`t

NIST TECHNICAL NOTE 1756

Generation of Large Directional Wind 

Speed Datasets from Smaller Synoptic 

Storm or Thunderstorm Data Samples

DongHun Yeo

NIST TECHNICAL NOTE 1756

Generation of Large Directional Wind 

Speed Datasets from Smaller Synoptic 

Storm or Thunderstorm Data Samples

DongHun Yeo

National Windstorm Impact Reduction Program

Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8611

August 2012

U.S. Department of Commerce

Dr. Rebecca Blank, Acting Secretary

National Institute of Standards and Technology

Dr. Patrick D. Gallagher, Director
Disclaimers

(1) The policy of the NIST is to use the International System of Units in its technical communications. In this document however, works of authors outside NIST are cited which describe 

measurements in certain non-SI units. Thus, it is more practical to include the non-SI unit measurements from these references.

(2) Certain trade names or company products or procedures may be mentioned in the text to 

specify adequately the experimental procedure or equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products or procedures are the best available for the purpose.
iii

Abstract

For structures sensitive to wind directionality, methods for the estimation of wind effects require 

the use of time series of directional wind speeds covering time periods exceeding the length of 

the Mean Recurrence Interval of interest in design. This study proposes a procedure for 

generating such time series from relatively short wind data sets. First, a procedure is developed 

for estimating the parameters of the distributions of the directional wind speeds, given that in the 

size of the data sample any one directional sector can in some instances be small. Once the 

distribution parameters are estimated, a simple Monte Carlo procedure is used for the data 

generation. The wind speed data being generated can be used within the framework of the 

Database-Assisted Design approach to determine wind effects on buildings by accounting for 

wind directionality.

Keywords: Directional wind speeds; Mean recurrence intervals; Extreme value statistics; 

Synthetic wind speed data; Monte Carlo simulation; Generalized Pareto distribution. 
iv

Acknowledgements

The author would like to thank E. Simiu and F. T. Lombardo of the National Institute of 

Standards and Technology for valuable advice and for providing wind speed datasets used in this 

work.
v

Contents

Abstract ..................................................................................................................... iii

Acknowledgements............................................................................................................ iv

Contents .......................................................................................................................v

List of Figures.................................................................................................................... vi

List of Tables .................................................................................................................... vii

Nomenclature................................................................................................................... viii

1. Introduction.................................................................................................................1

2. Methodology...............................................................................................................2

2.1 Measured Data Samples in Elemental and Consolidated Sectors...............................2

2.2 Probabilistic Modeling of Extreme Wind Speeds 

Using Directional Sector Data Sets.............................................................................2

2.3 Requisite Number of Generated Synthetic Windstorms.............................................4

2.4 Generation of Large Directional Data Sets by Monte Carlo Simulations ..................5

3. Application..................................................................................................................7

3.1 Small Sets of Measured Directional Wind Speed Data ..............................................7

3.2 GPD Parameter Estimation.........................................................................................9

3.3 Generation of Large Directional Wind Speed Datasets 

by Monte Carlo Simulation.......................................................................................12

4. Conclusions...............................................................................................................15

References .....................................................................................................................16
vi

List of Figures

Fig. 1 Construction of non-directional wind speed datasets from directional data ........................ 4

Fig. 2 Procedure for estimation of GPD parameters....................................................................... 6

Fig. 3 Series of synoptic wind speeds, ASOS data (Newark, NJ) .................................................. 7

Fig. 4 Histogram of measured wind speeds of synoptic wind data (Newark, NJ).......................... 8

Fig. 5 Histogram of measured wind speeds in directional sectors.................................................. 8

Fig. 6 Estimated tail length parameters versus threshold and number of threshold exceedances 10

Fig. 7 Estimated scale parameters versus threshold and number of threshold exceedances ........ 10

Fig. 8 Wind speeds in directional sectors as functions of MRIs (

10

0

10

2

10

4

40

60

80

MRI [years]

v

1 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

4 [mph]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

7 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for original 

c;

10

4

rs]

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

4

rs]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

4

rs]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for adjusted c;

10

0

10

2

10

4

40

60

80

MRI [years]

v

1 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

4 [mph]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

7 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for c = -0.01) ...................................................................... 11

Fig. 9 Comparison of λi’s in elemental sectors for measured data and synthetic data.................. 13

Fig. 10 Histogram of synthetic wind speed data for MRI = 10,000 years (Newark, NJ)............. 13

Fig. 11 Synthetic wind speeds in elemental sectors...................................................................... 14
vii

List of Tables

Table 1. Estimated parameters of generalized Pareto distributions................................................ 9
viii

Nomenclature

ASOS Automated Surface Observing Systems

Fi Cumulative Density Function of GPD for sector i

GPD Generalized Pareto distribution

MRI Mean Recurrence Interval

N

MRI of wind speeds

Ni

MRI of wind speeds for sector i

POT Peaks over Threshold

ai GPD parameter for scale for sector i

ci GPD parameter for tail length (or shape) for sector i

cij Tail length parameter with threshold uij for sector i

d Total number of elemental sectors

m Total number of directional sectors

mi Total number of threshold wind speeds for estimation of GPD parameters for sector i

mph Miles per hour

nd,i Number of wind speeds above U in directional sector i

n0k Number of wind speeds not higher than U in elemental sector k

nk Number of wind speeds above U in elemental sector k

qi Probability that wind speeds in sector i are not larger than U

r Number of synthetic directional windstorms 

rmeas Number of measured directional windstorms

s Multiplier to obtain a sufficient number of synthetic windstorms 

ui Threshold of wind speeds for sector i

uij Threshold j of wind speeds for sector i

umax,i Maximum threshold of wind speeds for constant ci for sector i

umin,i Minimum threshold of wind speeds for constant ci for sector i
ix

U Maximum value of threshold wind speeds from all sectors

vi Time series of directional wind speeds for sector i

λ Mean yearly arrival rate of windstorm events

λi Mean yearly arrival rate of windstorm events for sector i

μ Random noise

1

1. Introduction

Inherent in the ASCE 7-10 Standard (ASCE 2010) wind loading provisions are approximations 

that may be acceptable for the design of ordinary structures but are deemed unacceptable for the 

design of special structures, including tall buildings. Among these approximations are those 

inherent in the use by ASCE 7-10 Standard of a blanket wind directionality factor in conjunction 

with non-directional wind speeds with a 300-year, 700-year, or 1,700-year Mean Recurrence 

Interval (MRI). Such use results in MRIs of wind effects equal to the MRIs of the design wind 

speeds that nominally induce those effects. For structures for which wind directionality effects 

are determined by taking into account explicitly directional aerodynamic, wind climatological, 

and dynamic information, the nominal identity between the MRI of the design wind speeds and 

the MRI of the wind effects of interest no longer holds. An effective method for doing so 

requires the development of time series of directional wind speeds covering time intervals longer 

than the MRIs considered in design (see, e.g., Yeo and Simiu, 2011). This is achieved for regions 

not prone to hurricanes through the use of simulation techniques that employ relatively short 

records of measured directional wind speeds. To avoid estimation errors due to the commingling

of wind speed data associated with different types of storm it is typically necessary to perform 

separate simulations for synoptic storm and thunderstorm data (Lombardo, Main and Simiu

2009). If the correlation between any two directional data sets is less than, say, 0.7, which is 

typically the case for sufficiently large central angles of the directional sectors, the effect of the 

correlation on the estimated wind effects is negligible, and the wind speed data contained in any 

two sectors may be assumed to be independent; this assumption is marginally conservative from 

a structural engineering viewpoint (Grigoriu 2009), and is used throughout this work. If the 

correlations are relatively large, which may be the case if the central angles are small (e.g., 5◦or 

10◦), a methodology may be used that accounts for the correlations and is based on a translation 

model for the d-dimensional wind speed vector whose components are the directional wind 

speeds in a windstorm event (d is the total number of elemental sectors); for details see Grigoriu

(2009). 

The methodology used in this work involves the following steps. First, a decision is made 

on the number of elemental sectors being considered. For example, it is in practice reasonable to 

consider elemental sectors with central angle 360/18 = 20

◦

. Second, it is checked whether the 

number of data in each elemental sector is sufficiently large to allow reasonably precise estimates of the requisite probability distributions. Third, if for some elemental sectors this is not the 

case, consolidated sectors are created as the union of two or more consecutive elemental sectors,

so that the number of data in the consolidated sectors be sufficiently large. Fourth, for each sector, whether consolidated or elemental, an Extreme Value probabilistic model is fitted to the respective data sample. Since ASOS data typically exceed a threshold of approximately 35 mph, it 

is appropriate to use the generalized Pareto distribution (GPD) in conjunction with the Peaks 

over Threshold (POT) approach. Fifth, each of the probabilistic models so obtained is used to 

generate the requisite simulated data sets corresponding to the respective consolidated or elemental data set. The size r of the time series of simulated storm events associated with the simulated data must be such that the ratio r/λ is equal to or exceeds s times the MRI of the wind effects considered in design, where s ≥ 2, say, and λ is the mean yearly arrival rate of the storm 

events at the location of interest. 
2

The following sections describe the methodology in some detail, and include an example of 

its application. The report ends with a set of conclusions. The software for implementing the 

methodology is available on www.nist.gov/wind. 

2. Methodology

2.1 Measured Data Samples in Elemental and Consolidated Sectors

The first step of the methodology consists of inspecting the set of measured data on the basis of 

which the simulations yielding the requisite synthetic sets are to be performed. That set is 

extracted from recorded measurements obtained over periods of, say, 10 years to 50 years. In the 

United States measured data are currently typically obtained from Automated Surface Observing 

Systems (ASOS) by using software described by Lombardo, Main and Simiu (2009) and available on www.nist.gov/wind. The data are subjected to post-processing aimed at ensuring 

micrometeorological homogeneity with respect to surface roughness, averaging time, and height 

above the surface. In addition, if the post-processed data are reported in terms of integer values, 

noise contained in the interval -0.5 mph < μ ≤ 0.5 mph is added to them to allow their distinct

ordering. For example, if a data set contains three 20 mph wind speeds, the addition of noise 

would result in three speeds with the distinct values 19.8764, 20.0004, and 19.1087, say.

Once the measured data set is available in its final form it is necessary to determine whether 

the data sets corresponding to each of the individual directional sectors of interest are sufficiently 

large to allow the application of POT methods of extreme value statistical analysis. If an elemental sector contains a sufficiently large number of data, then those data will be subjected to 

the requisite statistical analysis. If the number of data is not sufficient, then the data set considered for analysis consists of the data contained in a consolidated sector. A directional sector denotes either an elemental or a consolidated sector containing a number of data that is sufficiently 

large to allow a useful statistical analysis. For a consolidated sector consisting of two or more elemental sectors, only the largest of the two or more elemental sector wind speeds associated with 

any given windstorm event is considered in the analysis. For example, consider a consolidated 

sector formed of two elemental sectors. Assume that in a given storm event the wind speed is 45 

mph in one elemental sector and 49 mph in the second elemental sector. Then only the 49 mph 

speed is considered in the analysis of the consolidated sector data.

POT requires the definition of a threshold such that only data exceeding that threshold are 

considered in the extreme value analysis. The threshold being considered is determined as indicated in Section 2.2.

 

2.2 Probabilistic Modeling of Extreme Wind Speeds Using Directional Sector Data Sets 

The generalized Pareto distribution (GPD) is widely assumed to be an appropriate model of the 

extreme wind speeds (see, e.g., Simiu, 2011 and references therein). That is, for a directional 

sector i (elemental or consolidated), the distribution of the extreme wind speeds vi larger than the 

threshold ui is the GPD with parameters (ci, ai, ui, λi), where ci is the shape (i.e., tail length) 
3

parameter, ai is the scale parameter, ui is the threshold, and λi is the mean arrival rate, estimated 

as the sample size divided by the duration of the data record in years. 

The expression for the GPD is

1

1 1 for 0

( )

1 exp for 0

i

c

i i

i i

i

i i

i i

i

i

v u

c c

a

F v

v u

c

a



     

            

 

   



      

(1)

If the mean annual rate of arrival of the windstorms is unity (corresponding to one windstorm per year), then the mean recurrence interval of the speed vi is

Ni

= 1/[1-Fi(vi)]. However, if 

the mean rate of arrival is λi, then 

1 1 N F v i i i i  / { [ ( )]}. 

Equation 1 can be inverted to obtain the speed vi corresponding to the probability Fi. Then,

1

i i c

i i i i i

i

a

v N u N

c

( ) [ ( ) ]    

(2)

where vi ≥ ui for 

0 ic 

(i.e., for Extreme Value Type I (Gumbel) and Type II (Fréchet) 

distribution tails), and ui ≤ vi ≤ ui – ai/ci for ci < 0 (i.e., for Extreme Value Type III (reverse 

Weibull) distribution tails, for which vi has an upper bound).

The parameters ci and ai for the directional sector i may be estimated by the de Haan method 

(de Haan 1994). First, a parameter cij (j = 1, 2, 3,..., mi) is estimated and plotted as a function of 

successive threshold values uij. For example, values of the threshold in directional sector i can be 

uij = 35, 36,..., 72 mph. If uij is too high, the number of data available for analysis will be too 

small, meaning that the precision of the estimates will be inadequate. If uij is too low, the data set 

will contain data that are not representative of the extreme wind speeds, meaning that the estimates will be biased. Typically, for a certain range of threshold values the estimated tail length 

parameter cij will have an approximately constant value (see, e.g., Simiu, 2011, p. 155). This value is chosen to be the estimator ci of the tail length parameter for the ith directional sector. The 

smallest and the largest of the thresholds uij for which the tail length parameter has the approximate value ci are denoted by ui,min and ui

,max, respectively. The threshold ui,min determines the size 

of the sample used to determine the parameter ai in Eq. (1) (see, e.g., Simiu, 2011, p. 148). As 

was noted in Sect. 2.1, of the wind speeds within a consolidated sector that belong to the same

windstorm event, only the largest is included in data set being analyzed. 

In some cases the estimated tail length parameter ci is positive, meaning that the distribution 

tail is described by a Type II Extreme Value distribution. This has been shown to be typically the 

result of sampling errors in the parameter estimation and can result in unrealistically large estimates of extreme wind speeds with long MRIs (Simiu and Scanlan, 1996, p. 97). For this reason, 

if the estimated value of the GPD tail length parameter is ci > -0.01, the value used in the calculations should be taken as ci = -0.01 (corresponding to within a close approximation to a Gumbel 

distribution tail); if the estimated value is ci < -0.1, the value used in the calculations should be 

taken as ci = -0.1, thereby avoiding distribution tails that may be unconservatively short. (Note 
4

 Directional wind speeds Non-directional wind speeds

Windstorm 

event Sect. 1 Sect. 2 Sect. 3 Sect. 4

Windstorm 

event

Non-dir.

Sect.

1 25 34 58 69 1 69

2 31 70 21 37 2 70

3 45 44 37 24 3 45

4 60 29 52 53 4 60

5 36 51 48 41 5 51

6 45 38 33 35 6 45

7 32 63 67 41 7 67

8 40 32 25 49 8 40

For each storm

v = max(vi)

 Directional wind speeds Non-directional wind speeds

Windstorm 

event

Sect. 1 Sect. 2 Sect. 3 Sect. 4

Windstorm 

event

Non-dir.

Sect.

1 25 34 58 69 1 69

2 31 70 21 37 2 70

3 45 44 37 24 3 45

4 60 29 52 53 4 60

5 36 51 48 41 5 51

6 45 38 33 35 6 45

7 32 63 67 41 7 67

8 40 32 25 49 8 49

that, for practical purposes, distribution tails for which c = -0.01 differ insignificantly from tails 

of the Gumbel distribution, which correspond in the limit to c = 0, see Sect. 3.2.) The purpose of 

these recommendations, which have been adopted in this work, is to avoid strong deviations 

from the Gumbel distribution commonly accepted at this time in the standard- writing community in the U.S. 

2.3 Requisite Number of Generated Synthetic Windstorms

The first step in obtaining the requisite number of synthetic windstorms consists of determining 

the value of the threshold U = maxi(umin,i) (i = 1, 2, ..., m), where m is the total number of 

directional sectors. The second step consist of creating a vector, the components of which are the 

largest directional wind speeds maxi(vi) > U measured in each windstorm. An illustrative 

example of directional and non-directional wind speeds with m = 4 is shown in Fig. 1. The third 

step is the calculation of the mean arrival rate λ of the windstorms for which maxi(vi) > U.

Finally, given the MRI 

N

of interest in design (e.g., 700 years or 1,700 years), the requisite 

number of synthetic windstorms to be generated should cover a time interval equal to s times (s ≥ 

2, say) the MRI 

N

(see Simiu, 2011, p. 158). This will assure a more precise estimation of the 

wind speed with MRI

N.

Therefore, the number of windstorms to be generated is 

r s N  

(3)

Note that r windstorms induce precisely r sets of directional wind effects. 

Fig. 1 Construction of non-directional wind speed datasets from directional data
5

2.4 Generation of Large Directional Data Sets by Monte Carlo Simulations

The generation is performed independently for each of the elemental sectors k (k = 1, 2,..., d). 

For each k we have r = n0k + nk, where n0k and nk denote, respectively, the number of wind 

speeds in sector k that are at most equal to the threshold U and the number of wind speeds in 

sector k that are higher than U. 

Denote by qk the probability of measured wind speeds in sector k being larger than the 

threshold U, (i.e., qk = P(vk > U)). Then nk = qk r = (λk/λ) r, where λk and λ are, respectively, the 

mean yearly arrival rate of measured windstorms in sector k that are higher than U and the mean 

arrival rate of non-directional wind speeds that are higher than U. The nk data are generated by 

Monte Carlo simulation using the following GPD model:

1 1 k

c

k k k v U a F c 

    [ ( ) ]/

(4)

where F is a random number uniformly distributed between 0 and 1. The positioning of the nk

speeds among the r speeds of sector k is randomly selected between 1 and r. For convenience, 

the n0k wind speeds at most equal to U are assigned zero speeds.

The GPD parameters ak and ck used in Eq. (4) are estimated by the following procedure

(Fig. 2). If, for an elemental sector k, we have umax,k ≥ U ≡ maxi(umin,i), then the parameters of the 

GPD model are based on U. If umax,k < U, then two cases need to be considered. In the first case 

ck(umax,k ) ≥ ck(U). In this case the use of the parameter ck(U) would be unconservative. For this 

reason, even though the threshold is specified as U and the mean arrival rate of the wind speeds 

in excess of that threshold is based on that threshold, the tail length and the scale parameter will 

be based on umax,k. In the second case ck(umax,k) < ck(U). Then, for the sake of conservatism, it is 

assumed that ck(U) = -0.01, which is the largest possible value considered in the extreme value 

statistical analysis (see Sect. 2.2), and that the scale parameter is also chosen to correspond to 

umax,k. This choice is justified by the observation that basing the scale parameter on U can in this 

case result in unreliable estimates.

In the final step, wind speeds larger than U need to be randomly relocated in their respective 

elemental sectors if any windstorm event has zero wind speeds in all elemental sectors.
6

umin,k umax,k

Case 1

uk

ck

U

Case 2

umin,k umax,k uk

ck

U

Case 3

umin,k uk

ck

U

umax,k

Case 1 Case 2 Case 3

 

Yes

No

Yes No

Elemental sector k

 

 

 

 

 

 

Fig. 2 Procedure for estimation of GPD parameters
7

Mar1982 Sep1987 Mar1993 Sep1998 Feb2004 Aug2009

20

30

40

50

60

70

80

Date Wind speed [mph]

3. Application

3.1 Small Sets of Measured Directional Wind Speed Data

We employ the proposed probabilistic model of directional wind speeds to generate synthetic 

synoptic wind speed series data for large MRIs at Newark, New Jersey. For the calibration of the 

proposed model for directional synoptic wind speeds, we use observed wind speed data in 36 directions in 10o increments, taken from the Automated Surface Observing System (ASOS), a 

network of about 20000 standardized US weather stations (NCDC, 2011). The ASOS synoptic 

wind data are adjusted by transforming knots into mph, using wind speeds for 18 elemental sectors with 20o increments, at 10 m above the ground (Fig. 3). The data have a threshold wind 

speed of approximately 29 mph (i.e., ≈ 25 knots), and a length of record of 35.34 years (from 

January 1, 1977 to April 24, 2012). Thus, the annual rate of occurrence for the wind events is 

1212/35.34 year = 34.295 year

-1

. Figure 4 shows the distribution of directional speeds of 

synoptic winds at Newark, NJ. 

Fig. 3 Series of synoptic wind speeds, ASOS data (Newark, NJ)

This study uses a minimum number of 200 wind events for each directional sector. Because 

the directional data in each elemental sector are not sufficient to estimate parameters of the generalized Pareto distribution, some elemental sectors with too few data for statistical analysis are 

consolidated (i.e., 10o to 50o, 50o to 210o, and 210o to 250o) so that each consolidated sector has a 

sufficient number of data. Figure 4 shows the histogram of the directional wind speeds of the 

wind data and directional sectors determined by the requirement of minimum 200 windstorms. 

The vertical bars represent the number of wind speeds in each elemental sector. The horizontal 

line indicates the threshold number (200) of windstorm events. If the number of windstorm 

events in an elemental sector is lower than the threshold, the sector should be consolidated with 

one or more adjacent sectors to obtain a number of windstorm events with speeds higher than the 

threshold. The figure also shows that the data have 9 directional sectors that consist of 6 elemental sectors and 3 consolidated sectors. The histogram of the wind speeds for each directional 

sector is shown in Fig. 5. 
8

Wind speed distribution in elemental sectors (Min. No. per directional sector = 200)

30 40 50 60

0

20

40

60

80

100

v

1

 [mph]

nd,1

30 40 50 60

0

20

40

60

80

100

v

2

 [mph]

nd,2

30 40 50 60

0

20

40

60

80

100

v

3

 [mph]

nd,3

30 40 50 60

0

20

40

60

80

100

120

v

4

 [mph]

nd,4

30 40 50 60

0

50

100

150

v

5

 [mph]

nd,5

30 40 50 60

0

50

100

150

v

6

 [mph]

nd,6

30 40 50 60

0

50

100

150

200

v

7

 [mph]

nd,7

30 40 50 60

0

50

100

150

200

v

8

 [mph]

nd,8

30 40 50 60

0

20

40

60

80

100

v

9

 [mph]

nd,9

1 2 3 4 5 6 7 8

Directional sector

9

0 90 180 270 360

0

100

200

300

400

500

600

700

Wind storm distribution (Min. No. per directional sector = 200)

Direction [degrees] No. of windstorms

2 8 13 14 15 16 17 18

Elemental sector

1 3 4 5 6 7 9 10 11 12

Fig. 4 Histogram of measured wind speeds of synoptic wind data (Newark, NJ)

Fig. 5 Histogram of measured wind speeds in directional sectors
9

3.2 GPD Parameter Estimation

For the directional sector i, the GPD parameters (ci, ai,) based on the threshold wind speed ui are 

estimated by the de Haan method (de Haan 1994) and are summarized in Table 1. The range of 

threshold wind speeds from umin,i to umax,i for constant ci is obtained from the plots of GPD 

parameters based on the respective threshold wind speeds (Fig 6). The maximum of the umin,i values is U = 37 mph. 

The tail length parameter ci for directional sector i is calculated from the original ci as a 

function of umax,i and U, as explained in Sect. 2.4. For the first directional sector, because umax,1 = 

40 mph is higher than U = 37 mph, c1 becomes c1(umax,1) = -0.003, but as noted in Sect. 2.2, this 

value is adjusted to -0.01; the associated scale parameter a1 becomes a(umax,1) = 4.051 mph.

The number of windstorm events whose non-directional highest speed is larger than U is 

644, and the associated mean arrival rate λ is 18.22 (= 644 storms/35.34 years). For directional 

sector i the number of wind speeds above U, ni, is calculated using the expression ni = (λi/λ)r,

where the ratio of (λi/λ) is the probability of wind speeds for sector i being higher than the

threshold U, (i.e., qi = P(vi > U)). Once the GPD parameters are determined, the wind speeds corresponding to MRIs can be obtained using Eq.(2) as shown in Fig. 8. Figure 8 shows, for comparison, wind speeds obtained by using: 1) original parameters, 2) adjusted parameters as explained above, and 3) c = -0.01 and the original a that results in wind speeds based on Gumbellike distribution. For all directional sectors except the first one, the wind speeds estimated from 

the adjusted parameters are higher than the wind speeds from the original parameters and lower 

than the wind speeds based on the Gumbel parameters. These results are consistent with the purpose of the method that uses adjusted parameters, which yields reasonably conservative wind 

speeds for design of structures.

Table 1. Estimated parameters of generalized Pareto distributions

Directional 

sector

umin,i

[mph]

umax,i

[mph]

Original 

ci

Original

ai

[mph]

Adjusted

ci

Adjusted

ai

[mph]

λi

[year-1]

1 34 40 -0.003 4.051 -0.010 4.051 1.585

2 33 39 -0.042 6.002 -0.042 6.002 1.641

3 33 41 -0.305 5.321 -0.100 5.321 2.235

4 37 49 -0.352 8.879 -0.100 8.879 3.650

5 37 52 -0.273 8.291 -0.100 8.291 6.112

6 35 46 -0.249 7.186 -0.100 7.186 8.546

7 37 47 -0.163 6.196 -0.100 6.196 10.045

8 34 44 -0.201 5.782 -0.100 5.782 5.914

9 33 42 -0.135 4.596 -0.100 4.596 2.037
10

30 35 40 45 50 55 60

-3

-2

-1

0

u

1

 [mph]

c

1

30 35 40 45 50 55 60

-3

-2

-1

0

u

2

 [mph]

c

2

30 35 40 45 50 55 60

-3

-2

-1

0

u

3

 [mph]

c

3

30 35 40 45 50 55 60

-3

-2

-1

0

u

4

 [mph]

c

4

30 35 40 45 50 55 60

-3

-2

-1

0

u

5

 [mph]

c

5

30 35 40 45 50 55 60

-3

-2

-1

0

u

6

 [mph]

c

6

30 35 40 45 50 55 60

-3

-2

-1

0

u

7

 [mph]

c

7

30 35 40 45 50 55 60

-3

-2

-1

0

u

8

 [mph]

c

8

GPD shape parameters estimated by deHaan method (Zoomed; Min. no. per sector = 200 ; red for original; blue for adjusted parameters)

30 35 40 45 50 55 60

-3

-2

-1

0

u

9

 [mph]

c

9

200 92 28 9 2 2 0

346 180 94 54 25 7 2

702 465 224 102 40 12 3

Sample

size

Sample

size

Sample

size

202 87 35 18 6 4 2

488 281 157 86 38 12 3

530 289 130 54 14 3 0

Sample

size

Sample

size

Sample

size

240 108 47 11 3 0 0

610 394 208 103 34 11 5

281 117 40 10 4 0 0

Sample

size

Sample

size

Sample

size

30 35 40 45 50 55 60

0

10

20

30

u

1

 [mph]

a

1

30 35 40 45 50 55 60

0

5

10

15

20

25

u

2

 [mph]

a

2

30 35 40 45 50 55 60

0

10

20

30

u

3

 [mph]

a

3

30 35 40 45 50 55 60

0

10

20

30

u

4

 [mph]

a

4

30 35 40 45 50 55 60

0

5

10

15

u

5

 [mph]

a

5

30 35 40 45 50 55 60

0

5

10

15

20

u

6

 [mph]

a

6

30 35 40 45 50 55 60

0

5

10

15

20

u

7

 [mph]

a

7

30 35 40 45 50 55 60

0

10

20

30

40

u

8

 [mph]

a

8

GPD scale parameters estimated by deHaan method (Min. no. per sector = 200 ; red for original; blue for adjusted parameters)

30 35 40 45 50 55 60

0

5

10

15

u

9

 [mph]

a

9

200 92 28 9 2 2 0

346 180 94 54 25 7 2

702 465 224 102 40 12 3

Sample

size

Sample

size

Sample

size

202 87 35 18 6 4 2

488 281 157 86 38 12 3

530 289 130 54 14 3 0

Sample

size

Sample

size

Sample

size

240 108 47 11 3 0 0

610 394 208 103 34 11 5

281 117 40 10 4 0 0

Sample

size

Sample

size

Sample

size

Fig. 6 Estimated tail length parameters versus threshold and number of threshold exceedances

Fig. 7 Estimated scale parameters versus threshold and number of threshold exceedances
11

101 102 103 104 40

50

60

70

80

MRI [years]

v

1 [mph]

101 102 103 104 50

60

70

80

90

100

MRI [years]

v

2 [mph]

101 102 103 104 40

50

60

70

80

90

MRI [years]

v

3 [mph]

101 102 103 104 40

60

80

100

120

140

MRI [years]

v

4 [mph]

101 102 103 104 40

60

80

100

120

140

MRI [years]

v

5 [mph]

101 102 103 104 40

60

80

100

120

MRI [years]

v

6 [mph]

101 102 103 104 40

60

80

100

120

MRI [years]

v

7 [mph]

101 102 103 104 50

60

70

80

90

100

MRI [years]

v

8 [mph]

101 102 103 104 40

50

60

70

80

90

MRI [years]

v

9 [mph]

Fig. 8 Wind speeds in directional sectors as functions of MRIs

(

10

0

10

2

10

4

40

60

80

MRI [years]

1 

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for original c;

10

0

10

2

10

4

40

60

80

MRI [years]

v

1 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

4 [mph]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

7 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for adjusted c;

10

0

10

2

10

4

40

60

80

MRI [years]

v

1 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

2 [mph]

100102104

0

50

100

MRI [years]

v

3 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

4 [mph]

10

0

10

2

104

50

100

150

MRI [years]

v

5 [mph]

100102104

50

100

150

MRI [years]

v

6 [mph]

10

0

10

2

10

4

50

100

150

MRI [years]

v

7 [mph]

10

0

10

2

104

60

80

100

MRI [years]

v

8 [mph]

100102104

0

50

100

MRI [years]

v

9 [mph]

Original c

Adjusted c

c = -0.01

for c = -0.01)
12

3.3 Generation of Large Directional Wind Speed Datasets by Monte Carlo Simulation

Synthetic wind speeds for synoptic wind events in Newark, NJ have been generated in all elemental sectors by Monte Carlo simulation using adjusted directional sector parameters estimated 

by the de Haan method, as shown in the previous section. This study generates the time-series of 

directional synoptic wind speeds for 10,000 years to assure a precise estimation of the wind 

speed and the associated wind effects with MRIs of up to 1,700 years.

The synthetic data for synoptic wind events covering a period of 10,000 years correspond to

r = 211,900 wind events (Eq.(3)) in 18 elemental directions. Assume that the elemental sector k

belongs to the directional sector i. For elemental sector k the requisite number nk of wind speeds 

above the threshold U is calculated by using nk = (λi/λ) r = r qi. The wind speeds above U are 

generated nk times in by Monte Carlo simulation using Eq.(4) with estimated GPD parameters 

(ci, ai) in directional sector i. This approach provides conservative results for the elemental sectors that are associated with consolidated sectors. As shown in Figs. 9 and 10, for elemental sectors 1 to 12 belonging to the consolidated sectors 1, 2 and 3 (Fig. 4) the number of synthetic 

wind speeds is augmented. Figure 11 shows the distribution of the synthetic wind speeds in elemental sectors.
13

2 8 13 14 15 16 17 18

Elemental sector

1 3 4 5 6 7 9 10 11 12 0 90 180 270 360

0

1

2

3

4

5

x 104

Direction [degrees] No. of windstorm events

0 90 180 270 360

0

2

4

6

8

10

Direction [degrees]



i

Annual arrival rate above the max threshold (= 37 mph) Measured data

Synthetic data

2 8 13 14 15 16 17 18

Elemental sector

1 3 4 5 6 7 9 10 11 12

Fig. 9 Comparison of λi’s in elemental sectors for measured data and synthetic data

Fig. 10 Histogram of synthetic wind speed data for MRI = 10,000 years (Newark, NJ)
14

20 40 60 80

0

2000

4000

6000

v

1

 [mph]

n

1

30 40 50 60 70

0

2000

4000

6000

v

2

 [mph]

n

2

20 40 60 80 100

0

2000

4000

6000

v

3

 [mph]

n

3

20 40 60 80 100

0

2000

4000

6000

v

4

 [mph]

n

4

20 40 60 80 100

0

2000

4000

6000

v

5

 [mph]

n

5

20 40 60 80 100

0

2000

4000

6000

v

6

 [mph]

n

6

20 40 60 80 100

0

2000

4000

6000

v

7

 [mph]

n

7

20 40 60 80 100

0

2000

4000

6000

v

8

 [mph]

n

8

20 40 60 80 100

0

2000

4000

6000

v

9

 [mph]

n

9

20 40 60 80 100

0

2000

4000

6000

v

10 [mph]

n10

20 40 60 80

0

2000

4000

6000

v

11 [mph]

n11

20 40 60 80

0

2000

4000

6000

v

12 [mph]

n12

20 40 60 80 100

0

5000

10000

v

13 [mph]

n13

20 40 60 80 100

0

5000

10000

15000

v

14 [mph]

n14

20 40 60 80 100

0

1

2

3

x 104

v

15 [mph]

n15

20 40 60 80

0

1

2

3

x 104

v

16 [mph]

n16

20 40 60 80

0

5000

10000

15000

v

17 [mph]

n17

30 40 50 60 70

0

2000

4000

6000

v

18 [mph]

n18

Fig. 11 Synthetic wind speeds in elemental sectors
15

4. Conclusions

We proposed an algorithm to generate large sets of directional synoptic or thunderstorm wind 

speeds of sufficient size to allow the estimation of wind effects with long mean recurrence 

intervals. The probability model in the study was based on a generalized Pareto distribution 

under the assumption of directionally independent wind speeds. The Monte Carlo simulation 

procedure that uses this probability model was described in detail. The algorithm applies to 

measured data sets that are too small to allow reliable estimates of correlations between pairs of 

sectorial directional wind speeds. Reference is made to earlier published results according to 

which the assumption of independence is marginally conservative provided that the center angles 

of the directional sectors being considered are sufficiently large (say, 20°), and reference is made 

to results applicable to directional data sets exhibiting large correlations (e.g., larger than 0.7). 

An application was presented, for which the parameters of the distribution were estimated from 

the ASOS data by the de Haan method. The proposed algorithm uses adjusted distribution parameters to prevent unconservative wind speed estimates. Future research includes the use of 

simulated data to estimate sampling errors in the estimation of wind-induced effects on structures 

as functions of the size of the measured data sample. The software required to perform the simulation is available on www.nist.gov/wind.
16

References

ASCE (2010). Minimum design loads for buildings and other structures, American Society of 

Civil Engineers, Reston, VA.

de Haan, L. (1994). "Extreme Value Statistics." in Extreme value theory and applications, J. 

Galambos, J. Lechner, and E. Simiu, eds., Kluwer Academic Publishers, 93-122.

Galambos, J., Lechner, J., and Simiu, E. (1994). "Extreme Value Theory and Applications."

Kluwer Academic Publishers.

Grigoriu, M. (2009). Algorithms for generating large sets of synthetic directional wind speed 

data for hurricane, thunderstorm, and synoptic winds. NIST Technical Note 1626, 

National Institute of Standards and Technology, Gaithersburg, MD.

Lombardo, F. T., Main, J. A., and Simiu, E. (2009). "Automated extraction and classification of 

thunderstorm and non-thunderstorm wind data for extreme-value analysis." Journal of 

Wind Engineering and Industrial Aerodynamics, 97(3-4), 120-131.

National Climatic Data Center (NCDC) (2011). Data documentation for data set 3505 (DSI3505): <http://www1.ncdc.noaa.gov/pub/data/documentlibrary/tddoc/td3505.pdf> 

(accessed 05/17/12).

Simiu, E. (2011). Design of buildings for wind: a guide for ASCE 7-10 Standard users and 

designers of special structures, 2nd ed., John Wiley & Sons, Hoboken, NJ.

Simiu, E. and Scanlan, R. H. (1996). Wind effects on structures, 3rd ed., John Wiley & Sons.

Yeo, D. and Simiu, E. (2011). "High-rise reinforced concrete structures: Database-Assisted 

Design for wind." Journal of Structural Engineering, 137(11), 1340-1349.