. This is the same system used by the Offshore Code Comparison Collaboration Continuation (OC4)

project (Phase I). The rotor nacelle assembly (RNA) of the OWT is that of the NREL 5-MW baseline turbine [37].

The jacket support structure has four legs, four levels of X-braces, and mudbraces. This support structure has been

described in detail by Vorpahl et al. [38]. ,

3.4.1.1 OC4 Jacket Support Structure

The jacket support structure for the NREL 5-MW turbine is based on a reference design developed as part of the

European Union’s UpWind project [39]. The UpWind jacket is designed for a site with a water depth of 50 m. The

jacket consists of four legs, four levels of X-braces, and mudbraces. The top and bottom widths of the jacket are 8 m

and 12 m, respectively. A rigid concrete block with a weight of 660 tons and dimensions of 9.6 m (length) × 9.6 m

(width) × 4 m (height) is positioned at the top of the jacket and serves as the transition piece (TP) or platform that

connects the jacket with the tower of the baseline wind turbine. The geometric configuration and dimensions of the

members of the OC4 jacket support structure are presented in Fig. 3.15. The jacket is made up of a medium-grade

structural steel with a Young’s modulus of 210 GPa. The density is assumed to be 8500 kg/m3, which accounts for

paint, bolts, welds, and all other additional masses.

As marine growth can influence the overall loading and, thus, the dynamic behavior of the system, it is taken

into consideration in the model described herein as per DNV guidelines [40] and as given by Fisher and Kuehn [41].

The depth range with respect to the mean sea level (MSL) over which to consider marine growth is −40 ≤ zg(m) ≤

−2, its thickness, tg, is 100 mm, and its density, ρg, is 1,100 kg/m3

. The legs of the jacket structure are assumed to be

flooded by sea water with density, ρw, equal to 1,025 kg/m3; the braces are not assumed flooded.

There is a grouted connection between the piles and the jacket legs as shown in Fig. 3.16. The bottom of the

grouted connection is at z = −49.5 m and the upper end of the grout is at z = −45.5 m. The properties of the legs at

the lowest level (Level 4) and the piles are included in Fig. 3.15. The density of the grout material between the two

steel parts, ρG, is assumed to be 2,000 kg/m3

. As the stiffness of the two steel members together with the grout material is very high, the grouted part from MSL−49.5 m to MSL−45.5m (including pile, leg, and grout) is modeled as

rigid in Abaqus. The embedded length of the pile is assumed to be 47 m.

As shown in Fig. 3.17, the Abaqus model used in this study consists of a tower top mass, a tower, a transition

piece, and the jacket structure. All the separate parts in the model are connected via kinematic coupling constraints

in Abaqus. The rotor nacelle assembly (RNA) including the hub is modeled as a nodal mass without rotary inertia

and the transition piece between the baseline turbine and the jacket structure is modeled as a rigid body, where the

660 tons dead load of this transition piece is modeled as a rectangular body with the dimensions of 9.6 m (length)

× 9.6 m (width) × 4 m (height). Because the purpose of this study is not to evaluate localized stress concentration

at member joints or local buckling of members, all the jacket members are modeled using Euler-Bernoulli beam

elements.

In this study, member forces and reaction forces at a total of 13 locations (referred to as “sensor locations”)

are evaluated. Figure 3.18 provides detailed information on these sensor location. The structural response of braces

and legs are evaluated with respect to the member (local) coordinate system; for axial forces, positive values imply

tensile forces while negative values imply compressive forces.

3.4.1.2 Verification of the Abaqus Model

The Abaqus model is verified by comparison with the study presented by Popko et al. [42], which includes results

from the IEA Wind Task 30 OC4 Project Phase I, which was focused on the coupled simulation of an offshore

wind turbine with a jacket support structure. In the verification studies with our model, it is assumed that the jacket

structure is cut and clamped or fixed at the mudline.

43

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Comparison of Masses

Before comparing the wind turbine or support structure response with any other studies, we first consider the

structural mass as well as all additional mass in the model. This is done in Table 3.4. Structural mass includes the

jacket, transition piece, tower, and rotor-nacelle assembly (RNA), while additional mass includes marine growth and

water in the flooded legs. In general, a very good agreement is observed when our model is compared with that in

Popko et al. [42].

Table 3.4. Comparison of structural and additional mass in our Abaqus model with that in Popko et al. [42].

Structural Mass (kg) Additional mass (kg) Total

RNA Tower TP Jacket Flooded Marine

Leg Growth

Abaqus Model 350 216 660 674 204 180 2290

Popko et al. [42] 350 220 660 677 200 177 2290

Difference 0 -4 0 -3 +4 +3 0

Comparison of Natural Frequencies

An eigenvalue analysis is performed to obtain natural frequencies based on our Abaqus model, which are

then compared with the natural frequencies evaluated with an Ansys model used by Song et al. [43]. The natural

frequencies for the Abaqus and Ansys models are presented in Table 3.5. Generally, values from the two models are

in a good agreement with each other. Small discrepancies are expected as the two models include a different number

of degrees of freedom (DOF) and somewhat dissimilar structural modeling assumptions. As shown in Fig. 3.19,

Popko et al. [42] also provides eigenvalue analysis results based on various OWT modeling codes used as part of the

OC4 project. Eigenfrequencies of the first and second global fore-aft and side-to-side modes in the figure are very

close to eigenfrequencies for the same modes determined using our Abaqus model.

Table 3.5. Natural frequencies of the OC4 wind turbine system.

Mode Natural frequencies (Hz)

Ansys Abaqus Difference

(Song et al.) (this study) |%|

1 0.3190 0.3333 4.4

2 0.3190 0.3333 4.4

3 1.1936 1.2155 1.8

4 1.1936 1.2155 1.8

5 3.4425 3.3643 2.2

6 4.1253 4.4354 7.5

7 4.1253 4.4354 7.5

8 5.3391 5.3242 0.2

9 6.6953 6.6084 1.2

10 6.6953 6.6084 1.2

Comparison of Turbine Response

As further verification of the Abaqus model, we consider two response measures under regular wave loading:

(1) the fore-aft shear force at the base of the jacket structure; and (2) the out-of-plane displacement (i.e., in the foreaft direction, x) of the central joint of the X-brace at Level 2 on Side 2 (S2) (see Fig. 3.15). Our response calculations

are compared with those presented in Popko et al. [42].

First, the fore-aft shear force is evaluated for the offshore wind turbine excited using a regular Airy wave (H = 6

m, T = 10 sec). As shown in Fig. 3.20, good agreement is seen for the evaluated fore-aft force between our model

and others reported in Popko et al. [42]. Next, the out-of-plane displacement (effectively, in the fore-aft direction) is

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considered for the offshore wind turbine excited by a regular 9th-order stream function wave (H = 8 m, T = 10 sec).

In Fig. 3.21, the surface wave elevation resulting from using this stream function is compared with the surface wave

elevation based on Airy wave theory used with our Abaqus model (the wave profiles for the 9th-order stream function

and the Airy theory cases are very similar). Figure 3.22 shows that the X-brace out-of-plane displacement evaluated

from our Abaqus model (thick black line) matches well with results presented in Popko et al. [42].

3.4.1.3 Modeling Soil-Pile Interaction

Because the interaction between the soil and the embedded pile changes the dynamic characteristics of wind turbine,

this interaction effect is considered in our Abaqus model of the jacket support structure. In our model, this interaction represented by a p-y curve model specified in the American Petroleum Institute (API) RP2A guidelines [44].

The p-y curve method for designing offshore pile foundations has been utilized by the offshore oil and gas industry for decades and is based largely on work performed in the early 1970s [45, 46]. The method approximates the

stiffness of the soil-pile system by a number of discrete nonlinear soil springs arranged along the length of the pile.

These springs act independently of one another and therefore do not affect the displacement of neighboring springs.

The lateral resistance of the pile is represented by p-y curves, with “p” representing the lateral resistance and “y”

representing the lateral displacement of the pile. The soil profile assumed for the design of the OC4 Jacket [39] is

used to evaluate the lateral soil stiffness characteristics and is presented in Table 3.6.

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N

0 0.2 0.4 0.6 0.8 1

(a) At 40 hours (Hs = 9.3

m; Uz=10m = 26.9 m/s).

N

0 0.2 0.4 0.6 0.8 1

(b) At 40 hours + 1 min (Hs =

9.3 m; Uz=10m = 27.2 m/s).

N

0 0.2 0.4 0.6 0.8 1

(c) At 40 hours + 10 min (Hs =

9.4 m; Uz=10m = 26.9 m/s).

N

0 0.2 0.4 0.6 0.8 1

(d) At 40 hours + 60 min (Hs =

9.9 m; Uz=10m = 28.4 m/s).

Figure 3.6. Variation with time of Hurricane Sandy wave spectra (at and after 40

hours) at the location of Site No. 1 with 50-m water depth (blue arrow: wave direction; red arrow: wind direction). Only very small changes are seen over one hour.

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Frequency wave spectrum(m2

−sec)

hour

f(Hz)

10 20 30 40 50 60 70

0.1

0.2

0.3

0.4

0

5

10

15

20

25

Normalized frequency wave spectrum

hour

f(Hz)

10 20 30 40 50 60 70

0.1

0.2

0.3

0.4

0

0.2

0.4

0.6

0.8

Figure 3.7. Variation with time of the frequency-dependent wave spectrum during Hurricane Sandy (at the

location of Site No. 1 with 50-m water depth. Normalization to unity with variation in time is also shown.)

Directional spreading of wave energy (m2/rad)

hour

θ(rad)

10 20 30 40 50 60 70

−3

−2

−1

0

1

2

0

1

2

3

4

5

Normalized wave energy

hour

θ(rad)

10 20 30 40 50 60 70

−3

−2

−1

0

1

2

0

0.2

0.4

0.6

0.8

Figure 3.8. Variation with time of the directional-dependent wave spreading function during Hurricane Sandy (at the location of Site No. 1 with 50-

m water depth. Normalization to unity with variation in time is also shown.)

47

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,   ,   	 , 


,   


, 

,   , 

 









′, , 
′, ′, 



, 

 

	

	


	





	

 T T








	 ,  ! 	 ,  
  	 ,  
  		 ,  


T 


 
 0


 
 0

0 0 1

T 


 0 


0 1 0


 0 


	, 	 		

Figure 3.9. Procedure for simulation of the turbulent wind field during Hurricane Sandy.

hour

z(m)

10 20 30 40 50 60 70

0

50

100

150

200

0

10

20

30

40

(a) Horizontal mean wind speed.

hour

z(m)

10 20 30 40 50 60 70

0

50

100

150

200

0

0.05

0.1

0.15

0.2

(b) Vertical mean wind speed.

Figure 3.10. Variation with time of the horizontal mean wind speed and the vertical mean wind speed (at the location of Site No. 1 with 50-m water depth).

48

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20 25 30 35 40 45

0

50

100

150

200

250

300

350

400

wind speed(m/s)

z(m)

WRF

Log−law

Figure 3.11. Mean wind shear interpolated from the WRF output for Hurricane Sandy versus

that estimated by the classical log law (corresponding to the time, 40 hours, and at Site No. 1).

FAST

Abaqus

wind

Wave

Wave

wind

Tower top

load

Coupled Uncoupled

ൎ

Tower top

load

Figure 3.12. Coupled and uncoupled modeling approach for

an offshore wind turbine with a jacket support structure.

49

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(1) (2) (3) WAVE WIND WIND

N

ଶߠ ଷߠ

WIND

N

ଵߠ

Figure 3.13. Three considerations in evaluating the response

of a jacket-type structure supporting an offshore wind turbine.

50

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/5.

\
O

*WD

*GKIJV


\
O

9CVGT&GRVJ


O

04'./9

6WTDKPG

,CEMGV

5WRRQTV

5GC$GF

Figure 3.14. Schematic diagram of the jacket-supported NREL 5-MW wind turbine model.

51

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Level 1

Level 4

Level 3

Level 2

Z = 16.1m

Z = 4.3m

Z = -8.9m

Z = -24.6m

Z = -43.1m

L1

Y

X

L2

L3 L4

S1

S4

S3

S2

(Top View)

Component Color Outer

Dia.(m)

Thickness

(mm)

X- and mud brace Grey 0.8 20

Leg (Level 4) Blue 1.2 50

Leg (Level 1-3) Red 1.2 35

Leg crossing TP Not shown 1.2 40

Pile Black 2.082 60

Figure 3.15. Geometric configuration and dimensions of members of the OC4 jacket support structure.

MSL -45.5m: Grout top

Grout Material

MSL -50m: Mudline

Properties: Leg lowest level

Properties: Pile

MSL -49.5: Grout bottom

Figure 3.16. Grouted leg and pile connection for the jacket support structure.

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Jacket pile Concrete TP

(660 ton)

NACELLE

(350 ton)

TOWER

Figure 3.17. Abaqus modeling of the OC4 reference jacket structure used in this study.

BRA-S-L1

LEG-SW-L1

BRA-W-L1

BRA-S-L2

LEG-SW-L2

BRA-W-L2

BRA-S-L3

LEG-SW-L3 BRA-W-L3

BRA-S-L4

LEG-SW-L4

BRA-W-L4

LEG-SW-MUD

NO. Sensor

Name

Location Member

type

1 BRA-W-L1 On side 2(west) at level 1 Brace

2 BRA-W-L2 On side 2(west) at level 2 Brace

3 BRA-W-L3 On side 2(west) at level 3 Brace

4 BRA-W-L4 On side 2(west) at level 4 Brace

5 BRA-S-L1 On side 3(west) at level 1 Brace

6 BRA-S-L2 On side 3(west) at level 2 Brace

7 BRA-S-L3 On side 3(west) at level 3 Brace

8 BRA-S-L4 On side 4(west) at level 4 Brace

9 LEG-SW-L1 Leg3(south west) at level 1 Leg

10 LEG-SW-L2 Leg3(south west) at level 2 Leg

11 LEG-SW-L3 Leg3(south west) at level 3 Leg

12 LEG-SW-L4 Leg3(south west) at level 4 Leg

13 LEG-SW-MUD Leg3(south west) at 

mudline

Reaction

Figure 3.18. Sensor names and locations for the dynamic response

analyses of the offshore wind turbine and jacket support structure.

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Frequency [Hz] 

Fraunhofer IWES / ADCoS-Offshore

Risø DTU / HAWC2

GLGH / Bladed V4.0

POSTECH / Bladed V3.85

CGC / Bladed V3.80

IFE / 3Dfloat

Fedem Technology AS / FEDEM WindPower

CeSOS-NTNU / USFOS-vpOne

NTUA / GAST

SWE / Flex5-Poseidon

REpower /ANSYS

LUH / Flex5-Poseidon

ABS / ANSYS-BModes

NTNU / ASHES

ECN-WMC / Phatas-WMCfem

ABAQUS

Figure 3.19. Natural frequencies based on various OWT modeling codes [42].

ABAQUS

Figure 3.20. Fore-aft shear force at the mudline for our Abaqus

model and comparison with results presented in Popko et al. [42].

54

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0 2 4 6 8 10

−4

−2

0

2

4

6

time(sec)

η(m)

Airy

Stream

Figure 3.21. Surface wave elevation evaluated using Airy theory and a 9

th-order stream function approach.

ABAQUS

Figure 3.22. Out-of-plane deflection at center of X-brace at Level 2 on Side 2 of

our Abqaus model and comparison with results presented in Popko et al. [42].

55

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Table 3.6. Soil properties assumed for the jacket support structure [39].

Depth (m) Soil type γ

′

(kN/m3) φ (deg) cu (kPa) ε50(%)

0-3 SAND 10 36.0

3-5 SAND 10 36.0

5-7 CLAY 10 60.0 0.7

7-10 SAND 10 37.0

10-13 SAND 10 35.0

13-15 SAND 10 35.0

15-18 SAND 10 37.5

18-47 SAND 10 37.5

γ

′

: effective soil weight

φ: angle of internal friction

cu: undrained shear strength

ε50: strain that occurs at one-half of the maximum stress

ε50: in laboratory undrained compression test

Table 3.7. Development of sand p-y curves [44].

1. Theoretical ultimate bearing capacity

for wedge failure, pus

pus = (C1z+C2D)γ

′

z

2. Theoretical ultimate bearing capacity

for flow failure, pud

pud = C3Dγ

′

z

3. Governing ultimate bearing capacity,

pu

pu = min(pus, pud)

4. Develop p-y curve p = Apu tanh

kz

Apu

y



D: Average pile diameter from surface to depth

A: Factor to account for cyclic loading condition (take A = 0.9)

C1, C2, and C3: Coefficients determined from Figure 6.8.6-1 in API [44]

k: Initial modulus of subgrade reaction determined from Figure 6.8.7-1 in API [44]

In the API guidelines, p-y curves for sand and clay are developed using the procedures presented in Tables 3.7

and 3.8, respectively. Figures 3.23a and 3.23b present characteristic shapes of the p-y curves for sand and clay,

respectively. In our Abaqus model, the lateral stiffness of the soil is modeled using a nonlinear spring element,

SPRING1. Table 3.9 shows the effect of soil-structure interaction on the eigenfrequencies of the model; consideration of soil-structure interaction (SSI) effects leads to noticeable reduction in the system natural frequencies.

3.4.2 Hydrodynamic Loads and Associated Response on Jacket Members during Hurricane

Sandy

The hydrodynamic loading experienced by a jacket member is comprised of drag and inertia force components.

Morison’s equation is used to compute the hydrodynamic load per unit member length, ∆f , as follows:

∆f = ∆fD +∆fM =

1

2

CDρDur|ur|+

πD

2

4

CMρwu ̇r (3.23)

where ∆fD and ∆fM are the drag and inertia forces per unit length, respectively, CD is the drag coefficient taken as

1.0, and CM is the inertia coefficient taken as 2.0. Also, in Eq. 3.23, ur and  ̇ur, respectively, are the “relative” velocity

and acceleration (accounting for the motions of the water particles and the structure), ρw is the density of water, and

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Table 3.8. Development of clay p-y curves [44].

Static Loading

1. Compute ultimate soil resistance, pu

pu1 =

"

3+

γ

′

cu

z+

J

D

z

#

cuD

pu2 = 0.9cuD

pu = min(pu1, pu2)

2. Compute deflection at one-half the

ultimate soil resistance, y50

y50 = 2.5ε50D

3. Develop p-y curves

p

pu

= 0.5



y

y50 1/3

Dynamic Loading

1. Develop p-y curves Construct p-y curve in the same manner as for

static loading for values of p < 0.72pu

2. Determine transition depth, zr zr =

6cuD

γ

′D+Jcu

3. If depth z ≥ zr p = 0.72pu f or y > 3y50

4. If depth z < zr

p = 0.72pu at y = 3y50

p = 0.72pu



z

zr



at y = 15y50

Table 3.9. Variation of system natural frequencies under different foundation modeling assumptions.

Mode Natural frequencies (Hz)

Abaqus Abaqus Difference

(clamped at mudline) (including SSI) |%|

1 0.3333 0.3053 8.4

2 0.3333 0.3053 8.4

3 1.2155 0.9592 21.0

4 1.2155 0.9592 21.0

5 3.3643 2.3932 28.8

6 4.4354 3.4427 22.3

7 4.4354 3.4427 22.3

8 5.3242 4.7326 11.1

9 6.6084 5.1140 22.6

10 6.6084 5.1140 22.6

57

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(a) Representative p-y curves for sand.









 

. 	

. 	







	 
 



  


(b) Representative p-y curve for clay.

Figure 3.23. Characteristic Shapes of the p-y curves used in this study.

58

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D is the diameter of the jacket member. In the case of linear Gaussian waves, the inertia force in Morison’s equation

is a Gaussian process as it is a linear of the water particle acceleration which is a Gaussian process; the drag force,

however, is a non-Gaussian process as it is a nonlinear function of the water particle velocity.

We are interested in the response of the jacket support structure as various locations—braces, legs, and at the

mudline. The four response measures that we consider here are: axial force in brace, BRA-W-L4; axial force in

leg, LEG-SW-L4; vertical reaction force, Fz

, at mudline, LEG-SW-MUD; and bending moment, My, at mudline,

LEG-SW-MUD. Refer to Fig. 3.18 which helps to identify these response variables and their locations on the jacket

structure. Response statistics are for hydrodynamic loading alone and apply to a single hour during Hurricane Sandy

for the wind turbine at Site No. 1.

Table 3.10 summarizes response statistics considering hydrodynamic drag and inertia loads separately as well as

in combined (total) effect. Based on an estimate of the number of upcrossings of the mean of the response process,

one can compute a theoretical peak factor for response extremes, assuming the process were Gaussian [47]. As

shown in Table 3.10 for the axial force in brace, BRA-W-L4, the response due to inertia forces has skewness close to

zero, kurtosis close to 3, and peak factor close to the corresponding Gaussian peak factor—all of these findings are

in line with expected Gaussian characteristics of the response due to inertial load effects alone. Similar observations

can be made as well for the other response measures’ statistics under inertia loads, as can be seen in Tables 3.11,

3.12, and 3.13. In contrast, the response due to drag forces has a significantly higher kurtosis and a peak factor

larger than the corresponding Gaussian peak factor—therefore, the response due to drag forces is clearly strongly

non-Gaussian.

Table 3.10. Statistics of the axial force in a brace, BRA-W-L4, due to hydrodynamic loading

during Hurricane Sandy (corresponding to 50 hours after 00:00 UTC on October 28, 2012).

Axial force in a brace member, BRA-W-L4

drag inertia total

Mean (kN) 212 162 210

Max (kN) 1053 668 1100

Min (kN) -1334 -1084 -1499

SD (kN) 271 299 403

Skewness 0.31 -0.10 0.16

Kurtosis 6.62 2.79 3.35

Peak Factor (PF)1 4.66 3.08 3.25

PF (Gaussian)2 2.97 3.02 3.00

1 PF = Maximum(|Max− Mean|,|Min− Mean|)/SD

1 SD = standard deviation

2 Peak factor evaluated from the mean upcrossing rate

2 of the process, assuming it were Gaussian

Agarwal [48] studied the relative importance of drag and inertia forces to the tower base bending moment of an

offshore wind turbine supported by a monopile, which was a cylinder of 6 m diameter installed in 20 meters of water.

It was found in that study that the response due to hydrodynamic loading was dominated by inertia forces and the

response was close to a Gaussian process. However, the OC4 reference jacket support structure used in the present

study is composed of brace members of 1.0 m diameter and leg members of 1.2 m diameter, which are much smaller

sized sections than the monopile studied by Agarwal [48]. Thus, the relative contribution of drag to inertia forces

toward the total response is greatly increased in our study. From Tables 3.10, 3.11, 3.12, and 3.13, it is clear that

inertia and drag force effects are of comparable importance for all the response variables studied. The ratios of the

maximum response due to drag loads alone to the maximum response due to inertia loads alone are about 1.23, 1.00,

0.90, and 1.33, respectively, for the brace axial force (BRA-W-L4), the leg axial force (LEG-SW-L4), the vertical

reaction force at mudline (Fy at LEG-SW-MUD), and the bending moment at mudline (My at LEG-SW-MUD); the

corresponding ratios for the response standard deviation are about 0.91, 0.92, 0.98, and 0.90, respectively.

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Table 3.11. Statistics of the axial force in a leg, LEG-SW-L4, due to hydrodynamic loading

during Hurricane Sandy (corresponding to 50 hours after 00:00 UTC on October 28, 2012).

Axial force in a leg, LEG-SW-L4

drag inertia total

Mean (kN) -3237 -3110 -3231

Max (kN) 629 -1394 853

Min (kN) -5332 -5319 -5760

SD (kN) 533 577 781

Skewness 1.12 -0.17 0.47

Kurtosis 10.05 3.05 4.33

Peak Factor(PF) 7.26 3.83 5.23

PF (Gaussian) 3.02 3.06 3.03

Table 3.12. Statistics of the vertical reaction force, Fz, at the mudline, LEG-SW-MUD, due to hydrodynamic loading during Hurricane Sandy (corresponding to 50 hours after 00:00 UTC on October 28, 2012).

Vertical reaction force at mudline, LEG-SW-MUD

drag inertia total

Mean (kN) -3330 -3575 -3326

Max (kN) 3024 -467 3501

Min (kN) -5877 -6538 -6409

SD (kN) 874 890 1259

Skewness 2.22 -0.08 0.99

Kurtosis 12.88 3.44 5.87

Peak Factor(PF) 7.27 3.49 5.42

PF (Gaussian) 3.01 3.05 3.02

We note from the preceding results that although the drag and inertia contributions to the different response

variables are comparable, the response due to the combined or total hydrodynamic load effects, accounting for drag

and inertia, depends on the location and type of the evaluated response. For example, for axial force evaluated in

a brace (BRA-W-L4) and for the mudline reaction moment, My (at LEG-SW-MUD), the computed response extreme peak factors are quite close to the peak factors theoretically estimated based on the assumption of a Gaussian

response process. This implies that the 1-hour maximum values of these two response variables during Hurricane

Sandy can be estimated based on Gaussian response assumptions. In contrast, the computed response extreme peak

factors for the axial force in a leg (LEG-SW-L4) and for the mudline vertical reaction force, Fz (at LEG-SW-MUD)

are significantly higher than the corresponding Gaussian peak factors.

3.4.3 Effect of Hurricane-Induced Currents

For the case of a monopile-supported offshore wind turbine, because the contribution of drag loads to the total

hydrodynamic loads is insignificant as was shown by Agarwal [48], we might expect that the contribution of wave

currents to the total response would also be negligible in that case. In the present study, we know that drag load

effects for the OC4 jacket support structure are of comparable importance to the inertia load effects. Since the drag

load effects must include the contribution from ocean currents, we are interested in learning to what extent these

currents influence the total response.

For Hurricane Sandy, available depth-dependent ocean current velocities from HYCOM are vectorially combined with the wave particle velocities before computing drag forces. Figure 3.24 shows the variation with time of

the ocean current velocities, evaluated by post-processing HYCOM output at Site No. 1, during the UMCM simulation of Hurricane Sandy. Figure 3.25 shows how the ocean current velocity components, ucx and ucy, influence the

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Table 3.13. Statistics of the bending moment, My, at the mudline, LEG-SW-MUD, due to hydrodynamic

loading during Hurricane Sandy (corresponding to 50 hours after 00:00 UTC on October 28, 2012).

Bending moment at mudline, LEG-SW-MUD

drag inertia total

Mean (kN) 61 -2 57

Max (kN) 1641 1290 1846

Min (kN) -1714 -1170 -1779

SD (kN) 393 438 582

Skewness -0.35 0.09 -0.17

Kurtosis 6.36 2.73 3.17

Peak Factor(PF) 4.52 2.95 3.16

PF (Gaussian) 2.98 3.01 3.01

axial force in a brace (BRA-W-L4); including the ocean currents increases the maximum axial force in the brace by

about 19% (from 1255 kN to 1499 kN).

3.4.4 Hydrodynamic versus Aerodynamic Loads

In this section, we evaluate the relative importance of hydrodynamic loads versus aerodynamic loads toward different

jacket response measures. Figures 3.28 and 3.31 show, respectively, simulated time series of axial forces in diagonal

braces on Side 2 and in leg L3 at different vertical levels (refer to Fig. 3.15). These time series plots are taken from

a 1-hour simulation during Hurricane Sandy. In the brace members, while the wind load effect is dominant at the

upper levels of the jacket (e.g., Level 1), the wave load effect becomes dominant at the lower level (e.g. Levels 2-4).

In contrast, the axial force in the leg member (L3), even at the lowest levels, is significantly affected by both wind

and wave loads.

Figure 3.32 shows maximum mudline reaction forces and moments evaluated from 1-hour simulations (carried

out every 10 hours) over a period from 10 to 60 hours into the UMCM simulation of Hurricane Sandy. As can be

seen in this figure, the contribution of wind loads to the various mudline reaction forces and moments is not significant. It is only for the vertical reaction force, Fz

, at the mudline that the wind loads are relatively more important, but

even there, when wind and wave load effects are combined, the very largest maximum Fz value (which occurs at 50

hours) shows that the total effect on the 1-hour maximum Fz of wind and waves together is almost the same as that

due to waves alone.

3.5 Discussion and Conclusions

In-depth studies of the response, during Hurricane Sandy, of a 5-MW offshore wind turbine with a jacket support

structure have been presented. To evaluate the response of offshore wind turbines during the evolution of this hurricane, ten mid-Atlantic potential offshore wind plant sites were selected. The track and intensity of Hurricane Sandy

were numerically simulated by a fully coupled atmospheric-wave-ocean model, UMCM.

Based on directional wave spectra resulting from the UMCM output, hurricane-generated wave kinematics were

simulated using second-order wave theory that was presented in Chapter 2. It was shown that wave spectra based on

the first 1 minute each hour could be used to represent the entire 1-hour period and to simulate waves for that hour as

needed for subsequent turbine response computations.

While the vertical wind shear profile for Hurricane Ike in Chapter 2 was estimated using the classical log law,

in this chapter, we used wind field data from the WRF output, updated every 10 minutes and provided at several

elevations, to stochastically simulate needed wind velocity fields for Hurricane Sandy. The WRF output for Hurricane Sandy provided mean wind velocity data at 6 different levels up to 200 m above the surface. The vertical

61

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Current speed (m/s): to east direction

hour

z(m)

10 20 30 40 50 60 70

−50

−40

−30

−20

−10

0

−0.4

−0.2

0

0.2

0.4

0.6

Current speed (m/s): to north direction

hour

z(m)

10 20 30 40 50 60 70

−50

−40

−30

−20

−10

0

−1

−0.5

0

0.5

Figure 3.24. Variation with time of the depth-dependent current velocities during Hurricane Sandy (at the 50-m water depth location within Site No. 1).

wind profile that resulted, based on the WRF output, showed significant difference from the log law, which ignores

atmospheric stability effects. Because the mean wind velocity and wind direction during the hurricane show some

variation with time in each hour, the time-varying non-turbulent part of the full wind field was developed by using

an interpolation function based on six 10-min sampled wind field data values from the WRF output. The turbulent

wind part was stochastically simulated using standard Kaimal power spectra and coherence functions; the reference

wind velocity and friction velocity needed to define parameters of the Kaimal power spectra were evaluated using the

10-min wind speed and friction velocity values provided as part of the WRF output.

Due to the limitation of available software tools, an uncoupled modeling scheme was used to analyze the response of an offshore wind turbine with a jacket support structure. While in a coupled modeling approach, aerodynamic and hydrodynamic load effects can be evaluated simultaneously, an uncoupled modeling approach requires

separate computational steps to evaluate the aerodynamic loads and the hydrodynamic loads. The aerodynamic

load effects on the turbine rotor was first evaluated using a wind turbine model in FAST with a fixed base; the rotor

aerodynamic loads were then applied as point loads at the top of a model of a tower that was supported by a jacket

structure in Abaqus. Before evaluating the response of the offshore wind turbine with the jacket support during Hurricane Sandy, the uncoupled model was verified by comparing masses, natural frequencies, and the turbine response

in regular waves against results presented in the OC4 project report. For verification purposes, it was assumed that

the jacket structure was fixed at the mudline. We found that the masses, the natural frequencies, and the turbine response in regular waves, evaluated using our uncoupled model, were all comparable to the results presented in the

OC4 project report.

Because interaction between the soil and an embedded pile can change the dynamic characteristics of the wind

turbine, this interaction effect was included in our Abaqus model of the jacket support structure. In this model, the

interaction between the soil and the embedded pile was modeled using the p-y curve approach specified in the American Petroleum Institute (API) RP2A guidelines. The soil profile used for the design of the OC4 jacket was used

62

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-10

-5

0

5

10

-5

0

5

-5

0

5

400 420 440 460 480 500

-1500

-1000

-500

0

500

1000

1500

Time(sec)

with current

without current

Wave Elevation(m) 

࢛࢞ at z = -5m (m/s) (࢞ࢉ࢛ = 0.10m/s)

࢛࢟ at z = -5m (m/s) (࢟ࢉ࢛ = -0.63m/s)

Axial force at BRA-W-L4(kN) 

Figure 3.25. Time series at Site No. 1 of the wave elevation, the near-surface x-direction wave

and current velocities, the near-surface y-direction wave and current velocities, and the axial force in a brace, BRA-W-L4, after including and excluding the ocean current contribution

(corresponding to 50 hours after 00:00 UTC on October 28, 2012 during Hurricane Sandy).

63

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40

50

60

-10

0

10

-400

-200

0

200

-400

0

400

800

-1000

0

1000

200 220 240 260 280 300

-1000

0

1000

2000

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at BRA-W-L1 (kN) 

Axial force at BRA-W-L2(kN) 

Axial force at BRA-W-L3(kN) 

Axial force at BRA-W-L4(kN) 

(a) only wind loads.

Figure 3.26. Time history of diagonal brace axial forces on Side 2 at various vertical levels of the jacket support structure at Site No. 1 during Hurricane Sandy (only wind loads).

64

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40

50

60

-10

0

10

-400

-200

0

200

-400

0

400

800

-1000

0

1000

200 220 240 260 280 300

-1000

0

1000

2000

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at BRA-W-L1(kN) 

Axial force at BRA-W-L2(kN) 

Axial force at BRA-W-L3(kN) 

Axial force at BRA-W-L4(kN) 

(a) only wave loads.

Figure 3.27. Time history of diagonal brace axial forces on Side 2 at various vertical levels of the jacket support structure at Site No. 1 during Hurricane Sandy (only wave loads).

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40

50

60

-10

0

10

-400

-200

0

200

-400

0

400

800

-1000

0

1000

200 220 240 260 280 300

-1000

0

1000

2000

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at BRA-W-L1(kN) 

Axial force at BRA-W-L2(kN) 

Axial force at BRA-W-L3(kN) 

Axial force at BRA-W-L4(kN) 

(a) considering wind and wave loads.

Figure 3.28. Time history of diagonal brace axial forces on Side 2 at various vertical levels of the

jacket support structure at Site No. 1 during Hurricane Sandy (considering wind and wave loads).

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40

50

60

-10

0

10

-8000

-4000

0

-8000

-4000

0

-8000

-4000

0

200 220 240 260 280 300

-8000

-4000

0

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at LEG-SW-L1(kN) 

Axial force at LEG-SW-L2(kN) 

Axial force at LEG-SW-L3(kN) 

Axial force at LEG-SW-L4(kN) 

(a) only wind loads.

Figure 3.29. Time history of leg (L3) axial forces at various vertical levels of the

jacket support structure at Site No. 1 during Hurricane Sandy (only wind loads).

67

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40

50

60

-10

0

10

-8000

-4000

0

-8000

-4000

0

-8000

-4000

0

200 220 240 260 280 300

-8000

-4000

0

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at LEG-SW-L1(kN) 

Axial force at LEG-SW-L2(kN) 

Axial force at LEG-SW-L3(kN) 

Axial force at LEG-SW-L4(kN) 

(a) only wave loads.

Figure 3.30. Time history of leg (L3) axial forces at various vertical levels of the

jacket support structure at Site No. 1 during Hurricane Sandy (only wave loads).

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40

50

60

-10

0

10

-8000

-4000

0

-8000

-4000

0

-8000

-4000

0

200 220 240 260 280 300

-8000

-4000

0

Time(sec)

Hub height wind velocity(m/s) 

Wave Elevation(m) 

Axial force at LEG-SW-L1(kN) 

Axial force at LEG-SW-L2(kN) 

Axial force at LEG-SW-L3(kN) 

Axial force at LEG-SW-L4(kN) 

(a) considering wind and wave loads.

Figure 3.31. Time history of leg (L3) axial forces at various vertical levels of the jacket support structure at Site No. 1 during Hurricane Sandy (considering wind and wave loads).

69

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10 20 30 40 50 60

0

0.5

1

1.5

2

2.5

3

Time after 00:00 UTC 2012-10-28(hours)

Fx(MN)

only wave

only wind

wind+wave

10 20 30 40 50 60

0

1

2

3

4

5

6

7

8

9

Time after 00:00 UTC 2012-10-28(hours)

Mx(MN-m)

only wave

only wind

wind+wave

(a) x-direction.

10 20 30 40 50 60

0

2

4

6

8

10

12

14

16

18

Time after 00:00 UTC 2012-10-28(hours)

My(MN-m)

only wave

only wind

wind+wave

10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time after 00:00 UTC 2012-10-28(hours)

Fy(MN)

only wave

only wind

wind+wave

(b) y-direction.

10 20 30 40 50 60

0

5

10

15

20

25

Time after 00:00 UTC 2012-10-28(hours)

Fz(MN)

only wave

only wind

wind+wave

10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time after 00:00 UTC 2012-10-28(hours)

Mz(MN-m)

only wave

only wind

wind+wave

(c) z-direction.

Figure 3.32. Maximum mudline reaction forces (LEG-SW-MUD) at Site No. 1 during Hurricane Sandy.

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to evaluate the soil lateral stiffness characteristics. Because soil-structure interaction effects can significantly influence the overall dynamic characteristics of the structural system, we evaluated the effect of different soil-interaction

models on overall system eigenfrequencies.

In turbine response studies related to Hurricane Sandy, we first studied the hydrodynamic loads experienced

by a jacket member. As was shown by Agarwal [48], hydrodynamic loading on a monopile-supported wind turbine

is dominated by inertia force and the turbine response can then be close to a Gaussian process, especially for linear

waves. With the OC4 reference jacket used in this study, composed of brace members of 1.0 m diameter and leg

members of 1.2 m diameter, which are more slender than the 6-meter diameter monopile studied by Agarwal [48],

we found that drag load effects were comparable to inertia load effects and that the nonlinearity and non-Gaussian

character of the total hydrodynamic load effect increased. As a results, maximum response values estimated based

on Gaussian assumptions were significantly different from the actual response maxima computed in hour-long

simulations during Hurricane Sandy.

We also evaluated the effect of ocean currents on turbine response during Hurricane Sandy. Because drag load

effects for the OC4 jacket are comparable in importance to inertia load effects and because drag loads depend on

current velocities, the effect of including ocean currents toward the total response was found to be non-negligible as

was seen when we studied maximum axial forces in a jacket brace member. This finding suggests that it is important

to have fully coupled wave and ocean current inputs for realistic evaluation of the response of an offshore wind

turbine during a hurricane.

Finally, we evaluated the relative importance of hydrodynamic versus aerodynamic loads on the overall jacket

response during Hurricane Sandy. We found that the relative contribution of wind and wave loads varied depending

on the type and location of the jacket member being considered. For a diagonal brace member’s axial forces that

were studied, while the wind load effect was found to be dominant at upper levels in the jacket, the wave load effect

was dominant at the lower levels. In contrast, the axial force in a leg member at lower level was significantly influenced by both wind and wave loads. The contribution of wind load effects to the total mudline vertical reaction force

was found to be insignificant.

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4 Summary and Conclusions

4.1 Summary of Research Objectives

The simulation of a coupled wind, wave, and current inputs based on UMCM output and the response evaluation

of an offshore wind turbine using these coupled inputs were the primary goals of this study. In particular, we had

three main research objectives: (i) to investigate the characteristics of hurricane-generated wind, waves, and currents;

(ii) to generate time series input of turbulent wind fields and wave kinematics using the hurricane simulation output;

and (iii) to predict and interpret the turbine response during Hurricanes Ike (2008) and Sandy (2012) using the

assembled turbulent wind fields, wave kinematics, and current fields.

4.2 Summary of the Problem Descriptions

In order to assess the risks to potential U.S. offshore wind farms from the destructive environmental conditions

induced by hurricanes, Hurricane Ike(2008) and Sandy(2012) were numerically simulated by a state-of-the-art hurricane numerical simulation model, the University of Miami Coupled Model (UMCM). We used the wind, wave, and

current output data provided from these numerical simulations of the two hurricanes. UMCM consists of atmosphere

(WRF), ocean surface wave (UMWM), and ocean (HYCOM) component models.

We selected two and ten sites, respectively, for Hurricanes Ike (2008) and Sandy (2008). For Ike, single turbine units at the two sites in the Gulf of Mexico were studied. For Sandy, a detailed turbine response at one of ten

potential mid-Atlantic wind energy development sites was undertaken.

The coupled wind and wave fields at selected locations were stochastically simulated and we evaluated the

turbine response of a 5-MW offshore wind turbine supported by a monopile or a jacket structure over important

periods when the storm is close to making landfall.

For Hurricane Ike, we investigated:

• swell versus wind seas;

• the effect of yaw misalignment;

• the effect of blade pitch angle variation and control;

• the effect of blade azimuthal position on loads; and

• the effect of turbine parking strategies.

Also, under the assumption of zero yaw misalignment and of blades pitched to feather for Hurricane Sandy, we

investigated:

• hydrodynamic loads and associated response on jacket members;

• the effect of hurricane-induced currents; and

• a comparison of hurricane-induced hydrodynamic versus aerodynamic loads.

4.3 Conclusions

4.3.1 Modeling Hurricane Ike’s Influence

Because hurricane directional waves can be thought of as composed of two wave components, swell and wind seas,

which have different characteristics, their characteristics are evaluated after separating swell and wind seas from the

directional wave spectra resulting from the UMCM output by the wave age criterion. The mean wave frequencies

of swell components are significantly lower than resonant frequencies associated with tower bending. Also, the

72

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variation of mean wave frequency and wave direction corresponding to swell is relatively insignificant because the

evolution is not as strongly affected by the local wind.

While the contribution from hydrodynamic loading to the tower response is only very slightly influenced by

the amount of yaw misalignment, the aerodynamic loading contribution is significantly influenced by it. The significantly lower turbine loads in the case of zero yaw misalignment highlights the importance of a reliable yaw backup

power system, which is strongly recommended since a grid failure during a hurricane could result in loss of the

needed yaw control.

Blade pitch control is important during the hurricane; as expected, blades pitched to feather result in the lowest

tower response maxima.

While the tower base fore-aft moment in a case with zero yaw error does not vary greatly for different blade

azimuthal positions, the tower base side-to-side moment is seen to vary by a considerably larger amount. In general,

though not at all times during the hurricane, largest and smallest tower load maxima occurred for rotor configurations

where one blade is in the 0 and 180 degree azimuthal position, respectively.

While the tower base fore-aft moment in a case with zero yaw error is not significantly different with the different turbine parking strategies, the tower base side-to-side moment is seen to be noticeably different and the parkedstandstill case leads to systematically larger loads than the idling case during the hurricane.

4.3.2 Modeling Hurricane Sandy’s Influence

First, we evaluated the nature of the hydrodynamic loads experienced by a jacket member. The small section size

of jacket members makes the drag load effect comparable to the inertia load effect; it also makes the nonlinearity

of the total hydrodynamic load effect increase. Consequently, this high nonlinearity of the response process makes

differences between actual response maxima relative to Gaussian-based maxima significant.

We also evaluated the effect of ocean currents on the overall turbine response. Because the drag load effects

for the selected OC4 jacket are of comparable importance to the inertia load effect and because drag loads include

contributions from the ocean current, we found that the influence of ocean currents on the total response was nonnegligible. This was confirmed by studying maximum axial forces in a diagonal brace member of the jacket structure.

The relative importance of hydrodynamic and aerodynamic loads was also investigated. We found that the

relative contribution of wind versus wave loads depends on the type and location of the jacket member of interest.

For example, in the brace members studied, while wind load effects were dominant at the higher levels of the jacket

structure, wave load effects were dominant at the lower levels. Axial forces in leg members at the lower level, however, were significantly affected by both wind and wave loads. The contribution of wind load effects on total mudline

reaction forces was not significant.

73

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Appendices

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Appendix A

UMCM input files

A.1 Hurricane Ike Simulation

A.1.1 WRF(namelist.input)

&time_control

run_days = 8,

run_hours = 0,

run_minutes = 0,

run_seconds = 0,

start_year = 2008, 2008, 2008,

start_month = 09, 09, 09,

start_day = 08, 08, 08,

start_hour = 12, 12, 12,

start_minute = 00, 00, 00,

start_second = 00, 00, 00,

end_year = 2008, 2008, 2008,

end_month = 09, 09, 09,

end_day = 13, 13, 13,

end_hour = 12, 12, 12,

end_minute = 00, 00, 00,

end_second = 00, 00, 00,

interval_seconds = 21600

input_from_file = .true.,.false.,.false.,

history_interval = 60, 60, 60

frames_per_outfile = 1, 1, 1,

restart = .f.,

restart_interval = 360,

io_form_history = 2

io_form_restart = 2

io_form_input = 2

io_form_boundary = 2

debug_level = 0

input_from_hires = .f., .t., .t.,

rsmas_data_path = "/home/disk/manta9/joe/topo/ts",

/

&domains

sr_x = 0, 0, 0,

sr_y = 0, 0, 0,

time_step = 60,

time_step_fract_num = 0,

time_step_fract_den = 1,

max_dom = 3,

s_we = 1, 1, 1,

e_we = 400, 700, 331,

s_sn = 1, 1, 1,

e_sn = 360, 502, 331,

s_vert = 1, 1, 1,

e_vert = 36, 36, 36,

num_metgrid_levels = 22

eta_levels = 1.000, 0.996, 0.992, 0.988, 0.983, 0.970, 0.954,

0.934, 0.909, 0.880, 0.845, 0.807,

0.765, 0.719, 0.672, 0.622, 0.571,

0.520, 0.468, 0.420, 0.376, 0.335,

0.298, 0.263, 0.231, 0.202, 0.175,

0.150, 0.127, 0.106, 0.088, 0.070,

0.055, 0.040, 0.026, 0.000

use_surface = .false.

dx = 12000, 4000, 1333.33,

dy = 12000, 4000, 1333.33,

grid_id = 1, 2, 3,

parent_id = 0, 1, 2,

i_parent_start = 1, 35, 473,

j_parent_start = 1, 85, 90,

parent_grid_ratio = 1, 3, 3,

parent_time_step_ratio = 1, 3, 3,

feedback = 1,

smooth_option = 0

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vortex_interval = 20, 20, 20, 20,

max_vortex_speed = 40, 40, 40, 40,

time_to_move = 0, 9999, 0

corral_dist = 0, 25, 25, 25,

/

&physics

mp_physics = 4, 4, 4,

ra_lw_physics = 1, 1, 1,

ra_sw_physics = 1, 1, 1,

radt = 15, 15, 15,

sf_sfclay_physics = 1, 1, 1,

sf_surface_physics = 1, 1, 1,

bl_pbl_physics = 1, 1, 1,

bldt = 0, 0, 0,

cu_physics = 1, 0, 0,

cudt = 5, 0, 0,

isfflx = 1,

isftcflx = 2,

ifsnow = 0,

icloud = 1,

surface_input_source = 1,

num_soil_layers = 5,

sf_urban_physics = 0,

mp_zero_out = 0,

maxiens = 1,

maxens = 3,

maxens2 = 3,

maxens3 = 16,

ensdim = 144,

slope_rad = 0,

topo_shading = 0,

omlcall = 0,

oml_hml0 = 100,

oml_gamma = 0.14,

/

&fdda

grid_fdda = 1, 0, 0,

gfdda_inname = "wrffdda_d<domain>",

gfdda_end_h = 24, 24, 24,

gfdda_interval_m = 360, 360, 360,

fgdt = 0, 0, 0,

fgdtzero = 0, 0, 0,

if_no_pbl_nudging_uv = 0, 0, 0,

if_no_pbl_nudging_t = 0, 0, 0,

if_no_pbl_nudging_ph = 0, 0, 0,

if_zfac_uv = 0, 0, 0,

k_zfac_uv = 10, 10, 10,

if_zfac_t = 0, 0, 0,

k_zfac_t = 10, 10, 10,

if_zfac_ph = 0, 0, 0,

k_zfac_ph = 10, 10, 10,

dk_zfac_uv = 1, 1, 1,

dk_zfac_t = 1, 1, 1,

dk_zfac_ph = 1, 1, 1,

guv = 0.0003, 0.0000, 0.0000,

gt = 0.0000, 0.0000, 0.0000,

gph = 0.0000, 0.0000, 0.0000,

if_ramping = 1,

dtramp_min = 60.0,

io_form_gfdda = 2,

/

&dynamics

iso_temp = 0.,

w_damping = 1,

diff_opt = 1,

km_opt = 4,

diff_6th_opt = 0,

diff_6th_factor = 0.12,

base_temp = 290.

damp_opt = 0,

zdamp = 5000., 5000., 5000.,

dampcoef = 0.2, 0.2, 0.2

khdif = 0, 0, 0,

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kvdif = 0, 0, 0,

non_hydrostatic = .true., .true., .true.,

moist_adv_opt = 0, 0, 0,

scalar_adv_opt = 0, 0, 0,

use_baseparam_fr_nml = .true.

/

&bdy_control

spec_bdy_width = 5,

spec_zone = 1,

relax_zone = 4,

specified = .true., .false.,.false.,

nested = .false., .true., .true.,

/

&grib2

/

&namelist_quilt

nio_tasks_per_group = 0,

nio_groups = 1,

/

A.1.2 UMWM(main.nml)

&DOMAIN

isGlobal = .F. ! Global (.T.) or regional (.F.)

mm = 1195 ! Domain size in x

nm = 1075 ! Domain size in y

om = 37 ! Number of frequency bins

pm = 36 ! Number of directions

fmin = 0.0313 ! Lowest frequency bin [Hz]

fmax = 2.0 ! Highest frequency bin [Hz]

fprog = 0.5 ! Highest prognostic frequency bin [Hz]

startTimeStr = ’2008-09-08_12:00:00’ ! Simulation start time

stopTimeStr = ’2008-09-13_12:00:00’ ! Simulation end time

dtg = 60 ! Global (I/O) time step [s]

restart = .f. ! Restart from file

/

&PHYSICS

g = 9.80665 ! Gravitational acceleration [m/s^2]

nu_air = 1.56E-5 ! Kinematic viscosity of air [m^2/s]

nu_water = 0.9E-6 ! Kinematic viscosity of water [m^2/s]

sfct = 0.07 ! Surface tension [N/m]

kappa = 0.4 ! Von Karman constant

z = 10. ! Height of the input wind speed [m]

gustiness = 0.0 ! Random wind gustiness factor (should be between 0 and 0.2)

dmin = 20. ! Depth limiter [m]

explim = 1.1 ! Exponent limiter (0.69 ~ 100% growth)

sin_fac = 0.11 ! Input factor from following winds

sin_diss1 = 0.10 ! Damping factor from opposing winds

sin_diss2 = 0.01 ! Damping factor from swell overrunning wind

sds_fac = 42. ! Breaking dissipation factor

sds_power = 2.5 ! Saturation spectrum power

mss_fac = 120. ! Mean-square-slope adjustment to Sds

snl_fac = 5. ! Wave energy downshifting factor

sdt_fac = 0.01 ! Dissipation due to turbulence factor

sbf_fac = 0.003 ! Bottom friction coefficient [m/s]

sbp_fac = 0.003 ! Bottom percolation coefficient [m/s]

/

&GRID

gridFromFile = .T. ! Set to .T. if lon/lat fields are input from file

delx = 12000 ! Grid spacing in x [m] if gridFromFile = .F.

dely = 12000 ! Grid spacing in y [m] if gridFromFile = .F.

topoFromFile = .T. ! Set to .T. to input bathymetry from file

dpt = 1000 ! Constant water depth [m] if topoFromFile = .F.

fillEstuaries = .F. ! Set to .T. to fill cells with 3 land neighbours

fillLakes = .F. ! Set to .T. to fill user chosen seas/lakes

/

&FORCING

winds = .F. ! Wind input from file

currents = .F. ! Currents input from file

air_density = .F. ! Air density input from file

water_density = .F. ! Water density input from file

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/

&FORCING_CONSTANT

wspd0 = 25 ! Wind speed [m/s]

wdir0 = 0. ! Wind direction [rad]

uc0 = 0. ! x-component ocean current [m/s]

vc0 = 0. ! y-component ocean current [m/s]

rhoa0 = 1.2 ! Air density [kg/m^3]

rhow0 = 1025 ! Water density [kg/m^3]

/

&OUTPUT

outgrid = 1 ! Gridded output interval [hours]

outspec =-1 ! Spectrum output interval [hours]

outrst = 6 ! Restart output interval [hours]

xpl = 600 ! Grid cell in x for stdout (screen)

ypl = 400 ! Grid cell in y for stdout (screen)

stokes = .T. ! Output Stokes drift velocity fields

/

&STOKES

depths = 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30 35 40 50 60 70 80 90 100

A.1.3 HYCOM(blkdat.input)

ERA-15 forcing; flx-s14w; LWcorr; precip+2mm; SSSrlx; FCT2 tsadvc.; 0-tracer.

Sigma0; GDEM3 init; KPP mixed layer; SeaWiFS mon KPAR; nested in ATLd0.08 2.6;

S-Z(15-11): dp00/f/x/i=3m/1.125/12m/1m; ds=1m/1.125/4m; src_2.2.34;

12345678901234567890123456789012345678901234567890123456789012345678901234567890

22 ’iversn’ = hycom version number x10

201 ’iexpt ’ = experiment number x10

1000 ’idm ’ = longitudinal array size

1000 ’jdm ’ = latitudinal array size

700 ’itest ’ = grid point where detailed diagnostics are desired

700 ’jtest ’ = grid point where detailed diagnostics are desired

32 ’kdm ’ = number of layers

32 ’nhybrd’ = number of hybrid levels (0=all isopycnal)

14 ’nsigma’ = number of sigma levels (nhybrd-nsigma z-levels)

3.0 ’dp00 ’ = deep z-level spacing minimum thickness (m)

450.0 ’dp00x ’ = deep z-level spacing maximum thickness (m)

1.18 ’dp00f ’ = deep z-level spacing stretching factor (1.0=const.space)

0.5 ’ds00 ’ = shallow z-level spacing minimum thickness (m)

75.0 ’ds00x ’ = shallow z-level spacing maximum thickness (m)

1.18 ’ds00f ’ = shallow z-level spacing stretching factor (1.0=const.space)

1.0 ’dp00i ’ = deep iso-pycnal spacing minimum thickness (m)

6.0 ’isotop’ = shallowest depth for isopycnal layers (m, <0 from file)

35.0 ’saln0 ’ = initial salinity value (psu), only used for iniflg<2

1 ’locsig’ = locally-referenced pot. density for stability (0=F,1=T)

2 ’kapref’ = thermobaric ref. state (-1=input,0=none,1,2,3=constant)

2 ’thflag’ = reference pressure flag (0=Sigma-0, 2=Sigma-2)

34.0 ’thbase’ = reference density (sigma units)

0 ’vsigma’ = spacially varying isopycnal target densities (0=F,1=T)

28.10 ’sigma ’ = layer 1 isopycnal target density (sigma units)

28.90 ’sigma ’ = layer 2 isopycnal target density (sigma units)

29.70 ’sigma ’ = layer 3 isopycnal target density (sigma units)

30.50 ’sigma ’ = layer 4 isopycnal target density (sigma units)

30.95 ’sigma ’ = layer 5 isopycnal target density (sigma units)

31.50 ’sigma ’ = layer 6 isopycnal target density (sigma units)

32.05 ’sigma ’ = layer 7 isopycnal target density (sigma units)

32.60 ’sigma ’ = layer 8 isopycnal target density (sigma units)

33.15 ’sigma ’ = layer 9 isopycnal target density (sigma units)

33.70 ’sigma ’ = layer 10 isopycnal target density (sigma units)

34.25 ’sigma ’ = layer 11 isopycnal target density (sigma units)

34.75 ’sigma ’ = layer 12 isopycnal target density (sigma units)

35.15 ’sigma ’ = layer 13 isopycnal target density (sigma units)

35.50 ’sigma ’ = layer 14 isopycnal target density (sigma units)

35.80 ’sigma ’ = layer 15 isopycnal target density (sigma units)

36.04 ’sigma ’ = layer 16 isopycnal target density (sigma units)

36.20 ’sigma ’ = layer 17 isopycnal target density (sigma units)

36.38 ’sigma ’ = layer 18 isopycnal target density (sigma units)

36.52 ’sigma ’ = layer 19 isopycnal target density (sigma units)

36.62 ’sigma ’ = layer 20 isopycnal target density (sigma units)

36.70 ’sigma ’ = layer 21 isopycnal target density (sigma units)

36.77 ’sigma ’ = layer 22 isopycnal target density (sigma units)

36.83 ’sigma ’ = layer 23 isopycnal target density (sigma units)

36.89 ’sigma ’ = layer 24 isopycnal target density (sigma units)

36.97 ’sigma ’ = layer 25 isopycnal target density (sigma units)

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37.02 ’sigma ’ = layer 26 isopycnal target density (sigma units)

37.06 ’sigma ’ = layer 27 isopycnal target density (sigma units)

37.10 ’sigma ’ = layer 28 isopycnal target density (sigma units)

37.17 ’sigma ’ = layer 29 isopycnal target density (sigma units)

37.30 ’sigma ’ = layer 30 isopycnal target density (sigma units)

37.42 ’sigma ’ = layer 31 isopycnal target density (sigma units)

37.48 ’sigma ’ = layer 32 isopycnal target density (sigma units)

3 ’iniflg’ = initial state flag (0=levl, 1=zonl, 2=clim)

0 ’jerlv0’ = initial jerlov water type (1 to 5; 0 to use KPAR)

3 ’yrflag’ = days in year flag (0=360, 1=366, 2=366J1, 3=actual)

0 ’sshflg’ = diagnostic SSH flag (0=SSH,1=SSH&stericSSH)

0.0416667 ’dsurfq’ = number of days between model diagnostics at the surface

0.0416667 ’diagfq’ = number of days between model diagnostics

0.0 ’proffq’ = number of days between model diagnostics at selected locs

0.0 ’tilefq’ = number of days between model diagnostics on selected tiles

0.0 ’meanfq’ = number of days between model diagnostics (time averaged)

9999.0 ’rstrfq’ = number of days between model restart output

1.0 ’bnstfq’ = number of days between baro nesting archive input

1.0 ’nestfq’ = number of days between 3-d nesting archive input

0.125 ’cplifq’ = number of days (or time steps) between sea ice coupling

120.0 ’baclin’ = baroclinic time step (seconds), int. divisor of 86400

5.0 ’batrop’ = barotropic time step (seconds), int. div. of baclin/2

0 ’incflg’ = incremental update flag (0=no, 1=yes, 2=full-velocity)

100 ’incstp’ = no. timesteps for full update (1=direct insertion)

1 ’incupf’ = number of days of incremental updating input

0.125 ’wbaro ’ = barotropic time smoothing weight

1 ’btrlfr’ = leapfrog barotropic time step (0=F,1=T)

0 ’btrmas’ = barotropic is mass conserving (0=F,1=T)

8.0 ’hybrlx’ = HYBGEN: inverse relaxation coefficient (time steps)

0.01 ’hybiso’ = HYBGEN: Use PCM if layer is within hybiso of target density

3 ’hybmap’ = hybrid remapper flag (0=PCM, 1=PLM, 2=PPM, 3=WENO-like)

0 ’hybflg’ = hybrid generator flag (0=T&S, 1=th&S, 2=th&T)

0 ’advflg’ = thermal advection flag (0=T&S, 1=th&S, 2=th&T)

2 ’advtyp’ = scalar advection type (0=PCM,1=MPDATA,2=FCT2,4=FCT4)

2 ’momtyp’ = momentum advection type (2=2nd order, 4=4th order)

-1.0 ’slip ’ = +1 for free-slip, -1 for non-slip boundary conditions

0.05 ’visco2’ = deformation-dependent Laplacian viscosity factor

0.0 ’visco4’ = deformation-dependent biharmonic viscosity factor

0.0 ’facdf4’ = speed-dependent biharmonic viscosity factor

0.003 ’veldf2’ = diffusion velocity (m/s) for Laplacian momentum dissip.

0.02 ’veldf4’ = diffusion velocity (m/s) for biharmonic momentum dissip.

0.0 ’thkdf2’ = diffusion velocity (m/s) for Laplacian thickness diffus.

0.01 ’thkdf4’ = diffusion velocity (m/s) for biharmonic thickness diffus.

0.005 ’temdf2’ = diffusion velocity (m/s) for Laplacian temp/saln diffus.

1.0 ’temdfc’ = temp diffusion conservation (0.0,1.0 all dens,temp resp.)

0.0 ’vertmx’ = diffusion velocity (m/s) for momentum at MICOM M.L.base

0.05 ’cbar ’ = rms flow speed (m/s) for linear bottom friction

2.2e-3 ’cb ’ = coefficient of quadratic bottom friction

0.0 ’drglim’ = limiter for explicit friction (1.0 none, 0.0 implicit)

0.0 ’drgscl’ = scale factor for tidal drag (0.0 for no tidal drag)

500.0 ’thkdrg’ = thickness of bottom boundary layer for tidal drag (m)

10.0 ’thkbot’ = thickness of bottom boundary layer (m)

0.02 ’sigjmp’ = minimum density jump across interfaces (kg/m**3)

0.3 ’tmljmp’ = equivalent temperature jump across mixed-layer (degC)

15.0 ’thkmls’ = reference mixed-layer thickness for SSS relaxation (m)

0.0 ’thkmlt’ = reference mixed-layer thickness for SST relaxation (m)

5.0 ’thkriv’ = nominal thickness of river inflow (m)

20.0 ’thkfrz’ = maximum thickness of near-surface freezing zone (m)

0 ’iceflg’ = sea ice model flag (0=none,1=energy loan,2=coupled/esmf)

0.0 ’tfrz_0’ = ENLN: ice melting point (degC) at S=0psu

-0.054 ’tfrz_s’ = ENLN: gradient of ice melting point (degC/psu)

0.0 ’ticegr’ = ENLN: temp. grad. inside ice (deg/m); =0 use surtmp

0.5 ’hicemn’ = ENLN: minimum ice thickness (m)

10.0 ’hicemx’ = ENLN: maximum ice thickness (m)

0 ’ntracr’ = number of tracers (0=none,negative to initialize)

0 ’trcflg’ = tracer flags (one digit per tr, most sig. replicated)

240 ’tsofrq’ = number of time steps between anti-drift offset calcs

0.0 ’tofset’ = temperature anti-drift offset (degC/century)

0.0 ’sofset’ = salnity anti-drift offset (psu/century)

1 ’mlflag’ = mixed layer flag (0=none,1=KPP,2-3=KT,4=PWP,5=MY,6=GISS)

1 ’pensol’ = KT: activate penetrating solar rad. (0=F,1=T)

999.0 ’dtrate’ = KT: maximum permitted m.l. detrainment rate (m/day)

19.2 ’thkmin’ = KT/PWP: minimum mixed-layer thickness (m)

1 ’dypflg’ = KT/PWP: diapycnal mixing flag (0=none, 1=KPP, 2=explicit)

240 ’mixfrq’ = KT/PWP: number of time steps between diapycnal mix calcs

1.e-7 ’diapyc’ = KT/PWP: diapycnal diffusivity x buoyancy freq. (m**2/s**2)

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0.25 ’rigr ’ = PWP: critical gradient richardson number

0.65 ’ribc ’ = PWP: critical bulk richardson number

0.7 ’rinfty’ = KPP: maximum gradient richardson number (shear inst.)

0.25 ’ricr ’ = KPP: critical bulk richardson number

0.0 ’bldmin’ = KPP: minimum surface boundary layer thickness (m)

1200.0 ’bldmax’ = K-PROF: maximum surface boundary layer thickness (m)

0.7 ’cekman’ = KPP/KT: scale factor for Ekman depth

1.0 ’cmonob’ = KPP: scale factor for Monin-Obukov depth

0 ’bblkpp’ = KPP: activate bottom boundary layer (0=F,1=T)

1 ’shinst’ = KPP: activate shear instability mixing (0=F,1=T)

1 ’dbdiff’ = KPP: activate double diffusion mixing (0=F,1=T)

1 ’nonloc’ = KPP: activate nonlocal b. layer mixing (0=F,1=T)

0 ’botdiw’ = K-PROF: activate bot.enhan.int.wav mixing (0=F,1=T)

1 ’difout’ = K-PROF: output visc/diff coffs in archive (0=F,1=T)

0 ’difsmo’ = K-PROF: number of layers with horiz smooth diff coeffs

50.0e-4 ’difm0 ’ = KPP: max viscosity due to shear instability (m**2/s)

50.0e-4 ’difs0 ’ = KPP: max diffusivity due to shear instability (m**2/s)

0.3e-4 ’difmiw’ = KPP: background/internal wave viscosity (m**2/s)

0.1e-4 ’difsiw’ = KPP: background/internal wave diffusivity (m**2/s)

10.0e-4 ’dsfmax’ = KPP: salt fingering diffusivity factor (m**2/s)

1.9 ’rrho0 ’ = KPP: salt fingering rp=(alpha*delT)/(beta*delS)

98.96 ’cs ’ = KPP: value for nonlocal flux term

10.0 ’cstar ’ = KPP: value for nonlocal flux term

0.0 ’cv ’ = KPP: buoyancy frequency ratio (0.0 to use a fn. of N)

5.0 ’c11 ’ = KPP: value for turb velocity scale

2 ’hblflg’ = KPP: b. layer interp. flag (0=const.,1=linear,2=quad.)

2 ’niter ’ = KPP: iterations for semi-implicit soln. (2 recomended)

0 ’fltflg’ = FLOATS: synthetic float flag (0=no; 1=yes)

4 ’nfladv’ = FLOATS: advect every nfladv bacl. time steps (even, >=4)

1 ’nflsam’ = FLOATS: output (0=every nfladv steps; >0=no. of days)

0 ’intpfl’ = FLOATS: horiz. interp. (0=2nd order+n.n.; 1=n.n. only)

0 ’iturbv’ = FLOATS: add horiz. turb. advection velocity (0=no; 1=yes)

1 ’ismpfl’ = FLOATS: sample water properties at float (0=no; 1=yes)

4.63e-6 ’tbvar ’ = FLOATS: horizontal turb. vel. variance scale (m**2/s**2)

0.4 ’tdecri’ = FLOATS: inverse decorrelation time scale (1/day)

2 ’lbflag’ = lateral barotropic bndy flag (0=none, 1=port, 2=input)

2 ’tidflg’ = TIDES: tidal forcing flag (0=none,1=open-bdy,2=bdy&body)

11111111 ’tidcon’ = TIDES: 1 digit per (Q1K2P1N2O1K1S2M2), 0=off,1=on

0.06 ’tidsal’ = TIDES: scalar self attraction and loading factor (<0: file)

1 ’tidgen’ = TIDES: generic time (0=F,1=T)

1.0 ’tidrmp’ = TIDES: ramp time (days)

0.0 ’tid_t0’ = TIDES: origin for ramp time (model day)

12 ’clmflg’ = climatology frequency flag (6=bimonthly, 12=monthly)

2 ’wndflg’ = wind stress input flag (0=none,1=u/v-grid,2,3=p-grid)

1 ’ustflg’ = ustar forcing flag (3=input,1,2=wndspd,4=stress)

3 ’flxflg’ = thermal forcing flag (0=none,3=net-flux,1,2,4=sst-based)

0 ’empflg’ = E-P forcing flag (0=none,3=net_E-P, 1,2,4=sst-bas_E)

0 ’dswflg’ = diurnal shortwave flag (0=none,1=daily to diurnal corr.)

0 ’sssflg’ = SSS relaxation flag (0=none,1=clim,-1=clim&rmx)

0 ’lwflag’ = longwave (SST) flag (0=none,1=clim,2=atmos)

0 ’sstflg’ = SST relaxation flag (0=none,1=clim,2=atmos,3=observed)

0 ’icmflg’ = ice mask flag (0=none,1=clim,2=atmos,3=obs/coupled)

0 ’flxoff’ = net flux offset flag (0=F,1=T)

0 ’flxsmo’ = smooth surface fluxes (0=F,1=T)

0 ’relax ’ = activate lateral boundary nudging (0=F,1=T)

0 ’trcrlx’ = activate lat. bound. tracer nudging (0=F,1=T)

0 ’priver’ = rivers as a precipitation bogas (0=F,1=T)

0 ’epmass’ = treat evap-precip as a mass exchange (0=F,1=T)

A.2 Hurricane Sandy Simulation

A.2.1 WRF(namelist.input)

&time_control

run_days = 7,

run_hours = 0,

run_minutes = 0,

run_seconds = 0,

start_year = 2012, 2012, 2012,

start_month = 10, 10, 10,

start_day = 27, 27, 27,

start_hour = 00, 00, 00,

start_minute = 00, 00, 00,

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start_second = 00, 00, 00,

end_year = 2012, 2012, 2012,

end_month = 10, 10, 10,

end_day = 31, 31, 31,

end_hour = 00, 00, 00,

end_minute = 00, 00, 00,

end_second = 00, 00, 00,

interval_seconds = 21600

input_from_file = .t., .f., .f.,

input_from_hires = .f., .t., .t.,

history_interval = 60, 60, 60,

frames_per_outfile = 1, 1, 1,

restart = .f.,

restart_interval = 360,

io_form_history = 2

io_form_restart = 2

io_form_input = 2

io_form_boundary = 2

debug_level = 0

rsmas_data_path = "/home/disk/manta9/joe/topo/ts",

/

&domains

hypsometric_opt = 1,

time_step = 60,

time_step_fract_num = 0,

time_step_fract_den = 1,

max_dom = 2,

s_we = 1, 1, 1,

e_we = 400, 562, 361,

s_sn = 1, 1, 1,

e_sn = 360, 622, 361,

s_vert = 1, 1, 1,

e_vert = 36, 36, 36,

num_metgrid_levels = 27

eta_levels = 1.000, 0.996, 0.992, 0.988, 0.983, 0.970, 0.954,

0.934, 0.909, 0.880, 0.845, 0.807,

0.765, 0.719, 0.672, 0.622, 0.571,

0.520, 0.468, 0.420, 0.376, 0.335,

0.298, 0.263, 0.231, 0.202, 0.175,

0.150, 0.127, 0.106, 0.088, 0.070,

0.055, 0.040, 0.026, 0.000

use_surface = .false.

dx = 12000, 4000, 1333.33,

dy = 12000, 4000, 1333.33,

grid_id = 1, 2, 3,

parent_id = 0, 1, 2,

i_parent_start = 1, 130, 257,

j_parent_start = 1, 130, 205,

parent_grid_ratio = 1, 3, 3,

parent_time_step_ratio = 1, 3, 3,

feedback = 1,

smooth_option = 0

vortex_interval = 20, 20, 20,

max_vortex_speed = 40, 40, 40,

time_to_move = 0, 9999, 0,

corral_dist = 0, 15, 15,

track_level = 85000

/

&physics

mp_physics = 4, 4, 4,

ra_lw_physics = 4, 4, 4,

ra_sw_physics = 4, 4, 4,

radt = 15, 15, 15,

sf_sfclay_physics = 1, 1, 1,

sf_surface_physics = 1, 1, 1,

bl_pbl_physics = 1, 1, 1,

bldt = 0, 0, 0,

cu_physics = 1, 0, 0,

cudt = 5, 0, 0,

kfeta_trigger = 2,

isfflx = 1,

isftcflx = 2,

ifsnow = 0,

icloud = 1,

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surface_input_source = 1,

num_soil_layers = 5,

sf_urban_physics = 0,

mp_zero_out = 0,

maxiens = 1,

maxens = 3,

maxens2 = 3,

maxens3 = 16,

ensdim = 144,

slope_rad = 0,

topo_shading = 0,

omlcall = 0,

oml_hml0 = 100,

oml_gamma = 0.14,

stoch_force_opt = 0, 0, 0, ! turns SKEBS on (0=off)

stoch_vertstruc_opt = 1, 1, 1, ! makes SKEBS pattern vary with height

tot_backscat_psi = 1E-05, ! default perturbation amplitude for streamfunction field

tot_backscat_t = 1E-06, !default perturbation amplitude for temperature field

nens = 9, !random seed

/

&fdda

grid_fdda = 0, 0, 0,

gfdda_inname = "wrffdda_d<domain>",

gfdda_end_h = 120, 120, 24,

gfdda_interval_m = 360, 360, 360,

fgdt = 0, 0, 0,

fgdtzero = 0, 0, 0,

if_no_pbl_nudging_uv = 0, 0, 0,

if_no_pbl_nudging_t = 0, 0, 0,

if_no_pbl_nudging_ph = 0, 0, 0,

if_zfac_uv = 0, 0, 0,

k_zfac_uv = 10, 10, 10,

if_zfac_t = 0, 0, 0,

k_zfac_t = 10, 10, 10,

if_zfac_ph = 0, 0, 0,

k_zfac_ph = 10, 10, 10,

dk_zfac_uv = 1, 1, 1,

dk_zfac_t = 1, 1, 1,

dk_zfac_ph = 1, 1, 1,

guv = 0.0003, 0.0000, 0.0000,

gt = 0.0000, 0.0000, 0.0000,

gph = 0.0000, 0.0000, 0.0000,

if_ramping = 1,

dtramp_min = 60.0,

io_form_gfdda = 2,

/

&dynamics

iso_temp = 0.,

w_damping = 1,

diff_opt = 1,

km_opt = 4,

diff_6th_opt = 0,

diff_6th_factor = 0.12,

base_temp = 290.

damp_opt = 0,

zdamp = 5000., 5000., 5000.,

dampcoef = 0.2, 0.2, 0.2

khdif = 0, 0, 0,

kvdif = 0, 0, 0,

non_hydrostatic = .true., .true., .true.,

moist_adv_opt = 0, 0, 0,

scalar_adv_opt = 0, 0, 0,

use_baseparam_fr_nml = .true.

/

&bdy_control

spec_bdy_width = 5,

spec_zone = 1,

relax_zone = 4,

specified = .true., .false.,.false.,

nested = .false., .true., .true.,

perturb_bdy = 1, !boundary perturbations on (0=off)

/

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&grib2

/

&namelist_quilt

nio_tasks_per_group = 0,

nio_groups = 1,

/

A.2.2 UMWM(main.nml)

&DOMAIN

isGlobal = .F. ! Global (.T.) or regional (.F.)

mm = 1195 ! Domain size in x

nm = 1075 ! Domain size in y

om = 37 ! Number of frequency bins

pm = 36 ! Number of directions

fmin = 0.0313 ! Lowest frequency bin [Hz]

fmax = 2.0 ! Highest frequency bin [Hz]

fprog = 0.5 ! Highest prognostic frequency bin [Hz]

startTimeStr = ’2008-09-08_00:00:00’ ! Simulation start time

stopTimeStr = ’2008-09-08_01:00:00’ ! Simulation end time

dtg = 60 ! Global (I/O) time step [s]

restart = .f. ! Restart from file

/

&PHYSICS

g = 9.80665 ! Gravitational acceleration [m/s^2]

nu_air = 1.56E-5 ! Kinematic viscosity of air [m^2/s]

nu_water = 0.9E-6 ! Kinematic viscosity of water [m^2/s]

sfct = 0.07 ! Surface tension [N/m]

kappa = 0.4 ! Von Karman constant

z = 10. ! Height of the input wind speed [m]

gustiness = 0.0 ! Random wind gustiness factor (should be between 0 and 0.2)

dmin = 20. ! Depth limiter [m]

explim = 1.1 ! Exponent limiter (0.69 ~ 100% growth)

sin_fac = 0.11 ! Input factor from following winds

sin_diss1 = 0.10 ! Damping factor from opposing winds

sin_diss2 = 0.01 ! Damping factor from swell overrunning wind

sds_fac = 42. ! Breaking dissipation factor

sds_power = 2.5 ! Saturation spectrum power

mss_fac = 120. ! Mean-square-slope adjustment to Sds

snl_fac = 5. ! Wave energy downshifting factor

sdt_fac = 0.01 ! Dissipation due to turbulence factor

sbf_fac = 0.003 ! Bottom friction coefficient [m/s]

sbp_fac = 0.003 ! Bottom percolation coefficient [m/s]

/

&GRID

gridFromFile = .T. ! Set to .T. if lon/lat fields are input from file

delx = 12000 ! Grid spacing in x [m] if gridFromFile = .F.

dely = 12000 ! Grid spacing in y [m] if gridFromFile = .F.

topoFromFile = .T. ! Set to .T. to input bathymetry from file

dpt = 1000 ! Constant water depth [m] if topoFromFile = .F.

fillEstuaries = .F. ! Set to .T. to fill cells with 3 land neighbours

fillLakes = .F. ! Set to .T. to fill user chosen seas/lakes

/

&FORCING

winds = .F. ! Wind input from file

currents = .F. ! Currents input from file

air_density = .F. ! Air density input from file

water_density = .F. ! Water density input from file

/

&FORCING_CONSTANT

wspd0 = 25 ! Wind speed [m/s]

wdir0 = 0. ! Wind direction [rad]

uc0 = 0. ! x-component ocean current [m/s]

vc0 = 0. ! y-component ocean current [m/s]

rhoa0 = 1.2 ! Air density [kg/m^3]

rhow0 = 1030 !

Water density [kg/m^3]

/

&OUTPUT

outgrid = 1 ! Gridded output interval [hours]

outspec = 1 ! Spectrum output interval [hours]

outrst = 6 ! Restart output interval [hours]

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xpl = 400 ! Grid cell in x for stdout (screen)

ypl = 500 ! Grid cell in y for stdout (screen)

stokes = .T. ! Output Stokes drift velocity fields

/

&STOKES

depths = 0 0.2 0.4 0.6 0.8 1 2 5 10 30 50 100

A.2.3 HYCOM(blkdat.input)

ERA-15 forcing; flx-s14w; LWcorr; precip+2mm; SSSrlx; FCT2 tsadvc.; 0-tracer.

Sigma0; GDEM3 init; KPP mixed layer; SeaWiFS mon KPAR; nested in ATLd0.08 2.6;

S-Z(15-11): dp00/f/x/i=3m/1.125/12m/1m; ds=1m/1.125/4m; src_2.2.34;

12345678901234567890123456789012345678901234567890123456789012345678901234567890

22 ’iversn’ = hycom version number x10

201 ’iexpt ’ = experiment number x10

1000 ’idm ’ = longitudinal array size

1000 ’jdm ’ = latitudinal array size

700 ’itest ’ = grid point where detailed diagnostics are desired

700 ’jtest ’ = grid point where detailed diagnostics are desired

32 ’kdm ’ = number of layers

32 ’nhybrd’ = number of hybrid levels (0=all isopycnal)

14 ’nsigma’ = number of sigma levels (nhybrd-nsigma z-levels)

3.0 ’dp00 ’ = deep z-level spacing minimum thickness (m)

450.0 ’dp00x ’ = deep z-level spacing maximum thickness (m)

1.18 ’dp00f ’ = deep z-level spacing stretching factor (1.0=const.space)

0.5 ’ds00 ’ = shallow z-level spacing minimum thickness (m)

75.0 ’ds00x ’ = shallow z-level spacing maximum thickness (m)

1.18 ’ds00f ’ = shallow z-level spacing stretching factor (1.0=const.space)

1.0 ’dp00i ’ = deep iso-pycnal spacing minimum thickness (m)

6.0 ’isotop’ = shallowest depth for isopycnal layers (m, <0 from file)

35.0 ’saln0 ’ = initial salinity value (psu), only used for iniflg<2

1 ’locsig’ = locally-referenced pot. density for stability (0=F,1=T)

2 ’kapref’ = thermobaric ref. state (-1=input,0=none,1,2,3=constant)

2 ’thflag’ = reference pressure flag (0=Sigma-0, 2=Sigma-2)

34.0 ’thbase’ = reference density (sigma units)

0 ’vsigma’ = spacially varying isopycnal target densities (0=F,1=T)

28.10 ’sigma ’ = layer 1 isopycnal target density (sigma units)

28.90 ’sigma ’ = layer 2 isopycnal target density (sigma units)

29.70 ’sigma ’ = layer 3 isopycnal target density (sigma units)

30.50 ’sigma ’ = layer 4 isopycnal target density (sigma units)

30.95 ’sigma ’ = layer 5 isopycnal target density (sigma units)

31.50 ’sigma ’ = layer 6 isopycnal target density (sigma units)

32.05 ’sigma ’ = layer 7 isopycnal target density (sigma units)

32.60 ’sigma ’ = layer 8 isopycnal target density (sigma units)

33.15 ’sigma ’ = layer 9 isopycnal target density (sigma units)

33.70 ’sigma ’ = layer 10 isopycnal target density (sigma units)

34.25 ’sigma ’ = layer 11 isopycnal target density (sigma units)

34.75 ’sigma ’ = layer 12 isopycnal target density (sigma units)

35.15 ’sigma ’ = layer 13 isopycnal target density (sigma units)

35.50 ’sigma ’ = layer 14 isopycnal target density (sigma units)

35.80 ’sigma ’ = layer 15 isopycnal target density (sigma units)

36.04 ’sigma ’ = layer 16 isopycnal target density (sigma units)

36.20 ’sigma ’ = layer 17 isopycnal target density (sigma units)

36.38 ’sigma ’ = layer 18 isopycnal target density (sigma units)

36.52 ’sigma ’ = layer 19 isopycnal target density (sigma units)

36.62 ’sigma ’ = layer 20 isopycnal target density (sigma units)

36.70 ’sigma ’ = layer 21 isopycnal target density (sigma units)

36.77 ’sigma ’ = layer 22 isopycnal target density (sigma units)

36.83 ’sigma ’ = layer 23 isopycnal target density (sigma units)

36.89 ’sigma ’ = layer 24 isopycnal target density (sigma units)

36.97 ’sigma ’ = layer 25 isopycnal target density (sigma units)

37.02 ’sigma ’ = layer 26 isopycnal target density (sigma units)

37.06 ’sigma ’ = layer 27 isopycnal target density (sigma units)

37.10 ’sigma ’ = layer 28 isopycnal target density (sigma units)

37.17 ’sigma ’ = layer 29 isopycnal target density (sigma units)

37.30 ’sigma ’ = layer 30 isopycnal target density (sigma units)

37.42 ’sigma ’ = layer 31 isopycnal target density (sigma units)

37.48 ’sigma ’ = layer 32 isopycnal target density (sigma units)

3 ’iniflg’ = initial state flag (0=levl, 1=zonl, 2=clim)

0 ’jerlv0’ = initial jerlov water type (1 to 5; 0 to use KPAR)

3 ’yrflag’ = days in year flag (0=360, 1=366, 2=366J1, 3=actual)

0 ’sshflg’ = diagnostic SSH flag (0=SSH,1=SSH&stericSSH)

0.0416667 ’dsurfq’ = number of days between model diagnostics at the surface

0.0416667 ’diagfq’ = number of days between model diagnostics

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0.0 ’proffq’ = number of days between model diagnostics at selected locs

0.0 ’tilefq’ = number of days between model diagnostics on selected tiles

0.0 ’meanfq’ = number of days between model diagnostics (time averaged)

9999.0 ’rstrfq’ = number of days between model restart output

1.0 ’bnstfq’ = number of days between baro nesting archive input

1.0 ’nestfq’ = number of days between 3-d nesting archive input

0.125 ’cplifq’ = number of days (or time steps) between sea ice coupling

120.0 ’baclin’ = baroclinic time step (seconds), int. divisor of 86400

5.0 ’batrop’ = barotropic time step (seconds), int. div. of baclin/2

0 ’incflg’ = incremental update flag (0=no, 1=yes, 2=full-velocity)

100 ’incstp’ = no. timesteps for full update (1=direct insertion)

1 ’incupf’ = number of days of incremental updating input

0.125 ’wbaro ’ = barotropic time smoothing weight

1 ’btrlfr’ = leapfrog barotropic time step (0=F,1=T)

0 ’btrmas’ = barotropic is mass conserving (0=F,1=T)

8.0 ’hybrlx’ = HYBGEN: inverse relaxation coefficient (time steps)

0.01 ’hybiso’ = HYBGEN: Use PCM if layer is within hybiso of target density

3 ’hybmap’ = hybrid remapper flag (0=PCM, 1=PLM, 2=PPM, 3=WENO-like)

0 ’hybflg’ = hybrid generator flag (0=T&S, 1=th&S, 2=th&T)

0 ’advflg’ = thermal advection flag (0=T&S, 1=th&S, 2=th&T)

2 ’advtyp’ = scalar advection type (0=PCM,1=MPDATA,2=FCT2,4=FCT4)

2 ’momtyp’ = momentum advection type (2=2nd order, 4=4th order)

-1.0 ’slip ’ = +1 for free-slip, -1 for non-slip boundary conditions

0.05 ’visco2’ = deformation-dependent Laplacian viscosity factor

0.0 ’visco4’ = deformation-dependent biharmonic viscosity factor

0.0 ’facdf4’ = speed-dependent biharmonic viscosity factor

0.003 ’veldf2’ = diffusion velocity (m/s) for Laplacian momentum dissip.

0.02 ’veldf4’ = diffusion velocity (m/s) for biharmonic momentum dissip.

0.0 ’thkdf2’ = diffusion velocity (m/s) for Laplacian thickness diffus.

0.01 ’thkdf4’ = diffusion velocity (m/s) for biharmonic thickness diffus.

0.005 ’temdf2’ = diffusion velocity (m/s) for Laplacian temp/saln diffus.

1.0 ’temdfc’ = temp diffusion conservation (0.0,1.0 all dens,temp resp.)

0.0 ’vertmx’ = diffusion velocity (m/s) for momentum at MICOM M.L.base

0.05 ’cbar ’ = rms flow speed (m/s) for linear bottom friction

2.2e-3 ’cb ’ = coefficient of quadratic bottom friction

0.0 ’drglim’ = limiter for explicit friction (1.0 none, 0.0 implicit)

0.0 ’drgscl’ = scale factor for tidal drag (0.0 for no tidal drag)

500.0 ’thkdrg’ = thickness of bottom boundary layer for tidal drag (m)

10.0 ’thkbot’ = thickness of bottom boundary layer (m)

0.02 ’sigjmp’ = minimum density jump across interfaces (kg/m**3)

0.3 ’tmljmp’ = equivalent temperature jump across mixed-layer (degC)

15.0 ’thkmls’ = reference mixed-layer thickness for SSS relaxation (m)

0.0 ’thkmlt’ = reference mixed-layer thickness for SST relaxation (m)

5.0 ’thkriv’ = nominal thickness of river inflow (m)

20.0 ’thkfrz’ = maximum thickness of near-surface freezing zone (m)

0 ’iceflg’ = sea ice model flag (0=none,1=energy loan,2=coupled/esmf)

0.0 ’tfrz_0’ = ENLN: ice melting point (degC) at S=0psu

-0.054 ’tfrz_s’ = ENLN: gradient of ice melting point (degC/psu)

0.0 ’ticegr’ = ENLN: temp. grad. inside ice (deg/m); =0 use surtmp

0.5 ’hicemn’ = ENLN: minimum ice thickness (m)

10.0 ’hicemx’ = ENLN: maximum ice thickness (m)

0 ’ntracr’ = number of tracers (0=none,negative to initialize)

0 ’trcflg’ = tracer flags (one digit per tr, most sig. replicated)

240 ’tsofrq’ = number of time steps between anti-drift offset calcs

0.0 ’tofset’ = temperature anti-drift offset (degC/century)

0.0 ’sofset’ = salnity anti-drift offset (psu/century)

1 ’mlflag’ = mixed layer flag (0=none,1=KPP,2-3=KT,4=PWP,5=MY,6=GISS)

1 ’pensol’ = KT: activate penetrating solar rad. (0=F,1=T)

999.0 ’dtrate’ = KT: maximum permitted m.l. detrainment rate (m/day)

19.2 ’thkmin’ = KT/PWP: minimum mixed-layer thickness (m)

1 ’dypflg’ = KT/PWP: diapycnal mixing flag (0=none, 1=KPP, 2=explicit)

240 ’mixfrq’ = KT/PWP: number of time steps between diapycnal mix calcs

1.e-7 ’diapyc’ = KT/PWP: diapycnal diffusivity x buoyancy freq. (m**2/s**2)

0.25 ’rigr ’ = PWP: critical gradient richardson number

0.65 ’ribc ’ = PWP: critical bulk richardson number

0.7 ’rinfty’ = KPP: maximum gradient richardson number (shear inst.)

0.25 ’ricr ’ = KPP: critical bulk richardson number

0.0 ’bldmin’ = KPP: minimum surface boundary layer thickness (m)

1200.0 ’bldmax’ = K-PROF: maximum surface boundary layer thickness (m)

0.7 ’cekman’ = KPP/KT: scale factor for Ekman depth

1.0 ’cmonob’ = KPP: scale factor for Monin-Obukov depth

0 ’bblkpp’ = KPP: activate bottom boundary layer (0=F,1=T)

1 ’shinst’ = KPP: activate shear instability mixing (0=F,1=T)

1 ’dbdiff’ = KPP: activate double diffusion mixing (0=F,1=T)

1 ’nonloc’ = KPP: activate nonlocal b. layer mixing (0=F,1=T)

0 ’botdiw’ = K-PROF: activate bot.enhan.int.wav mixing (0=F,1=T)

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1 ’difout’ = K-PROF: output visc/diff coffs in archive (0=F,1=T)

0 ’difsmo’ = K-PROF: number of layers with horiz smooth diff coeffs

50.0e-4 ’difm0 ’ = KPP: max viscosity due to shear instability (m**2/s)

50.0e-4 ’difs0 ’ = KPP: max diffusivity due to shear instability (m**2/s)

0.3e-4 ’difmiw’ = KPP: background/internal wave viscosity (m**2/s)

0.1e-4 ’difsiw’ = KPP: background/internal wave diffusivity (m**2/s)

10.0e-4 ’dsfmax’ = KPP: salt fingering diffusivity factor (m**2/s)

1.9 ’rrho0 ’ = KPP: salt fingering rp=(alpha*delT)/(beta*delS)

98.96 ’cs ’ = KPP: value for nonlocal flux term

10.0 ’cstar ’ = KPP: value for nonlocal flux term

0.0 ’cv ’ = KPP: buoyancy frequency ratio (0.0 to use a fn. of N)

5.0 ’c11 ’ = KPP: value for turb velocity scale

2 ’hblflg’ = KPP: b. layer interp. flag (0=const.,1=linear,2=quad.)

2 ’niter ’ = KPP: iterations for semi-implicit soln. (2 recomended)

0 ’fltflg’ = FLOATS: synthetic float flag (0=no; 1=yes)

4 ’nfladv’ = FLOATS: advect every nfladv bacl. time steps (even, >=4)

1 ’nflsam’ = FLOATS: output (0=every nfladv steps; >0=no. of days)

0 ’intpfl’ = FLOATS: horiz. interp. (0=2nd order+n.n.; 1=n.n. only)

0 ’iturbv’ = FLOATS: add horiz. turb. advection velocity (0=no; 1=yes)

1 ’ismpfl’ = FLOATS: sample water properties at float (0=no; 1=yes)

4.63e-6 ’tbvar ’ = FLOATS: horizontal turb. vel. variance scale (m**2/s**2)

0.4 ’tdecri’ = FLOATS: inverse decorrelation time scale (1/day)

2 ’lbflag’ = lateral barotropic bndy flag (0=none, 1=port, 2=input)

2 ’tidflg’ = TIDES: tidal forcing flag (0=none,1=open-bdy,2=bdy&body)

11111111 ’tidcon’ = TIDES: 1 digit per (Q1K2P1N2O1K1S2M2), 0=off,1=on

0.06 ’tidsal’ = TIDES: scalar self attraction and loading factor (<0: file)

1 ’tidgen’ = TIDES: generic time (0=F,1=T)

1.0 ’tidrmp’ = TIDES: ramp time (days)

0.0 ’tid_t0’ = TIDES: origin for ramp time (model day)

12 ’clmflg’ = climatology frequency flag (6=bimonthly, 12=monthly)

1 ’wndflg’ = wind stress input flag (0=none,1=u/v-grid,2,3=p-grid)

2 ’ustflg’ = ustar forcing flag (3=input,1,2=wndspd,4=stress)

3 ’flxflg’ = thermal forcing flag (0=none,3=net-flux,1,2,4=sst-based)

0 ’empflg’ = E-P forcing flag (0=none,3=net_E-P, 1,2,4=sst-bas_E)

0 ’dswflg’ = diurnal shortwave flag (0=none,1=daily to diurnal corr.)

0 ’sssflg’ = SSS relaxation flag (0=none,1=clim,-1=clim&rmx)

0 ’lwflag’ = longwave (SST) flag (0=none,1=clim,2=atmos)

0 ’sstflg’ = SST relaxation flag (0=none,1=clim,2=atmos,3=observed)

0 ’icmflg’ = ice mask flag (0=none,1=clim,2=atmos,3=obs/coupled)

0 ’flxoff’ = net flux offset flag (0=F,1=T)

0 ’flxsmo’ = smooth surface fluxes (0=F,1=T)

0 ’relax ’ = activate lateral boundary nudging (0=F,1=T)

0 ’trcrlx’ = activate lat. bound. tracer nudging (0=F,1=T)

0 ’priver’ = rivers as a precipitation bogas (0=F,1=T)

0 ’epmass’ = treat evap-precip as a mass exchange (0=F,1=T)

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Appendix B

List of UMCM output

B.1 List of WRF output

dimensions:

Time = UNLIMITED; // (1 currently

DateStrLen = 19;

west_east = 399;

south_north = 359;

bottom_top = 35;

bottom_top_stag = 36;

soil_layers_stag = 5;

west_east_stag = 400;

south_north_stag = 360;

variables:

char Times(Time=1, DateStrLen=19);

float XLAT(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LATITUDE, SOUTH IS NEGATIVE";

:units = "degree_north";

:stagger = "";

float XLONG(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LONGITUDE, WEST IS NEGATIVE";

:units = "degree_east";

:stagger = "";

float LU_INDEX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LAND USE CATEGORY";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float ZNU(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "eta values on half (mass) levels";

:units = "";

:stagger = "";

float ZNW(Time=1, bottom_top_stag=36);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "eta values on full (w) levels";

:units = "";

:stagger = "Z";

float ZS(Time=1, soil_layers_stag=5);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "DEPTHS OF CENTERS OF SOIL LAYERS";

:units = "m";

:stagger = "Z";

float DZS(Time=1, soil_layers_stag=5);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "THICKNESSES OF SOIL LAYERS";

:units = "m";

:stagger = "Z";

float VAR_SSO(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "variance of subgrid-scale orography";

:units = "m2";

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:stagger = "";

:coordinates = "XLONG XLAT";

float LAP_HGT(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Laplacian of orography";

:units = "m";

:stagger = "";

:coordinates = "XLONG XLAT";

float U(Time=1, bottom_top=35, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "x-wind component";

:units = "m s-1";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float V(Time=1, bottom_top=35, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "y-wind component";

:units = "m s-1";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float W(Time=1, bottom_top_stag=36, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "z-wind component";

:units = "m s-1";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float PH(Time=1, bottom_top_stag=36, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "perturbation geopotential";

:units = "m2 s-2";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float PHB(Time=1, bottom_top_stag=36, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "base-state geopotential";

:units = "m2 s-2";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float T(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "perturbation potential temperature (theta-t0)";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

float HFX_FORCE(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "SCM ideal surface sensible heat flux";

:units = "W m-2";

:stagger = "";

float LH_FORCE(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "SCM ideal surface latent heat flux";

:units = "W m-2";

:stagger = "";

float TSK_FORCE(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

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:description = "SCM ideal surface skin temperature";

:units = "W m-2";

:stagger = "";

float HFX_FORCE_TEND(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "SCM ideal surface sensible heat flux tendency";

:units = "W m-2 s-1";

:stagger = "";

float LH_FORCE_TEND(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "SCM ideal surface latent heat flux tendency";

:units = "W m-2 s-1";

:stagger = "";

float TSK_FORCE_TEND(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "SCM ideal surface skin temperature tendency";

:units = "W m-2 s-1";

:stagger = "";

float MU(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "perturbation dry air mass in column";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float MUB(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "base state dry air mass in column";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float NEST_POS(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "-";

:units = "-";

:stagger = "";

:coordinates = "XLONG XLAT";

float P(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "perturbation pressure";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float PB(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "BASE STATE PRESSURE";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float FNM(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "upper weight for vertical stretching";

:units = "";

:stagger = "";

float FNP(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "lower weight for vertical stretching";

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:units = "";

:stagger = "";

float RDNW(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "inverse d(eta) values between full (w) levels";

:units = "";

:stagger = "";

float RDN(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "inverse d(eta) values between half (mass) levels";

:units = "";

:stagger = "";

float DNW(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "d(eta) values between full (w) levels";

:units = "";

:stagger = "";

float DN(Time=1, bottom_top=35);

:FieldType = 104; // int

:MemoryOrder = "Z ";

:description = "d(eta) values between half (mass) levels";

:units = "";

:stagger = "";

float CFN(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "extrapolation constant";

:units = "";

:stagger = "";

float CFN1(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "extrapolation constant";

:units = "";

:stagger = "";

float P_HYD(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "hydrostatic pressure";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float Q2(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "QV at 2 M";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float T2(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TEMP at 2 M";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

float TH2(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "POT TEMP at 2 M";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

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float PSFC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SFC PRESSURE";

:units = "Pa";

:stagger = "";

:coordinates = "XLONG XLAT";

float U10(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "U at 10 M";

:units = "m s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float V10(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "V at 10 M";

:units = "m s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float RDX(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "INVERSE X GRID LENGTH";

:units = "";

:stagger = "";

float RDY(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "INVERSE Y GRID LENGTH";

:units = "";

:stagger = "";

float RESM(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "TIME WEIGHT CONSTANT FOR SMALL STEPS";

:units = "";

:stagger = "";

float ZETATOP(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "ZETA AT MODEL TOP";

:units = "";

:stagger = "";

float CF1(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "2nd order extrapolation constant";

:units = "";

:stagger = "";

float CF2(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "2nd order extrapolation constant";

:units = "";

:stagger = "";

float CF3(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "2nd order extrapolation constant";

:units = "";

:stagger = "";

int ITIMESTEP(Time=1);

:FieldType = 106; // int

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:MemoryOrder = "0 ";

:description = "";

:units = "";

:stagger = "";

float XTIME(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "minutes since simulation start";

:units = "";

:stagger = "";

float QVAPOR(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Water vapor mixing ratio";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float QCLOUD(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Cloud water mixing ratio";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float QRAIN(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Rain water mixing ratio";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float QICE(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Ice mixing ratio";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float QSNOW(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Snow mixing ratio";

:units = "kg kg-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float SHDMAX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ANNUAL MAX VEG FRACTION";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SHDMIN(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ANNUAL MIN VEG FRACTION";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOALB(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ANNUAL MAX SNOW ALBEDO IN FRACTION";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

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float TSLB(Time=1, soil_layers_stag=5, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "SOIL TEMPERATURE";

:units = "K";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float SMOIS(Time=1, soil_layers_stag=5, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "SOIL MOISTURE";

:units = "m3 m-3";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float SH2O(Time=1, soil_layers_stag=5, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "SOIL LIQUID WATER";

:units = "m3 m-3";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float SMCREL(Time=1, soil_layers_stag=5, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "RELATIVE SOIL MOISTURE";

:units = "";

:stagger = "Z";

:coordinates = "XLONG XLAT";

float SEAICE(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SEA ICE FLAG";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float XICEM(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SEA ICE FLAG (PREVIOUS STEP)";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SFROFF(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SURFACE RUNOFF";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float UDROFF(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "UNDERGROUND RUNOFF";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

int IVGTYP(Time=1, south_north=359, west_east=399);

:FieldType = 106; // int

:MemoryOrder = "XY ";

:description = "DOMINANT VEGETATION CATEGORY";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

int ISLTYP(Time=1, south_north=359, west_east=399);

:FieldType = 106; // int

:MemoryOrder = "XY ";

:description = "DOMINANT SOIL CATEGORY";

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:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float VEGFRA(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "VEGETATION FRACTION";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float GRDFLX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "GROUND HEAT FLUX";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float ACGRDFLX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED GROUND HEAT FLUX";

:units = "J m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float ACSNOM(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED MELTED SNOW";

:units = "kg m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOW(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SNOW WATER EQUIVALENT";

:units = "kg m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOWH(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "PHYSICAL SNOW DEPTH";

:units = "m";

:stagger = "";

:coordinates = "XLONG XLAT";

float CANWAT(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "CANOPY WATER";

:units = "kg m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float SSTSK(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SKIN SEA SURFACE TEMPERATURE";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

float LAI(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Leaf area index";

:units = "area/area";

:stagger = "";

:coordinates = "XLONG XLAT";

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float VAR(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "OROGRAPHIC VARIANCE";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float MAPFAC_M(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on mass grid";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float MAPFAC_U(Time=1, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on u-grid";

:units = "";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float MAPFAC_V(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on v-grid";

:units = "";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float MAPFAC_MX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on mass grid, x direction";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float MAPFAC_MY(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on mass grid, y direction";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float MAPFAC_UX(Time=1, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on u-grid, x direction";

:units = "";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float MAPFAC_UY(Time=1, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on u-grid, y direction";

:units = "";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float MAPFAC_VX(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on v-grid, x direction";

:units = "";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float MF_VX_INV(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Inverse map scale factor on v-grid, x direction";

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:units = "";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float MAPFAC_VY(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Map scale factor on v-grid, y direction";

:units = "";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float F(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Coriolis sine latitude term";

:units = "s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float E(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Coriolis cosine latitude term";

:units = "s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float SINALPHA(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Local sine of map rotation";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float COSALPHA(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Local cosine of map rotation";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float HGT(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "Terrain Height";

:units = "m";

:stagger = "";

:coordinates = "XLONG XLAT";

float TAUX_ESMF(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "WIND STRESS X-COMPONENT FROM UMCM";

:units = "N/m^2";

:stagger = "";

:coordinates = "XLONG XLAT";

float TAUY_ESMF(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "WIND STRESS Y-COMPONENT FROM UMCM";

:units = "N/m^2";

:stagger = "";

:coordinates = "XLONG XLAT";

float TSK(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SURFACE SKIN TEMPERATURE";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

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float P_TOP(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "PRESSURE TOP OF THE MODEL";

:units = "Pa";

:stagger = "";

float T00(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "BASE STATE TEMPERATURE";

:units = "K";

:stagger = "";

float P00(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "BASE STATE PRESURE";

:units = "Pa";

:stagger = "";

float TLP(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "BASE STATE LAPSE RATE";

:units = "";

:stagger = "";

float TISO(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "TEMP AT WHICH THE BASE T TURNS CONST";

:units = "K";

:stagger = "";

float MAX_MSTFX(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "Max map factor in domain";

:units = "";

:stagger = "";

float MAX_MSTFY(Time=1);

:FieldType = 104; // int

:MemoryOrder = "0 ";

:description = "Max map factor in domain";

:units = "";

:stagger = "";

float RAINC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED TOTAL CUMULUS PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINSH(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED SHALLOW CUMULUS PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINNC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED TOTAL GRID SCALE PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float PRATEC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

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:description = "PRECIP RATE FROM CUMULUS SCHEME";

:units = "mm s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float PRATESH(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "PRECIP RATE FROM SHALLOW CUMULUS SCHEME";

:units = "mm s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINCV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP CUMULUS PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINSHV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP SHALLOW CUMULUS PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINNCV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP NONCONVECTIVE PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float RAINBL(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "PBL TIME-STEP TOTAL PRECIPITATION";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOWNC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED TOTAL GRID SCALE SNOW AND ICE";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float GRAUPELNC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED TOTAL GRID SCALE GRAUPEL";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float HAILNC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED TOTAL GRID SCALE HAIL";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOWNCV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP NONCONVECTIVE SNOW AND ICE";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

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float GRAUPELNCV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP NONCONVECTIVE GRAUPEL";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float HAILNCV(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TIME-STEP NONCONVECTIVE HAIL";

:units = "mm";

:stagger = "";

:coordinates = "XLONG XLAT";

float REFL_10CM(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "Radar reflectivity (lamda = 10 cm)";

:units = "dBZ";

:stagger = "";

:coordinates = "XLONG XLAT";

float CLDFRA(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "CLOUD FRACTION";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SWDOWN(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "DOWNWARD SHORT WAVE FLUX AT GROUND SURFACE";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float GLW(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "DOWNWARD LONG WAVE FLUX AT GROUND SURFACE";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float SWNORM(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "NORMAL SHORT WAVE FLUX AT GROUND SURFACE (SLOPE-DEPENDENT)";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float OLR(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "TOA OUTGOING LONG WAVE";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float XLAT_U(Time=1, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LATITUDE, SOUTH IS NEGATIVE";

:units = "degree_north";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float XLONG_U(Time=1, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XY ";

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:description = "LONGITUDE, WEST IS NEGATIVE";

:units = "degree_east";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float XLAT_V(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LATITUDE, SOUTH IS NEGATIVE";

:units = "degree_north";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float XLONG_V(Time=1, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LONGITUDE, WEST IS NEGATIVE";

:units = "degree_east";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float ALBEDO(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ALBEDO";

:units = "-";

:stagger = "";

:coordinates = "XLONG XLAT";

float CLAT(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "COMPUTATIONAL GRID LATITUDE, SOUTH IS NEGATIVE";

:units = "degree_north";

:stagger = "";

:coordinates = "XLONG XLAT";

float ALBBCK(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "BACKGROUND ALBEDO";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float EMISS(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SURFACE EMISSIVITY";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float NOAHRES(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "RESIDUAL OF THE NOAH SURFACE ENERGY BUDGET";

:units = "W m{-2}";

:stagger = "";

:coordinates = "XLONG XLAT";

float TMN(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SOIL TEMPERATURE AT LOWER BOUNDARY";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

float XLAND(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LAND MASK (1 FOR LAND, 2 FOR WATER)";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

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float UST(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "U* IN SIMILARITY THEORY";

:units = "m s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float PBLH(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "PBL HEIGHT";

:units = "m";

:stagger = "";

:coordinates = "XLONG XLAT";

float HFX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "UPWARD HEAT FLUX AT THE SURFACE";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float QFX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "UPWARD MOISTURE FLUX AT THE SURFACE";

:units = "kg m-2 s-1";

:stagger = "";

:coordinates = "XLONG XLAT";

float LH(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LATENT HEAT FLUX AT THE SURFACE";

:units = "W m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float ACHFX(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED UPWARD HEAT FLUX AT THE SURFACE";

:units = "J m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float ACLHF(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "ACCUMULATED UPWARD LATENT HEAT FLUX AT THE SURFACE";

:units = "J m-2";

:stagger = "";

:coordinates = "XLONG XLAT";

float SNOWC(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "FLAG INDICATING SNOW COVERAGE (1 FOR SNOW COVER)";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SR(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "fraction of frozen precipitation";

:units = "-";

:stagger = "";

:coordinates = "XLONG XLAT";

int SAVE_TOPO_FROM_REAL(Time=1);

:FieldType = 106; // int

:MemoryOrder = "0 ";

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:description = "1=original topo from real/0=topo modified by WRF";

:units = "flag";

:stagger = "";

float VERTSTRUCC(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "vertical structure for stoch. forcing";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float VERTSTRUCS(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "vertical structure for stoch. forcing";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float RU_TENDF_STOCH(Time=1, bottom_top=35, south_north=359, west_east_stag=400);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "stochastic forcing, U";

:units = "m/s";

:stagger = "X";

:coordinates = "XLONG_U XLAT_U";

float RV_TENDF_STOCH(Time=1, bottom_top=35, south_north_stag=360, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "stochastic forcing, V";

:units = "m/s";

:stagger = "Y";

:coordinates = "XLONG_V XLAT_V";

float RT_TENDF_STOCH(Time=1, bottom_top=35, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XYZ";

:description = "stochastic forcing, T";

:units = "K/s";

:stagger = "";

:coordinates = "XLONG XLAT";

int SEED1(Time=1);

:FieldType = 106; // int

:MemoryOrder = "0 ";

:description = "RANDOM SEED NUMBER 1";

:units = "";

:stagger = "";

int SEED2(Time=1);

:FieldType = 106; // int

:MemoryOrder = "0 ";

:description = "RANDOM SEED NUMBER 2";

:units = "";

:stagger = "";

float LANDMASK(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "LAND MASK (1 FOR LAND, 0 FOR WATER)";

:units = "";

:stagger = "";

:coordinates = "XLONG XLAT";

float SST(Time=1, south_north=359, west_east=399);

:FieldType = 104; // int

:MemoryOrder = "XY ";

:description = "SEA SURFACE TEMPERATURE";

:units = "K";

:stagger = "";

:coordinates = "XLONG XLAT";

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B.2 List of UMWM output

dimensions:

x = 1195;

y = 1075;

f = 37;

th = 36;

z = 19;

variables:

float z(z=19);

:description = "Depth";

:units = "m";

float u_stokes(z=19, y=1075, x=1195);

:description = "Stokes drift x-component";

:units = "m/s";

float v_stokes(z=19, y=1075, x=1195);

:description = "Stokes drift y-component";

:units = "m/s";

float frequency(f=37);

:description = "Frequency";

:units = "Hz";

float theta(th=36);

:description = "Directions";

:units = "rad";

float lon(y=1075, x=1195);

:description = "Longitude";

:units = "degrees East";

float lat(y=1075, x=1195);

:description = "Latitude";

:units = "degrees North";

int seamask(y=1075, x=1195);

:description = "Seamask";

:units = "non-dimensional";

float depth(y=1075, x=1195);

:description = "Ocean depth";

:units = "m";

float wspd(y=1075, x=1195);

:description = "Wind speed";

:units = "m/s";

float wdir(y=1075, x=1195);

:description = "Water density";

:units = "kg/m^3";

float uc(y=1075, x=1195);

:description = "Ocean current y-component";

:units = "m/s";

float vc(y=1075, x=1195);

float rhoa(y=1075, x=1195);

float rhow(y=1075, x=1195);

float momx(y=1075, x=1195);

:description = "Momentum, x-component";

:units = "kgm/s";

float momy(y=1075, x=1195);

:description = "Momentum, y-component";

:units = "kgm/s";

float cgmxx(y=1075, x=1195);

:description = "Cg*Momentum, xx-component";

:units = "kgm^2/s^2";

103

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float cgmxy(y=1075, x=1195);

:description = "Cg*Momentum, xy-component";

:units = "kgm^2/s^2";

float cgmyy(y=1075, x=1195);

:description = "Cg*Momentum, yy-component";

:units = "kgm^2/s^2";

float taux_form(y=1075, x=1195);

:description = "Form drag, x-component";

:units = "N/m^2";

float tauy_form(y=1075, x=1195);

:description = "Form drag, y-component";

:units = "N/m^2";

float taux_form_1(y=1075, x=1195);

:description = "Form drag, part 1, x-component";

:units = "N/m^2";

float tauy_form_1(y=1075, x=1195);

:description = "Form drag, part 1, y-component";

:units = "N/m^2";

float taux_form_2(y=1075, x=1195);

:description = "Form drag, part 2, x-component";

:units = "N/m^2";

float tauy_form_2(y=1075, x=1195);

:description = "Form drag, part 2, y-component";

:units = "N/m^2";

float taux_form_3(y=1075, x=1195);

:description = "Form drag, part 3, x-component";

:units = "N/m^2";

float tauy_form_3(y=1075, x=1195);

:description = "Form drag, part 3, y-component";

:units = "N/m^2";

float taux_skin(y=1075, x=1195);

:description = "Skin drag, x-component";

:units = "N/m^2";

float tauy_skin(y=1075, x=1195);

:description = "Skin drag, y-component";

:units = "N/m^2";

float taux_ocn(y=1075, x=1195);

:description = "Momentum flux from breaking waves to ocean top, x-component";

:units = "N/m^2";

float tauy_ocn(y=1075, x=1195);

:description = "Momentum flux from breaking waves to ocean top, y-component";

:units = "N/m^2";

float taux_bot(y=1075, x=1195);

:description = "Momentum flux from waves to ocean bottom, x-component";

:units = "N/m^2";

float tauy_bot(y=1075, x=1195);

:description = "Momentum flux from waves to ocean bottom, y-component";

:units = "N/m^2";

float taux_snl(y=1075, x=1195);

:description = "Momentum flux due to Snl, x-component";

:units = "N/m^2";

float tauy_snl(y=1075, x=1195);

:description = "Momentum flux due to Snl, y-component";

:units = "N/m^2";

float tailatmx(y=1075, x=1195);

:description = "Atmosphere tail stress part, x-component";

:units = "N/m^2";

104

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float tailatmy(y=1075, x=1195);

:description = "Atmosphere tail stress part, y-component";

:units = "N/m^2";

float tailocnx(y=1075, x=1195);

:description = "Ocean tail stress part, x-component";

:units = "N/m^2";

float tailocny(y=1075, x=1195);

:description = "Ocean tail stress part, y-component";

:units = "N/m^2";

float cd(y=1075, x=1195);

:description = "Drag coefficient of air";

:units = "non-dimensional";

float ust(y=1075, x=1195);

:description = "Friction velocity of air";

:units = "m/s";

float swh(y=1075, x=1195);

:description = "Significant wave height";

:units = "m";

float mss(y=1075, x=1195);

:description = "Mean-squared slope";

:units = "non-dimensional";

float mwp(y=1075, x=1195);

:description = "Mean wave period";

:units = "s";

float mwl(y=1075, x=1195);

:description = "Mean wavelength";

:units = "m";

float mwd(y=1075, x=1195);

:description = "Mean wave direction";

:units = "rad";

float dwp(y=1075, x=1195);

:description = "Dominant wave period";

:units = "s";

float dwl(y=1075, x=1195);

:description = "Dominant wavelength";

:units = "m";

float dwd(y=1075, x=1195);

:description = "Dominant wave direction";

:units = "rad";

float dcp0(y=1075, x=1195);

:description = "Dominant phase speed, intrinsic";

:units = "m/s";

float dcg0(y=1075, x=1195);

:description = "Dominant group speed, intrinsic";

:units = "m/s";

float dcp(y=1075, x=1195);

:description = "Dominant phase speed";

:units = "m/s";

float dcg(y=1075, x=1195);

:description = "Dominant group speed";

:units = "m/s";

}

B.3 List of HYCOM output

dimensions:

MT = UNLIMITED; // (1 currently

105

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Latitude = 1000;

Longitude = 1000;

Depth = 40;

variables:

double MT(MT=1);

:long_name = "time";

:units = "days since 1900-12-31 00:00:00";

:calendar = "gregorian";

:axis = "T";

double Date(MT=1);

:long_name = "date";

:units = "day as %Y%m%d.%f";

:C_format = "%13.4f";

:FORTRAN_format = "(f13.4)";

float Depth(Depth=40);

:standard_name = "depth";

:units = "m";

:positive = "down";

:axis = "Z";

float Latitude(Latitude=1000);

:standard_name = "latitude";

:units = "degrees_north";

:axis = "Y";

float Longitude(Longitude=1000);

:standard_name = "longitude";

:units = "degrees_east";

:point_spacing = "even";

:axis = "X";

float u(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "eastward_sea_water_velocity";

:units = "m/s";

:_FillValue = 1.2676506E30f; // float

:valid_range = -1.975024f, 1.876598f; // float

:long_name = " u-veloc. [20.1H]";

float v(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "northward_sea_water_velocity";

:units = "m/s";

:_FillValue = 1.2676506E30f; // float

:valid_range = -1.3474879f, 2.665912f; // float

:long_name = " v-veloc. [20.1H]";

float w_velocity(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "upward_sea_water_velocity";

:units = "m/s";

:_FillValue = 1.2676506E30f; // float

:valid_range = -0.037467636f, 0.017186552f; // float

:long_name = " w-veloc. [20.1H]";

float water_temp(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "sea_water_temperature";

:units = "degC";

:_FillValue = 1.2676506E30f; // float

:valid_range = 2.6080048f, 30.902374f; // float

:long_name = " temp [20.1H]";

float salinity(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "sea_water_salinity";

:units = "psu";

:_FillValue = 1.2676506E30f; // float

:valid_range = 12.106584f, 38.24341f; // float

:long_name = " salinity [20.1H]";

float pot_density(MT=1, Depth=40, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "sea_water_potential_density";

106

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:units = "sigma";

:_FillValue = 1.2676506E30f; // float

:valid_range = 13.050988f, 36.986603f; // float

:long_name = " p.dens [20.1H]";

float bathymetry(MT=1, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:units = "m";

:_FillValue = 1.2676506E30f; // float

:valid_range = 9.999999f, 8477.0f; // float

:long_name = " bathymetry [20.1H]";

float ilt(MT=1, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "ocean_mixed_layer_thickness";

:units = "m";

:_FillValue = 1.2676506E30f; // float

:valid_range = 1.0797554f, 1146.0001f; // float

:long_name = " ILT (0.50 degC) [20.1H]";

float mlt(MT=1, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "ocean_mixed_layer_thickness";

:units = "m";

:_FillValue = 1.2676506E30f; // float

:valid_range = 0.715755f, 1146.0001f; // float

:long_name = " MLT (0.50 kg/m3) [20.1H]";

float ssh(MT=1, Latitude=1000, Longitude=1000);

:coordinates = "Date";

:standard_name = "sea_surface_elevation";

:units = "m";

:_FillValue = 1.2676506E30f; // float

:valid_range = -0.95362926f, 0.84672445f; // float

:long_name = " sea surf. height [20.1H]";

107

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Appendix C

Fourier coefficients for wave kinematics

C.1 Wave Surface Elevation

C.1.1 First-Order

X

(1)

im = aim · exp(−ιεim)· exp(−ι(~kim ·~x)) (1)

where~x = (x,y) is a point on the horizontal x-y plane; ι =

√

−1 and~kim =



|~ki|cosθm,|~ki|sinθm



; ωiis the angular frequency; ~kiis the wave number which is

related to the frequency, ωi, through the linear dispersion relation, ω

2

i = g|~ki

|tanh(|~ki|h) (where h is the water depth).

C.1.2 Second-Order

X

(2)±

i jmn = aimajn · exp(−sgn(ω

±

i j)ιε

±

i jmn)·K

±

i jmn

· exp(−sgn(ω

±

i j )ι(~kim ·~x±~kjn ·~x))

(2)

where,

ε

±

i jmn = εim ±ε jn and ω

±

i j = ωi ±ωj (3)

sgn(x) =







1 x > 0

0 x = 0

−1 x < 0

(4)

C.2 Wave Particle Velocity

C.2.1 First-Order

U

(1)

x,im = aim · exp(−ιεim)ωi

cosh[|~ki|(h+z)]

sinh(|~ki|h)

cosθm · exp(−ι(~kim ·~x)) (5)

U

(1)

y,im = aim · exp(−ιεim)ωi

cosh[|~ki|(h+z)]

sinh(|~ki|h)

sinθm · exp(−ι(~kim ·~x)) (6)

U

(1)

z,im = (ι)aim · exp(−ιεim)ωi

sinh[|~ki|(h+z)]

sinh(|~ki|h)

· exp(−ι(~kim ·~x)) (7)

C.2.2 Second-Order

U

(2±)

x,i jmn = aimajn · exp(−sgn(ω

±

i j)ιε

±

i jmn)·B

±

i jmn ·(|~ki

|cosθm ±|~kj

|cosθn)

· exp(−sgn(ω

±

i j)ι(~kim ·~x±~kjn ·~x))

(8)

U

(2±)

x,i jmn = aimajn · exp(−sgn(ω

±

i j)ιε

±

i jmn)·B

±

i jmn ·(|~ki

|sinθm ±|~kj|sinθn)

· exp(−sgn(ω

±

i j )ι(~kim ·~x±~kjn ·~x))

(9)

U

(2±)

x,i jmn = (ι)· aimajn · exp(−sgn(ω

±

i j)ιε

±

i jmn)·B

±

i jmn · k

±

i jmn ·tanh[k

±

i jmn(h+z)]

· exp(−sgn(ω

±

i j)ι(~kim ·~x±~kjn ·~x))

(10)

108

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C.3 Wave Particle Acceleration

C.3.1 First-Order

U ̇

(1)

x,im = (ι)·ωi

·U

(1)

x,im (11)

U ̇

(1)

y,im = (ι)·ωi

·U

(1)

y,im (12)

U ̇

(1)

z,im = (ι)·ωi

·U

(1)

z,im (13)

C.3.2 Second-Order

U ̇

(2±)

x,i jmn = (ι)·ω

±

i j ·U

(2±)

x,i jmn (14)

U ̇

(2±)

y,i jmn = (ι)·ωi j

± ·U

(2±)

y,i jmn (15)

U ̇

(2±)

z,i jmn = (ι)·ωi j

± ·U

(2±)

z,i jmn (16)

C.4 Dynamic Pressure

C.4.1 First-Order

P

(1)

im = (ρwg)· aim · exp(−ιεim)ωi

cosh[|~ki|(h+z)]

cosh(|~ki|h)

· exp(−ι(~kim ·~x)) (17)

C.4.2 Second-Order (only second-order potential term)

P

(2±)

i jmn = (ρw)· aimajn · exp(−sgn(ω

±

i j)ιε

±

i jmn)·B

±

i jmn ·ω

±

i j

· exp(−sgn(ω

±

i j )ι(~kim ·~x±~kjn ·~x))

(18)

109

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Appendix D

FAST input files for the parked NREL 5-MW baseline turbine

D.1 Primary Input File(∗.fst)

--------------------------------------------------------------------------------

------- FAST INPUT FILE --------------------------------------------------------

NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.

Properties from Dutch Offshore Wind Energy Converter (DOWEC) 6MW Pre-Design (10046_00

---------------------- SIMULATION CONTROL --------------------------------------

False Echo - Echo input data to "echo.out" (flag)

1 ADAMSPrep - ADAMS preprocessor mode {1: Run FAST, 2: use FAST as a preproc

1 AnalMode - Analysis mode {1: Run a time-marching simulation, 2: create a

3 NumBl - Number of blades (-)

4000.0 TMax - Total run time (s)

0.01000 DT - Integration time step (s)

---------------------- TURBINE CONTROL -----------------------------------------

0 YCMode - Yaw control mode {0: none, 1: user-defined from routine UserYa

9999.9 TYCOn - Time to enable active yaw control (s) [unused when YCMode=0

0 PCMode - Pitch control mode {0: none, 1: user-defined from routine Pitc

0.0 TPCOn - Time to enable active pitch control (s) [unused when PCMode=0]

0 VSContrl - Variable-speed control mode {0: none, 1: simple VS, 2: user-de

9999.9 VS_RtGnSp - Rated generator speed for simple variable-speed generator c

9999.9 VS_RtTq - Rated generator torque/constant generator torque in Region

9999.9 VS_Rgn2K - Generator torque constant in Region 2 for simple variable-s

9999.9 VS_SlPc - Rated generator slip percentage in Region 2 1/2 for simple

2 GenModel - Generator model {1: simple, 2: Thevenin, 3: user-defined fr

True GenTiStr - Method to start the generator {T: timed using TimGenOn, F:

True GenTiStp - Method to stop the generator {T: timed using TimGenOf, F: w

9999.9 SpdGenOn - Generator speed to turn on the generator for a startup (HSS

9999.9 TimGenOn - Time to turn on the generator for a startup (s) [used only

9999.9 TimGenOf - Time to turn off the generator (s) [used only when GenTiStp

1 HSSBrMode - HSS brake model {1: simple, 2: user-defined from routine UserH

0 THSSBrDp - Time to initiate deployment of the HSS brake (s)

9999.9 TiDynBrk - Time to initiate deployment of the dynamic generator brake

9999.9 TTpBrDp(1) - Time to initiate deployment of tip brake 1 (s)

9999.9 TTpBrDp(2) - Time to initiate deployment of tip brake 2 (s)

9999.9 TTpBrDp(3) - Time to initiate deployment of tip brake 3 (s) [unused for

9999.9 TBDepISp(1) - Deployment-initiation speed for the tip brake on blade 1 (r

9999.9 TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (r

9999.9 TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (r

9999.9 TYawManS - Time to start override yaw maneuver and end standard yaw co

9999.9 TYawManE - Time at which override yaw maneuver reaches final yaw angle

0.0 NacYawF - Final yaw angle for yaw maneuvers (degrees)

9999.9 TPitManS(1) - Time to start override pitch maneuver for blade 1 and end s

9999.9 TPitManS(2) - Time to start override pitch maneuver for blade 2 and end s

9999.9 TPitManS(3) - Time to start override pitch maneuver for blade 3 and end s

9999.9 TPitManE(1) - Time at which override pitch maneuver for blade 1 reaches f

9999.9 TPitManE(2) - Time at which override pitch maneuver for blade 2 reaches f

9999.9 TPitManE(3) - Time at which override pitch maneuver for blade 3 reaches f

90.0 BlPitch(1) - Blade 1 initial pitch (degrees)

90.0 BlPitch(2) - Blade 2 initial pitch (degrees)

90.0 BlPitch(3) - Blade 3 initial pitch (degrees) [unused for 2 blade

90.0 B1PitchF(1) - Blade 1 final pitch for pitch maneuvers (degrees)

90.0 B1PitchF(2) - Blade 2 final pitch for pitch maneuvers (degrees)

90.0 B1PitchF(3) - Blade 3 final pitch for pitch maneuvers (degrees) [

---------------------- ENVIRONMENTAL CONDITIONS --------------------------------

9.80665 Gravity - Gravitational acceleration (m/s^2)

---------------------- FEATURE FLAGS -------------------------------------------

True FlapDOF1 - First flapwise blade mode DOF (flag)

True FlapDOF2 - Second flapwise blade mode DOF (flag)

True EdgeDOF - First edgewise blade mode DOF (flag)

False TeetDOF - Rotor-teeter DOF (flag) [unused for 3 blades]

True DrTrDOF - Drivetrain rotational-flexibility DOF (flag)

True GenDOF - Generator DOF (flag)

False YawDOF - Yaw DOF (flag)

True TwFADOF1 - First fore-aft tower bending-mode DOF (flag)

True TwFADOF2 - Second fore-aft tower bending-mode DOF (flag)

True TwSSDOF1 - First side-to-side tower bending-mode DOF (flag)

True TwSSDOF2 - Second side-to-side tower bending-mode DOF (flag)

True CompAero - Compute aerodynamic forces (flag)

False CompNoise - Compute aerodynamic noise (flag)

---------------------- INITIAL CONDITIONS --------------------------------------

110

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0.0 OoPDefl - Initial out-of-plane blade-tip displacement (meters)

0.0 IPDefl - Initial in-plane blade-tip deflection (meters)

0.0 TeetDefl - Initial or fixed teeter angle (degrees) [unused for 3 blades]

0.0 Azimuth - Initial azimuth angle for blade 1 (degrees)

0.0 RotSpeed - Initial or fixed rotor speed (rpm)

0.0 NacYaw - Initial or fixed nacelle-yaw angle (degrees)

0.0 TTDspFA - Initial fore-aft tower-top displacement (meters)

0.0 TTDspSS - Initial side-to-side tower-top displacement (meters)

---------------------- TURBINE CONFIGURATION -----------------------------------

63.0 TipRad - The distance from the rotor apex to the blade tip (meters)

1.5 HubRad - The distance from the rotor apex to the blade root (meters)

1 PSpnElN - Number of the innermost blade element which is still part of t

0.0 UndSling - Undersling length [distance from teeter pin to the rotor apex]

0.0 HubCM - Distance from rotor apex to hub mass [positive downwind] (mete

-5.01910 OverHang - Distance from yaw axis to rotor apex [3 blades] or teeter pin

1.9 NacCMxn - Downwind distance from the tower-top to the nacelle CM (meters

0.0 NacCMyn - Lateral distance from the tower-top to the nacelle CM (meters

1.75 NacCMzn - Vertical distance from the tower-top to the nacelle CM (meters

87.6 TowerHt - Height of tower above ground level [onshore] or MSL [offshore

1.96256 Twr2Shft - Vertical distance from the tower-top to the rotor shaft (meter

0.0 TwrRBHt - Tower rigid base height (meters)

-5.0 ShftTilt - Rotor shaft tilt angle (degrees)

0.0 Delta3 - Delta-3 angle for teetering rotors (degrees) [unused for 3 bla

-2.5 PreCone(1) - Blade 1 cone angle (degrees)

-2.5 PreCone(2) - Blade 2 cone angle (degrees)

-2.5 PreCone(3) - Blade 3 cone angle (degrees) [unused for 2 blades]

0.0 AzimB1Up - Azimuth value to use for I/O when blade 1 points up (degrees)

---------------------- MASS AND INERTIA ----------------------------------------

0.0 YawBrMass - Yaw bearing mass (kg)

240.00E3 NacMass - Nacelle mass (kg)

56.78E3 HubMass - Hub mass (kg)

0.0 TipMass(1) - Tip-brake mass, blade 1 (kg)

0.0 TipMass(2) - Tip-brake mass, blade 2 (kg)

0.0 TipMass(3) - Tip-brake mass, blade 3 (kg) [unused for 2 blades]

2607.89E3 NacYIner - Nacelle inertia about yaw axis (kg m^2)

534.116 GenIner - Generator inertia about HSS (kg m^2)

115.926E3 HubIner - Hub inertia about rotor axis [3 blades] or teeter axis [2 bl

---------------------- DRIVETRAIN ----------------------------------------------

90.0 GBoxEff - Gearbox efficiency (%)

94.4 GenEff - Generator efficiency [ignored by the Thevenin and user-define

97.0 GBRatio - Gearbox ratio (-)

False GBRevers - Gearbox reversal {T: if rotor and generator rotate in oppos

0.5162E3 HSSBrTqF - Fully deployed HSS-brake torque (N-m)

0 HSSBrDT - Time for HSS-brake to reach full deployment once initiated (sec)

DynBrkFi - File containing a mech-gen-torque vs HSS-speed curve for a dynamic brak

867.637E6 DTTorSpr - Drivetrain torsional spring (N-m/rad)

6.215E6 DTTorDmp - Drivetrain torsional damper (N-m/(rad/s))

---------------------- SIMPLE INDUCTION GENERATOR ------------------------------

9999.9 SIG_SlPc - Rated generator slip percentage (%) [used only when VSContr

9999.9 SIG_SySp - Synchronous (zero-torque) generator speed (rpm) [used only

9999.9 SIG_RtTq - Rated torque (N-m) [used only when VSContrl=0 and GenModel=

9999.9 SIG_PORt - Pull-out ratio (Tpullout/Trated) (-) [used only when VSCont

---------------------- THEVENIN-EQUIVALENT INDUCTION GENERATOR -----------------

9999.9 TEC_Freq - Line frequency [50 or 60] (Hz) [used only when VSContrl=0 a

9998 TEC_NPol - Number of poles [even integer > 0] (-) [used only when VSCo

9999.9 TEC_SRes - Stator resistance (ohms) [used only when VSContrl=0 and Gen

9999.9 TEC_RRes - Rotor resistance (ohms) [used only when VSContrl=0 and GenM

9999.9 TEC_VLL - Line-to-line RMS voltage (volts) [used only when VSContrl=0

9999.9 TEC_SLR - Stator leakage reactance (ohms) [used only when VSContrl=0

9999.9 TEC_RLR - Rotor leakage reactance (ohms) [used only when VSContrl=0 a

9999.9 TEC_MR - Magnetizing reactance (ohms) [used only when VSContrl=0 and

---------------------- PLATFORM ------------------------------------------------

0 PtfmModel - Platform model {0: none, 1: onshore, 2: fixed bottom o

"NRELOffshrBsline5MW_Platform_Monopile_RF.dat" PtfmFile - Name of file contai

---------------------- TOWER ---------------------------------------------------

99 TwrNodes - Number of tower nodes used for analysis (-)

"NRELOffshrBsline5MW_Tower_Onshore.dat" TwrFile - Name of file containin

---------------------- NACELLE-YAW ---------------------------------------------

9028.32E6 YawSpr - Nacelle-yaw spring constant (N-m/rad)

19.16E6 YawDamp - Nacelle-yaw damping constant (N-m/(rad/s))

0.0 YawNeut - Neutral yaw position--yaw spring force is zero at this yaw (de

---------------------- FURLING -------------------------------------------------

False Furling - Read in additional model properties for furling turbine (fl

FurlFile - Name of file containing furling properties (quoted string) [unused when

---------------------- ROTOR-TEETER --------------------------------------------

0 TeetMod - Rotor-teeter spring/damper model {0: none, 1: standard, 2: use

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0.0 TeetDmpP - Rotor-teeter damper position (degrees) [used only for 2 blades

0.0 TeetDmp - Rotor-teeter damping constant (N-m/(rad/s)) [used only for 2 b

0.0 TeetCDmp - Rotor-teeter rate-independent Coulomb-damping moment (N-m) [us

0.0 TeetSStP - Rotor-teeter soft-stop position (degrees) [used only for 2 bla

0.0 TeetHStP - Rotor-teeter hard-stop position (degrees) [used only for 2 bla

0.0 TeetSSSp - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used

0.0 TeetHSSp - Rotor-teeter hard-stop linear-spring constant (N-m/rad) [used

---------------------- TIP-BRAKE -----------------------------------------------

0.0 TBDrConN - Tip-brake drag constant during normal operation, Cd*Area (m^2)

0.0 TBDrConD - Tip-brake drag constant during fully-deployed operation, Cd*Ar

0.0 TpBrDT - Time for tip-brake to reach full deployment once released (sec

---------------------- BLADE ---------------------------------------------------

"NRELOffshrBsline5MW_Blade.dat" BldFile(1) - Name of file containin

"NRELOffshrBsline5MW_Blade.dat" BldFile(2) - Name of file containin

"NRELOffshrBsline5MW_Blade.dat" BldFile(3) - Name of file containin

---------------------- AERODYN -------------------------------------------------

"NRELOffshrBsline5MW_AeroDyn.ipt" ADFile - Name of file containin

---------------------- NOISE ---------------------------------------------------

NoiseFile - Name of file containing aerodynamic noise input parameters (quoted stri

---------------------- ADAMS ---------------------------------------------------

"NRELOffshrBsline5MW_ADAMSSpecific.dat" ADAMSFile - Name of file containin

---------------------- LINEARIZATION CONTROL -----------------------------------

"NRELOffshrBsline5MW_Linear.dat" LinFile - Name of file containin

---------------------- OUTPUT --------------------------------------------------

True SumPrint - Print summary data to "<RootName>.fsm" (flag)

1 OutFileFmt - Format for tabular (time-marching) output file(s) (1: text

True TabDelim - Generate a tab-delimited tabular output file. (flag)

"ES10.3E2" OutFmt - Format used for tabular output except time. Resulting fiel

0 TStart - Time to begin tabular output (s)

10 DecFact - Decimation factor for tabular output {1: output every

10.0 SttsTime - Amount of time between screen status messages (sec)

-3.09528 NcIMUxn - Downwind distance from the tower-top to the nacelle IMU (mete

0.0 NcIMUyn - Lateral distance from the tower-top to the nacelle IMU (meter

2.23336 NcIMUzn - Vertical distance from the tower-top to the nacelle IMU (meter

1.912 ShftGagL - Distance from rotor apex [3 blades] or teeter pin [2 blades] t

3 NTwGages - Number of tower nodes that have strain gages for output [0 to

10,11,12 TwrGagNd - List of tower nodes that have strain gages [1 to TwrNodes]

3 NBlGages - Number of blade nodes that have strain gages for output [0 to

5,9,13 BldGagNd - List of blade nodes that have strain gages [1 to BldNodes] (

OutList - The next line(s) contains a list of output parameters. See OutList.txt

"WindVxi , WindVyi , WindVzi" - Longitudinal, lateral,

"GenPwr , GenTq" - Electrical generator p

"OoPDefl1 , IPDefl1 , TwstDefl1" - Blade 1 out-of-plane a

"BldPitch1" - Blade 1 pitch angle

"Azimuth" - Blade 1 azimuth angle

"RotSpeed , GenSpeed" - Low-speed shaft and hi

"TTDspFA , TTDspSS , TTDspTwst" - Tower fore-aft and sid

"Spn2MLxb1, Spn2MLyb1" - Blade 1 local edgewise

"RootFxc1 , RootFyc1 , RootFzc1" - Out-of-plane shear, in

"RootMxc1 , RootMyc1 , RootMzc1" - In-plane bending, out-

"RotTorq , LSSGagMya, LSSGagMza" - Rotor torque and low-s

"YawBrFxp , YawBrFyp , YawBrFzp" - Fore-aft shear, side-t

"YawBrMxp , YawBrMyp , YawBrMzp" - Side-to-side bending,

"TwrBsFxt , TwrBsFyt , TwrBsFzt" - Fore-aft shear, side-t

"TwrBsMxt , TwrBsMyt , TwrBsMzt" - Side-to-side bending,

"NacYaw, YawPos"

"RootMxb1 , RootMyb1 , RootMzb1" - Blade 1 edgewise, flap

"NacYawErr, HorWndDir"

"WaveElev"

END of FAST input file (the word "END" must appear in the first 3 columns of this las

--------------------------------------------------------------------------------

D.2 AeroDyn Input Files(∗.ipt)

NREL 5.0 MW offshore baseline aerodynamic input properties; Compatible with AeroDyn v1

SI SysUnits - System of units used for input and output [must be SI for FA

STEADY StallMod - Dynamic stall included [BEDDOES or STEADY] (unquoted string)

NO_CM UseCm - Use aerodynamic pitching moment model? [USE_CM or NO_CM] (unq

EQUIL InfModel - Inflow model [DYNIN or EQUIL] (unquoted string)

NONE IndModel - Induction-factor model [NONE or WAKE or SWIRL] (unquoted stri

0.005 AToler - Induction-factor tolerance (convergence criteria) (-)

PRANDtl TLModel - Tip-loss model (EQUIL only) [PRANDtl, GTECH, or NONE] (unquo

PRANDtl HLModel - Hub-loss model (EQUIL only) [PRANdtl or NONE] (unquoted stri

"userwind" WindFile - Name of file containing wind data (quoted stri

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90.0 HH - Wind reference (hub) height [TowerHt+Twr2Shft+OverHang*SIN(Shf

0.0 TwrShad - Tower-shadow velocity deficit (-)

9999.9 ShadHWid - Tower-shadow half width (m)

9999.9 T_Shad_Refpt- Tower-shadow reference point (m)

1.225 AirDens - Air density (kg/m^3)

1.464E-5 KinVisc - Kinematic air viscosity [CURRENTLY IGNORED] (m^2/sec)

0.0125 DTAero - Time interval for aerodynamic calculations (sec)

8 NumFoil - Number of airfoil files (-)

"AeroData\Cylinder1.dat" FoilNm - Names of the airfoil fi

"AeroData\Cylinder2.dat"

"AeroData\DU40_A17.dat"

"AeroData\DU35_A17.dat"

"AeroData\DU30_A17.dat"

"AeroData\DU25_A17.dat"

"AeroData\DU21_A17.dat"

"AeroData\NACA64_A17.dat"

17 BldNodes - Number of blade nodes used for analysis (-)

RNodes AeroTwst DRNodes Chord NFoil PrnElm

2.8667 13.308 2.7333 3.542 1 PRINT

5.6000 13.308 2.7333 3.854 1 PRINT

8.3333 13.308 2.7333 4.167 2 PRINT

11.7500 13.308 4.1000 4.557 3 PRINT

15.8500 11.480 4.1000 4.652 4 PRINT

19.9500 10.162 4.1000 4.458 4 PRINT

24.0500 9.011 4.1000 4.249 5 PRINT

28.1500 7.795 4.1000 4.007 6 PRINT

32.2500 6.544 4.1000 3.748 6 PRINT

36.3500 5.361 4.1000 3.502 7 PRINT

40.4500 4.188 4.1000 3.256 7 PRINT

44.5500 3.125 4.1000 3.010 8 PRINT

48.6500 2.319 4.1000 2.764 8 PRINT

52.7500 1.526 4.1000 2.518 8 PRINT

56.1667 0.863 2.7333 2.313 8 PRINT

58.9000 0.370 2.7333 2.086 8 PRINT

61.6333 0.106 2.7333 1.419 8 PRINT

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Appendix E

Abaqus files for modeling the jacket support structure

E.1 Phyton script to read field output from .odb(∗.py)

from odbAccess import *

from textRepr import *

from abaqusConstants import *

import odbAccess

odb=openOdb(path=’myjob.odb’)

mySteps = odb.steps

numSteps = len(mySteps)

for i in range(numSteps):

stepKey = mySteps.keys()[i]

step = mySteps[stepKey]

numFrames = len(step.frames)

regS1 = odb.rootAssembly.instances[’PART-1-1’].nodeSets[’BC_NODE’]

regU1 = odb.rootAssembly.instances[’PART-1-1’].nodeSets[’ZERO_POINT’]

regL1 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’LEG1_MEMB1’]

regL2 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’LEG2_MEMB1’]

regL3 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’LEG3_MEMB1’]

regL4 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’LEG4_MEMB1’]

regB1M1 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA1_MEMB1’]

regB2M1 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA2_MEMB1’]

regB3M1 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA3_MEMB1’]

regB4M1 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA4_MEMB1’]

regB1M2 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA1_MEMB2’]

regB2M2 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA2_MEMB2’]

regB3M2 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA3_MEMB2’]

regB4M2 = odb.rootAssembly.instances[’PART-1-1’].elementSets[’BRA4_MEMB2’]

frameRepository = step.frames

moment_out =open(’abaqus_moment1.txt’,’w’)

force_out =open(’abaqus_force1.txt’,’w’)

disp_out_zero =open(’abaqus_disp_zero.txt’,’w’)

L1_out =open(’abaqus_L1.txt’,’w’)

L2_out =open(’abaqus_L2.txt’,’w’)

L3_out =open(’abaqus_L3.txt’,’w’)

L4_out =open(’abaqus_L4.txt’,’w’)

B1M1_out =open(’abaqus_B1M1.txt’,’w’)

B2M1_out =open(’abaqus_B2M1.txt’,’w’)

B3M1_out =open(’abaqus_B3M1.txt’,’w’)

B4M1_out =open(’abaqus_B4M1.txt’,’w’)

B1M2_out =open(’abaqus_B1M2.txt’,’w’)

B2M2_out =open(’abaqus_B2M2.txt’,’w’)

B3M2_out =open(’abaqus_B3M2.txt’,’w’)

B4M2_out =open(’abaqus_B4M2.txt’,’w’)

for frame in frameRepository:

RForce =frame.fieldOutputs[’RF’]

RMoment =frame.fieldOutputs[’RM’]

UDisp =frame.fieldOutputs[’U’]

URDisp =frame.fieldOutputs[’UR’]

SForce =frame.fieldOutputs[’SF’]

SMoment =frame.fieldOutputs[’SM’]

Time = frame.frameValue

FX = RForce.getSubset(region=regS1).values[0].data[0]

FY = RForce.getSubset(region=regS1).values[0].data[1]

FZ = RForce.getSubset(region=regS1).values[0].data[2]

MX = RMoment.getSubset(region=regS1).values[0].data[0]

MY = RMoment.getSubset(region=regS1).values[0].data[1]

MZ = RMoment.getSubset(region=regS1).values[0].data[2]

U_zero1 = UDisp.getSubset(region=regU1).values[0].data[0]

U_zero2 = UDisp.getSubset(region=regU1).values[0].data[1]

U_zero3 = UDisp.getSubset(region=regU1).values[0].data[2]

UR_zero1 = URDisp.getSubset(region=regU1).values[0].data[0]

UR_zero2 = URDisp.getSubset(region=regU1).values[0].data[1]

UR_zero3 = URDisp.getSubset(region=regU1).values[0].data[2]

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L1_F1 = SForce.getSubset(region=regL1).values[0].data[0]

L1_F2 = SForce.getSubset(region=regL1).values[0].data[1]

L1_F3 = SForce.getSubset(region=regL1).values[0].data[2]

L1_M1 = SMoment.getSubset(region=regL1).values[0].data[0]

L1_M2 = SMoment.getSubset(region=regL1).values[0].data[1]

L1_M3 = SMoment.getSubset(region=regL1).values[0].data[2]

L2_F1 = SForce.getSubset(region=regL2).values[0].data[0]

L2_F2 = SForce.getSubset(region=regL2).values[0].data[1]

L2_F3 = SForce.getSubset(region=regL2).values[0].data[2]

L2_M1 = SMoment.getSubset(region=regL2).values[0].data[0]

L2_M2 = SMoment.getSubset(region=regL2).values[0].data[1]

L2_M3 = SMoment.getSubset(region=regL2).values[0].data[2]

L3_F1 = SForce.getSubset(region=regL3).values[0].data[0]

L3_F2 = SForce.getSubset(region=regL3).values[0].data[1]

L3_F3 = SForce.getSubset(region=regL3).values[0].data[2]

L3_M1 = SMoment.getSubset(region=regL3).values[0].data[0]

L3_M2 = SMoment.getSubset(region=regL3).values[0].data[1]

L3_M3 = SMoment.getSubset(region=regL3).values[0].data[2]

L4_F1 = SForce.getSubset(region=regL4).values[0].data[0]

L4_F2 = SForce.getSubset(region=regL4).values[0].data[1]

L4_F3 = SForce.getSubset(region=regL4).values[0].data[2]

L4_M1 = SMoment.getSubset(region=regL4).values[0].data[0]

L4_M2 = SMoment.getSubset(region=regL4).values[0].data[1]

L4_M3 = SMoment.getSubset(region=regL4).values[0].data[2]

B1M1_F1 = SForce.getSubset(region=regB1M1).values[0].data[0]

B1M1_F2 = SForce.getSubset(region=regB1M1).values[0].data[1]

B1M1_F3 = SForce.getSubset(region=regB1M1).values[0].data[2]

B1M1_M1 = SMoment.getSubset(region=regB1M1).values[0].data[0]

B1M1_M2 = SMoment.getSubset(region=regB1M1).values[0].data[1]

B1M1_M3 = SMoment.getSubset(region=regB1M1).values[0].data[2]

B2M1_F1 = SForce.getSubset(region=regB2M1).values[0].data[0]

B2M1_F2 = SForce.getSubset(region=regB2M1).values[0].data[1]

B2M1_F3 = SForce.getSubset(region=regB2M1).values[0].data[2]

B2M1_M1 = SMoment.getSubset(region=regB2M1).values[0].data[0]

B2M1_M2 = SMoment.getSubset(region=regB2M1).values[0].data[1]

B2M1_M3 = SMoment.getSubset(region=regB2M1).values[0].data[2]

B3M1_F1 = SForce.getSubset(region=regB3M1).values[0].data[0]

B3M1_F2 = SForce.getSubset(region=regB3M1).values[0].data[1]

B3M1_F3 = SForce.getSubset(region=regB3M1).values[0].data[2]

B3M1_M1 = SMoment.getSubset(region=regB3M1).values[0].data[0]

B3M1_M2 = SMoment.getSubset(region=regB3M1).values[0].data[1]

B3M1_M3 = SMoment.getSubset(region=regB3M1).values[0].data[2]

B4M1_F1 = SForce.getSubset(region=regB4M1).values[0].data[0]

B4M1_F2 = SForce.getSubset(region=regB4M1).values[0].data[1]

B4M1_F3 = SForce.getSubset(region=regB4M1).values[0].data[2]

B4M1_M1 = SMoment.getSubset(region=regB4M1).values[0].data[0]

B4M1_M2 = SMoment.getSubset(region=regB4M1).values[0].data[1]

B4M1_M3 = SMoment.getSubset(region=regB4M1).values[0].data[2]

B1M2_F1 = SForce.getSubset(region=regB1M2).values[0].data[0]

B1M2_F2 = SForce.getSubset(region=regB1M2).values[0].data[1]

B1M2_F3 = SForce.getSubset(region=regB1M2).values[0].data[2]

B1M2_M1 = SMoment.getSubset(region=regB1M2).values[0].data[0]

B1M2_M2 = SMoment.getSubset(region=regB1M2).values[0].data[1]

B1M2_M3 = SMoment.getSubset(region=regB1M2).values[0].data[2]

B2M2_F1 = SForce.getSubset(region=regB2M2).values[0].data[0]

B2M2_F2 = SForce.getSubset(region=regB2M2).values[0].data[1]

B2M2_F3 = SForce.getSubset(region=regB2M2).values[0].data[2]

B2M2_M1 = SMoment.getSubset(region=regB2M2).values[0].data[0]

B2M2_M2 = SMoment.getSubset(region=regB2M2).values[0].data[1]

B2M2_M3 = SMoment.getSubset(region=regB2M2).values[0].data[2]

B3M2_F1 = SForce.getSubset(region=regB3M2).values[0].data[0]

B3M2_F2 = SForce.getSubset(region=regB3M2).values[0].data[1]

B3M2_F3 = SForce.getSubset(region=regB3M2).values[0].data[2]

B3M2_M1 = SMoment.getSubset(region=regB3M2).values[0].data[0]

B3M2_M2 = SMoment.getSubset(region=regB3M2).values[0].data[1]

B3M2_M3 = SMoment.getSubset(region=regB3M2).values[0].data[2]

B4M2_F1 = SForce.getSubset(region=regB4M2).values[0].data[0]

B4M2_F2 = SForce.getSubset(region=regB4M2).values[0].data[1]

B4M2_F3 = SForce.getSubset(region=regB4M2).values[0].data[2]

B4M2_M1 = SMoment.getSubset(region=regB4M2).values[0].data[0]

B4M2_M2 = SMoment.getSubset(region=regB4M2).values[0].data[1]

B4M2_M3 = SMoment.getSubset(region=regB4M2).values[0].data[2]

force_out.write(str(Time)+" "+str(FX)+" "+str(FY)+" "+str(FZ)+"\n")

moment_out.write(str(Time)+" "+str(MX)+" "+str(MY)+" "+str(MZ)+"\n")

disp_out_zero.write(str(Time)+" "+str(U_zero1)+" "+str(U_zero2)+" "+str(U_zero3)

+" "+str(UR_zero1)+" "+str(UR_zero2)+" "+str(UR_zero3)+"\n")

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L1_out.write(str(Time)+" "+str(L1_F1)+" "+str(L1_F2)+" "+str(L1_F3)+" "+str(L1_M1)

+" "+str(L1_M2)+" "+str(L1_M3)+"\n")

L2_out.write(str(Time)+" "+str(L2_F1)+" "+str(L2_F2)+" "+str(L2_F3)+" "+str(L2_M1)

+" "+str(L2_M2)+" "+str(L2_M3)+"\n")

L3_out.write(str(Time)+" "+str(L3_F1)+" "+str(L3_F2)+" "+str(L3_F3)+" "+str(L3_M1)

+" "+str(L3_M2)+" "+str(L3_M3)+"\n")

L4_out.write(str(Time)+" "+str(L4_F1)+" "+str(L4_F2)+" "+str(L4_F3)+" "+str(L4_M1)

+" "+str(L4_M2)+" "+str(L4_M3)+"\n")

B1M1_out.write(str(Time)+" "+str(B1M1_F1)+" "+str(B1M1_F2)+" "+str(B1M1_F3)+" "

+str(B1M1_M1)+" "+str(B1M1_M2)+" "+str(B1M1_M3)+"\n")

B2M1_out.write(str(Time)+" "+str(B2M1_F1)+" "+str(B2M1_F2)+" "+str(B2M1_F3)+" "

+str(B2M1_M1)+" "+str(B2M1_M2)+" "+str(B2M1_M3)+"\n")

B3M1_out.write(str(Time)+" "+str(B3M1_F1)+" "+str(B3M1_F2)+" "+str(B3M1_F3)+" "

+str(B3M1_M1)+" "+str(B3M1_M2)+" "+str(B3M1_M3)+"\n")

B4M1_out.write(str(Time)+" "+str(B4M1_F1)+" "+str(B4M1_F2)+" "+str(B4M1_F3)+" "

+str(B4M1_M1)+" "+str(B4M1_M2)+" "+str(B4M1_M3)+"\n")

B1M2_out.write(str(Time)+" "+str(B1M2_F1)+" "+str(B1M2_F2)+" "+str(B1M2_F3)+" "

+str(B1M2_M1)+" "+str(B1M2_M2)+" "+str(B1M2_M3)+"\n")

B2M2_out.write(str(Time)+" "+str(B2M2_F1)+" "+str(B2M2_F2)+" "+str(B2M2_F3)+" "

+str(B2M2_M1)+" "+str(B2M2_M2)+" "+str(B2M2_M3)+"\n")

B3M2_out.write(str(Time)+" "+str(B3M2_F1)+" "+str(B3M2_F2)+" "+str(B3M2_F3)+" "

+str(B3M2_M1)+" "+str(B3M2_M2)+" "+str(B3M2_M3)+"\n")

B4M2_out.write(str(Time)+" "+str(B4M2_F1)+" "+str(B4M2_F2)+" "+str(B4M2_F3)+" "

+str(B4M2_M1)+" "+str(B4M2_M2)+" "+str(B4M2_M3)+"\n")

moment_out=open(’abaqus_moment2.txt’,’w’)

force_out=open(’abaqus_force2.txt’,’w’)

for frame in frameRepository:

RForce =frame.fieldOutputs[’RF’]

RMoment=frame.fieldOutputs[’RM’]

Time = frame.frameValue

FX = RForce.getSubset(region=regS1).values[1].data[0]

FY = RForce.getSubset(region=regS1).values[1].data[1]

FZ = RForce.getSubset(region=regS1).values[1].data[2]

MX = RMoment.getSubset(region=regS1).values[1].data[0]

MY = RMoment.getSubset(region=regS1).values[1].data[1]

MZ = RMoment.getSubset(region=regS1).values[1].data[2]

force_out.write(str(Time)+" "+str(FX)+" "+str(FY)+" "+str(FZ)+"\n")

moment_out.write(str(Time)+" "+str(MX)+" "+str(MY)+" "+str(MZ)+"\n")

moment_out=open(’abaqus_moment3.txt’,’w’)

force_out=open(’abaqus_force3.txt’,’w’)

for frame in frameRepository:

RForce =frame.fieldOutputs[’RF’]

RMoment=frame.fieldOutputs[’RM’]

Time = frame.frameValue

FX = RForce.getSubset(region=regS1).values[2].data[0]

FY = RForce.getSubset(region=regS1).values[2].data[1]

FZ = RForce.getSubset(region=regS1).values[2].data[2]

MX = RMoment.getSubset(region=regS1).values[2].data[0]

MY = RMoment.getSubset(region=regS1).values[2].data[1]

MZ = RMoment.getSubset(region=regS1).values[2].data[2]

force_out.write(str(Time)+" "+str(FX)+" "+str(FY)+" "+str(FZ)+"\n")

moment_out.write(str(Time)+" "+str(MX)+" "+str(MY)+" "+str(MZ)+"\n")

moment_out=open(’abaqus_moment4.txt’,’w’)

force_out=open(’abaqus_force4.txt’,’w’)

for frame in frameRepository:

RForce =frame.fieldOutputs[’RF’]

RMoment=frame.fieldOutputs[’RM’]

Time = frame.frameValue

FX = RForce.getSubset(region=regS1).values[3].data[0]

FY = RForce.getSubset(region=regS1).values[3].data[1]

FZ = RForce.getSubset(region=regS1).values[3].data[2]

MX = RMoment.getSubset(region=regS1).values[3].data[0]

MY = RMoment.getSubset(region=regS1).values[3].data[1]

MZ = RMoment.getSubset(region=regS1).values[3].data[2]

force_out.write(str(Time)+" "+str(FX)+" "+str(FY)+" "+str(FZ)+"\n")

moment_out.write(str(Time)+" "+str(MX)+" "+str(MY)+" "+str(MZ)+"\n")

odb.close()

116

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
E.2 Abaqus Input File(∗.inp)

*Heading

*Preprint, echo=NO, model=NO, history=NO, contact=NO

**

** PARTS

**

*Part, name=PART-1

*Node

1, 6000., 6000., -50000.

2, 6000., 6000., -45000.

3, 5967., 5967., -44001.

4, 5939., 5939., -43127.

5, 5333., 5333., -24614.

6, -6000., 6000., -50000.

7, -6000., 6000., -45000.

8, -5967., 5967., -44001.

9, -5939., 5939., -43127.

10, -5333., 5333., -24614.

11, -6000., -6000., -50000.

12, -6000., -6000., -45000.

13, -5967., -5967., -44001.

14, -5939., -5939., -43127.

15, -5333., -5333., -24614.

16, 6000., -6000., -50000.

17, 6000., -6000., -45000.

18, 5967., -5967., -44001.

19, 5939., -5939., -43127.

20, 5333., -5333., -24614.

21, 4820., 4820., -8922.

22, 4385., 4385., 4378.

23, 4016., 4016., 15651.

24, 4000., 4000., 16150.

25, -4820., 4820., -8922.

26, -4385., 4385., 4378.

27, -4016., 4016., 15651.

28, -4000., 4000., 16150.

29, -4820., -4820., -8922.

30, -4385., -4385., 4378.

31, -4016., -4016., 15651.

32, -4000., -4000., 16150.

33, 4820., -4820., -8922.

34, 4385., -4385., 4378.

35, 4016., -4016., 15651.

36, 4000., -4000., 16150.

41, 5620., 0., -33373.

42, -5620., 0., -33373.

43, 0., 5620., -33373.

44, 0., -5620., -33373.

45, 5064., 0., -16371.

46, -5064., 0., -16371.

47, 0., 5064., -16371.

48, 0., -5064., -16371.

49, 4592., 0., -1958.

50, -4592., 0., -1958.

51, 0., 4592., -1958.

52, 0., -4592., -1958.

53, 4193., 0., 10262.

54, -4193., 0., 10262.

55, 0., 4193., 10262.

56, 0., -4193., 10262.

57, 4000., 4000., 20150.

58, -4000., 4000., 20150.

59, 4000., -4000., 20150.

60, -4000., -4000., 20150.

61, 0., 0., 16150.

62, 0., 0., 18150.

63, 0., 0., 20150.

1001, 0., 0., 21150.

1011, 0., 0., 32150.

1021, 0., 0., 42150.

1031, 0., 0., 54150.

1041, 0., 0., 64150.

1051, 0., 0., 74150.

1061, 0., 0., 83150.

1071, 0., 0., 88150.

117

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10041, 5863, 5863, -40813

10042, 5787, 5787, -38499

10043, 5711, 5711, -36185

10044, 5636, 5636, -33871

10045, 5560, 5560, -31557

10046, 5484, 5484, -29243

10047, 5408, 5408, -26929

10081, -5864., 5863., -40813.

10082, -5788., 5787., -38499.

10083, -5712., 5711., -36185.

10084, -5636., 5636., -33871.

10085, -5561., 5560., -31557.

10086, -5485., 5484., -29243.

10087, -5409., 5408., -26929.

10121, -5864., -5864., -40813.

10122, -5788., -5788., -38499.

10123, -5712., -5712., -36185.

10124, -5636., -5636., -33871.

10125, -5561., -5561., -31557.

10126, -5485., -5485., -29243.

10127, -5409., -5409., -26929.

10161, 5863., -5864., -40813.

10162, 5787., -5788., -38499.

10163, 5711., -5712., -36185.

10164, 5636., -5636., -33871.

10165, 5560., -5561., -31557.

10166, 5484., -5485., -29243.

10167, 5408., -5409., -26929.

10171, 5268., 5268., -22653.

10172, 5204., 5204., -20691.

10173, 5140., 5140., -18730.

10174, 5076., 5076., -16768.

10175, 5012., 5012., -14807.

10176, 4948., 4948., -12845.

10177, 4884., 4884., -10884.

10181, 4765., 4765., -7260.

10182, 4711., 4711., -5597.

10183, 4656., 4656., -3935.

10184, 4602., 4602., -2272.

10185, 4548., 4548., -610.

10186, 4493., 4493., 1053.

10187, 4439., 4439., 2715.

10191, 4338., 4338., 5787.

10192, 4292., 4292., 7196.

10193, 4246., 4246., 8605.

10194, 4200., 4200., 10014.

10195, 4154., 4154., 11423.

10196, 4108., 4108., 12832.

10197, 4062., 4062., 14241.

10211, -5269., 5268., -22653.

10212, -5205., 5204., -20691.

10213, -5141., 5140., -18730.

10214, -5077., 5076., -16768.

10215, -5013., 5012., -14807.

10216, -4949., 4948., -12845.

10217, -4885., 4884., -10884.

10221, -4766., 4765., -7260.

10222, -4712., 4711., -5597.

10223, -4657., 4656., -3935.

10224, -4603., 4602., -2272.

10225, -4549., 4548., -610.

10226, -4494., 4493., 1053.

10227, -4440., 4439., 2715.

10231, -4339., 4338., 5787.

10232, -4293., 4292., 7196.

10233, -4247., 4246., 8605.

10234, -4201., 4200., 10014.

10235, -4155., 4154., 11423.

10236, -4109., 4108., 12832.

10237, -4063., 4062., 14241.

10251, -5269., -5269., -22653.

10252, -5205., -5205., -20691.

10253, -5141., -5141., -18730.

10254, -5077., -5077., -16768.

10255, -5013., -5013., -14807.

10256, -4949., -4949., -12845.

118

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10257, -4885., -4885., -10884.

10261, -4766., -4766., -7260.

10262, -4712., -4712., -5597.

10263, -4657., -4657., -3935.

10264, -4603., -4603., -2272.

10265, -4549., -4549., -610.

10266, -4494., -4494., 1053.

10267, -4440., -4440., 2715.

10271, -4339., -4339., 5787.

10272, -4293., -4293., 7196.

10273, -4247., -4247., 8605.

10274, -4201., -4201., 10014.

10275, -4155., -4155., 11423.

10276, -4109., -4109., 12832.

10277, -4063., -4063., 14241.

10291, 5268., -5269., -22653.

10292, 5204., -5205., -20691.

10293, 5140., -5141., -18730.

10294, 5076., -5077., -16768.

10295, 5012., -5013., -14807.

10296, 4948., -4949., -12845.

10297, 4884., -4885., -10884.

10301, 4765., -4766., -7260.

10302, 4711., -4712., -5597.

10303, 4656., -4657., -3935.

10304, 4602., -4603., -2272.

10305, 4548., -4549., -610.

10306, 4493., -4494., 1053.

10307, 4439., -4440., 2715.

10311, 4338., -4339., 5787.

10312, 4292., -4293., 7196.

10313, 4246., -4247., 8605.

10314, 4200., -4201., 10014.

10315, 4154., -4155., 11423.

10316, 4108., -4109., 12832.

10317, 4062., -4063., 14241.

10371, 4475., 5967., -44001.

10372, 2983., 5967., -44001.

10373, 1491., 5967., -44001.

10374, 0., 5967., -44001.

10375, -1492., 5967., -44001.

10376, -2984., 5967., -44001.

10377, -4476., 5967., -44001.

10381, -5967., 4475., -44001.

10382, -5967., 2983., -44001.

10383, -5967., 1491., -44001.

10384, -5967., 0., -44001.

10385, -5967., -1492., -44001.

10386, -5967., -2984., -44001.

10387, -5967., -4476., -44001.

10391, -4476., -5967., -44001.

10392, -2984., -5967., -44001.

10393, -1492., -5967., -44001.

10394, 0., -5967., -44001.

10395, 1491., -5967., -44001.

10396, 2983., -5967., -44001.

10397, 4475., -5967., -44001.

10401, 5967., -4476., -44001.

10402, 5967., -2984., -44001.

10403, 5967., -1492., -44001.

10404, 5967., 0., -44001.

10405, 5967., 1491., -44001.

10406, 5967., 2983., -44001.

10407, 5967., 4475., -44001.

10411, 5859., 4454., -40689.

10412, 5779., 2969., -38250.

10413, 5699., 1484., -35812.

10421, 5548., -1334., -31184.

10422, 5476., -2667., -28994.

10423, 5404., -4000., -26804.

10431, 5859., -4455., -40689.

10432, 5779., -2970., -38250.

10433, 5699., -1485., -35812.

10441, 5548., 1333., -31184.

10442, 5476., 2666., -28994.

10443, 5404., 3999., -26804.

119

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10451, -5860., 4454., -40689.

10452, -5780., 2969., -38250.

10453, -5700., 1484., -35812.

10461, -5549., -1334., -31184.

10462, -5477., -2667., -28994.

10463, -5405., -4000., -26804.

10471, -5860., -4455., -40689.

10472, -5780., -2970., -38250.

10473, -5700., -1485., -35812.

10481, -5549., 1333., -31184.

10482, -5477., 2666., -28994.

10483, -5405., 3999., -26804.

10491, 4454., 5859., -40689.

10492, 2969., 5779., -38250.

10493, 1484., 5699., -35812.

10501, -1334., 5548., -31184.

10502, -2667., 5476., -28994.

10503, -4000., 5404., -26804.

10511, -4455., 5859., -40689.

10512, -2970., 5779., -38250.

10513, -1485., 5699., -35812.

10521, 1333., 5548., -31184.

10522, 2666., 5476., -28994.

10523, 3999., 5404., -26804.

10531, 4454., -5860., -40689.

10532, 2969., -5780., -38250.

10533, 1484., -5700., -35812.

10541, -1334., -5549., -31184.

10542, -2667., -5477., -28994.

10543, -4000., -5405., -26804.

10551, -4455., -5860., -40689.

10552, -2970., -5780., -38250.

10553, -1485., -5700., -35812.

10561, 1333., -5549., -31184.

10562, 2666., -5477., -28994.

10563, 3999., -5405., -26804.

10571, 5265., 3999., -22554.

10572, 5198., 2666., -20493.

10573, 5131., 1333., -18432.

10581, 5003., -1205., -14509.

10582, 4942., -2410., -12647.

10583, 4881., -3615., -10785.

10591, 5265., -4000., -22554.

10592, 5198., -2667., -20493.

10593, 5131., -1334., -18432.

10601, 5003., 1205., -14509.

10602, 4942., 2410., -12647.

10603, 4881., 3615., -10785.

10611, -5266., 3999., -22554.

10612, -5199., 2666., -20493.

10613, -5132., 1333., -18432.

10621, -5003., -1205., -14509.

10622, -4942., -2410., -12647.

10623, -4881., -3615., -10785.

10631, -5266., -4000., -22554.

10632, -5199., -2667., -20493.

10633, -5132., -1334., -18432.

10641, -5003., 1205., -14509.

10642, -4942., 2410., -12647.

10643, -4881., 3615., -10785.

10651, 3999., 5265., -22554.

10652, 2666., 5198., -20493.

10653, 1333., 5131., -18432.

10661, -1205., 5003., -14509.

10662, -2410., 4942., -12647.

10663, -3615., 4881., -10785.

10671, -4000., 5265., -22554.

10672, -2667., 5198., -20493.

10673, -1334., 5131., -18432.

10681, 1205., 5003., -14509.

10682, 2410., 4942., -12647.

10683, 3615., 4881., -10785.

10691, 3999., -5266., -22554.

10692, 2666., -5199., -20493.

10693, 1333., -5132., -18432.

10701, -1205., -5003., -14509.

120

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10702, -2410., -4942., -12647.

10703, -3615., -4881., -10785.

10711, -4000., -5266., -22554.

10712, -2667., -5199., -20493.

10713, -1334., -5132., -18432.

10721, 1205., -5003., -14509.

10722, 2410., -4942., -12647.

10723, 3615., -4881., -10785.

10731, 4763., 3615., -7181.

10732, 4706., 2410., -5440.

10733, 4649., 1205., -3699.

10741, 4540., -1097., -374.

10742, 4488., -2193., 1210.

10743, 4436., -3289., 2794.

10751, 4763., -3615., -7181.

10752, 4706., -2410., -5440.

10753, 4649., -1205., -3699.

10761, 4540., 1096., -374.

10762, 4488., 2192., 1210.

10763, 4436., 3288., 2794.

10771, -4763., 3615., -7181.

10772, -4706., 2410., -5440.

10773, -4649., 1205., -3699.

10781, -4541., -1097., -374.

10782, -4489., -2193., 1210.

10783, -4437., -3289., 2794.

10791, -4763., -3615., -7181.

10792, -4706., -2410., -5440.

10793, -4649., -1205., -3699.

10801, -4541., 1096., -374.

10802, -4489., 2192., 1210.

10803, -4437., 3288., 2794.

10811, 3615., 4763., -7181.

10812, 2410., 4706., -5440.

10813, 1205., 4649., -3699.

10821, -1097., 4540., -374.

10822, -2193., 4488., 1210.

10823, -3289., 4436., 2794.

10831, -3615., 4763., -7181.

10832, -2410., 4706., -5440.

10833, -1205., 4649., -3699.

10841, 1096., 4540., -374.

10842, 2192., 4488., 1210.

10843, 3288., 4436., 2794.

10851, 3615., -4763., -7181.

10852, 2410., -4706., -5440.

10853, 1205., -4649., -3699.

10861, -1097., -4541., -374.

10862, -2193., -4489., 1210.

10863, -3289., -4437., 2794.

10871, -3615., -4763., -7181.

10872, -2410., -4706., -5440.

10873, -1205., -4649., -3699.

10881, 1096., -4541., -374.

10882, 2192., -4489., 1210.

10883, 3288., -4437., 2794.

10891, 4337., 3288., 5849.

10892, 4289., 2192., 7320.

10893, 4241., 1096., 8791.

10901, 4148., -1004., 11609.

10902, 4104., -2008., 12956.

10903, 4060., -3012., 14303.

10911, 4337., -3289., 5849.

10912, 4289., -2193., 7320.

10913, 4241., -1097., 8791.

10921, 4148., 1004., 11609.

10922, 4104., 2008., 12956.

10923, 4060., 3012., 14303.

10931, -4337., 3288., 5849.

10932, -4289., 2192., 7320.

10933, -4241., 1096., 8791.

10941, -4149., -1004., 11609.

10942, -4105., -2008., 12956.

10943, -4061., -3012., 14303.

10951, -4337., -3289., 5849.

10952, -4289., -2193., 7320.

121

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10953, -4241., -1097., 8791.

10961, -4149., 1004., 11609.

10962, -4105., 2008., 12956.

10963, -4061., 3012., 14303.

10971, 3288., 4337., 5849.

10972, 2192., 4289., 7320.

10973, 1096., 4241., 8791.

10981, -1004., 4148., 11609.

10982, -2008., 4104., 12956.

10983, -3012., 4060., 14303.

10991, -3289., 4337., 5849.

10992, -2193., 4289., 7320.

10993, -1097., 4241., 8791.

11001, 1004., 4148., 11609.

11002, 2008., 4104., 12956.

11003, 3012., 4060., 14303.

11011, 3288., -4337., 5849.

11012, 2192., -4289., 7320.

11013, 1096., -4241., 8791.

11021, -1004., -4149., 11609.

11022, -2008., -4105., 12956.

11023, -3012., -4061., 14303.

11031, -3289., -4337., 5849.

11032, -2193., -4289., 7320.

11033, -1097., -4241., 8791.

11041, 1004., -4149., 11609.

11042, 2008., -4105., 12956.

11043, 3012., -4061., 14303.

21001 , 6000 , 6000 , -51000

21002 , 6000 , 6000 , -52000

21003 , 6000 , 6000 , -53000

21004 , 6000 , 6000 , -54000

21005 , 6000 , 6000 , -55000

21006 , 6000 , 6000 , -56000

21007 , 6000 , 6000 , -57000

21008 , 6000 , 6000 , -58000

21009 , 6000 , 6000 , -59000

21010 , 6000 , 6000 , -60000

21011 , 6000 , 6000 , -61000

21012 , 6000 , 6000 , -62000

21013 , 6000 , 6000 , -63000

21014 , 6000 , 6000 , -64000

21015 , 6000 , 6000 , -65000

21016 , 6000 , 6000 , -66000

21017 , 6000 , 6000 , -67000

21018 , 6000 , 6000 , -68000

21019 , 6000 , 6000 , -69000

21020 , 6000 , 6000 , -70000

21021 , 6000 , 6000 , -71000

21022 , 6000 , 6000 , -72000

21023 , 6000 , 6000 , -73000

21024 , 6000 , 6000 , -74000

21025 , 6000 , 6000 , -75000

21026 , 6000 , 6000 , -76000

21027 , 6000 , 6000 , -77000

21028 , 6000 , 6000 , -78000

21029 , 6000 , 6000 , -79000

21030 , 6000 , 6000 , -80000

21031 , 6000 , 6000 , -81000

21032 , 6000 , 6000 , -82000

21033 , 6000 , 6000 , -83000

21034 , 6000 , 6000 , -84000

21035 , 6000 , 6000 , -85000

21036 , 6000 , 6000 , -86000

21037 , 6000 , 6000 , -87000

21038 , 6000 , 6000 , -88000

21039 , 6000 , 6000 , -89000

21040 , 6000 , 6000 , -90000

21041 , 6000 , 6000 , -91000

21042 , 6000 , 6000 , -92000

21043 , 6000 , 6000 , -93000

21044 , 6000 , 6000 , -94000

21045 , 6000 , 6000 , -95000

21046 , 6000 , 6000 , -96000

21047 , 6000 , 6000 , -97000

21048 , 6000 , 6000 , -98000

122

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
21049 , 6000 , 6000 , -99000

21050 , 6000 , 6000 , -100000

22001 , -6000 , 6000 , -51000

22002 , -6000 , 6000 , -52000

22003 , -6000 , 6000 , -53000

22004 , -6000 , 6000 , -54000

22005 , -6000 , 6000 , -55000

22006 , -6000 , 6000 , -56000

22007 , -6000 , 6000 , -57000

22008 , -6000 , 6000 , -58000

22009 , -6000 , 6000 , -59000

22010 , -6000 , 6000 , -60000

22011 , -6000 , 6000 , -61000

22012 , -6000 , 6000 , -62000

22013 , -6000 , 6000 , -63000

22014 , -6000 , 6000 , -64000

22015 , -6000 , 6000 , -65000

22016 , -6000 , 6000 , -66000

22017 , -6000 , 6000 , -67000

22018 , -6000 , 6000 , -68000

22019 , -6000 , 6000 , -69000

22020 , -6000 , 6000 , -70000

22021 , -6000 , 6000 , -71000

22022 , -6000 , 6000 , -72000

22023 , -6000 , 6000 , -73000

22024 , -6000 , 6000 , -74000

22025 , -6000 , 6000 , -75000

22026 , -6000 , 6000 , -76000

22027 , -6000 , 6000 , -77000

22028 , -6000 , 6000 , -78000

22029 , -6000 , 6000 , -79000

22030 , -6000 , 6000 , -80000

22031 , -6000 , 6000 , -81000

22032 , -6000 , 6000 , -82000

22033 , -6000 , 6000 , -83000

22034 , -6000 , 6000 , -84000

22035 , -6000 , 6000 , -85000

22036 , -6000 , 6000 , -86000

22037 , -6000 , 6000 , -87000

22038 , -6000 , 6000 , -88000

22039 , -6000 , 6000 , -89000

22040 , -6000 , 6000 , -90000

22041 , -6000 , 6000 , -91000

22042 , -6000 , 6000 , -92000

22043 , -6000 , 6000 , -93000

22044 , -6000 , 6000 , -94000

22045 , -6000 , 6000 , -95000

22046 , -6000 , 6000 , -96000

22047 , -6000 , 6000 , -97000

22048 , -6000 , 6000 , -98000

22049 , -6000 , 6000 , -99000

22050 , -6000 , 6000 , -100000

23001 , 6000 , -6000 , -51000

23002 , 6000 , -6000 , -52000

23003 , 6000 , -6000 , -53000

23004 , 6000 , -6000 , -54000

23005 , 6000 , -6000 , -55000

23006 , 6000 , -6000 , -56000

23007 , 6000 , -6000 , -57000

23008 , 6000 , -6000 , -58000

23009 , 6000 , -6000 , -59000

23010 , 6000 , -6000 , -60000

23011 , 6000 , -6000 , -61000

23012 , 6000 , -6000 , -62000

23013 , 6000 , -6000 , -63000

23014 , 6000 , -6000 , -64000

23015 , 6000 , -6000 , -65000

23016 , 6000 , -6000 , -66000

23017 , 6000 , -6000 , -67000

23018 , 6000 , -6000 , -68000

23019 , 6000 , -6000 , -69000

23020 , 6000 , -6000 , -70000

23021 , 6000 , -6000 , -71000

23022 , 6000 , -6000 , -72000

23023 , 6000 , -6000 , -73000

23024 , 6000 , -6000 , -74000

123

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
23025 , 6000 , -6000 , -75000

23026 , 6000 , -6000 , -76000

23027 , 6000 , -6000 , -77000

23028 , 6000 , -6000 , -78000

23029 , 6000 , -6000 , -79000

23030 , 6000 , -6000 , -80000

23031 , 6000 , -6000 , -81000

23032 , 6000 , -6000 , -82000

23033 , 6000 , -6000 , -83000

23034 , 6000 , -6000 , -84000

23035 , 6000 , -6000 , -85000

23036 , 6000 , -6000 , -86000

23037 , 6000 , -6000 , -87000

23038 , 6000 , -6000 , -88000

23039 , 6000 , -6000 , -89000

23040 , 6000 , -6000 , -90000

23041 , 6000 , -6000 , -91000

23042 , 6000 , -6000 , -92000

23043 , 6000 , -6000 , -93000

23044 , 6000 , -6000 , -94000

23045 , 6000 , -6000 , -95000

23046 , 6000 , -6000 , -96000

23047 , 6000 , -6000 , -97000

23048 , 6000 , -6000 , -98000

23049 , 6000 , -6000 , -99000

23050 , 6000 , -6000 , -100000

24001 , -6000 , -6000 , -51000

24002 , -6000 , -6000 , -52000

24003 , -6000 , -6000 , -53000

24004 , -6000 , -6000 , -54000

24005 , -6000 , -6000 , -55000

24006 , -6000 , -6000 , -56000

24007 , -6000 , -6000 , -57000

24008 , -6000 , -6000 , -58000

24009 , -6000 , -6000 , -59000

24010 , -6000 , -6000 , -60000

24011 , -6000 , -6000 , -61000

24012 , -6000 , -6000 , -62000

24013 , -6000 , -6000 , -63000

24014 , -6000 , -6000 , -64000

24015 , -6000 , -6000 , -65000

24016 , -6000 , -6000 , -66000

24017 , -6000 , -6000 , -67000

24018 , -6000 , -6000 , -68000

24019 , -6000 , -6000 , -69000

24020 , -6000 , -6000 , -70000

24021 , -6000 , -6000 , -71000

24022 , -6000 , -6000 , -72000

24023 , -6000 , -6000 , -73000

24024 , -6000 , -6000 , -74000

24025 , -6000 , -6000 , -75000

24026 , -6000 , -6000 , -76000

24027 , -6000 , -6000 , -77000

24028 , -6000 , -6000 , -78000

24029 , -6000 , -6000 , -79000

24030 , -6000 , -6000 , -80000

24031 , -6000 , -6000 , -81000

24032 , -6000 , -6000 , -82000

24033 , -6000 , -6000 , -83000

24034 , -6000 , -6000 , -84000

24035 , -6000 , -6000 , -85000

24036 , -6000 , -6000 , -86000

24037 , -6000 , -6000 , -87000

24038 , -6000 , -6000 , -88000

24039 , -6000 , -6000 , -89000

24040 , -6000 , -6000 , -90000

24041 , -6000 , -6000 , -91000

24042 , -6000 , -6000 , -92000

24043 , -6000 , -6000 , -93000

24044 , -6000 , -6000 , -94000

24045 , -6000 , -6000 , -95000

24046 , -6000 , -6000 , -96000

24047 , -6000 , -6000 , -97000

24048 , -6000 , -6000 , -98000

24049 , -6000 , -6000 , -99000

24050 , -6000 , -6000 , -100000

124

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
*Element, type=B31

1001, 63, 1001

1011, 1001, 1011

1021, 1011, 1021

1031, 1021, 1031

1041, 1031, 1041

1051, 1041, 1051

1061, 1051, 1061

1071, 1061, 1071

10010, 1, 2

10020, 2, 3

10030, 3, 4

10050, 6, 7

10060, 7, 8

10070, 8, 9

10041, 4, 10041

10042, 10041, 10042

10043, 10042, 10043

10044, 10043, 10044

10045, 10044, 10045

10046, 10045, 10046

10047, 10046, 10047

10048, 10047, 5

10081, 9, 10081

10082, 10081, 10082

10083, 10082, 10083

10084, 10083, 10084

10085, 10084, 10085

10086, 10085, 10086

10087, 10086, 10087

10088, 10087, 10

10090, 11, 12

10100, 12, 13

10110, 13, 14

10121, 14, 10121

10122, 10121, 10122

10123, 10122, 10123

10124, 10123, 10124

10125, 10124, 10125

10126, 10125, 10126

10127, 10126, 10127

10128, 10127, 15

10130, 16, 17

10140, 17, 18

10150, 18, 19

10161, 19, 10161

10162, 10161, 10162

10163, 10162, 10163

10164, 10163, 10164

10165, 10164, 10165

10166, 10165, 10166

10167, 10166, 10167

10168, 10167, 20

10171, 5, 10171

10172, 10171, 10172

10173, 10172, 10173

10174, 10173, 10174

10175, 10174, 10175

10176, 10175, 10176

10177, 10176, 10177

10178, 10177, 21

10181, 21, 10181

10182, 10181, 10182

10183, 10182, 10183

10184, 10183, 10184

10185, 10184, 10185

10186, 10185, 10186

10187, 10186, 10187

10188, 10187, 22

10191, 22, 10191

10192, 10191, 10192

10193, 10192, 10193

10194, 10193, 10194

10195, 10194, 10195

10196, 10195, 10196

10197, 10196, 10197

125

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10198, 10197, 23

10200, 23, 24

10211, 10, 10211

10212, 10211, 10212

10213, 10212, 10213

10214, 10213, 10214

10215, 10214, 10215

10216, 10215, 10216

10217, 10216, 10217

10218, 10217, 25

10221, 25, 10221

10222, 10221, 10222

10223, 10222, 10223

10224, 10223, 10224

10225, 10224, 10225

10226, 10225, 10226

10227, 10226, 10227

10228, 10227, 26

10231, 26, 10231

10232, 10231, 10232

10233, 10232, 10233

10234, 10233, 10234

10235, 10234, 10235

10236, 10235, 10236

10237, 10236, 10237

10238, 10237, 27

10240, 27, 28

10251, 15, 10251

10252, 10251, 10252

10253, 10252, 10253

10254, 10253, 10254

10255, 10254, 10255

10256, 10255, 10256

10257, 10256, 10257

10258, 10257, 29

10261, 29, 10261

10262, 10261, 10262

10263, 10262, 10263

10264, 10263, 10264

10265, 10264, 10265

10266, 10265, 10266

10267, 10266, 10267

10268, 10267, 30

10271, 30, 10271

10272, 10271, 10272

10273, 10272, 10273

10274, 10273, 10274

10275, 10274, 10275

10276, 10275, 10276

10277, 10276, 10277

10278, 10277, 31

10280, 31, 32

10291, 20, 10291

10292, 10291, 10292

10293, 10292, 10293

10294, 10293, 10294

10295, 10294, 10295

10296, 10295, 10296

10297, 10296, 10297

10298, 10297, 33

10301, 33, 10301

10302, 10301, 10302

10303, 10302, 10303

10304, 10303, 10304

10305, 10304, 10305

10306, 10305, 10306

10307, 10306, 10307

10308, 10307, 34

10311, 34, 10311

10312, 10311, 10312

10313, 10312, 10313

10314, 10313, 10314

10315, 10314, 10315

10316, 10315, 10316

10317, 10316, 10317

10318, 10317, 35

126

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10320, 35, 36

10371, 3, 10371

10372, 10371, 10372

10373, 10372, 10373

10374, 10373, 10374

10375, 10374, 10375

10376, 10375, 10376

10377, 10376, 10377

10378, 10377, 8

10381, 8, 10381

10382, 10381, 10382

10383, 10382, 10383

10384, 10383, 10384

10385, 10384, 10385

10386, 10385, 10386

10387, 10386, 10387

10388, 10387, 13

10391, 13, 10391

10392, 10391, 10392

10393, 10392, 10393

10394, 10393, 10394

10395, 10394, 10395

10396, 10395, 10396

10397, 10396, 10397

10398, 10397, 18

10401, 18, 10401

10402, 10401, 10402

10403, 10402, 10403

10404, 10403, 10404

10405, 10404, 10405

10406, 10405, 10406

10407, 10406, 10407

10408, 10407, 3

10411, 4, 10411

10412, 10411, 10412

10413, 10412, 10413

10414, 10413, 41

10421, 41, 10421

10422, 10421, 10422

10423, 10422, 10423

10424, 10423, 20

10431, 19, 10431

10432, 10431, 10432

10433, 10432, 10433

10434, 10433, 41

10441, 41, 10441

10442, 10441, 10442

10443, 10442, 10443

10444, 10443, 5

10451, 9, 10451

10452, 10451, 10452

10453, 10452, 10453

10454, 10453, 42

10461, 42, 10461

10462, 10461, 10462

10463, 10462, 10463

10464, 10463, 15

10471, 14, 10471

10472, 10471, 10472

10473, 10472, 10473

10474, 10473, 42

10481, 42, 10481

10482, 10481, 10482

10483, 10482, 10483

10484, 10483, 10

10491, 4, 10491

10492, 10491, 10492

10493, 10492, 10493

10494, 10493, 43

10501, 43, 10501

10502, 10501, 10502

10503, 10502, 10503

10504, 10503, 10

10511, 9, 10511

10512, 10511, 10512

10513, 10512, 10513

127

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10514, 10513, 43

10521, 43, 10521

10522, 10521, 10522

10523, 10522, 10523

10524, 10523, 5

10531, 19, 10531

10532, 10531, 10532

10533, 10532, 10533

10534, 10533, 44

10541, 44, 10541

10542, 10541, 10542

10543, 10542, 10543

10544, 10543, 15

10551, 14, 10551

10552, 10551, 10552

10553, 10552, 10553

10554, 10553, 44

10561, 44, 10561

10562, 10561, 10562

10563, 10562, 10563

10564, 10563, 20

10571, 5, 10571

10572, 10571, 10572

10573, 10572, 10573

10574, 10573, 45

10581, 45, 10581

10582, 10581, 10582

10583, 10582, 10583

10584, 10583, 33

10591, 20, 10591

10592, 10591, 10592

10593, 10592, 10593

10594, 10593, 45

10601, 45, 10601

10602, 10601, 10602

10603, 10602, 10603

10604, 10603, 21

10611, 10, 10611

10612, 10611, 10612

10613, 10612, 10613

10614, 10613, 46

10621, 46, 10621

10622, 10621, 10622

10623, 10622, 10623

10624, 10623, 29

10631, 15, 10631

10632, 10631, 10632

10633, 10632, 10633

10634, 10633, 46

10641, 46, 10641

10642, 10641, 10642

10643, 10642, 10643

10644, 10643, 25

10651, 5, 10651

10652, 10651, 10652

10653, 10652, 10653

10654, 10653, 47

10661, 47, 10661

10662, 10661, 10662

10663, 10662, 10663

10664, 10663, 25

10671, 10, 10671

10672, 10671, 10672

10673, 10672, 10673

10674, 10673, 47

10681, 47, 10681

10682, 10681, 10682

10683, 10682, 10683

10684, 10683, 21

10691, 20, 10691

10692, 10691, 10692

10693, 10692, 10693

10694, 10693, 48

10701, 48, 10701

10702, 10701, 10702

10703, 10702, 10703

128

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10704, 10703, 29

10711, 15, 10711

10712, 10711, 10712

10713, 10712, 10713

10714, 10713, 48

10721, 48, 10721

10722, 10721, 10722

10723, 10722, 10723

10724, 10723, 33

10731, 21, 10731

10732, 10731, 10732

10733, 10732, 10733

10734, 10733, 49

10741, 49, 10741

10742, 10741, 10742

10743, 10742, 10743

10744, 10743, 34

10751, 33, 10751

10752, 10751, 10752

10753, 10752, 10753

10754, 10753, 49

10761, 49, 10761

10762, 10761, 10762

10763, 10762, 10763

10764, 10763, 22

10771, 25, 10771

10772, 10771, 10772

10773, 10772, 10773

10774, 10773, 50

10781, 50, 10781

10782, 10781, 10782

10783, 10782, 10783

10784, 10783, 30

10791, 29, 10791

10792, 10791, 10792

10793, 10792, 10793

10794, 10793, 50

10801, 50, 10801

10802, 10801, 10802

10803, 10802, 10803

10804, 10803, 26

10811, 21, 10811

10812, 10811, 10812

10813, 10812, 10813

10814, 10813, 51

10821, 51, 10821

10822, 10821, 10822

10823, 10822, 10823

10824, 10823, 26

10831, 25, 10831

10832, 10831, 10832

10833, 10832, 10833

10834, 10833, 51

10841, 51, 10841

10842, 10841, 10842

10843, 10842, 10843

10844, 10843, 22

10851, 33, 10851

10852, 10851, 10852

10853, 10852, 10853

10854, 10853, 52

10861, 52, 10861

10862, 10861, 10862

10863, 10862, 10863

10864, 10863, 30

10871, 29, 10871

10872, 10871, 10872

10873, 10872, 10873

10874, 10873, 52

10881, 52, 10881

10882, 10881, 10882

10883, 10882, 10883

10884, 10883, 34

10891, 22, 10891

10892, 10891, 10892

10893, 10892, 10893

129

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10894, 10893, 53

10901, 53, 10901

10902, 10901, 10902

10903, 10902, 10903

10904, 10903, 35

10911, 34, 10911

10912, 10911, 10912

10913, 10912, 10913

10914, 10913, 53

10921, 53, 10921

10922, 10921, 10922

10923, 10922, 10923

10924, 10923, 23

10931, 26, 10931

10932, 10931, 10932

10933, 10932, 10933

10934, 10933, 54

10941, 54, 10941

10942, 10941, 10942

10943, 10942, 10943

10944, 10943, 31

10951, 30, 10951

10952, 10951, 10952

10953, 10952, 10953

10954, 10953, 54

10961, 54, 10961

10962, 10961, 10962

10963, 10962, 10963

10964, 10963, 27

10971, 22, 10971

10972, 10971, 10972

10973, 10972, 10973

10974, 10973, 55

10981, 55, 10981

10982, 10981, 10982

10983, 10982, 10983

10984, 10983, 27

10991, 26, 10991

10992, 10991, 10992

10993, 10992, 10993

10994, 10993, 55

11001, 55, 11001

11002, 11001, 11002

11003, 11002, 11003

11004, 11003, 23

11011, 34, 11011

11012, 11011, 11012

11013, 11012, 11013

11014, 11013, 56

11021, 56, 11021

11022, 11021, 11022

11023, 11022, 11023

11024, 11023, 31

11031, 30, 11031

11032, 11031, 11032

11033, 11032, 11033

11034, 11033, 56

11041, 56, 11041

11042, 11041, 11042

11043, 11042, 11043

11044, 11043, 35

11050, 24, 57

11060, 28, 58

11070, 32, 60

11080, 36, 59

20001, 61, 62

20002, 62, 63,

21001, 1, 21001

21002, 21001, 21002

21003, 21002, 21003

21004, 21003, 21004

21005, 21004, 21005

21006, 21005, 21006

21007, 21006, 21007

21008, 21007, 21008

21009, 21008, 21009

130

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
21010, 21009, 21010

21011, 21010, 21011

21012, 21011, 21012

21013, 21012, 21013

21014, 21013, 21014

21015, 21014, 21015

21016, 21015, 21016

21017, 21016, 21017

21018, 21017, 21018

21019, 21018, 21019

21020, 21019, 21020

21021, 21020, 21021

21022, 21021, 21022

21023, 21022, 21023

21024, 21023, 21024

21025, 21024, 21025

21026, 21025, 21026

21027, 21026, 21027

21028, 21027, 21028

21029, 21028, 21029

21030, 21029, 21030

21031, 21030, 21031

21032, 21031, 21032

21033, 21032, 21033

21034, 21033, 21034

21035, 21034, 21035

21036, 21035, 21036

21037, 21036, 21037

21038, 21037, 21038

21039, 21038, 21039

21040, 21039, 21040

21041, 21040, 21041

21042, 21041, 21042

21043, 21042, 21043

21044, 21043, 21044

21045, 21044, 21045

21046, 21045, 21046

21047, 21046, 21047

21048, 21047, 21048

21049, 21048, 21049

21050, 21049, 21050

22001, 6, 22001

22002, 22001, 22002

22003, 22002, 22003

22004, 22003, 22004

22005, 22004, 22005

22006, 22005, 22006

22007, 22006, 22007

22008, 22007, 22008

22009, 22008, 22009

22010, 22009, 22010

22011, 22010, 22011

22012, 22011, 22012

22013, 22012, 22013

22014, 22013, 22014

22015, 22014, 22015

22016, 22015, 22016

22017, 22016, 22017

22018, 22017, 22018

22019, 22018, 22019

22020, 22019, 22020

22021, 22020, 22021

22022, 22021, 22022

22023, 22022, 22023

22024, 22023, 22024

22025, 22024, 22025

22026, 22025, 22026

22027, 22026, 22027

22028, 22027, 22028

22029, 22028, 22029

22030, 22029, 22030

22031, 22030, 22031

22032, 22031, 22032

22033, 22032, 22033

22034, 22033, 22034

22035, 22034, 22035

131

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
22036, 22035, 22036

22037, 22036, 22037

22038, 22037, 22038

22039, 22038, 22039

22040, 22039, 22040

22041, 22040, 22041

22042, 22041, 22042

22043, 22042, 22043

22044, 22043, 22044

22045, 22044, 22045

22046, 22045, 22046

22047, 22046, 22047

22048, 22047, 22048

22049, 22048, 22049

22050, 22049, 22050

23001, 16, 23001

23002, 23001, 23002

23003, 23002, 23003

23004, 23003, 23004

23005, 23004, 23005

23006, 23005, 23006

23007, 23006, 23007

23008, 23007, 23008

23009, 23008, 23009

23010, 23009, 23010

23011, 23010, 23011

23012, 23011, 23012

23013, 23012, 23013

23014, 23013, 23014

23015, 23014, 23015

23016, 23015, 23016

23017, 23016, 23017

23018, 23017, 23018

23019, 23018, 23019

23020, 23019, 23020

23021, 23020, 23021

23022, 23021, 23022

23023, 23022, 23023

23024, 23023, 23024

23025, 23024, 23025

23026, 23025, 23026

23027, 23026, 23027

23028, 23027, 23028

23029, 23028, 23029

23030, 23029, 23030

23031, 23030, 23031

23032, 23031, 23032

23033, 23032, 23033

23034, 23033, 23034

23035, 23034, 23035

23036, 23035, 23036

23037, 23036, 23037

23038, 23037, 23038

23039, 23038, 23039

23040, 23039, 23040

23041, 23040, 23041

23042, 23041, 23042

23043, 23042, 23043

23044, 23043, 23044

23045, 23044, 23045

23046, 23045, 23046

23047, 23046, 23047

23048, 23047, 23048

23049, 23048, 23049

23050, 23049, 23050

24001, 11, 24001

24002, 24001, 24002

24003, 24002, 24003

24004, 24003, 24004

24005, 24004, 24005

24006, 24005, 24006

24007, 24006, 24007

24008, 24007, 24008

24009, 24008, 24009

24010, 24009, 24010

24011, 24010, 24011

132

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
24012, 24011, 24012

24013, 24012, 24013

24014, 24013, 24014

24015, 24014, 24015

24016, 24015, 24016

24017, 24016, 24017

24018, 24017, 24018

24019, 24018, 24019

24020, 24019, 24020

24021, 24020, 24021

24022, 24021, 24022

24023, 24022, 24023

24024, 24023, 24024

24025, 24024, 24025

24026, 24025, 24026

24027, 24026, 24027

24028, 24027, 24028

24029, 24028, 24029

24030, 24029, 24030

24031, 24030, 24031

24032, 24031, 24032

24033, 24032, 24033

24034, 24033, 24034

24035, 24034, 24035

24036, 24035, 24036

24037, 24036, 24037

24038, 24037, 24038

24039, 24038, 24039

24040, 24039, 24040

24041, 24040, 24041

24042, 24041, 24042

24043, 24042, 24043

24044, 24043, 24044

24045, 24044, 24045

24046, 24045, 24046

24047, 24046, 24047

24048, 24047, 24048

24049, 24048, 24049

24050, 24049, 24050

*Element, TYPE=SPRING1, ELSET=SPR_xdir1

31001, 21001

32001, 22001

33001, 23001

34001, 24001

*Element, TYPE=SPRING1, ELSET=SPR_xdir2

31002, 21002

32002, 22002

33002, 23002

34002, 24002

*Element, TYPE=SPRING1, ELSET=SPR_xdir3

31003, 21003

32003, 22003

33003, 23003

34003, 24003

*Element, TYPE=SPRING1, ELSET=SPR_xdir4

31004, 21004

32004, 22004

33004, 23004

34004, 24004

*Element, TYPE=SPRING1, ELSET=SPR_xdir5

31005, 21005

32005, 22005

33005, 23005

34005, 24005

*Element, TYPE=SPRING1, ELSET=SPR_xdir6

31006, 21006

32006, 22006

33006, 23006

34006, 24006

*Element, TYPE=SPRING1, ELSET=SPR_xdir7

31007, 21007

32007, 22007

33007, 23007

34007, 24007

*Element, TYPE=SPRING1, ELSET=SPR_xdir8

31008, 21008

133

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
32008, 22008

33008, 23008

34008, 24008

*Element, TYPE=SPRING1, ELSET=SPR_xdir9

31009, 21009

32009, 22009

33009, 23009

34009, 24009

*Element, TYPE=SPRING1, ELSET=SPR_xdir10

31010, 21010

32010, 22010

33010, 23010

34010, 24010

*Element, TYPE=SPRING1, ELSET=SPR_xdir11

31011, 21011

32011, 22011

33011, 23011

34011, 24011

*Element, TYPE=SPRING1, ELSET=SPR_xdir12

31012, 21012

32012, 22012

33012, 23012

34012, 24012

*Element, TYPE=SPRING1, ELSET=SPR_xdir13

31013, 21013

32013, 22013

33013, 23013

34013, 24013

*Element, TYPE=SPRING1, ELSET=SPR_xdir14

31014, 21014

32014, 22014

33014, 23014

34014, 24014

*Element, TYPE=SPRING1, ELSET=SPR_xdir15

31015, 21015

32015, 22015

33015, 23015

34015, 24015

*Element, TYPE=SPRING1, ELSET=SPR_xdir16

31016, 21016

32016, 22016

33016, 23016

34016, 24016

*Element, TYPE=SPRING1, ELSET=SPR_xdir17

31017, 21017

32017, 22017

33017, 23017

34017, 24017

*Element, TYPE=SPRING1, ELSET=SPR_xdir18

31018, 21018

32018, 22018

33018, 23018

34018, 24018

*Element, TYPE=SPRING1, ELSET=SPR_xdir19

31019, 21019

32019, 22019

33019, 23019

34019, 24019

*Element, TYPE=SPRING1, ELSET=SPR_xdir20

31020, 21020

32020, 22020

33020, 23020

34020, 24020

*Element, TYPE=SPRING1, ELSET=SPR_xdir21

31021, 21021

32021, 22021

33021, 23021

34021, 24021

*Element, TYPE=SPRING1, ELSET=SPR_xdir22

31022, 21022

32022, 22022

33022, 23022

34022, 24022

*Element, TYPE=SPRING1, ELSET=SPR_xdir23

31023, 21023

32023, 22023

134

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
33023, 23023

34023, 24023

*Element, TYPE=SPRING1, ELSET=SPR_xdir24

31024, 21024

32024, 22024

33024, 23024

34024, 24024

*Element, TYPE=SPRING1, ELSET=SPR_xdir25

31025, 21025

32025, 22025

33025, 23025

34025, 24025

*Element, TYPE=SPRING1, ELSET=SPR_xdir26

31026, 21026

32026, 22026

33026, 23026

34026, 24026

*Element, TYPE=SPRING1, ELSET=SPR_xdir27

31027, 21027

32027, 22027

33027, 23027

34027, 24027

*Element, TYPE=SPRING1, ELSET=SPR_xdir28

31028, 21028

32028, 22028

33028, 23028

34028, 24028

*Element, TYPE=SPRING1, ELSET=SPR_xdir29

31029, 21029

32029, 22029

33029, 23029

34029, 24029

*Element, TYPE=SPRING1, ELSET=SPR_xdir30

31030, 21030

32030, 22030

33030, 23030

34030, 24030

*Element, TYPE=SPRING1, ELSET=SPR_xdir31

31031, 21031

32031, 22031

33031, 23031

34031, 24031

*Element, TYPE=SPRING1, ELSET=SPR_xdir32

31032, 21032

32032, 22032

33032, 23032

34032, 24032

*Element, TYPE=SPRING1, ELSET=SPR_xdir33

31033, 21033

32033, 22033

33033, 23033

34033, 24033

*Element, TYPE=SPRING1, ELSET=SPR_xdir34

31034, 21034

32034, 22034

33034, 23034

34034, 24034

*Element, TYPE=SPRING1, ELSET=SPR_xdir35

31035, 21035

32035, 22035

33035, 23035

34035, 24035

*Element, TYPE=SPRING1, ELSET=SPR_xdir36

31036, 21036

32036, 22036

33036, 23036

34036, 24036

*Element, TYPE=SPRING1, ELSET=SPR_xdir37

31037, 21037

32037, 22037

33037, 23037

34037, 24037

*Element, TYPE=SPRING1, ELSET=SPR_xdir38

31038, 21038

32038, 22038

33038, 23038

135

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
34038, 24038

*Element, TYPE=SPRING1, ELSET=SPR_xdir39

31039, 21039

32039, 22039

33039, 23039

34039, 24039

*Element, TYPE=SPRING1, ELSET=SPR_xdir40

31040, 21040

32040, 22040

33040, 23040

34040, 24040

*Element, TYPE=SPRING1, ELSET=SPR_xdir41

31041, 21041

32041, 22041

33041, 23041

34041, 24041

*Element, TYPE=SPRING1, ELSET=SPR_xdir42

31042, 21042

32042, 22042

33042, 23042

34042, 24042

*Element, TYPE=SPRING1, ELSET=SPR_xdir43

31043, 21043

32043, 22043

33043, 23043

34043, 24043

*Element, TYPE=SPRING1, ELSET=SPR_xdir44

31044, 21044

32044, 22044

33044, 23044

34044, 24044

*Element, TYPE=SPRING1, ELSET=SPR_xdir45

31045, 21045

32045, 22045

33045, 23045

34045, 24045

*Element, TYPE=SPRING1, ELSET=SPR_xdir46

31046, 21046

32046, 22046

33046, 23046

34046, 24046

*Element, TYPE=SPRING1, ELSET=SPR_xdir47

31047, 21047

32047, 22047

33047, 23047

34047, 24047

*Element, TYPE=SPRING1, ELSET=SPR_xdir48

31048, 21048

32048, 22048

33048, 23048

34048, 24048

*Element, TYPE=SPRING1, ELSET=SPR_xdir49

31049, 21049

32049, 22049

33049, 23049

34049, 24049

*Element, TYPE=SPRING1, ELSET=SPR_xdir50

31050, 21050

32050, 22050

33050, 23050

34050, 24050

*Element, TYPE=SPRING1, ELSET=SPR_ydir1

41001, 21001

42001, 22001

43001, 23001

44001, 24001

*Element, TYPE=SPRING1, ELSET=SPR_ydir2

41002, 21002

42002, 22002

43002, 23002

44002, 24002

*Element, TYPE=SPRING1, ELSET=SPR_ydir3

41003, 21003

42003, 22003

43003, 23003

44003, 24003

136

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
*Element, TYPE=SPRING1, ELSET=SPR_ydir4

41004, 21004

42004, 22004

43004, 23004

44004, 24004

*Element, TYPE=SPRING1, ELSET=SPR_ydir5

41005, 21005

42005, 22005

43005, 23005

44005, 24005

*Element, TYPE=SPRING1, ELSET=SPR_ydir6

41006, 21006

42006, 22006

43006, 23006

44006, 24006

*Element, TYPE=SPRING1, ELSET=SPR_ydir7

41007, 21007

42007, 22007

43007, 23007

44007, 24007

*Element, TYPE=SPRING1, ELSET=SPR_ydir8

41008, 21008

42008, 22008

43008, 23008

44008, 24008

*Element, TYPE=SPRING1, ELSET=SPR_ydir9

41009, 21009

42009, 22009

43009, 23009

44009, 24009

*Element, TYPE=SPRING1, ELSET=SPR_ydir10

41010, 21010

42010, 22010

43010, 23010

44010, 24010

*Element, TYPE=SPRING1, ELSET=SPR_ydir11

41011, 21011

42011, 22011

43011, 23011

44011, 24011

*Element, TYPE=SPRING1, ELSET=SPR_ydir12

41012, 21012

42012, 22012

43012, 23012

44012, 24012

*Element, TYPE=SPRING1, ELSET=SPR_ydir13

41013, 21013

42013, 22013

43013, 23013

44013, 24013

*Element, TYPE=SPRING1, ELSET=SPR_ydir14

41014, 21014

42014, 22014

43014, 23014

44014, 24014

*Element, TYPE=SPRING1, ELSET=SPR_ydir15

41015, 21015

42015, 22015

43015, 23015

44015, 24015

*Element, TYPE=SPRING1, ELSET=SPR_ydir16

41016, 21016

42016, 22016

43016, 23016

44016, 24016

*Element, TYPE=SPRING1, ELSET=SPR_ydir17

41017, 21017

42017, 22017

43017, 23017

44017, 24017

*Element, TYPE=SPRING1, ELSET=SPR_ydir18

41018, 21018

42018, 22018

43018, 23018

44018, 24018

*Element, TYPE=SPRING1, ELSET=SPR_ydir19

137

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
41019, 21019

42019, 22019

43019, 23019

44019, 24019

*Element, TYPE=SPRING1, ELSET=SPR_ydir20

41020, 21020

42020, 22020

43020, 23020

44020, 24020

*Element, TYPE=SPRING1, ELSET=SPR_ydir21

41021, 21021

42021, 22021

43021, 23021

44021, 24021

*Element, TYPE=SPRING1, ELSET=SPR_ydir22

41022, 21022

42022, 22022

43022, 23022

44022, 24022

*Element, TYPE=SPRING1, ELSET=SPR_ydir23

41023, 21023

42023, 22023

43023, 23023

44023, 24023

*Element, TYPE=SPRING1, ELSET=SPR_ydir24

41024, 21024

42024, 22024

43024, 23024

44024, 24024

*Element, TYPE=SPRING1, ELSET=SPR_ydir25

41025, 21025

42025, 22025

43025, 23025

44025, 24025

*Element, TYPE=SPRING1, ELSET=SPR_ydir26

41026, 21026

42026, 22026

43026, 23026

44026, 24026

*Element, TYPE=SPRING1, ELSET=SPR_ydir27

41027, 21027

42027, 22027

43027, 23027

44027, 24027

*Element, TYPE=SPRING1, ELSET=SPR_ydir28

41028, 21028

42028, 22028

43028, 23028

44028, 24028

*Element, TYPE=SPRING1, ELSET=SPR_ydir29

41029, 21029

42029, 22029

43029, 23029

44029, 24029

*Element, TYPE=SPRING1, ELSET=SPR_ydir30

41030, 21030

42030, 22030

43030, 23030

44030, 24030

*Element, TYPE=SPRING1, ELSET=SPR_ydir31

41031, 21031

42031, 22031

43031, 23031

44031, 24031

*Element, TYPE=SPRING1, ELSET=SPR_ydir32

41032, 21032

42032, 22032

43032, 23032

44032, 24032

*Element, TYPE=SPRING1, ELSET=SPR_ydir33

41033, 21033

42033, 22033

43033, 23033

44033, 24033

*Element, TYPE=SPRING1, ELSET=SPR_ydir34

41034, 21034

138

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
42034, 22034

43034, 23034

44034, 24034

*Element, TYPE=SPRING1, ELSET=SPR_ydir35

41035, 21035

42035, 22035

43035, 23035

44035, 24035

*Element, TYPE=SPRING1, ELSET=SPR_ydir36

41036, 21036

42036, 22036

43036, 23036

44036, 24036

*Element, TYPE=SPRING1, ELSET=SPR_ydir37

41037, 21037

42037, 22037

43037, 23037

44037, 24037

*Element, TYPE=SPRING1, ELSET=SPR_ydir38

41038, 21038

42038, 22038

43038, 23038

44038, 24038

*Element, TYPE=SPRING1, ELSET=SPR_ydir39

41039, 21039

42039, 22039

43039, 23039

44039, 24039

*Element, TYPE=SPRING1, ELSET=SPR_ydir40

41040, 21040

42040, 22040

43040, 23040

44040, 24040

*Element, TYPE=SPRING1, ELSET=SPR_ydir41

41041, 21041

42041, 22041

43041, 23041

44041, 24041

*Element, TYPE=SPRING1, ELSET=SPR_ydir42

41042, 21042

42042, 22042

43042, 23042

44042, 24042

*Element, TYPE=SPRING1, ELSET=SPR_ydir43

41043, 21043

42043, 22043

43043, 23043

44043, 24043

*Element, TYPE=SPRING1, ELSET=SPR_ydir44

41044, 21044

42044, 22044

43044, 23044

44044, 24044

*Element, TYPE=SPRING1, ELSET=SPR_ydir45

41045, 21045

42045, 22045

43045, 23045

44045, 24045

*Element, TYPE=SPRING1, ELSET=SPR_ydir46

41046, 21046

42046, 22046

43046, 23046

44046, 24046

*Element, TYPE=SPRING1, ELSET=SPR_ydir47

41047, 21047

42047, 22047

43047, 23047

44047, 24047

*Element, TYPE=SPRING1, ELSET=SPR_ydir48

41048, 21048

42048, 22048

43048, 23048

44048, 24048

*Element, TYPE=SPRING1, ELSET=SPR_ydir49

41049, 21049

42049, 22049

139

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
43049, 23049

44049, 24049

*Element, TYPE=SPRING1, ELSET=SPR_ydir50

41050, 21050

42050, 22050

43050, 23050

44050, 24050

*Elset, elset=TP_BEAM

20001, 20002

*Elset, elset=BEAM1

10371, 10372, 10373, 10374, 10375, 10376, 10377, 10378

10381, 10382, 10383, 10384, 10385, 10386, 10387, 10388

10391, 10392, 10393, 10394, 10395, 10396, 10397, 10398

10401, 10402, 10403, 10404, 10405, 10406, 10407, 10408

10411, 10412, 10413, 10414, 10421, 10422, 10423, 10424

10431, 10432, 10433, 10434, 10441, 10442, 10443, 10444

10451, 10452, 10453, 10454, 10461, 10462, 10463, 10464

10471, 10472, 10473, 10474, 10481, 10482, 10483, 10484

10491, 10492, 10493, 10494, 10501, 10502, 10503, 10504

10511, 10512, 10513, 10514, 10521, 10522, 10523, 10524

10531, 10532, 10533, 10534, 10541, 10542, 10543, 10544

10551, 10552, 10553, 10554, 10561, 10562, 10563, 10564

10571, 10572, 10573, 10574, 10581, 10582, 10583, 10584

10591, 10592, 10593, 10594, 10601, 10602, 10603, 10604

10611, 10612, 10613, 10614, 10621, 10622, 10623, 10624

10631, 10632, 10633, 10634, 10641, 10642, 10643, 10644

10651, 10652, 10653, 10654, 10661, 10662, 10663, 10664

10671, 10672, 10673, 10674, 10681, 10682, 10683, 10684

10691, 10692, 10693, 10694, 10701, 10702, 10703, 10704

10711, 10712, 10713, 10714, 10721, 10722, 10723, 10724

10731, 10732, 10733, 10734, 10741, 10742, 10743, 10744

10751, 10752, 10753, 10754, 10761, 10762, 10763, 10764

10771, 10772, 10773, 10774, 10781, 10782, 10783, 10784

10791, 10792, 10793, 10794, 10801, 10802, 10803, 10804

10811, 10812, 10813, 10814, 10821, 10822, 10823, 10824

10831, 10832, 10833, 10834, 10841, 10842, 10843, 10844

10851, 10852, 10853, 10854, 10861, 10862, 10863, 10864

10871, 10872, 10873, 10874, 10881, 10882, 10883, 10884

10891, 10892, 10893, 10894, 10901, 10902, 10903, 10904

10911, 10912, 10913, 10914, 10921, 10922, 10923, 10924

10931, 10932, 10933, 10934, 10941, 10942, 10943, 10944

10951, 10952, 10953, 10954, 10961, 10962, 10963, 10964

10971, 10972, 10973, 10974, 10981, 10982, 10983, 10984

10991, 10992, 10993, 10994, 11001, 11002, 11003, 11004

11011, 11012, 11013, 11014, 11021, 11022, 11023, 11024

11031, 11032, 11033, 11034, 11041, 11042, 11043, 11044

*Elset, elset=BEAM2

10020, 10030, 10060, 10070, 10081, 10082, 10083, 10084

10085, 10086, 10087, 10088, 10100, 10110, 10121

10122, 10123, 10124, 10125, 10126, 10127, 10128, 10140

10150, 10161, 10162, 10163, 10164, 10165, 10166, 10167

10168, 10041, 10042, 10043, 10044, 10045, 10046, 10047

10048

*Elset, elset=BEAM3

10171, 10172, 10173, 10174, 10175, 10176, 10177, 10178

10181, 10182, 10183, 10184, 10185, 10186, 10187, 10188

10191, 10192, 10193, 10194, 10195, 10196, 10197, 10198

10200, 10211, 10212, 10213, 10214, 10215, 10216, 10217

10218, 10221, 10222, 10223, 10224, 10225, 10226, 10227

10228, 10231, 10232, 10233, 10234, 10235, 10236, 10237

10238, 10240, 10251, 10252, 10253, 10254, 10255, 10256

10257, 10258, 10261, 10262, 10263, 10264, 10265, 10266

10267, 10268, 10271, 10272, 10273, 10274, 10275, 10276

10277, 10278, 10280, 10291, 10292, 10293, 10294, 10295

10296, 10297, 10298, 10301, 10302, 10303, 10304, 10305

10306, 10307, 10308, 10311, 10312, 10313, 10314, 10315

10316, 10317, 10318, 10320

*Elset, elset=BEAM4, generate

11050, 11080, 10

*Elset, elset=PILE, generate

10010, 10130, 40

21001, 21050, 1

22001, 22050, 1

23001, 23050, 1

24001, 24050, 1

*Elset, elset=TW1

140

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
1001,

*Elset, elset=TW2

1011,

*Elset, elset=TW3

1021,

*Elset, elset=TW4

1031,

*Elset, elset=TW5

1041,

*Elset, elset=TW6

1051,

*Elset, elset=TW7

1061,

*Elset, elset=TW8

1071,

*Nset, nset=TW_top_node

1071,

*Nset, nset=TP_slave_node

24, 28, 32, 36, 57, 58, 59, 60, 61, 63

*Nset, nset=X2S2

49, 50, 51, 52

*Nset, nset=TP_master_node

62,

*Nset, nset=BC_node, generate

21050, 24050, 1000

*SPRING, ELSET=SPR_xdir1, nonlinear

1

-92700, -200

-88460, -7

-78678, -5

-51463, -2

0, 0

51463, 2

78678, 5

88460, 7

92700, 200

*SPRING, ELSET=SPR_xdir2, nonlinear

1

-241200, -200

-229684, -9

-203713, -6

-132675, -3

0, 0

132675, 3

203713, 6

229684, 9

241200, 200

*SPRING, ELSET=SPR_xdir3, nonlinear

1

-445500, -200

-423651, -11

-375082, -7

-243627, -4

0, 0

243627, 4

375082, 7

423651, 11

445500, 200

*SPRING, ELSET=SPR_xdir4, nonlinear

1

-547200, -200

-525026, -17

-470522, -11

-311498, -6

0, 0

311498, 6

470522, 11

525026, 17

547200, 200

*SPRING, ELSET=SPR_xdir5, nonlinear

1

-787500, -200

-751842, -19

-669132, -13

-438120, -6

0, 0

141

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438120, 6

669132, 13

751842, 19

787500, 200

*SPRING, ELSET=SPR_xdir6, nonlinear

1

-198000, -525

-336600, -315

-475200, -105

-330000, -35

0, 0

330000, 35

475200, 105

336600, 315

198000, 525

*SPRING, ELSET=SPR_xdir7, nonlinear

1

-248500, -525

-379850, -315

-511200, -105

-355000, -35

0, 0

355000, 35

511200, 105

379850, 315

248500, 525

*SPRING, ELSET=SPR_xdir8, nonlinear

1

-2505600, -200

-2380588, -20

-2105253, -13

-1365055, -7

0, 0

1365055, 7

2105253, 13

2380588, 20

2505600, 200

*SPRING, ELSET=SPR_xdir9, nonlinear

1

-3094200, -200

-2940972, -22

-2602129, -15

-1688508, -7

0, 0

1688508, 7

2602129, 15

2940972, 22

3094200, 200

*SPRING, ELSET=SPR_xdir10, nonlinear

1

-3744000, -200

-3559751, -24

-3150933, -16

-2045917, -8

0, 0

2045917, 8

3150933, 16

3559751, 24

3744000, 200

*SPRING, ELSET=SPR_xdir11, nonlinear

1

-3722400, -200

-3537689, -29

-3129671, -19

-2030412, -10

0, 0

2030412, 10

3129671, 19

3537689, 29

3722400, 200

*SPRING, ELSET=SPR_xdir12, nonlinear

1

-4363200, -200

-4166643, -32

-3709493, -21

-2430070, -11

142

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
0, 0

2430070, 11

3709493, 21

4166643, 32

4363200, 200

*SPRING, ELSET=SPR_xdir13, nonlinear

1

-5054400, -200

-4821302, -34

-4285850, -23

-2801053, -11

0, 0

2801053, 11

4285850, 23

4821302, 34

5054400, 200

*SPRING, ELSET=SPR_xdir14, nonlinear

1

-5796000, -200

-5523141, -36

-4903174, -24

-3197898, -12

0, 0

3197898, 12

4903174, 24

5523141, 36

5796000, 200

*SPRING, ELSET=SPR_xdir15, nonlinear

1

-6588000, -200

-6272154, -38

-5561459, -25

-3620601, -13

0, 0

3620601, 13

5561459, 25

6272154, 38

6588000, 200

*SPRING, ELSET=SPR_xdir16, nonlinear

1

-9417600, -200

-8991304, -36

-8002343, -24

-5239773, -12

0, 0

5239773, 12

8002343, 24

8991304, 36

9417600, 200

*SPRING, ELSET=SPR_xdir17, nonlinear

1

-10557000, -200

-10031500, -37

-8872656, -25

-5754420, -12

0, 0

5754420, 12

8872656, 25

10031500, 37

10557000, 200

*SPRING, ELSET=SPR_xdir18, nonlinear

1

-11761200, -200

-11179488, -39

-9892261, -26

-6419832, -13

0, 0

6419832, 13

9892261, 26

11179488, 39

11761200, 200

*SPRING, ELSET=SPR_xdir19, nonlinear

1

-13030200, -200

-12389443, -41

-10967137, -27

143

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
-7121558, -14

0, 0

7121558, 14

10967137, 27

12389443, 41

13030200, 200

*SPRING, ELSET=SPR_xdir20, nonlinear

1

-14363999, -200

-13661364, -43

-12097285, -29

-7859598, -14

0, 0

7859598, 14

12097285, 29

13661364, 43

14363999, 200

*SPRING, ELSET=SPR_xdir21, nonlinear

1

-15762598, -200

-14995252, -45

-13282704, -30

-8633951, -15

0, 0

8633951, 15

13282704, 30

14995252, 45

15762598, 200

*SPRING, ELSET=SPR_xdir22, nonlinear

1

-17225995, -200

-16391106, -47

-14523394, -31

-9444618, -16

0, 0

9444618, 16

14523394, 31

16391106, 47

17225995, 200

*SPRING, ELSET=SPR_xdir23, nonlinear

1

-18754190, -200

-17848926, -49

-15819354, -33

-10291597, -16

0, 0

10291597, 16

15819354, 33

17848926, 49

18754190, 200

*SPRING, ELSET=SPR_xdir24, nonlinear

1

-20347180, -200

-19368712, -51

-17170585, -34

-11174891, -17

0, 0

11174891, 17

17170585, 34

19368712, 51

20347180, 200

*SPRING, ELSET=SPR_xdir25, nonlinear

1

-22004963, -200

-20950463, -53

-18577087, -35

-12094497, -18

0, 0

12094497, 18

18577087, 35

20950463, 53

22004963, 200

*SPRING, ELSET=SPR_xdir26, nonlinear

1

-23727534, -200

-22594181, -55

144

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
-20038858, -37

-13050416, -18

0, 0

13050416, 18

20038858, 37

22594181, 55

23727534, 200

*SPRING, ELSET=SPR_xdir27, nonlinear

1

-25514888, -200

-24299864, -57

-21555900, -38

-14042649, -19

0, 0

14042649, 19

21555900, 38

24299864, 57

25514888, 200

*SPRING, ELSET=SPR_xdir28, nonlinear

1

-27367015, -200

-26067513, -59

-23128212, -39

-15071194, -20

0, 0

15071194, 20

23128212, 39

26067513, 59

27367015, 200

*SPRING, ELSET=SPR_xdir29, nonlinear

1

-29283903, -200

-27897127, -61

-24755794, -41

-16136052, -20

0, 0

16136052, 20

24755794, 41

27897127, 61

29283903, 200

*SPRING, ELSET=SPR_xdir30, nonlinear

1

-31265537, -200

-29788707, -63

-26438646, -42

-17237224, -21

0, 0

17237224, 21

26438646, 42

29788707, 63

31265537, 200

*SPRING, ELSET=SPR_xdir31, nonlinear

1

-33311896, -200

-31651966, -64

-27992780, -43

-18152233, -21

0, 0

18152233, 21

27992780, 43

31651966, 64

33311896, 200

*SPRING, ELSET=SPR_xdir32, nonlinear

1

-35422954, -200

-33664837, -66

-29780565, -44

-19318982, -22

0, 0

19318982, 22

29780565, 44

33664837, 66

35422954, 200

*SPRING, ELSET=SPR_xdir33, nonlinear

1

-37598676, -200

145

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
-35739673, -68

-31623620, -45

-20522045, -23

0, 0

20522045, 23

31623620, 45

35739673, 68

37598676, 200

*SPRING, ELSET=SPR_xdir34, nonlinear

1

-39839023, -200

-37876476, -70

-33521946, -47

-21761421, -23

0, 0

21761421, 23

33521946, 47

37876476, 70

39839023, 200

*SPRING, ELSET=SPR_xdir35, nonlinear

1

-42143944, -200

-40075244, -72

-35475543, -48

-23037111, -24

0, 0

23037111, 24

35475543, 48

40075244, 72

42143944, 200

*SPRING, ELSET=SPR_xdir36, nonlinear

1

-44513381, -200

-42335978, -74

-37484409, -49

-24349113, -25

0, 0

24349113, 25

37484409, 49

42335978, 74

44513381, 200

*SPRING, ELSET=SPR_xdir37, nonlinear

1

-46947262, -200

-44658677, -76

-39548546, -51

-25697429, -25

0, 0

25697429, 25

39548546, 51

44658677, 76

46947262, 200

*SPRING, ELSET=SPR_xdir38, nonlinear

1

-49069898, -200

-46639826, -77

-41258491, -51

-26764840, -26

0, 0

26764840, 26

41258491, 51

46639826, 77

49069898, 200

*SPRING, ELSET=SPR_xdir39, nonlinear

1

-50361212, -200

-47867190, -77

-42344241, -51

-27469178, -26

0, 0

27469178, 26

42344241, 51

47867190, 77

50361212, 200

*SPRING, ELSET=SPR_xdir40, nonlinear

1

146

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
-51652525, -200

-49094553, -77

-43429991, -51

-28173516, -26

0, 0

28173516, 26

43429991, 51

49094553, 77

51652525, 200

*SPRING, ELSET=SPR_xdir41, nonlinear

1

-52943838, -200

-50321917, -77

-44515740, -51

-28877853, -26

0, 0

28877853, 26

44515740, 51

50321917, 77

52943838, 200

*SPRING, ELSET=SPR_xdir42, nonlinear

1

-54235151, -200

-51549281, -77

-45601490, -51

-29582191, -26

0, 0

29582191, 26

45601490, 51

51549281, 77

54235151, 200

*SPRING, ELSET=SPR_xdir43, nonlinear

1

-55526464, -200

-52776645, -77

-46687240, -51

-30286529, -26

0, 0

30286529, 26

46687240, 51

52776645, 77

55526464, 200

*SPRING, ELSET=SPR_xdir44, nonlinear

1

-56817777, -200

-54004009, -77

-47772990, -51

-30990867, -26

0, 0

30990867, 26

47772990, 51

54004009, 77

56817777, 200

*SPRING, ELSET=SPR_xdir45, nonlinear

1

-58109090, -200

-55231373, -77

-48858739, -51

-31695205, -26

0, 0

31695205, 26

48858739, 51

55231373, 77

58109090, 200

*SPRING, ELSET=SPR_xdir46, nonlinear

1

-59400403, -200

-56458736, -77

-49944489, -51

-32399543, -26

0, 0

32399543, 26

49944489, 51

56458736, 77

59400403, 200

*SPRING, ELSET=SPR_xdir47, nonlinear

147

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
1

-60691717, -200

-57686100, -77

-51030239, -51

-33103881, -26

0, 0

33103881, 26

51030239, 51

57686100, 77

60691717, 200

*SPRING, ELSET=SPR_xdir48, nonlinear

1

-61983030, -200

-58913464, -77

-52115989, -51

-33808219, -26

0, 0

33808219, 26

52115989, 51

58913464, 77

61983030, 200

*SPRING, ELSET=SPR_xdir49, nonlinear

1

-63274343, -200

-60140828, -77

-53201739, -51

-34512556, -26

0, 0

34512556, 26

53201739, 51

60140828, 77

63274343, 200

*SPRING, ELSET=SPR_xdir50, nonlinear

1

-64565656, -200

-61368192, -77

-54287488, -51

-35216894, -26

0, 0

35216894, 26

54287488, 51

61368192, 77

64565656, 200

*SPRING, ELSET=SPR_ydir1, nonlinear

2

-92700, -200

-88460, -7

-78678, -5

-51463, -2

0, 0

51463, 2

78678, 5

88460, 7

92700, 200

*SPRING, ELSET=SPR_ydir2, nonlinear

2

-241200, -200

-229684, -9

-203713, -6

-132675, -3

0, 0

132675, 3

203713, 6

229684, 9

241200, 200

*SPRING, ELSET=SPR_ydir3, nonlinear

2

-445500, -200

-423651, -11

-375082, -7

-243627, -4

0, 0

243627, 4

375082, 7

423651, 11

445500, 200

148

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
*SPRING, ELSET=SPR_ydir4, nonlinear

2

-547200, -200

-525026, -17

-470522, -11

-311498, -6

0, 0

311498, 6

470522, 11

525026, 17

547200, 200

*SPRING, ELSET=SPR_ydir5, nonlinear

2

-787500, -200

-751842, -19

-669132, -13

-438120, -6

0, 0

438120, 6

669132, 13

751842, 19

787500, 200

*SPRING, ELSET=SPR_ydir6, nonlinear

2

-198000, -525

-336600, -315

-475200, -105

-330000, -35

0, 0

330000, 35

475200, 105

336600, 315

198000, 525

*SPRING, ELSET=SPR_ydir7, nonlinear

2

-248500, -525

-379850, -315

-511200, -105

-355000, -35

0, 0

355000, 35

511200, 105

379850, 315

248500, 525

*SPRING, ELSET=SPR_ydir8, nonlinear

2

-2505600, -200

-2380588, -20

-2105253, -13

-1365055, -7

0, 0

1365055, 7

2105253, 13

2380588, 20

2505600, 200

*SPRING, ELSET=SPR_ydir9, nonlinear

2

-3094200, -200

-2940972, -22

-2602129, -15

-1688508, -7

0, 0

1688508, 7

2602129, 15

2940972, 22

3094200, 200

*SPRING, ELSET=SPR_ydir10, nonlinear

2

-3744000, -200

-3559751, -24

-3150933, -16

-2045917, -8

0, 0

2045917, 8

3150933, 16

3559751, 24

149

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
3744000, 200

*SPRING, ELSET=SPR_ydir11, nonlinear

2

-3722400, -200

-3537689, -29

-3129671, -19

-2030412, -10

0, 0

2030412, 10

3129671, 19

3537689, 29

3722400, 200

*SPRING, ELSET=SPR_ydir12, nonlinear

2

-4363200, -200

-4166643, -32

-3709493, -21

-2430070, -11

0, 0

2430070, 11

3709493, 21

4166643, 32

4363200, 200

*SPRING, ELSET=SPR_ydir13, nonlinear

2

-5054400, -200

-4821302, -34

-4285850, -23

-2801053, -11

0, 0

2801053, 11

4285850, 23

4821302, 34

5054400, 200

*SPRING, ELSET=SPR_ydir14, nonlinear

2

-5796000, -200

-5523141, -36

-4903174, -24

-3197898, -12

0, 0

3197898, 12

4903174, 24

5523141, 36

5796000, 200

*SPRING, ELSET=SPR_ydir15, nonlinear

2

-6588000, -200

-6272154, -38

-5561459, -25

-3620601, -13

0, 0

3620601, 13

5561459, 25

6272154, 38

6588000, 200

*SPRING, ELSET=SPR_ydir16, nonlinear

2

-9417600, -200

-8991304, -36

-8002343, -24

-5239773, -12

0, 0

5239773, 12

8002343, 24

8991304, 36

9417600, 200

*SPRING, ELSET=SPR_ydir17, nonlinear

2

-10557000, -200

-10031500, -37

-8872656, -25

-5754420, -12

0, 0

5754420, 12

8872656, 25

150

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
10031500, 37

10557000, 200

*SPRING, ELSET=SPR_ydir18, nonlinear

2

-11761200, -200

-11179488, -39

-9892261, -26

-6419832, -13

0, 0

6419832, 13

9892261, 26

11179488, 39

11761200, 200

*SPRING, ELSET=SPR_ydir19, nonlinear

2

-13030200, -200

-12389443, -41

-10967137, -27

-7121558, -14

0, 0

7121558, 14

10967137, 27

12389443, 41

13030200, 200

*SPRING, ELSET=SPR_ydir20, nonlinear

2

-14363999, -200

-13661364, -43

-12097285, -29

-7859598, -14

0, 0

7859598, 14

12097285, 29

13661364, 43

14363999, 200

*SPRING, ELSET=SPR_ydir21, nonlinear

2

-15762598, -200

-14995252, -45

-13282704, -30

-8633951, -15

0, 0

8633951, 15

13282704, 30

14995252, 45

15762598, 200

*SPRING, ELSET=SPR_ydir22, nonlinear

2

-17225995, -200

-16391106, -47

-14523394, -31

-9444618, -16

0, 0

9444618, 16

14523394, 31

16391106, 47

17225995, 200

*SPRING, ELSET=SPR_ydir23, nonlinear

2

-18754190, -200

-17848926, -49

-15819354, -33

-10291597, -16

0, 0

10291597, 16

15819354, 33

17848926, 49

18754190, 200

*SPRING, ELSET=SPR_ydir24, nonlinear

2

-20347180, -200

-19368712, -51

-17170585, -34

-11174891, -17

0, 0

11174891, 17

151

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
17170585, 34

19368712, 51

20347180, 200

*SPRING, ELSET=SPR_ydir25, nonlinear

2

-22004963, -200

-20950463, -53

-18577087, -35

-12094497, -18

0, 0

12094497, 18

18577087, 35

20950463, 53

22004963, 200

*SPRING, ELSET=SPR_ydir26, nonlinear

2

-23727534, -200

-22594181, -55

-20038858, -37

-13050416, -18

0, 0

13050416, 18

20038858, 37

22594181, 55

23727534, 200

*SPRING, ELSET=SPR_ydir27, nonlinear

2

-25514888, -200

-24299864, -57

-21555900, -38

-14042649, -19

0, 0

14042649, 19

21555900, 38

24299864, 57

25514888, 200

*SPRING, ELSET=SPR_ydir28, nonlinear

2

-27367015, -200

-26067513, -59

-23128212, -39

-15071194, -20

0, 0

15071194, 20

23128212, 39

26067513, 59

27367015, 200

*SPRING, ELSET=SPR_ydir29, nonlinear

2

-29283903, -200

-27897127, -61

-24755794, -41

-16136052, -20

0, 0

16136052, 20

24755794, 41

27897127, 61

29283903, 200

*SPRING, ELSET=SPR_ydir30, nonlinear

2

-31265537, -200

-29788707, -63

-26438646, -42

-17237224, -21

0, 0

17237224, 21

26438646, 42

29788707, 63

31265537, 200

*SPRING, ELSET=SPR_ydir31, nonlinear

2

-33311896, -200

-31651966, -64

-27992780, -43

-18152233, -21

0, 0

152

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
18152233, 21

27992780, 43

31651966, 64

33311896, 200

*SPRING, ELSET=SPR_ydir32, nonlinear

2

-35422954, -200

-33664837, -66

-29780565, -44

-19318982, -22

0, 0

19318982, 22

29780565, 44

33664837, 66

35422954, 200

*SPRING, ELSET=SPR_ydir33, nonlinear

2

-37598676, -200

-35739673, -68

-31623620, -45

-20522045, -23

0, 0

20522045, 23

31623620, 45

35739673, 68

37598676, 200

*SPRING, ELSET=SPR_ydir34, nonlinear

2

-39839023, -200

-37876476, -70

-33521946, -47

-21761421, -23

0, 0

21761421, 23

33521946, 47

37876476, 70

39839023, 200

*SPRING, ELSET=SPR_ydir35, nonlinear

2

-42143944, -200

-40075244, -72

-35475543, -48

-23037111, -24

0, 0

23037111, 24

35475543, 48

40075244, 72

42143944, 200

*SPRING, ELSET=SPR_ydir36, nonlinear

2

-44513381, -200

-42335978, -74

-37484409, -49

-24349113, -25

0, 0

24349113, 25

37484409, 49

42335978, 74

44513381, 200

*SPRING, ELSET=SPR_ydir37, nonlinear

2

-46947262, -200

-44658677, -76

-39548546, -51

-25697429, -25

0, 0

25697429, 25

39548546, 51

44658677, 76

46947262, 200

*SPRING, ELSET=SPR_ydir38, nonlinear

2

-49069898, -200

-46639826, -77

-41258491, -51

-26764840, -26

153

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
0, 0

26764840, 26

41258491, 51

46639826, 77

49069898, 200

*SPRING, ELSET=SPR_ydir39, nonlinear

2

-50361212, -200

-47867190, -77

-42344241, -51

-27469178, -26

0, 0

27469178, 26

42344241, 51

47867190, 77

50361212, 200

*SPRING, ELSET=SPR_ydir40, nonlinear

2

-51652525, -200

-49094553, -77

-43429991, -51

-28173516, -26

0, 0

28173516, 26

43429991, 51

49094553, 77

51652525, 200

*SPRING, ELSET=SPR_ydir41, nonlinear

2

-52943838, -200

-50321917, -77

-44515740, -51

-28877853, -26

0, 0

28877853, 26

44515740, 51

50321917, 77

52943838, 200

*SPRING, ELSET=SPR_ydir42, nonlinear

2

-54235151, -200

-51549281, -77

-45601490, -51

-29582191, -26

0, 0

29582191, 26

45601490, 51

51549281, 77

54235151, 200

*SPRING, ELSET=SPR_ydir43, nonlinear

2

-55526464, -200

-52776645, -77

-46687240, -51

-30286529, -26

0, 0

30286529, 26

46687240, 51

52776645, 77

55526464, 200

*SPRING, ELSET=SPR_ydir44, nonlinear

2

-56817777, -200

-54004009, -77

-47772990, -51

-30990867, -26

0, 0

30990867, 26

47772990, 51

54004009, 77

56817777, 200

*SPRING, ELSET=SPR_ydir45, nonlinear

2

-58109090, -200

-55231373, -77

-48858739, -51

154

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
-31695205, -26

0, 0

31695205, 26

48858739, 51

55231373, 77

58109090, 200

*SPRING, ELSET=SPR_ydir46, nonlinear

2

-59400403, -200

-56458736, -77

-49944489, -51

-32399543, -26

0, 0

32399543, 26

49944489, 51

56458736, 77

59400403, 200

*SPRING, ELSET=SPR_ydir47, nonlinear

2

-60691717, -200

-57686100, -77

-51030239, -51

-33103881, -26

0, 0

33103881, 26

51030239, 51

57686100, 77

60691717, 200

*SPRING, ELSET=SPR_ydir48, nonlinear

2

-61983030, -200

-58913464, -77

-52115989, -51

-33808219, -26

0, 0

33808219, 26

52115989, 51

58913464, 77

61983030, 200

*SPRING, ELSET=SPR_ydir49, nonlinear

2

-63274343, -200

-60140828, -77

-53201739, -51

-34512556, -26

0, 0

34512556, 26

53201739, 51

60140828, 77

63274343, 200

*SPRING, ELSET=SPR_ydir50, nonlinear

2

-64565656, -200

-61368192, -77

-54287488, -51

-35216894, -26

0, 0

35216894, 26

54287488, 51

61368192, 77

64565656, 200

*******************************************

** new sets for outputs at legs and braces

*******************************************

*Nset, nset=ZERO_POINT, generate

10741, 10881, 20

*Elset, elset=LEG1_MEMB1

10271,

*Elset, elset=LEG2_MEMB1

10261,

*Elset, elset=LEG3_MEMB1

10251,

*Elset, elset=LEG4_MEMB1

10121,

*Elset, elset=BRA1_MEMB1

11031,

155

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
*Elset, elset=BRA2_MEMB1

10871,

*Elset, elset=BRA3_MEMB1

10711,

*Elset, elset=BRA4_MEMB1

10551,

*Elset, elset=BRA1_MEMB2

10951,

*Elset, elset=BRA2_MEMB2

10791,

*Elset, elset=BRA3_MEMB2

10631,

*Elset, elset=BRA4_MEMB2

10471,

*Elset, elset=PILE_END

10050,

** Section: Section-6-TW1 Profile: Profile-6

*Beam Section, elset=TW1, material=STEEL, temperature=GRADIENTS, section=PIPE

2800., 32.

0.,-1.,0.

** Section: Section-7-TW2 Profile: Profile-7

*Beam Section, elset=TW2, material=STEEL, temperature=GRADIENTS, section=PIPE

2788., 32.

0.,-1.,0.

** Section: Section-8-TW3 Profile: Profile-8

*Beam Section, elset=TW3, material=STEEL, temperature=GRADIENTS, section=PIPE

2659., 30.

0.,-1.,0.

** Section: Section-9-TW4 Profile: Profile-9

*Beam Section, elset=TW4, material=STEEL, temperature=GRADIENTS, section=PIPE

2541., 28.

0.,-1.,0.

** Section: Section-10-TW5 Profile: Profile-10

*Beam Section, elset=TW5, material=STEEL, temperature=GRADIENTS, section=PIPE

2400., 24.

0.,-1.,0.

** Section: Section-11-TW6 Profile: Profile-11

*Beam Section, elset=TW6, material=STEEL, temperature=GRADIENTS, section=PIPE

2282., 22.

0.,-1.,0.

** Section: Section-12-TW7 Profile: Profile-12

*Beam Section, elset=TW7, material=STEEL, temperature=GRADIENTS, section=PIPE

2164., 30.

0.,-1.,0.

** Section: Section-13-TW8 Profile: Profile-13

*Beam Section, elset=TW8, material=STEEL, temperature=GRADIENTS, section=PIPE

2059., 30.

0.,-1.,0.

** Section: Section-1-PILE Profile: Profile-1

*Beam Section, elset=PILE, material=STEEL, temperature=GRADIENTS, section=PIPE

1041., 60.

0.,-1.,0.

** Section: Section-3-BEAM2 Profile: Profile-3

*Beam Section, elset=BEAM2, material=STEEL, temperature=GRADIENTS, section=PIPE

600., 50.

0.,-1.,0.

** Section: Section-4-BEAM3 Profile: Profile-4

*Beam Section, elset=BEAM3, material=STEEL, temperature=GRADIENTS, section=PIPE

600., 35.

0.,0.,-1.

** Section: Section-2-BEAM1 Profile: Profile-2

*Beam Section, elset=BEAM1, material=STEEL, temperature=GRADIENTS, section=PIPE

400., 20.

0.,0.,-1.

** Section: Section-5-BEAM4 Profile: Profile-5

*Beam Section, elset=BEAM4, material=STEEL, temperature=GRADIENTS, section=PIPE

600., 40.

0.,-1.,0.

** Section: Section-6-TP_BEAM Profile: Profile-6

*Beam Section, elset=TP_BEAM, material=CONCRETE, temperature=GRADIENTS, section=RECT

9600, 9600

0.,-1.,0.

*Element, type=MASS, elset=NAC_mass

50002, 1071

*Mass, elset=NAC_mass

350000.,

156

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*End Part

** --------------------------------

** ASSEMBLY

** --------------------------------

*Assembly, name=Assembly

**

*Instance, name=PART-1-1, part=PART-1

*End Instance

*Nset, nset=TW_TOP, instance=PART-1-1

1071,

*Nset, nset=TP_BOTTOM, instance=PART-1-1

61,

*Nset, nset=JACKET_TOP, instance=PART-1-1

24, 28, 32, 36

*Surface, type=NODE, name=TRANSITION_PIECE_BOTTOM

JACKET_TOP, 1.

** Constraint: TP_JACKET

*Coupling, constraint name=TP_JACKET, ref node = TP_BOTTOM, surface=TRANSITION_PIECE_BOTTOM

*Kinematic

** Constraint: Constraint-2

**MPC

**TIE, PART-1-1.TP_slave_node, PART-1-1.TP_master_node

*End Assembly

** --------------------------------

** MATERIALS

** --------------------------------

*Material, name=STEEL

*Damping, beta=0.01

*Density

7.85e-06,

*Elastic

2.1e+08, 0.3

*Material, name=RIGID_MASS

*Damping, beta=0.01

*Density

7.85e-06,

*Elastic

2.9e+27, 0.0

*Material, name=CONCRETE

*Damping, alpha=3.18005, beta=0.216071

*Density

1.806e-06,

*Elastic

2.1e+08, 0.3

** --------------------------------

** Amplitude

** --------------------------------

*Amplitude, name=Fx_amp, INPUT=YawBrFxp.out

*Amplitude, name=Fy_amp, INPUT=YawBrFyp.out

*Amplitude, name=Fz_amp, INPUT=YawBrFzp.out

*Amplitude, name=Mx_amp, INPUT=YawBrMxp.out

*Amplitude, name=My_amp, INPUT=YawBrMyp.out

*Amplitude, name=Mz_amp, INPUT=YawBrMzp.out

** --------------------------------

** BOUNDARY CONDITIONS

** --------------------------------

** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre

*Boundary

**PART-1-1.BC_node, ENCASTRE

PART-1-1.BC_node, 3, 3

**PART-1-1.BC_node, 2, 2

PART-1-1.BC_node, 6, 6

** --------------------------------

** Define Hydrodynamic load

** --------------------------------

*AQUA

-50000, 0.0, 9800, 1026.05e-09

*WAVE,TYPE=GRIDDED, DATA FILE=gridwave_3d_P1.binary

0.,0.,0.,1.,0.

**----------------------------------

** STEP: dynamic analysis step

**----------------------------------

*Step, name=Step-2, nlgeom=YES, inc=400000

*Dynamic, application=TRANSIENT FIDELITY

**Dynamic

1,600,1e-08,0.10

157

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**----------------------------------

** Wind LOADS

**----------------------------------

** Name: CFORCE-1 Type: Moment

*Cload, follower, amplitude=MZ_AMP

TW_TOP, 6, 0.0001

** Name: CFORCE-2 Type: Moment

*Cload, follower, amplitude=MY_AMP

TW_TOP, 5, 0.0001

** Name: CFORCE-3 Type: Moment

*Cload, follower, amplitude=MX_AMP

TW_TOP, 4, 0.0001

** Name: CFORCE-4 Type: Concentrated force

*Cload, follower, amplitude=FZ_AMP

TW_TOP, 3, 0.0001

** Name: CFORCE-5 Type: Concentrated force

*Cload, follower, amplitude=FY_AMP

TW_TOP, 2, 0.0001

** Name: CFORCE-6 Type: Concentrated force

*Cload, follower, amplitude=FX_AMP

TW_TOP, 1, 0.0001

**----------------------------------

** WAVE LOADS

**----------------------------------

*DLOAD

, GRAV, 9800, 0., 0., -1.

*DLOAD

PART-1-1.BEAM1, FI, , 1000. , 2. , 0.

PART-1-1.BEAM2, FI, , 1400. , 2. , 0.

PART-1-1.BEAM3, FI, , 1400. , 2. , 0.

PART-1-1.BEAM4, FI, , 1400. , 2. , 0.

*DLOAD

PART-1-1.BEAM1, FDD, , 1000. , 1.

PART-1-1.BEAM2, FDD, , 1400. , 1.

PART-1-1.BEAM3, FDD, , 1400. , 1.

PART-1-1.BEAM4, FDD, , 1400. , 1.

**DLOAD

**PART-1-1.BEAM1, PB, , 1000.

**PART-1-1.BEAM2, PB, , 1400.

**PART-1-1.BEAM3, PB, , 1400.

**PART-1-1.BEAM4, PB, , 1400.

**

** OUTPUT REQUESTS

**

**Restart, write, frequency=0

**

** FIELD OUTPUT: F-Output-2

**

*OUTPUT,FIELD, Frequency=1

*NODE OUTPUT, NSET=PART-1-1.BC_node

RF

*NODE OUTPUT, NSET=PART-1-1.X2S2

U

*ELEMENT OUTPUT, ELSET=PART-1-1.TW1

SF

*NODE OUTPUT, NSET=PART-1-1.ZERO_POINT

U

*NODE OUTPUT, NSET=PART-1-1.TW_top_node

U

*ELEMENT OUTPUT, ELSET=PART-1-1.LEG1_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.LEG2_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.LEG3_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.LEG4_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA1_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA2_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA3_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA4_MEMB1

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA1_MEMB2

158

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SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA2_MEMB2

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA3_MEMB2

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.BRA4_MEMB2

SF

*ELEMENT OUTPUT, ELSET=PART-1-1.PILE_END

SF

*End Step

159

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Appendix F. The University of Miami Coupled Model 

for Combined Simulation of Hurricane Wind and Wave 

Fields 

Summary of University of Miami Work 

This project aimed to develop a meteorologically-based simulation and design tool that addresses 

uncertain risks to U.S. offshore wind farms from destructive wind and wave conditions in the 

hurricane-prone Gulf of Mexico and U.S. Eastern Seaboard wind energy development sites. This 

process involves adapting a leading, coupled, atmosphere-wave-ocean model developed by the 

research group at the University of Miami (UM) for hurricane research and prediction to provide 

correlated wind and wave fields as input to the NREL-developed FAST turbine design tools. The 

University of Miami Coupled Model (UMCM) has been configured to provide high-resolution 

coupled model simulations of hurricanes for use in the analysis of wind and wave loads 

conducted by the University of Texas (UT). We have completed the UMCM simulations of two 

major hurricanes: Hurricane Ike (2008) over the Gulf of Mexico and Superstorm Sandy (2012) 

over the U.S. Eastern Seaboard. The UMCM model output was provided to both NREL and UT 

groups during the course of this project for studies of downscaling wind and wave effects to 

turbine scale. Documentation of the UMCM software and model output is included here. This 

appendix focuses on scientific results and model evaluation with observations of Hurricane Ike 

and Superstorm Sandy. 

Objectives 

The main objectives of this work are to 1) configure and test the UMCM over the Gulf of 

Mexico and the U.S. East Coast/Atlantic Seaboard for use in predicting wind turbine loads, 2) 

conduct coupled atmosphere-wave-ocean model experiments using UMCM to better understand 

the wind, surface waves, and ocean currents in hurricanes near landfall and their impacts on 

offshore wind turbines, and 3) provide UMCM simulations of hurricanes over the Gulf of 

Mexico and for downscaling studies at turbine and structural scales. Figure F1 shows a 

schematic of the coupled system and conceptual model for this project. 

The UMCM was developed for research and prediction of marine and coastal weather systems 

including tropical cyclones and winter storms. It is a fully coupled atmosphere-wave-ocean 

model that consists of three model components: the Weather Research and Forecasting (WRF) 

model, the University of Miami Wave Model (UMWM), and the Hybrid Coordinate Ocean 

Model (HYCOM). We have developed a unified air-sea interface module that couples multiple 

atmosphere, wave, and ocean models using the Earth System Modeling Framework (ESMF). It 

provides a physically based and computationally efficient coupling at the air-sea interface that is 

flexible for use in a multi-model system and portable for transition to the next-generation 

coupled atmosphere-wave/ocean-land models. The UMCM has been tested and evaluated using 

the coupled air-sea observations collected in recent field campaigns in the Northern seas and 

Gulf of Mexico and for tropical cyclones in the Atlantic and Pacific basins. The UMCM is used 

to provide fully coupled model predictions of wind, ocean wave, and current fields as input to 

turbine design calculations. 

163 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Figure F1. Schematic of the fully coupled atmosphere-wave-ocean modeling system University of 

Miami Coupled Model that consists of WRF (atmospheric model), University of Miami Wave Model 

(wave model), and the Hybrid Coordinate Ocean Model (HYCOM) (ocean circulation model), as 

well as the meteorological and oceanic variables in the coupled system 

The development of the UMCM is based on basic coupled atmosphere-wave-ocean coupling 

physics described in Chen et al. (2007, 2013). The latest version includes a standardized, unified, 

air-sea coupling module, which provides routines that are compatible with different atmosphere, 

wave and ocean component models. The development of the Earth System Modeling Framework 

(ESMF (Hill et al. 2004), a software library for geophysical model coupling, made the design 

and development of the unified air-sea coupled model feasible. ESMF provides the facilities for 

grid and field data manipulation, as well as conventions for coupled model software design and 

parallel processing. The UMCM can be constructed using different atmosphere, wave, and ocean 

circulation models, connected together through an ESMF coupling interface. 

UMCM Component Model Descriptions 

Atmosphere Model 

The atmospheric model in UMCM is the Weather Research and Forecasting (WRF) model V3.5 

with Advanced Research WRF (ARW) dynamical core (Skamarock et al. 2008). WRF is a stateof-the-art non-hydrostatic atmospheric model with a large number of model physics options and 

a storm-following, moving nest capability for hurricane forecasting. It is defined on a 12 km 

horizontal resolution domain with 36 vertical levels and spans the area from 103.0 W to 55.0 W 

in longitude, and from 7.0 N to 45.0 N in latitude. There are two square-shaped, vortexfollowing, inner nests of 4 km and 1.3 km horizontal resolution that are 2,000 km and 440 km 

wide, respectively. The surface layer is based on Monin-Obukhov theory and the boundary layer 

parameterization is based on the Yonsei University scheme (YSU, Hong et al. 2006). The cloud 

microphysics is based on the single-moment 5-species scheme WSM5 (Hong et al. 2004), which 

is used on 1.3 and 4 km nested domains. The Kain-Fritsch cumulus parameterization is based on 

the 12 km domain (Kain and Fritsch 1993) in addition to WSM5. WRF passes the vertical wind 

164 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
profile and air density to the wave model and radiative and heat fluxes and precipitation rate to 

the ocean circulation model. 

Ocean Surface Wave Model 

The ocean wave model in UMCM is the University of Miami Wave Model (UMWM) V1.1.0 

(Donelan et al. 2012), a spectral ocean wave model that predicts wave energy spectra and 

atmosphere and ocean momentum fluxes based on input winds and ocean currents. UMWM is 

initialized from a calm state, and the full wave development for the initial atmospheric 

conditions happens within 6 hours. The model covers the same domain as the WRF parent 

domain, except that it is defined on a 4 km horizontal resolution. The wave energy spectrum is 

defined on 36 directional bins and 37 frequency bins ranging from 0.0313 Hz to 2 Hz. UMWM 

passes vectorial atmosphere stress to the atmosphere model, and vectorial ocean stress to the 

ocean circulation model. 

Ocean Circulation Model 

The ocean circulation model in UMCM is the HYbrid Coordinate Ocean Model (HYCOM) 

V2.2.34 (Wallcraft et al. 2009). It is a 3-dimensional hydrostatic ocean model with a hybrid 

vertical coordinate, z-level in shallow water, terrain-following σ-coordinate in intermediate 

water, and isopycnal (constant density) in deep water. In this study, we use the nonlocal Kprofile vertical-mixing scheme by Large et al. (1994). Its domain is defined on a 0.04 degree 

(deg) horizontal resolution grid that spans almost as large a domain as that of WRF and UMWM, 

and with 32 vertical levels. In this region, the grid spacing of 0.04 deg corresponds to the spacing 

between 3,250 m in the north, and 4,400 m in the south of the domain. Thus, the grid spacing 

closely matches that of the UMWM grid and the WRF inner 4 km nest. HYCOM passes seasurface temperature to the atmosphere model and surface current field and water density to the 

wave model. The air-sea interface module is defined on an exchange grid that covers the WRF 

and UMWM domains, at the horizontal resolution of 4 km. All fields are interpolated to the 

exchange grid, on which the calculation of air-sea exchange is defined, and are co-located in 

discrete time. In the current model configuration, fields from WRF and UMWM are exchanged 

every 60 seconds (s), whereas HYCOM fields are exchanged every 120 s. 

Initial and Lateral Boundary Conditions 

The WRF model initial and lateral boundary conditions are from the National Center for 

Environmental Prediction (NCEP) Global Forecasting System (GFS) 6-hourly fields at 0.5 deg 

horizontal resolution. The initial and boundary conditions for the ocean model are provided by 

the global, data-assimilated, 0.08 deg horizontal resolution daily HYCOM fields. Figure F2 

shows an example of the UMCM domains and model forecast of Hurricane Sandy initialized by 

the global GFS and HYCOM fields at 0000 UTC on 28 October 2012. 

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Figure F2. UMCM model forecast of surface wind (left) and sea surface temperature and 

precipitating cloud fields (right) for Hurricane Sandy at 0600 UTC on October 29, 2012 

Combined Models 

Each of the three component models in UMCM have separate origins and were originally 

designed to simulate their respective physical systems separately. The unified air-sea interface 

serves not only as a coupler but also includes coupling computations related to air-sea heat, 

moisture, and momentum fluxes that are done consistently at each coupling time step. The 

common grid is configured at the highest horizontal grid spacing of the three component models. 

In the current coupling configuration, it is set to 1.3 km, which is consistent with WRF. The 

UMWM and HYCOM grid resolution is at 4 km. The coupling time step for between the 

atmosphere-wave models is 1 minute and for the ocean model is 2 minutes. 

The WRF model incorporates two-way interacting moving nests at an increasing resolution over 

a storm and which follows it as it moves. In the specific configuration used for simulations of 

Hurricane Ike, the outermost domain has a 12 km horizontal resolution. This resolution provides 

forcing for the lateral boundaries of a 4 km middle resolution domain, which in turn provides 

forcing for the lateral boundaries of a moving 1.33 km fine-resolution domain centered over the 

hurricane using a vortex-tracking algorithm developed at the UM. The outermost domain of 

WRF is initialized and forced using output from a global weather forecast model, typically the 

National Weather Service’s GFS or the European Center’s Integrated Forecast System (IFS) 

models. The influence of observational data (from satellites, aircraft, etc.) has been incorporated 

in the global forecast data. UMCM can also assimilate additional, more localized observational 

data as it runs. 

Completed Work at the University of Miami 

 UM group has completed the coupled atmosphere-wave-ocean model simulation of

Hurricane Ike (2008) and forecast of Superstorm Sandy (2012) using the University of

Miami Coupled Model (UMCM). UMCM has 1.3 km grid resolution for the atmosphere

and 4 km for the wave and ocean model components. The UMCM full model fields

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(including all veridical levels and nested horizontal model grids) were made available at 

an hourly output. 

 A site-specific, high-frequency model output at 1-minute intervals for 10 sites along the

eastern seaboard selected by the UT group. This special model output was provided for

the UT group in support of their downscale modeling effort. The 1-min coupled model

output includes winds, ocean surface wave height, and 2-D wave spectra and other

surface variables. In addition to the wind and wave data, UM also provided the ocean

current profiles at each site for UT, which may be of value for estimating loads both

above and below the ocean surface.

 At NREL and UT request, we have also produced full model fields at 10-minute interval,

which is higher frequency than the normal 1-hour interval output. The full fields include

3D winds, temperature, humidity, significant wave height and wave periods, 3D ocean

currents, temperature, and so on. UM provided the full UMCM output to NREL for 1)

future research applications, 2) advanced visualization of high-resolution atmospherewave-ocean fields in hurricanes at NREL, and 3) open distribution online for users

outside NREL (see Appendix G).

Results 

Superstorm Sandy (2012) 

Superstorm Sandy formed as a tropical storm in the Caribbean Sea on 23 October 2012, and later 

intensified into a Category 1 hurricane of the western Atlantic Ocean. It interacted with a strong 

mid-latitude system and became a “superstorm” that made landfall over the U.S. northeastern 

coastal region. UM conducted a UMCM forecast starting at 0000 UTC on 27 October 2012, 

using the NOAA GFS model forecast fields as the initial and lateral boundary conditions for 

WRF and the global HYCOM forecast fields for the regional HYCOM in UMCM. Figure A3 

shows the UMCM forecast storm track and intensity (red lines) compared with the National 

Hurricane Center (NHC) best track data (black lines). Both the storm track and intensity were 

well-forecasted by UMCM. 

167 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Figure F3. The UMCM forecast (red) and National Hurricane Center best track data (black) of 

Superstorm Sandy track (top left) and intensity (bottom left). Model forecast (red) and the National 

Data Buoy Center (NDBC) buoy observation (black) of significant wave height (Hs), mean wave 

period (MWP), wind speed (WSPD), sea-surface temperature (SST), and 2-m air temperature (Tair). 

The UMCM is evaluated and verified with in-situ observations from the National Data Buoy 

Center (NDBC) buoys. An example of the model verification against the buoy observation is 

shown in Figure F3. NDBC 41002 was near the center of Superstorm Sandy when the storm 

passed the buoy location on 28 October 2012. 

Hurricanes have major impacts on the coastal ocean and land when making landfall. The 

characteristics of winds, surface waves, and ocean currents are shown in Figure A4. The storm 

impacts are asymmetric around the storm. On the right side of the center, the wind is mostly 

southeasterly and easterly onshore flow. The surface waves and sea surface height are the highest 

when Sandy was making landfall on 30 October. On the left side, the wind changed direction 

before and after landfall. The wave height peaked before the landfall and then decreased when 

the wind became offshore at and after the landfall. The 2-D wave spectra shows that the sea 

swells (long waves) dominated on the right side, whereas the wind-sea (short waves) and swell 

are both present on the left. 

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Figure F4. UMCM forecasts of wind speed (red) and direction (black), significant wave height (red), 

sea level height (black), and 2-D wave spectra (color coded for power of wave spectrum and red 

arrow represents wind vector) at three selected virtual turbine sites on the left, right, and near the 

center of Superstorm Sandy right before the landfall on 30 October 2012. 

There is a significant vertical wind shear from the surface to the 200 m level in Superstorm 

Sandy as shown in Figure F5. The wind speed varies from 25 to > 40 m s-1. 

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Figure F5. The UMCM forecast of wind speed (color) near the center of the storm at location 03C 

(marked on the surface wind speed map in Figure F3). The black vectors indicate wind directions. 

Hurricane Ike (2008) 

The UMCM forecast fields in Hurricane Ike (2008) have been verified against the in situ 

observations from the NDBC sites in the Gulf of Mexico during the hurricane passage in 

September 2008. The fields of verification include 10-m surface wind speed (WSPD), sea level 

pressure (SLP), surface air temperature (Ta), sea-surface temperature (SST), significant wave 

height (SWH), and mean wave period (MWP). The site-specific comparisons are subject to 

storm track forecast error. In order to evaluate hurricane-induced features, a storm-relative 

approach with correction for track error is usually used for verification at sites within the storm 

when it passed the site. Here we include examples from two nearshore sites that are outside of 

the storm with an Earth-relative reference, and two within the storm along the Hurricane Ike path 

with a storm-relative comparison (Figures F6 through F10). 

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Figure F6. Map of model storm track forecast compared with the National Hurricane Center (NHC) 

Best Track estimate and locations of the NDBC sites 

Figure F7. Comparison of UMCM forecasts and NDBC Buoy 42001 data 

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Figure F8. Comparison of UMCM forecasts and NDBC Buoy 42002 data 

Figure F9. Comparison of UMCM forecasts and NDBC Buoy 42007 data 

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Figure F10. Comparison of UMCM forecasts and NDBC Buoy 42020 data 

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References 

Chen, S. S., J. F. Price, W. Zhao, M. A. Donelan, and E. J. Walsh (2007), The CBLAST 

Hurricane program and the next-generation fully coupled atmosphere-wave-ocean models for 

hurricane research and prediction, Bull. American Meteor. Soc., 88, 311–317. 

Chen, S. S., W. Zhao, M. A. Donelan, and H. L. Tolman (2013), Directional wind-wave coupling 

in fully coupled atmosphere-wave-ocean models: Results from CBLAST-hurricane, J. Atmos. 

Sci., 70, 3198–3215. 

Donelan, M. A., M. Curcic, S. S. Chen, and A. K. Magnusson (2012), Modeling waves and wind 

stress, J. Geophys. Res., 117, C00J23. 

Hill, C., C. DeLuca, V. Balaji, M. Suarez, and A. da Silva (2004), Architecture of the Earth 

System Modeling Framework, Computing in Science and Engineering, 6, 18–28. 

Hong, S.-Y., J. Dudhia, and S.-H. Chen (2004), A revised approach to ice microphysical 

processes for the bulk parameterization of clouds and precipitation, Mon. Wea. Rev., 132, 103–

120. 

Hong, S.-Y., Y. Noh, and J. Dudhia (2006), A new vertical diffusion package with an explicit 

treatment of entrainment processes, Mon. Wea. Rev., 121, 2318–2341. 

Kain, J. S., and J. M. Fritsch (1993), Convective parameterization for mesoscale models: The 

Kain-Fritsch scheme, in The representation of cumulus convection in numerical models, edited 

by K. A. Emanuel and A. M. S. D. J. Raymond, Eds., p. 246pp. 

Large, W. G., J. C. McWilliams, and S. C. Doney (1994), Oceanic vertical mixing: A review and 

a model with a nonlocal boundary layer parameterization, Reviews of Geophysics, 32, 363–403. 

McWilliams, J. C., and P. P. Sullivan (2000), Vertical mixing by Langmuir circulations, Spill 

Science and Technology Bulletin, 6, 225–237. 

Wallcraft, A. J., E. J. Metzger, and S. N. Carroll (2009), Software design description for the 

HYbrid Coordinate Ocean Model (HYCOM) version 2.2, Tech. rep., nRL/MR/732009-9166. 

174 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Appendix G. Large Data Access System 

The University of Miami Combined Model (UMCM) pairs atmospheric Weather Research and 

Forecasting (WRF) data with University of Miami Wave Model (UMWM) and Hybrid 

Coordinate Ocean Model data. The data set hosted at the National Renewable Energy Laboratory 

(NREL) contains detailed data for hurricanes Ike (2010) and Sandy (2012), stored in a series of 

NetCDF-format files, totaling 1.3 Terabytes. The UMCM data store can be accessed at 

http://opendap.nrel.gov (also listed on http://data.gov at 

http://catalog.data.gov/dataset/combined-wind-wave-hurricane-model). Users internal to NREL 

can access the data slicing application at http://jett.hpc.nrel.gov. 

Each data set contains a number of files, one per time stamp, and each file contains a grid of 

measurements using a custom map projection. The details of the data and their resolution are as 

follows: 

 Ike

o Time resolution:

 1 sample/hour from 9/8 12:00 to 9/12 6:00

 1 sample/10 minute (min) from 9/12 6:00 to 9/13 9:00

 252 samples in time

 Sandy

o Time resolution:

 1 sample/10 min from 10/28 00:10 to 10/31 00:00

 432 samples in time.

At 58 additional sites, the data set contains higher resolution “spectral” data from the UMWM 

for Hurricane Sandy. Figure G1 shows the location of these points relative to the tracks of Ike 

and Sandy. Of those sites, 26 were selected as potential areas of interest for offshore wind 

development, and 32 were selected as validation locations for comparison with National Data 

Buoy Center (NDBC) data. At these locations, 4,319 samples are available, providing a 1 

min/sample resolution. 

175 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Data Access Systems 

Figure G1. Locations of 1 minute/sample resolution "spectral" data placed amidst storm tracks are 

indicated by the red balloons 

Source: Orthoimagery courtesy of Google Inc. 

Figure G2. Configuration of OpenDAP Hyrax server and slicing application for the database file 

system (DBFS) 

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The data is stored in the NREL data center in the native NetCDF format on the DBFS highperformance data store. Remote Web access to the data is provided by a Hyrax data server, 

which accepts queries using the OpenDAP protocol as well as a basic Web access. OpenDAP 

queries allow for arbitrary subsetting of the data using any number of client frameworks (e.g., 

Python, Matlab, etc.). In this way, only the necessary subset of data is retrieved from the server 

on the fly as computations are performed. Visualization can be accomplished similarly, by 

requesting a subset of relevant data. 

Additionally, staff at the NREL Computational Sciences Center have developed a custom Web 

framework for performing automatic time-series data extraction at an arbitrary location with any 

subset of model variables. In this way, National Wind Technology Center researchers can extract 

just those variables of greatest interest at exactly the sites they wish. These data “slices” are 

requested through a Web interface. Data extraction is fielded by a queue-based system and 

researchers are notified when their data is ready to download as spreadsheet by email. Figure G2 

shows the configured elements of this data access system. At the time of writing, this framework 

can only be accessed internally, but is designed for public access should that be deemed valuable 

at a later time. 

Analysis Example 

To provide an example of analysis opportunities using these resources, we identified three 

locations corresponding to points of interest for offshore wind turbine researchers. These 

locations are 03A (39.2691,-74.2267), 03B (39.1576, -73.9192), and 07A (36.934,-75.5453). 

Locations 03A and 03B are off the coast of Atlantic City along the direct path of Hurricane 

Sandy, amounting to a worst-case scenario for this storm. Location 07A is off the coast of 

Virginia outside the main path of the storm. Both locations are in a state of active wind turbine 

planning and development. Figure G3 and Figure G4 show the locations in detail with the path of 

Hurricane Sandy in blue. 

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Figure G3. Close-up of locations 03A and 03B 

Source: Orthoimagery courtesy of Google Inc. 

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Figure G4. Close-up of location 07A 

Source: Orthoimagery courtesy of Google Inc. 

Example time series for location 03B are given in Figures G5 through G8. Figure G5 and Figure 

G7 show the entire duration of the storm for 1 and 10 min resolutions, respectively. Figure G6 

and Figure G8 show a close-up view of data from this time series around the time the storm 

crosses over the location (i.e., at landfall). It is clear to see that the 10-min sample/snapshot in 

Figure G8 is beginning to reach the limits of usefulness in terms of the resolution; however, the 

main trends are still clear. The higher resolution in Figure G6 gives a crisp view of the behavior 

of the storm at landfall. 

The peak wind event for location 03B occurs at approximately 03:00 on 30 October 2012, 

reaching a maximum average wind speed of 32 m/s (71 mph). The maximum wave event is 

approximately 6 hours earlier, reaching 11 meter wave heights with a period of 11 seconds. 

Wind direction changes radically between these two events (max wave and max wind), from 

approximately 200 degrees (SSW) to 80 degrees (ENE). The change in wind direction creates a 

maximum wind-wave misalignment in this period of 30‒35 degrees. Sites 03A and 03B show 

similar patterns (see Figure G9 and Figure G10). Site 07A exhibits the greatest misalignment in 

wind and wave directions: nearly 70 degrees phase mismatch during a period of greater than 30 

m/s wind speeds and more than 10 m waves. Site 03A, which is more inland, appears quite 

similar to 03B, although less severe. 

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Figure G5. Time series at location 03B, 1 min/sample resolution 

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Figure G6. Time series at location 03B, 1 min/sample resolution, close-up at landfall 

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Figure G7. Time series at location 03B, 10 min/sample resolution, extracted with NREL data slice 

tool 

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Figure G8. Time series at location 03B, 10 min/sample resolution, close up at landfall 

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Figure G9. Time series at location 03A, 1 min/sample resolution 

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Figure G10. Time series for location 07A, 1 min/sample resolution 

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