•.'----------

1II11111~!~!!I! ----~~IJ~! ------Ilff

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Model Simulations of Ocean/Sea-Ice Interaction

in the Western Arctic in 1983

Katherine S. Hedstrom

Institute of Marine and Coastal Sciences

Rutgers University.

Dale B. Haidvogel

Institute of Marine and Coastal Sciences

Rutgers University

Sergio Signorini

National Science Foundation

. March 1995

r REPRODUCED BY: '·1 u.s. Deparbnent or Commerce --

I

, National Technlcallnfonnalion Service

Springfield, Virginia 22161

, . --I

This study was funded by the Alaska Outer Continental Shelf Region of the Minerals Management Service, U.S. Department of the Interior, Anchorage, Alaska, through Cooperative Agreement

14-35-0001-30675 with Rutgers University, Institute of Marine and Coastal Sciences.

The opinions, findings, conclusions, or recommendations expressed in this report or product are

those of the authors and do not necessarily reflect the views of the U.S. Department of the Interior,

nor does mention of trade names or commercial products constitute endorsement or recommendation for use by the Federal Government.

This document was prepared with Jb.1£X and xfig.

Acknowledgments

Computational resources for the simulations described here were provided by the Arctic Region

Supercomputing Center (ARSC) of the University of Alaska, Fairbanks. The authors thank the

ARSC and its stafffor their support. The atmospheric (wind and thermal forcing) datasets used in

this study were provided by Drs. John Walsh and Bill Chapman ofthe University of illinois. Dr. Bill

Hibler of Dartmouth University provided us with the initial version of his ice model. The National

Science Foundation (NSF) contributed some salary and travel support under an NSF-sponsored

"Independent Research/Development" plan.

An earlier phase of this work was carried out under an MMS contract to Greenhorne & O'Mara

(G&O). The people involved at that time include Sergio Signorini, Wayne Lasch, Barry Herchenroder, Chris Miller, J.S. Wei, Bill O'Brien, and Jim Hill. We thank G&O, and especially Bill

O'Brien, for help in transitioning the project to Rutgers University.

Development and testing of the SPEM model has been funded by grants from the Office of

Naval Research (SC-53789), the National Science Foundation (OCE 90-12754-01), the Minerals

Management Service (14-35-0001-30675), and the National Aeronautics and Space Administration

(GC-R-261348-006-C).

1
f~ II(ul1llllllllllljfllllllrn'

Executive Summary

A coupled ocean circulation / sea-ice model is used to simulate flow properties and sea-ice

evolution in the Western Arctic during the year 1983. The coupled system, employing a semispectral primitive equation ocean circulation model and the Hibler sea-ice model, is applied on

a uniform (20 km) horizontal grid, and is forced by daily surface geostrophic winds and monthly

thermodynamic fluxes. The Beaufort Gyre and its seasonal variability are reproduced to the extent

of our observational knowledge. In particular, reversal in the climatological (anti-cyclonic) sense

of the Beaufort Gyre is indicated in September and October.~mation mechanisms for the

Beaufort Undercurrent are not reproduced at the resolution employeCl~Inclusion of an eddy form

stress parameterization improves the degree of skill in'the Undercurrent region. Bulk properties of

the sea-ice distribution (ice concentration and thickness, and its seasonal growth and retreat) are

reproduced well by the coupled model~owever, the trajectories of individual ice floes are not well

simulated, indicative of omitted and/or 'Roody treated processes such as small-scale ice dynamics,

high wavenumber and frequency atmosp'iieric forcing, mesoscale baroclinic eddies, and fine-scale

bathymetry. '\

2
Report Authors

Dale Haidvogel:

Kate Kedstrom:

Sergio Signorini:

Other Key Personnel

None

Project Organization

Sections 3, 5, and 6

Sections 2, 3, and 5

Sections 1 and 4

3
Contents

1 Scientific Background

1.1 Geometry and Oceanographic Setting

1.2 Hydrography .

1.3 Sea Ice .

1.4 The Beaufort Sea.

1.5 The Bering Strait.

1.6 Previous Numerical Experiments

1.7 Summary .

2 Description of the Coupled Model

2.1 Ocean Model Formulation

2.2 Ice Model Formulation .

2.2.1 Model structure

2.3 Model coupling .....

2.4 Western Arctic configuration

2.4.1 Model geometry

2.4.2 Initial conditions .

2.4.3 Model forcing .

2.4.4 Viscosity, diffusion, timestep

2.4.5 Floats .

3 Results of the Central Simulation (C3)

4 Interannual Variability of Forcing Fields and Impact on Model Results

5 Parameter Studies

6 Overall Assessment and Desirable Improvements

Literature Cited

4

6

6

6

6

8

9

9

11

12

12

13

13

15

15

15

15

21

21

23

24

47

58

74

76
List of Figures

1 Overview of the Arctic circulation (Aagaard [2]) 7

2 The coupled ice-ocean model schematic ..... 16

3 The Western Arctic grid . . . . . . . . . . . . . . 17

4 The unfiltered bathymetry interpolated to the Western Arctic grid 18

5 The unfiltered bathymetry clipped to lie between 50 and 500 m . . 19

6 The bathymetry after clipping, smoothing, and adding a shelf along the Northern

and Eastern boundaries " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7 The area-averaged Levitus temperature profile and the temperature climatology. .. 22

8 The area-averaged Levitus salinity profile and the salinity climatology . . . . . . .. 22

9 Monthly mean wind fields. The maximum vector length corresponds to a wind of

8.4 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

10 Time series of the area-averaged ice thickness . . . . . . . . . . . . . . 27

11 Monthly mean streamfunction values. Contour interval is 0.2 Sv . . . . 29

12 Surface currents in the Chukchi Sea. The maximum speed is 0.27 m/s 31

13 Transects of the monthly mean along-shore current .... . . . . 33

14 Monthly mean fractional ice concentrations and velocity vectors. The maximum

speed is 0.23 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36

15 Monthly mean fractional ice concentrations from the JIC data, derived from satellite

Images. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

16 Number of weeks of ice cover over 50% in the model . . 41

17 Number of weeks of ice cover over 50% in the JIC data. ·42

18 Ice thickness from submarines, from Hibler [24] . . . . 43

19 Monthly mean ice thickness from the model, in meters . 44

20 Drifting buoy trajectories " . . . 46

21 Annual means of the incoming short-wave radiation for the years 1980 to 1989. The

units are Watts/m2 . . . . . . . • • . . . • . . . . . . . . . . . . . . . . . . . . . . .. 48

22 Annual means of the incoming long-wave radiation for the years 1980 to 1989. The

units are Watts/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . .. 50

23 Annual means of the surface air temperature for the years 1980 to 1989, in degrees

Kelvin . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52

24 Annual means of the surface pressure for the years 1980 to 1989, in millibars 54

25 (a) Four year average of the surface atmospheric pressure; (b) mean ice motion, both

from Colony and Thorndike [14] 57

26 Eddy-induced streamfunction. Contour interval is 0.2 Sv . . . . . . . . . . . . 60

27 Eddy-induced velocity vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

28 Streamfunction from eddy form stress experiment. Contour interval is 0.2 Sv . 62

29 Transects of the monthly mean along-shore current from the eddy form stress experiment 64

30 Fractional ice concentration and velocity from eddy form stress experiment. Maximum speed is 0.23 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 66

31 Streamfunction from variable Bering Strait transport experiment. Contour interval

is 0.2 Sv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

32 Ice thickness in meters from the variable Bering Strait transport experiment. . 71

33 Drifting buoy trajectories from the variable Bering Strait transport experiment. 73

5
1 Scientific Background

1.1 Geometry and Oceanographic Setting

The Arctic Ocean extends over an area of approximately 9 X 106 km2 and consists of two major

deep (> 3000 m) basins, the Canadian and the Eurasian, which are fringed by shallow shelf areas.

The basins are separated by the Lomonosov ridge over which the depth is roughly 1000 m. The

continental shelves occupy nearly one third of the total Arctic Ocean area and vary in width from

approximately 40 km at the Alaskan coast (Beaufort Sea), to about 800 km at the Siberian coast.

The Arctic Ocean is connected to adjacent seas by the Bering Strait, an open border in the Barents

Sea, the Fram Strait, and a number of narrow passages in the Canadian Archipelago.

The circulation in the Arctic Ocean is primarily driven by strong atmospheric forcing, the large

amount of fresh water runoff, and the influx of water from the North Pacific (via the Bering Strait).

In addition, the Arctic circulation 'is influenced by the existing complex topography and the effects

of perennial and seasonal ice cover. The effects of sea ice on the circulation are mainly related to

the role played by the ice in the transfer of momentum from the atmosphere to the ocean, and

to the thermohaline effects associated with brine rejection during freezing. Figure 1 (Aagaard [2])

illustrates the geometry and subsurface circulation of the Arctic Ocean. This Figure shows areas of

strong boundary currents (including the Beaufort Sea Undercurrent), the shallow exchanges with

the North Atlantic and North Pacific oceans, potential saline source areas, and areas likely to have

long-lived baroclinic eddies.

A distinctive feature of the western Arctic circulation is the Beaufort Gyre, which is a large

scale anticyclone. The Beaufort Sea contains the westward branch of the gyre; at least below the

upper 40-50 m, the principal kinematic feature over the outer shelf and slope of the Beaufort Sea

is the Beaufort Undercurrent, a strong flow which in the mean is directed eastward, but which is

subject to frequent (3 to 10 days) reversals toward the west. The reversals are normally associated

with upwelling onto the outer shelf. The undercurrent is very likely part of a basin-scale circulation

within the Arctic Ocean.

1.2 Hydrography

Bjork [6] provides a concise review of the vertical structure in the Arctic Ocean compiled from

Threshnikov and Baranov [43]. The upper layer of the Arctic Ocean is characterized by a mixed

layer of thickness between 25 and 50 m and temperature near the freezing point. The salinity

increases horizontally from about 30 ppt in the Beaufort Sea, to about 32 ppt near the Fram Strait.

Below the mixed layer is a halocline where the salinity increases to about 34 ppt at 100 m depth,

while the temperature is still near the freezing point. Below the halocline the temperature increases

and attains a maximum with temperatures above zero degrees Celsius. The corresponding layer

is called the Atlantic layer, and has a salinity of about 34.8 ppt. The upper boundary of the

Atlantic layer is situated approximately at 300 m in the Beaufort Sea and rises to near 200 m near

Greenland. The maximum temperature is between 0.4 and 10 Celsius over most parts of the basin

with the warmest water near the Fram Strait. The thickness of the Atlantic layer ranges between

500 and 800 m. Below the Atlantic layer the water is relatively homogeneous with temperature

between a and -0.90 Celsius, and salinity in the range of 34.90 and 34.95 ppt.

1.3 Sea Ice

The study of the seasonal and interannual variability of sea ice in the Arctic Ocean and adjacent

seas began in the early 1970's when hemispheric-scale observations of sea ice cover became possible.

All records prior to that time are spatially very incomplete. Parkinson [34], using passive microwave

data from the Nimbus 5 and Nimbus 7 satellites, determined baseline information on the interannual

6
_ Scronl boo"""'" a.nwna

HypocIIesaed - -... boundary 00ItT'W'ID

.... We:ak lIKenor Row

•••••<> =:~cn;:Mth

lonI--

(J _

.:-<:';.;i.: Ec:ktr-pnenurc area

o~

Figure 1: Overview of the Arctic circulation (Aagaard [2])

7
variability in monthly averaged sea ice distributions in the north polar region over the period 1973-

1987. The following is a summary of relevant information, compiled from Parkinson.

The spatial distributions of the ice in the Arctic Ocean and Canadian Archipelago have their

lowest variability in winter and highest variability in summer. Both regions are fully ice covered

in the central winter months to at least 30% ice concentration in each of the 15 years analyzed.

Although both regions retain considerable ice coverage throughout the year, the spatial distributions

of the summertime coverage can vary substantially from year to year. In both regions the highest

interannual variability is in September, and the second highest in August. There is a sharp drop in

variability from September to October, reflecting the consistency with which winter-like conditions

have set in by the end of October.

Much of the summer-time variability in the Arctic Ocean results from different patterns of ice

distribution rather than from changes in areal ice extent. This is substantiated by a census of

summer-time ice coverage from year-to-year, which indicates that the total areal coverage of ice- in

different summers is sometimes very close even though the distributions of the ice vary considerably.

For example, the Arctic Ocean ice extents in September 1973 and September 1974 differed by only

2%, although in 1973 there was a wide strip of open water north of Alaska and Canada eastward to

125 degrees W which did not exist in 1974. In contrast, there was much more open water north of

Svalbard and north of eastern Siberia in 1974 than in 1973. These September 1973-1974 contrasts

can be explained on the basis of ice responses to the different atmospheric forcings in the 2 years.

Additional literature on the variability and distribution of ice in the Arctic is available (for example, Walsh and Johnson [45], Walsh et al. [44], Bourke and Garret [8], Campbell et al. [10], Hibler

[23], Semtner [39]). Later in this paper we will provide a discussion on the validation of the simulated ice cover using weekly ice data from the National Oceanic and Atmospheric Administration

(NOAA)-NAVY Joint Ice Center (JIC) for 1983 (the chosen year for our model simulations).

1.4 The Beaufort Sea

Since the focus of this study is on the Alaskan nearshore and outer continental shelf areas, the

rest of this scientific review will concentrate in areas of the Beaufort Sea. Aagaard [1] showed

that substantially different circulation regimes prevail on the inner and outer Beaufort shelf, with a

demarcation zone between the regimes lying near the 50 m isobath. The inner shelf is strongly winddriven in summer and far less energetic in winter (although some wind effects probably persist even

under the fast ice close to shore). In contrast, the outer shelf circulation is energetic at low (subtidal) frequencies throughout the year. However, the inner and outer shelf regimes are not entirely

decoupled; cross-shelf flow is frequent and links the Beaufort Undercurrent with the nearshore

environment.

The Beaufort Undercurrent is a bathymetrically steered mean eastward flow (order of 10cm/s)

extending seaward from the 40-50 m isobaths to approximately the base of the continental slope.

There is indication that the flow increases with depth and that it is not locally driven. However,

even thoug,h there is no evidence that the undercurrent is maintained by local wind forcing, Aagaard

[1] shows that under strong easterly winds the current normally reverses; this appears to hold in

about 75-80% of the situations when the easterly winds exceeded 8-10 m/s.

Despite the seasonally varying wind field, as well as the large seasonal differences in the upperocean temperature and salinity fields, there is no evidence for a significant seasonal variability in

the subsurface circulation in the Beaufort Sea (Aagaard et al. [2]). However, the wind forcing

influence, and therefore the seasonal variability, is much stronger near the surface where as much

as 50% of the flow variability is wind related (J. Overland's personal communication based on a

st udy of the Beaufort circulation using Argos-tracked ice drifters).

8
1.5 The Bering Strait

In contrast to the small seasonal cycle observed in the Beaufort subsurface circulation, the Bering

Strait, and probably much of the Chukchi Sea, is characterized by a distinct seasonal cycle in the

transport which is highly correlated to wind variability. Coachman and Aagaard [12], in a study of

the annual and interannual variability of the transport through the Bering Strait, found: (1) the

long-term mean transport through the Bering Strait is 0.8 Sverdrups (Sv); (2) there is an annual

transport cycle of amplitude 0.6 Sv, with the maximum in June, the minimum in February, and a

secondary maximum in January probably associated with the North Pacific atmospheric blocking

ridge activity (White and Clark, [46]) which interrupts the passage of storms across that ocean;

and, (3) there is interannual variability marked by a number of low-flow years in the past two

decades, including three or four lowest-transport winter periods during this century. The long-term

mean transport through the Bering Strait is maintained by a mean sea level slope ('"" 10-6 ) down

to the north (Coachman and Aagaard, [11]). This slope is primarily a result of the steric level

difference between the Atlantic and Pacific Oceans (Coachman et al., [13J; Stigebrandt, [41]).

Coachman and Aagaard [12], propose a linear regression (0.82 correlation) between the transport and the wind component toward 192 degrees True to describe the variability of the transport

through the Bering Strait. Therefore, transport variability is given by the variability of the meridional wind. This interpretation is also supported by numerical model studies (Overland and Roach

[33J, and Spaulding et al. [40]).

1.6 Previous Numerical Experiments

Previous numerical model efforts that are relevant to the present study can be divided into three

main categories: (1) numerical/experimental studies related to small scale processes, where the

dynamics of turbulent fluxes at the ice-ocean interface were studied in detail in areas of polynias and

marginal ice zones; (2) mesoscale numerical studies applied to the flow in the Bering and Chukchi

seas; and, (3) large-scale numerical experiments applied to the entire Arctic Ocean, including

dynamic/thermodynamic atmosphere-ice-ocean interactions. The paucity of the data available for

the Arctic Ocean makes the use of numerical models an invaluable tool to provide both a full analysis

of current conditions b~sed on limited data and a prediction capability· for future conditions.

Previous modeling studies have included diverse approaches, utilizing one-dimensional, twodimensional, and three-dimensional formulations. These modeling efforts have included ice only,

ocean only, or coupled ice-ocean studies. For example, Pollard et al. [36], Lemke and Manley [30],

Lemke [29], Bjork [5], and Mellor and Kantha [31J have studied one-dimensional coupled ice-ocean

models to describe the seasonal variation of the ice and the upper few hundred meters of the Arctic

Ocean. A common denominator of these one-dimensional studies is that they have all demonstrated

that the inclusion of a mixed layer that can carry away the excess brine and salt via turbulent fluxes

from the surface is essential for a correct prediction of the ice thickness.

Bjork [5J developed a one-dimensional time-dependent model to study the vertical stratification

of the upper Arctic Ocean with emphasis on the halocline problem. The model is driven by

freshwater from land, ice production and export, Bering Strait inflow and wind. The model is

able to generate the Arctic mixed layer and shows the importance of the water coming from the

Bering Strait in retaining the halocline. However, the lower layers deviate much from the observed

temperature and salinity profiles, most likely because of the simplicity of the model dynamics.

Brasseur [9J, using a numerical inverse methodology based on a variational principle and finite

element discretization, generated dynamically consistent horizontal distributions of chemical tracers

and transport of water for areas of the northern Bering Sea, including the Bering Strait and Chukchi

Sea. These fields were reconstructed by using synoptic data collected from the ISHTAR (Inner Shelf

Transfer and Recycling project) NSF Research Project during the 1985 and 1986 cruises. The study

shows that the Anadyr Stream, a swift current flowing northeastward between St. Lawrence Island

9
and the Siberian Peninsula, is the main conduit of chemical tracers for the whole region; strong

permanent upwelling close to the Siberian coast was also detected by this study. For a typical

summer situation, the total transport through the Bering Strait was assessed to be 1.28Sv.

A prognostic two-dimensional model was used by Kantha and Mellor [27] to study the evolution

of the coupled ice-ocean behavior in the Bering Sea. They have found that the density structure and

the circulation beneath the ice, and the position of the ice edge, are quite sensitive to even small

changes in the relevant parameters governing the dynamics and thermodynamics of the system.

Several three-dimensional coupled ice-ocean models have been developed for the Arctic Ocean and

adjacent seas. Some relevant examples are the Semtner [39] model, which treated both the ice and

ocean prognostically, and the Hibler and Bryan [26] study, 'where the ocean is treated diagnostically.

Fleming and Semtner [19] conducted a fully prognostic study of the Arctic ice cover using a

coupled ice-ocean model (horizontal resolution of 100 km) described by Fleming [18]. The coupled

model system consists of the Semtner [38] ocean model combined with the three-layer thermodynamic ice model (Semtner [37]) and a modified Hibler [23] dynamic ice model. The study shows

that the vertical ocean heat flux appears to be the dominant mechanism controlling localized ice

area anomalies and the overall ice concentration. The model produces very reasonable simulations

of the ice edge position, particularly in the Barents and Greenland seas. However, consistent errors

in simulated ice concentration are identified in the numerical study, including exaggerated meltfreeze cycle and insufficient ice thickness. The authors point out that the lack of a mixed layer

formulation in the model dynamics, and the coarse vertical resolution (20 to 30 m in the upper

layers) for the model experiments are inadequate to properly represent the processes related to the

ocean's heat flux (e.g., vertical mixing, stratification, and diffusion).

Piacsek et al. [35] studied the Arctic ice cover and upper ocean with a coupled ice-ocean model.

The model uses the Hibler ice model coupled to a three-dimensional ocean model that consists

of a turbulent mixed layer (Mellor and Yamada [32]) and an inverse geostrophic model. The

horizontal grid resolution adopted.is """ 127 km, and the vertical grid resolution ranges from 2.5

m near the surface to """ 1700 m near the bottom. The model is forced with 12-hourly GCMderived (Naval Polar Oceanography Center) atmospheric fluxes for the year 1986, for which good

quality ice edge analyses and observed Arctic buoy tracks (Colony and Rigor [14]) were available

for comparisons. In general, the computed ice edge positions from the model have comparable

accuracy to previous three-dimensional coupled ice-ocean studies, with too much ice growth during

the winter in th'e Barents Sea and too little ice east of Greenland. However, some improvements in

the ice thickness distributions were achieved, with a monotonic increase of the ice thickness from

the Siberian coast east toward the Canadian archipelago with maximum winter values of 5-6 m.

There is generally close agreement between the model and observed buoy positions, but the model

tracks exhibit some loops which are missing in the observed track. The authors suggest that further

improvements in the modeled buoy tracks can be achieved by an increase in the horizontal model

resolution, an improvement of the atmospheric forcing (higher resolution winds), and the use of a

three-dimensional ocean model.

Hakkinen [21] simulated the Arctic ice-ocean system by coupling the Semtner [37] ice model to

the sigma coordinate ocean model described by Blumberg and Mellor [7]. The horizontal resolution

for the adopted orthogonal grid ranges from 28 to 150 km; there are 18 sigma levels in the vertical

grid. The model focuses on the interannual variability of the sea ice during the period 1955-

1975. The main conclusion is that the model results show the origin of the Great Salinity Anomaly

(GSA) to be in the Arctic, as suggested by Aagaard and Carmack [3] and support the view that the

Arctic may play an active role in climate change. The extensive ice cover of 1968 has been widely

speculated as the source of the GSA, a high-latitude freshwater event which circulated during the

1970's around the subpolar gyre and returned to the Greenland Sea in the early 1980's (Dickson et

al., [16]).

10
1.7 Summary

In summary, large-scale atmospheric forcing combined with the thermohaline forcing plays a major

role in maintaining the Arctic Ocean circulation (e.g., the Beaufort Gyre), while the nearshore

mesoscale winds constitute the major driving mechanism for the seasonal variability of near-surface

currents in the Beaufort and Chukchi seas. However, at least below the mixed layer, the shelf

circulation in the Beaufort Sea is remotely forced by the large-scale oceanic flow rather than by

local wind. Therefore, to appropriately model the Beaufort Sea circulation one must provide a

larger-scale framework within which the more local problem may be nested. In fact, the Beaufort

Shelf is sufficiently narrow that much of it is primarily driven by the adjacent deep ocean.

11
2 Description of the Coupled Model

The coupled model used in this study is made up of the Semi-spectral Primitive Equation Model

(SPEM) (Haidvogel et al. [20]) and the Hibler dynamic-thermodynamic ice model (Hibler [23]).

These two models and the coupling used are described in Hedstrom [22]. This section reviews the

equations used by the coupled model and describes the Western Arctic model configuration.

2.1 Ocean Model Formulation

The primitive equations in Cartesian coordinates can be written:

(1)

-pg

(2)

(3)

(7)

(4)

(5)

(6)

P = p(T,S,P)

&¢

&z Po

&uw &vw &ww _ 0

&x + &y +----a;- - ,

&vw _ &¢ -& + Vw . V'vw+ fuw = --a + Fv +1Jv t . y

~~ +v~ . V'T = FT +1JT

&S . at + v~ . \7 S = Fs +1)s

where, in standard notation:

(uw,vw,ww) = the (x,y,z) components of vector velocity v~

Po +p(x, y, z, t) = total in situ density

T(x, y, z, t) = potential temperature

S(x,y,z,t) = salinity

P = total pressure P - Pog z

¢(x,y,z,t) = dynamic pressure ¢= (Pjpo)

f(x, y) = Coriolis parameter

9 = acceleration of gravity

(Fu , Fv , FT, Fs) = forcing terms

and

(1J u , 1Jv , 1JT, 1)s) = diffusive terms.

Equations (1) and (2) express the momentum balance in the x- and y-directions, respectively. The

time evolution of the perturbation temperature and salinity fields, T(x, y, z, t) and S(x, y, z, t), are

governed by the advective-diffusive equations (3) and (4). The equation of state is given by equation

(5). In the Boussinesq approximation, density variations are neglected in the momentum equations

except in their contribution to the buoyancy force in the vertical momentum equation (6). Under

the hydrostatic approximation, it is further assumed that the vertical pressure gradient balances

the buoyancy force. Lastly, equation (7) expresses the continuity equation for an incompressible

fluid. For the moment, the effects of forcing and dissipation will be represented by the schematic

terms F and 1J, respectively.

12
(9)

(8)

2.2 Ice Model Formulation

Hibler [23J has described a model for the simulation of sea ice circulation and thickness. The model

has been tested over a seasonal cycle and the results are also shown in that article. This report

was derived from the documentation for the sea ice model written by Hibler [24] and describes the

model in its current form. In this documentation frequent reference will be made to Hibler [23]

which describes the model, and will hereafter be referred to as JP079.

2.2.1 Model structure

The overall structure consists of two principal components-the momentum equations and the ice

continuity equations. The momentum balance includes air and water stress, Coriolis force, internal

ice stress, inertial forces and ocean tilt as shown in equations (8) and (9) (from JP079).

aUi '- n f M aH x x M -a + MVi . v Ui = M Vi - g-a +Ta +Tw + Fx t x.

a~ _._ . aH y y T

Mat + MVi' V'v, - -Mfu, - Mg ay + Ta + Tw +,ry

Non1inear boundary layers for both the ocean-ice and air-ice surface stress are used.

Ta = PaCaIVgl(Vgcos¢+ k x Vgsin¢)

Tw = PwCwlvw - vii [(Vw - vi) cos 0+k x (vw - Vi) sin 0]

(10)

(11)

(12)

A key component of the momentum balance is the force due to the internal ice stress (Fx and

Fy ). This force is based on a constitutive law which relates the ice stress to the strain rate and

ice strength (equation (12)). For this model, a viscous-plastic behavior is used. Rigid plastic

behavior is approximated in this law by allowing the ice t? flow in a plastic manner for normal

strain rates and to creep in a linear viscous manner for small strain rates. The treatment of ice

as a viscous-plastic fluid was largely motivated by the desire to avoid the complexities associated

with elastic-plastic behavior under flow. The stress-strain relationship is given by

P

(J"ij = 2TJ fij +(( - TJ )fkkOij - 20ij.

The viscous-plastic terms (14) and (15) are found by taking the divergence of the stress tensor:

(Fx,Fy ) = V'.O'

a [ aUi aVi ] a [(aUi aVi)] Fx =- (TJ+()-+((-TJ)--P/2 +- TJ -+-

ax ax ay ay ay ax

a [ . aVi aUi ] a [(aUi aVi)] Fy = ay (1]+~)8Y+((-TJ)ax -P/2 + ax 1] ay + ax

where the nonlinear viscosities are given by

(13)

(14)

(IS)

(16) P

( = 1/2 2 [(fr1 + f~2)(1 +l/e 2 ) +4e-2fr2 +2fnf22(1- l/e 2 )]

( TJ = 2' (17) e

The "pressure gradient" term is also modeled as a term in the internal ice stress. This term

represents the resistance which ice has to being compressed (ice strength) and is a function of ice

thickness and concentration (equation (18)):

P = P"hexp[-C(I- A)].

13

(18)
The second major component of the model consists of continuity equations describing the evolution of the ice thickness characteristics. These equations are essentially a simplification to two

levels of the Thorndike et al. [42J ice thickness distribution model. In this version of Hibler's model

two categories of ice are assumed: thin ice « 1.0 m in thickness) and thick ice (> 1.0 m). To

keep track of these two categories, two parameters are calculated: the mean ice thickness per unit

area, h, and the compactness, A, which is defined as the fraction of area covered by thick ice. The

continuity equations describing the evolution of these parameters (equations (19) and (20)) also

include thermodynamic terms (Shand SA):

oh o(Uih) O(Vih) S V = - ---+ h+ h (19) ot ox oy

oA o(UiA) O(ViA) S V at =- (20) ox - oy + A + A

Sh = AG(~) +(1- A)G(O) (21 )

. { G(G)(l-A) if G(O) > 0, SA = ho '

0, if G(O) < 0,

+{ 0, if Sh > 0,

SbA (22) if Sh < O. 2h

The effects of dissipation are represented by the schematic terms V h and VA, which are the sum of

a Laplacian and biharmonic diffusion. The ice growth rate G is computed from the environmental

variables such as air temperature as described in Hibler [25J and Hedstrom [22J.

The variables used by the ice model are therefore:

(Ui, Vi) = the (x, y) components of vector velocity vi

h(x, y, t) = effective (area-averaged) ice thickness

ho = 1 m =ice cutoff thickness

A(x, y, t) = ice concentration

M (x, y, t) = ice mass (density times thickness)

G(h) = growth rate of ice of thickness h

H (x, y, t) = height of the ocean surface

(( x, y, t) = nonlinear bulk viscosity

TJ(x, y, t) = nonlinear shear viscosity

e = 2 = eccentricity of the elliptical yield curve

f( x, y) = Coriolis parameter

9 = 9.8 m s-2 = acceleration of gravity

O'ij(X, y, t) = stress tensor

fij(x, y, t) = strain rate tensor

P( x, y, t) = ice pressure or strength

(P*,C) = (2.75 X 104 ,20) = ice strength parameters

(Ta , Tw ) = air and water stresses

CVg , vw ) = air and water velocities

Ca = nonlinear air drag coefficient

14
Cw = 5.5 X 10-3 = water drag coefficient

(¢,O) = (250 ,250 ) = air and water turning angles

(Pa' Pw) == (1.3 kg m-3 , 1000 kgm- 3 ) = air and water densities

(Fx , Fy ) = viscous-plastic terms

(Sh, SA) = thermodynamic terms

and

(Vh, V A) = ice diffusion terms.

2.3 Model coupling

The model coupling consists of exchanging momentum and thermodynamic information between

the two models at every timestep. The models themselves remain largely unchanged..A driver

main program was created to initialize both model components and to call the ice and ocean main

subroutines at each timestep. The coupling is described more fully in Hedstrom [22].

2.4 Western Arctic configuration

The configuration of the coupled model consists of setting up the geometry information, the initial

conditions, the forcing fields, and choosing the viscosity and diffusion. A schematic of the model

with its inputs is shown in figure 2.

2.4.1 Model geometry

The ice model has thus far dictated the use of a rectangular, rather than a curvilinear, grid. A grid

with a uniform spacing of 20 km was used, covering the Western. Arctic, as shown in figure 3.

The second step is to define the mask for islands and other land areas included in the domain.

The mask used by the model is shown as the white areas in figure 4, and was derived from a

coastline file obtained from Joe Reid. The coastlines shown in the figures are from an improved

coastline database which was obtained more recently. Although there is some disagreement in the

exact placement of Wrangel Island and the New Siberia Islands, we have not updated the model

mask to reflect these changes.

The model bathymetry was determined in several steps. First, the ETOP05 bathymetry is

bilinearly interpolated to the grid, as shown in figure 4. This is done with the batht ub program

in gridpak (Wilkin and Hedstrom [47]). Second, the bathymetry is constrained to lie between 50

and 500 m in depth, as shown in figure 5. A larger depth range is more difficult to use and the

water below 500 m is assumed to be unimportant for the short timescales relevant to this project.

Third, a shelf is added to the Eastern and Northern boundaries. This shelf allows coastally trapped

waves to propagate around the domain rather than reflecting where the isobaths leave the domain.

Finally, the bathymetry is smoothed with a filter designed to reduce the fractional change in depth

from one gridpoint to the next, resulting in the bathymetry shown in figure 6. In figure .5 it can be

seen that there are places where the depth goes from 100 m to 500 m between adjacent gridpoints.

The vertical sigma coordinate system in the model follows the bottom contours, but this is only

sensible when the bathymetry is horizontally resolved by the grid.

2.4.2 Initial conditions

Both the ice and ocean components of the model require initial conditions. The model is assumed

to start from rest; the initial ice and ocean velocities, as well as the ocean streamfunction, are

set to zero. The initial ice concentration is set to 1.00 (complete ice cover) since· the model was

started on January 1. The initial ice thickness is set to a uniform value of 1.65 m, the thickness of

15
Ice model

(Hibler)

Ocean model

(SPEM)

Coupled

ice-ocean model

Figure 2: The coupled ice-ocean model schematic

16

Production run
Figure 3: The Western Arctic grid

17
-",ooE"03 -5.00£'02 5,1X£.02 I.OOE+OJ 1.SOC.OJ 2,00£...03 2.5(£.03 J.DOE"'OJ 3 50E"OJ •. OOE"QJ

Figure 4: The unfiltered bathymetry interpolated to the Western Arctic grid

18
50. 1.00E"02 1.50(+02 2.00['4"02 2.50E"02 3,ooE+02 3.5OE+02 4.00E+02 4.50E+02 5,ooE+02

Figure 5: The unfiltered bathymetry clipped to lie between 50 and 500 m

19
1.00E+02 1.50E+02 2.00E+02 2,50E+02 3.00E+02 3.50E+02 4.00E+02 4.50E+02

Figure 6: The bathymetry after clipping, smoothing, and adding a shelf along the Northern and

Eastern boundaries

20
1.5 m of water. This is not a realistic value, but it was assumed that the thickness would reach an

equilibrium after several years of integration.

The ocean temperature and salinity fields also require initial conditions. The Levitus T and S

fields were horizontally averaged and approximated by the functions:

.6 - 5.2ez/

300 +4.0ez

/

600

34.9 - 4.7ez

/

200 .

These approximate fields are used to initialize the model fields and the T and S climatologies and

are shown in Fig. 7 and 8. The rhobar field is initialized from the initial density field rather than

from a statement function.

2.4.3 Model forcing

The model is forced at the surface via imposed fluxes of momentum and heat, estimated from

geostrophic winds and thermal fields for the year 1983 (Prof. John Walsh, University of illinois).

The thermal fields are interpolated in time from monthly fields and therefore contain no higher

frequencies, while the winds are derived from daily surface pressure fields. These fields are on a

uniform 160 km grid and are bilinearly interpolated onto the model grid. They are also linearly

interpolated in time at each timestep. The model was run for five years with the 1983 forcing;

during each December 31 the fields are interpolated from the December 31 values to the previous

January 1 values.

Within the model, the wind and water stresses are applied directly to the ice momentum

equations. For the water momentum equations, the wind stress is applied where there is open

water, otherwise the ice stress is applied. The surface stresses are applied as a body force over an

upper mixed layer of 51 meters in thickness.

The ice model contains a thermal budget package described in Hibler [25] and Hedstrom [22].

This thermal budget requires the incoming shortwave and longwave radiation, the air temperature,

and the humidity as inputs. It also requires the water temperature, and provides outgoing radiation

and amount of ice growth or melt. This change in ice thickness in turn modifies the heat and salt

balances in the water.

A second type of forcing in the model is the barotropic inflow at the Bering Strait and the

barotropic outflow along the northern boundary. The transport through the domain is set at 0.8 Sv

and is imposed by the boundary conditions on 7/;.

A third forcing is a "nudging" on the temperature and salinity fields to the approximate Levitus

climatology on a timescale of 100 days. Without this nudging, the model climatology drifts and

the model develops an instability in a bay where net ice is produced.

2.4.4 Viscosity, diffusion, timestep

The ice component of the model has a built-in diffusion which automatically scales with the gridspacing, and is a sum of Laplacian and biharmonic smoothing on the ice thickness and concentration.

The ice momentum equations also contain smoothing operators with non-linear viscous coefficients.

The ocean component, on the other hand, has options for what smoothing to apply and at what

strength. We have chosen to use a horizontal Laplacian viscosity with a value of 4000 m2/ s and a

horizontal Laplacian diffusivity of 400 m2 / s on the deviation from the model T and S climatologies.

Applying the diffusion to the deviation from climatology prevents some troubles arising from the

along-sigma diffusion operator.

There is a bottom drag of 2.65 x 10- 4 m/s. The walls are free-slip in the water and no-slip in

the ice. Both components of the model have a timestep of 675 s.

21
o

-200

-400

-600

-800

-1000

-1200

-1400

Area-averaged Levitus

Our climatology

-1.8 -1.6 -1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0 .2 .4 .6

Figure 7: The area-averaged Levitus temperature profile and the temperature climatology

o

-200

-400

-600

-800

-1000

-1200

-1400

Area-averaged Levitus

Our climatology

30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0

Figure 8: The area-averaged Levitus salinity profile and the salinity climatology

22
2.4.5 Floats

. The model has the means oftracking simulated drifting buoys, or floats. These floats were originally

designed to follow the water motion, but have been modified to follow the ice instead. The float

software provides a choice of bilinear or bicubic interpolation from the model gridpoints to the float

locations. The bilinear option was chosen to maintain sensible float velocity values near the mask

boundaries.

All of the model floats are initially "stored" at a fixed position inside the land mask. The times

and locations of 26 floats released by Roger Colony's group in 1982 and 1983 are stored in a float

timestepping routine. Atevery timestep, a check is made to see if any model floats should be moved

to the release location of a real drifter. The floats are moved as a cluster of nine, centered on the

real drifter, and with a spacing of 20 km.

23
3 Results of the Central Simulation (C3)

Table 1 summarizes the five multi-year experiments conducted with the coupled model described in

§2. Of the five simulations, two (C1 and C2) were used to adjust several internal parameters of the

ice model-those associated with treatment of ice at the northern cross-Arctic (open) boundary,

and the iteration parameter used in the iterative solution of the ice momentum equations. Following

C1 and C2, a third experiment (C3) was conducted to serve as a central focus for model evaluation

during 1983. This central experiment will be discussed in detail next. Lastly, two experiments were

carried out to investigate sensitivity to the incorporation of an eddy form stress parameterization

(C4) and to the inclusion of time variability in the mass influx through the Bering Strait (C5).

These latter experiments are briefly described in §4.

The central experiment (C3) was spun up from a state of rest using perpetual-1983 winds and

surface fluxes as described in §2. The monthly averages of the daily surface geostr.ophic winds used

to force the coupled model are shown in Figure 9. The mean winds are anti-cyclonic throughout

much of the year, as expected from long-term climatology. Note however the reversal in the sense

of the applied winds during the months of September and, to a lesser degree, October. As we show

below, this wind reversal in late 1983 is associated with a reversal in the sense of the Beaufort Gyre

during the same period. This reversal during 1983 was also observed by Kozo and Robe [28]. A

discussion of interannual variability in the forcing fields is given in §4.

After four years of integration, various measures of model behavior have reached an approximate

equilibrium; see, e.g., area-averaged ice thickness (Fig. 10) which increases to approximately 3

meters during the fourth winter season. Other variables attain similar seasonally varying equilibria

by the end of year 4. Thereafter, simulated data were obtained from year 5 of experiment C3 for

analysis and evaluation.

The simulated ocean circulation during 1983 is shown in Figures 11-13 in the form of monthly

means obtained by simple averages over daily records obtained during year five of C3. Figure

11 shows the inferred monthly mean depth-integrated circulation (mass transport streamfunction,

contour interval of 0.2 Sverdrups) between zero and 500 meters. A net anticyclonic circulation,

Experiment

C1

C2

C3

C4

C5

Duration

1 2 3 4 5

Comments

ice boundary conditions

ice iteration parameter

central experiment

parameterized undercurrent

variable Bering Strait inflow

time (years)

Table 1: Table of experiments

24
Apr i 1

January

\ II" 111 T r 11'"

"11111111'""

\ III \ r r t ,,, II" I, """"""1"""'0,. Ill .... ' r 1,1'" Ilrl II """"""""""" (Im""r"/,, II "",',""'1",,' .... , I ",rrlltll " "1'11"""","" •••• 11" "",/ II """"""",.", , ••. I 1'" rllfl1 11 """,.""'•••••• •..• tl ! Illrrlllr /.1 ""'""'••• ,, ••••. ,

1 I' ! rlllrllt1 " "'1"/"""'" ".,., 'I I 11'1 r "111 II """," " ••••• , •• ,.

: II, r : l I ::: :: ~;:::::::::::::::...,

I 111111 II : rr ~: :::;::::::::::::::::: , 1\\1" \ 11 t '"~ ,'/., •• , ••••••• , I '1\\ I""" I r I ""r •••• ' ••••• ••••. '11\!,1",\, T I 1',',".' , \ \ 1 , \ \ \ 1 \ \ I 1 r II I I , , ••••••••••••••

\\\\\\\\\\\'1 "I" I ••••••••• , .••• , \\""\\\\\\\,,, I rl' ., •••••••• , •• ,

\\\\\\\\\\\\\,\ ,. I I I, ••••••••• , •••

\\\\\\\\,\""", II ••••••••••

\\\\\\\\\"""" " .. " .. , .. \ \""", , . """ , .. , ,., - - .. ,. "

'~~~~::::::::::::::::::::::: : :::: : , "",,---------------_ .

May

\\ \\\ .. , ", .. , , ..._-- ..... \" , " _-- ::~:'::::::::::::::::::- It... , ...... , , .. , ..... - - - - - ---

February

Figure 9: Monthly mean wind fields. The maximum vector length corresponds to a wind of 8.4

m/s

25
.. , ".,'."' , .. .. •• , -"'1 ,.,., Ill"'" ••••••••••. •• ••• , ,-" \"1111 """ •••••••••.•.

•••• , " II LI.,1 ., ••••••• ', •

• •••••• , •• " II. 1" ".- ••

• , •••••••• ! II' ,,,

" .•••••• , "1111 I .'. "'" •••• ,. "j I,. l ,.

, " I I' : ::::-

.::!<ti: :::::::::::::::: ., ", , " ",-" . ••••••• ", "' •••••••• " I I" •• , •

.......••..•••.......... ,"'l··' .. .................. ::::::::::::::::::

,

:::::::::::::::::::::::::::::;;:::;;::i:;~ • , ...... - - __ - - ... ", .. , ... I , , , , • , , •

~:~n~mmmmmmiifii!i:i!i~:i;· ....., " "

::: u:: ~:::::::::::::::::::::::::::::::: , .. , , ., , , .. , , ., , -

-~-~-------------------"""", ..... 7--"'C--~---""""''''''''''''''''''''''''''''''''''''''''''~'''' --~-~-_ . , , ,,,, \., . -- \ ,.. ~, ,

-- " ".. \ \ \ \ \, , . ... "\ \ \ '\ \ \ \ \ \ \ \ \ , . - J:3 - ", \\'\ '\ \\\\,, \" , .

•••••.·.1rr!II'I!i111ilili"ll;;llill.••. - •• ..". 1 I \ I \ \ \ , , ---- " ..

""'llllll~\\\\\\""'''''''''''''''''----''''''-'''''''''''''

·'·.llllllllllll\\\' ........ -~-----_.... ''''

.;;~J J,: i J; ; ; i ;;: ;' ,: :: :: =~::: =. " I I I I j j I I I I , , , • , • . • . •• . .... , .

//'I'lllil'III" •• ••····· .. ,I"" 1 I 1 I 1 J'" , , , ••. , •...... -.. , ~~~~~~~~~;IO"I';;;:::::::::::: : //////iI'''

////

/~.;,

"'h'

November

Figure 9: cont.

26
3.0

2.8

2.6

,,-....

C/')

....

Q) 2.4 +-

Q)

E'-'"

en 2.2 en

(1)

C

0 2.0

(1)

0 1.8

Q)

CJ)

0....

(1) 1.6

1.4

1.2

1.0

o 200 400 600 800 1000 1200

lime (days)

1400 1600 1800 2000

Figure 10: Time series of the area-averaged ice thickness

27
the model Beaufort Gyre, is produced during the majority of the year. Maximum transports are

achieved in the winter months, with the largest values occurring in December (12 Sv) and February

(7.8 Sv). A reversal in the sense of the Beaufort Gyre is suggested during September (8.6 Sv cyclonic

flow) and more weakly in October (1.6 Sv). Such reversals are known to occur despite the preference

on average for an anti-cyclonic sense of rotation (Aagaard et al. [4]). The above pattern correlates

well with the variability of the wind forcing.

The steady inflow of 0.8 Sverdrups at the Bering Strait is apparent in these monthly means,

though the imposed inflow is in most months dominated by the wind-driven component of the

circulation (Coachman and Aagaard, [12]). Note the placement of the mass outflow boundary

conditions along the northern cross-Arctic open boundary. The streamfunction contours emanating

from the Bering Strait are required to exit in a fixed pattern along the open edge, as shown in Fig.

11.

These streamfunction contours display a quasi-persistent meandering pattern of the Bering

Strait inflow, which is mostly confined within the Chukchi Sea. During most months, the flow

emanating from the Bering Strait, after meandering in the Chukchi Sea and heading east towards

Barrow, attaches itself to the edge of the Beaufort Gyre and continues north along the edge of the

Russian shelf towards the cross-Arctic open boundary. However, the above pattern is significantly

changed during Beaufort Gyre reversals. The streamfunction contours for September clearly show

the Bering Strait inflow attaching itself to the reversed Beaufort Gyre at a point near Barrow and

proceeding east along the Beaufort shelf edge. In October, when the Beaufort Gyre is still reversed

but much weaker than in September, the meandering of the Bering Strait inflow penetrates much

deeper into the Arctic (as far as the New Siberian Islands on the Russian shelf).

To the extent of our knowledge, the existence (and persistence) of the meandering of the Bering

Strait inflow is not documented in the literature. However, the model results can be interpreted

within a simple dynamic framework using the conservation of potential vorticity (e.g., [f + (]/ h = const) to understand the cause for the anticyclonic meandering pattern. The dynamics (in the

real world and in the model) are more complex than this simple vorticity balance (friction, wind

stress, nonlinear effects), but assuming that friction effects are second order to the potential vorticity

balance, the following simple dynamical concept should hold for situations during which the external

forcing (i.e., winds) is weak.

Since the model depth (h = 50 m) is constant in the Chukchi Sea and most of the Russian Shelf,

any changes in the planetary vorticity (1) must be compensated by changes in the relative vorticity

(() to preserve the potential vorticity of the flow. As the Bering Strait inflow penetrates north

into the Arctic it gains planetary vorticity by a rate proportional to the change in latitude (65N

at the strait to 70N in the Chukchi); this increase in f must be accompanied by a proportional

negative change in (, i.e., a gain of anticyclonic relative vorticity in the flow, thus generating a

clockwise meander. This meandering pattern can either be intensified or weakened depending upon

the strength and direction of the prevailing winds in the Chukchi Sea. For instance, the anticyclonic

meander is much better organized in September and October of 1983 when the winds were very

weak than during November through March when the winds were very strong and predominantly

easterly in the Chukchi Sea.

The model bathymetry retains some of the s'tructure of the Hope Sea Valley, but is missing some

of the shallower features of the Chukchi Sea. These shallow features are thought to be important

in stearing the flow, also due to the conservation of potential vorticity (T. Weingartner, C. Pease,

personal communication). However, there is a great deal of uncertainty concerning the flow in the

Chukchi Sea (A. Miinchow, personal communication). In particular, the baroclinic currents have

not been adequately measured since most current meters have been deployed near the bottom to

avoid the ice ridges. Also, more is known about the flow near the U.S. than near Russia.

A closer look at the monthly mean surface currents in the Chukchi Sea shows large monthly

fluctuations in pattern and amplitude (Fig. 12). Generally speaking, the surface influx of water

28
Figure 11: Monthly mean streamfunction values. Contour interval is 0.2 Sv

29
._. -.~'---:--:':'---:-:-:::": ":-:: ----

Figure 11: cant.

30
• I,' \' \ L I' \, ••••••••••

·\." \",., . ·\ .... , \ , , , .. '" \, , . """ " . ... """, ",. \

."" I \, ", ••

• " f'" , " .. ,

January

\ \ \,' \, \ I'" \ \ \ \ \ \ \ \'" .""" . ·, , , \ , .. , . . .\", _. I' \ \" .

, , . . . . I , / •• , • ~. .. \ , , .

, , , " # - - - - # - # - - ... " .

March

, \, \ \ I I •••• "\,,, . ,,' \ .. " . ., ,.. , .. ., ...... , . . "" . ,I \ .

. - \ . . - , , , .. .... ,\ \" .. ... \ , , ' . , , , .- .. -- - - , ", . /"1. •• ,,\, .

f I'''"~ .. __ .. ,\,, .

May

February

Figure 12: Surface currents m the Chukchi Sea. The maximum speed is 0.27 m/s

31
,,\ \ \,.. ., \ \" ..

""~""I, •• \, 'I ,\ . . ,.1,

. ., , , .... - - _. ,,\

, ,

July

September

••••• I I' \ 1 I I ••••••••• , •

.... " .. , \, \ .....

, " \ \' ..... ........ , , \, . .. " \, \ \ . . ,'" \ \,

., , , \ \ \ . , , \ ,, \ , . ,\\ \" . ,,\, .

November

Figure 12: cont.

32

\ \ , \ , .. , . \ \ \ \ , , - . I , I • , ••• , , •••

• , I I' " .

. ... \, \, , , ." \ \,

.... , \ \ \ . . .. \ \ \ ,

August

October

December
January

March

February

Apr i I

May June

!,'~Ai;}fW?I!!1 .". "{,I 1 I I I I I I I

-0. 135 -0 105 -0.075 -0.045 -0.015 0 .01 5 0.045 0.075 O. 105 O. 135

Figure 13: Transects of the monthly mean along-shore current in mJs. Positive is towards the west

and is shown with hashing. Note the reversal of the Beaufort Gyre in September and the lack of

an organized eastward flow corresponding to the model Beaufort Undercurrent.

33
Ju 1y

September

November

August

\

October

December

h\·0<;;,iPiibl·'····· :,;;.,';.1.1 I I I I I I I I

-0. 135 -0. 105 -0.075 -0.045 -0.015 0 .01 5 0.045 0.075 0 105 O. 135

Figure 13: cont.

34
through the Bering Strait bifurcates, with part turning eastwards along the Alaskan coast and the

remainder moving westwards along Siberia (see, e.g., January or November). However, occurrence

of more preferential flow patterns also exist-for example, during October when the majority of

the Bering Strait inflow appears to turn westward. Another common feature of the monthly mean

surface currents is an enhanced current off Point Barrow, possibly suggestive of flow separation.

Vigorous interaction with the Beaufort Gyre is indicated in most of the monthly means. The

existence and strength of an eastwards coastal current to the east of Point Barrow is closely tied to

the sense of the gyral circulation; reversal of the sense of the gyre during September results in an

enhanced eastward coastal current, while eastward penetration of the coastal current is suppressed

with an anti-cyclonic Beaufort Gyre.

As previously discussed, an important component of the observed circulation in the Beaufort

Sea is the Beaufort Undercurrent, a narrow eastward current commonly observed at depths below

approximately 40 meters along the continental slope in the Beaufort Sea. The Undercurrent is

reminiscent of other deep boundary currents-e.g, the California Undercurrent-in both structure

and placement relative to the underlying bathymetry; therefore, it is likely that common dynamical

processes are involved in both. One possibility is that eddy form stresses associated with the

interaction between bottom topography and ambient mesoscale eddies may support the observed

Undercurrent, as suggested and explored by Eby and Holloway [17]. Such processes are not explicitly

incorporated here, due to under-representation of the baroclinic deformation radius. And indeed,

transects of the along-shore velocity component along the continental shelf in the Beaufort Sea

(Fig. 13) show no apparent tendency to produce a deep eastward flow, except during periods

of Beaufort Gyre reversal. Clearly, the model at this resolution does not succeed in capturing

the formation mechanisms for the Beaufort Undercurrent. A proposed parameterization for these

omitted processes is explored in §5.

Although generally in qualitative agreement with expectations, the ocean circulation patterns

produced in the central simulation are difficult to evaluate quantitatively because of the lack of

pertinent observations during 1983. Fortunately, we are in a somewhat better position with respect

to the simulated patterns of ice concentration, thickness, and motion. For example, Figures 14

and 1.5 contain monthly mean maps of ice concentration as simulated by the model and as determined from satellite remote sensing by JIC. Both the model and observations indicate a uniformly

ice covered Arctic during the winter months (November through April). The earliest melting is

observed to occur along the East Siberian Islands in both, although the onset appears to be somewhat sooner in the model than in the JIC dataset (see May maps). Early melting also occurs in

the Bering Sea; however, the spatial coverage of our model, among other things, is inadequate to

reproduce this melting faithfully. Somewhat later, melting begins along CaI:lada and the Canadian

archipelago (see June maps), and along Wrangel Island (a local effect seen only in the JIC data).

At the height of the summer months, both model and observations show extensive regions of nearly

ice free water, most prominently in the Chukchi Sea and along the Russian Arctic shelf. The ice

edge rapidly advances in October in both datasets.

In comparison to JIC, model-predicted melting in the summer is somewhat too vigorous. Figures

16 and 17 summarize the yearly variations'in ice concentration by contouring the number of weeks

that ice concentration exceeds 50%. In the real (JIC) world, relatively ice-free regions (those

with .50% coverage less than 8 months in the year) include the Chukchi Sea, the Canadian outer

continental shelf, the New Siberia Islands, as well as the portion of the Bering Sea encompassed

by our regional window. The melting in all four of these regions is reproduced well by the coupled

model. In addition, however, the model produces a significant degree of melting along the Russian

continental shelf between Wrangel Island and the New Siberian Islands. The reasons for this

enhanced melting in the model is unclear, though it may be due to poor resolution in space (160 km)

and time (monthly) of the thermodynamic forcing fields. In addition, another source of inaccuracies

in the model ice distribution may be the limited accuracy of inflow of ice mass at the cross-Arctic

35
Apr

:: ::~ / / / ......-.: '/.1,.,: __ __ "' ",. I.

- / / /// ///' .,..~ / / / ". ~,,~, I , ,

'/~//~~// /~ // ~"~~f' •. , ",~ ~////~/~,,~ ?/ , ~~~,~, •••.

"',' / '~ ...... " "''','''~,J" . ",,, ,', "I"', "'~""~f, . ... " ..." ,... / ...... ,... '''''' ... """,~~ . 11',ll'/~.,',II'TI""",. . J '" , ,. , "'/.f r , I , , , , I' , I .

1II",IIII',IJIII',I" . • •••• , , , , J I , 1 , 1 I I f 1 I 1 1 .. r •••

• ••• • , , I I , , t , I 1 , , J l 1 • , , I • , •••••••

• _ ...• ' I'" 't'l" II' ,t,.,.,., . .. , , ••• r I J' ,r' 'JI r " ",.,., •• , ••• • • • , I I , • , , , , I , I , I 1 • • • • • • • •

• I , I , I 1 I I I ! I , , • • , , • • • • •

" I' II' II" I, •• T II""",

:!!!;!!!!!!!:;!! !;!;;.... :::~ •• I I, • I ••••• " •••• ••• _ •••• _ ••• ~~ ." 'I \.,. I. " •••••••••••

• • • , , •• I, ••• " ••• _ _ • • • • •

' " .. " .

q:.:: ::; -:; ........-.A.-o' ...- ;'. I,. ' • ~/ .., ',,// ,..... ......:: '/JI, ••

._ /."",,.,,,,,I',,.,r,,~~....., ,,,..,,,. / ,.,,/// ', ~, . ,; -. ,."";"// ,,..,./" ,,.. / ; ,~.,.

."""J,.", I'/~~ _ ~~~~~~~~ •••

lilt "I/J/",,.',, ,,.--~-7"'~ .. _ . , ",',JI";'//"" , , , .... ,, . ~',',ltJII"/".'// ",,, .. ,,',,., "'~ _ ..••

(]

' , , J I , I I r / , I , 1';'''''''' "" "',. +

• rl"'111""""""" _ ....•• .llf 1"1/' '111111""" .

..0._ .,, "{"III, rll """ •• , 0 . _ • • _ • • • , , t I , 1 r r / , , , , , • • • • • ,. . • • • • • • • • I , , f , I r J , t I , J • • • , • _ • ,

••••• ,,"'1 ,j 11" tl ,., j" ••••

.....• ' t, Ii 11'1' t "f' I',., •• • • • • . • I , -l t , t I , , 'I I I , • • ••

.11' I." t I ,t •• ,., •• ,.

0.80 0.90

Figure 14: Monthly mean fractional Ice concentrations and velocity vectors. The maximum speed

is 0.23 m/s

36
Figure 14: cant.

37
70. 80.

February

June

90.

Figure 15: Monthly mean fractional ice concentrations from the JIC data, derived from satellite

images

38
10. 20, 30. 40. 50. 60.

Figure 15: cont.

39

80.

August

October

90.
open boundary, as will be noted in the discussion of the variability of the forcing fields (§4).

Model-predicted ice thicknesses are in qualitative agreement with the few available observations.

Approximate contours of observed ice thickness obtained from submarine sonar data (Fig. 18),

composited by Hibler [25] from several years of data, suggest a systematic increase in ice thickness

from west to east with maximum thicknesses of order 6 meters along Canada and minima of two

meters or less along the Russian continental shelf. The coupled m"odel (Fig. 19) reproduces the

large-scale patterns of ice thickness reasonably well, showing maximum thicknesses of almost 5

meters during the winter along the coast of eastern Canada. Summertime melting reduces this

maximum to about 3 meters, but does not appear to change the overall patterns of thickness which

are maintained throughout the year by preferential ice drift from west to east.

The coupled model therefore appears to reproduce reasonably well several of the bulk properties

of the ice/ocean system during 1983. A much more stringent assessment of model performance is

how well the model simulates the Lagrangian trajectories of individual ice floes. We assess this

issue by producing simulated Lagrangian trajectories for ice particles released at the space/time

locations of 26 drifting buoys tracked in the Arctic in 1983. The method used to reconstruct the

ice trajectories is discussed briefly in §2, and also by Hedstrom [22].

A summary of the resulting trajectories, and their comparison to the observed motion of the

drifting buoys, is shown in Fig. 20. Overall, the comparison is not good. Although the mean

displacements undergone by the simulated drifters is not grossly different than that observed, there

is little agreement in the detailed motions experienced by the simulated and observed drifters.

Clearly, other influences omitted in the present simulations are at work in the real world which

produce small-scale sea ice motion and diffusion of ice particles. Likely processes in this category

include high wavenumber and frequency wind components [totally absent in our geostrophic winds

which have poor resolution in space (160 km) and time (24 hours)], mesoscale baroclinic eddies,

and small-scale bathymetry.

40
2.5 5.0 7.5 10. 12. 15. lB. 20. 22. 25. 2B. 30. 32. 35. 3B. 40. 42. 45. 4B. 50.

Figure 16: Number of weeks of ice cover over 50% in the model

41
2. 5. B. 10. 12. 15. lB. 20. 22. 25. 2B. 30. 32. 35. 3B. 40. 42. 45. 4B. 50.

Figure 17: Number of weeks of ice cover over 50% in the JIC data

42
ISO'

FlO. 6. Approximate contours (01) of observed ice thickness values obtained from submarine

sonar data lLeSchack. private communication). The solid conlours were obtained by LeSchaclc

from a composile analysis of both summer (1960. 1962) and winter data (1960), whereas the

dashed contours are from April 1977 data.

Figure 18: Ice thickness from submarines, from Hibler [24J

43
0.25 0.75 1.2 1.8 2.2 2.8 3.2 3.8 4.2 4.8

Figure 19: Monthly mean ice thickness from the model, in meters

44
Figure 19: cont.

45
if

+

Figure 20: Drifting buoy trajectories. The red tracks are from the buoys released by Roger Colony's

group while the black tracks are those made by model buoys. The model buoys have a + every ten

days. The two model buoys that go through Bering Strait were placed there after leaving via the

northern boundary and have no corresponding real buoys.

46
4 Interannual Variability of Forcing Fields and Impact on Model

Results

As discussed in §1.3, much of the interannual variability in the Arctic Ocean results from different

patterns of ice distribution rather than from changes in areal ice extent. In fact, the interannual

contrasts in the summer-time ice cover distribution can be explained on the basis of ice response

to the variability in atmospheric forcing from year to year.

The year 1983 was chosen for our numerical simulations because at the onset of the Minerals

Management Service (MMS) Project the Bering Sea was the primary focus of environmental impact

studies and 1983 was the year of the Marginal Ice Zone Experiment (MISEX) in the Bering Sea,

a study which generated high quality, comprehensive data sets for model validation. Later, the

emphasis was shifted to the Beaufort Sea and a decision was made to keep the 1983 forcing fields

since most of the data sets required to force the models (most notably the wind model) were already

unpacked and gridded.

To put the chosen year (1983) for model simulations into perspective, one must look at the

interannual changes in the atmospheric forcing, since both ice drift and ocean currents are strongly

correlated to the winds, as well as to changes in the thermodynamic forcing which may impose

some variability in the sea ice distribution. A 10-year segment of daily thermodynamic and atmospheric sea-level pressure fields was obtained from John Walsh at the University of Illinois for our

interannual analysis. Figures 21 through 23 show the yearly averaged thermodynamic forcing fields

which consist of short-wave and long-wave radiation, and surface air temperature. Inspection of

these figures reveals that there is no significant interannual variability in the mean yearly thermodynamic forcing fields covering the period of 1980 through 1989. Therefore, any interannual heat

flux changes are mostly related to the interaction between these forcing fields and the ice-ocean

coupled system (sea ice, snow cover, percentage of open water).

Figure 24 shows the yearly averaged surface atmospheric pressure fields for years 1980-1989.

The typical atmospheric pressure pattern for the Arctic Ocean consists of two large atmospheric

gyres, one anticyclone (high pressure) centered in the western Arctic, and one cyclone (low pressure)

centered approximately southwest of Greenland. The anticyclone over the western Arctic drives the

Beaufort Gyre, while the low pressure pattern off of Greenland causes a cyclonic wind flow which

imposes a cyclonic gyration of the ice drift and currents in the Greenland-Iceland-Norwegian Seas.

These circulation patterns have been documented in the numerous model studies of the Arctic

Ocean summarized in §1.6.

However, the interannual variability of the strength and location of these atmospheric gyres is

significant. The annual mean strength ofthese gyres is actually linked to the number and persistence

of circulation reversals at any given year. Inspection of figure 24 reveals that 1980, 1982, 1985,

1987, and 1988 were "typical" years, e.g., the yearly averaged pressure fields are characterized by

a well defined dual atmospheric gyre system. In contrast, 1981, 1983, 1984, 1986, and 1989 were

years having a very weak and/or displaced yearly averaged atmospheric high. Consequently, over

this 10-year period, there was an even split between "typical" (predominantly anticyclonic) and

"non-typical" (occurrence of sustained reversals) atmospheric circulation.

The year chosen for our model simulations was thus a "non-typical" year in this regard. Our

model results show that reversals of the Arctic atmospheric anticyclone causes corresponding reversals of the Beaufort Gyre ocean circulation and sea ice drift. Figures 11 through 14 illustrate

these reversals in September when both ice drift and the ocean model streamfunction exhibit a well

developed cyclonic Beaufort Gyre.

Another look at the climatological atmospheric pressure field over the Arctic Ocean for an

earlier period is presented by Colony and Thorndike [15]. Figure 25a, which is a reproduction

from the above paper, shows the mean surface atmospheric pressure (1979-1982) over the Arctic

Ocean. This figure shows a large-scale atmospheric high with a central pressure of nearly 1020

47
1980

1982

1984

1981

1983

1985

90. 100. 110. 120. 130. 140. 150. 160. 170. 180.

Figure 21: Annual means of the incoming short-wave radiation for the years 1980 to 1989. The

units are Watts/m2

48
1986 1987

1988 1989

90. 100. 110. 120. 130. 140. 150. 160. 170. 180.

Figure 21: cont.

49
1980

1982

1984

1981

1983

1985

200. 210. 220. 230. 240.' 250. 260. 270. 280. 290. 300. 310. 320. 330. 340. 350.

Figure 22: Annual means of the incoming long-wave radiation for the years 1980 to 1989. The

units are Watts/m2

50
1986 1987

1988 1989

200. 210. 220. 230, 240. 250. 260. 270. 280. 290. 300. 310. 320. 330. 340. 350.

Figure 22: cant.

51
1980

1982

1984

1981

1983

1985

240. 245. 250. 255. 260. 265. 270. 275. 280. 285.

Figure 23: Annual means of the surface air temperature for the years 1980 to 1989, in degrees

Kelvin

52
1986 1987

1988 1989

240. 245. 250. 255. 260. 265. 270. 275. 280. 285.

Figure 23: cant.

53
1980

1982

1984

1981

1983

1985

1002. 1004. 1006. 1008. 1010. 1012. 1014. 1016. 1018. 1020.

Figure 24: Annual means of the surface pressure for the years 1980 to 1989, in millibars

54
1986 1987

1988 1989

1002. 1004. 1006. 1008. 1010. 1012. 1014. 1016. 1018. 1020.

Figure 24: cant.

55
millibars extending over the entire western Arctic Ocean. As mentioned before, this large-scale

high pressure is coherent with the corresponding anticyclonic atmospheric flow which is the primary

driving mechanism for the Beaufort Gyre and the predominantly anticyclonic ice drift in the western

Arctic Ocean. Figure 25b, also reproduced from Colony and Thorndike [15], shows the long-term

climatological ice drift pattern in the Arctic Ocean based on objectively analyzed ice drift data

originating from a combination of research stations (1893-1972), trajectories of automatic data

buoys (1979-1982), and trajectories of research stations and automatic data buoys during AIDJEX

(1975-1976). The pattern that emerges from these data sets is a well defined anticyclonic ice drift

with speeds of up to 3 em/s near Barrow, Wrangel Island, and along the Fram Strait.

However, year-to-year and season-to-season ice drift variability, which deviates from the longterm climatological mean state, is to be expected since reversals of atmospheric forcing are not

uncommon. Our model results (Figs. 9 and 14) show a significant seasonal variability in the atmospheric forcing (geostrophic winds) and ice drift fields, with January through April and NovemberDecember being the months characterized by the typical mean patterns shown by Cs>lony and

Thorndike, whereas the model results for the other months display either very weak and disorganized ice drift patterns or a total reversal of the ice drift to a cyclonic pattern, as shown for the

month of September. In fact, the underestimation of the ice extent by the model over the Russian

continental shelf between Wrangel Island and the New Siberian Islands in September may be a result of ill-defined open boundary conditions for the ice model under the ice inflow regime imposed

by the atmospheric forcing reversal. The boundary conditions for the ice model were developed for

ice outflow situations only (e.g., Fram Strait), which preclude a consistent exchange of ice mass

through the large Arctic open boundary of our limited area grid under significant inflow situations.

Note that for most months (Fig. 14) the model results show a significant ice outflow through the

entire Arctic open boundary.

56
r--r-1

o 2 4 em s"

"/ '" ,

/ / / / "'- " \cn/ \

~ft-~ / --" -.... \. \. \ "I

/ )".../ - / "- "'- -.... " \. ' / , / / -'" "--, /

<, \

" \. \ !' "- I I '- / "

, \ \" \ ',I , , "- / \ "- \

\

" '1-', ... "-

'" / "

" \ V " '-'"- / ... ..... ", '\.. '" / ' '.

/ "-

I " ,

"

Figure 25: (a) Four year average of the surface atmospheric pressure;.(b) mean ice motion. both

from Colony and Thorndike [14]

57
5 Parameter Studies

Several early experiments were conducted to arrive at workable values for the many adjustable

parameters which together define the coupled model. For example, short initial experiments of

this sort were used to ascertain the maximum stable time step and the minimum usable values of

viscosity and diffusivity. The values thus identified have been used in the central experiment C3.

Two of these initial experiments require somewhat lengthier discussion, since they point out two

important areas of model sensitivity which might not (unlike time step, etc.) be readily appreciated

at the outset. In one experiment (C1) for instance, parameters internal to the Hibler ice model

were adjusted to stiffen the boundary conditions in the ice model along the northern (open) edge.

This was done by setting the ice strength and viscosities to one. tenth of the values just inside the

model domain, rather than setting them to zero. This caused the ice velocities to be much smaller,

the ice thickness to be larger, and the Beaufort gyre to be much weaker (since less momentum was

transferred through the ice to the ocean below). As this experience demonstrates, the ice model

is very sensitive to the details of the open boundary conditions used for both the ice and oceanic

model variables.

The ice momentum equations are solved using an implicit timestep with a line-relaxation scheme.

The solver iterates until the error is less than a specified tolerance value, set to 2 X 10-4 for most

of the computations. We were concerned about linear openings in the ice which tend to appear

during the course of the central experiment, and wondered if we were not fully converging to the

correct solution. To test this idea, we tried (C2) an error tolerance value of 2 x 10-6 . The results

did not qualitatively change; in particular, the linear features appeared in different places but did

not disappear. We return to the issue of the iterative ice solver below in the Discussion (§6).

We have already mentioned that the oceanic component of the model is not successful in producing an analogue of the observed Beaufort Undercurrent. This is perhaps not surprising given the

resolution currently employed (20 km, much greater than the local Rossby deformation radius) and

the consequent lack of any internal baroclinic processes which might give rise to the Undercurrent.

Though not the only candidate, mesoscale eddyItopography interactions (eddy form stresses) are

conspicuously absent at this resolution.

A parameterization for eddy form stresses has recently been proposed Eby and Holloway [17] for

use in non-eddy-resolving oceanic circulation models. In its present simple form, the parameterized

eddy form stress forcing is implemented as a relaxation of the model velocity field towards a

barotropic "climatology" suggested by a maximum entropy principle. The resulting streamfunction

climatology is a function of the bottom topography:

(23)

where L is an adjustable scale factor, here set to 3 km. The U and v climatologies are found from:

1 o1/Jn

U - ---- n - h oy

1 o1/Jn

V n = ---. h ox (24)

Relaxation of the model fields towards this climatology takes place in the viscous terms; in place

of a horizontal Laplacian viscosity on U and v, the viscosity is applied to the u and v fields after

the climatology has been subtracted

~(Vho(u - Un)) + ~(Vh o(u - Un))

ox ox oy oy ~( hO(v - Vn )) ~(ho(v - Vn ))

ox V ox + oy V oy . (25)

The rationale for the modification of the viscous terms is that eddy mixing in the ocean does not

always act to bring the flow towards a state of rest, but may (and typically does) "push" the ocean

system towards preferred states of motion typified by cyclonic circulation around basin edges.

58
The implementation of the Eby and Holloway parameterization is complicated by the need to

chose a value for the parameter L, and by an uncertainty in the treatment of the topography. For

reasons of numerical accuracy and stability, we have had to smooth the observed bottom topography

before using it in the model simulations. One issue is therefore: should we derive the eddy form

stress streamfunction from the original (observed) topography, or from the smoothed topography

ultimately employed in the model? After some thought, and conversations with Greg Holloway, it

was decided to do the former-that is, to base the eddy form stress parameterization on the original

unfiltered topography (although we had to cut it off above 50 m). Clearly, alternate treatments are

possible; however, the choice adopted here is likely to produce the strongest eddy form stresses,

and is therefore a best case scenario for the eddy form stress effects.

The resulting streamfunction and velocities climatologies are shown in figures 26 and 27, respectively. The large-scale patterns of eddy-induced circulation are cyclonic, with maximum velocities

of approximately 30 em/s occurring along the Siberian and Alaskan continental shelves. Because

we use the unsmoothed topography in the definition of these fields, small-scale variability in h is

retained, and is particularly apparent in the implied velocities.

Addition of the eddy form stress parameterization to the central experiment (experiment C4)

produces significant changes to the oceanic circulation. Figure 28 shows the monthly mean transport

streamfunction fields produced in experiment C4. These maps should be compared with those in

Figure 11, obtained from the central experiment. Several effects are striking. First, the large-scale

circulation patterns associated with the Beaufort Gyre are modified, with the appearance of net

cyclonic flow adjacent to the continental shelves. The eddy-induced cyclonic flow dominates the

wind-driven component of circulation in all months, though it is most apparent in the summer and

fall (see, e.g., October). Vertical sections of velocity taken across the Alaskan outer continental

shelf (Figure 29) show the eddy-induced currents to be persistent, strong [0(20) cm/sec], and nearly

depth-independent. Though this reverse (cyclonic) sense of circulation, and its placement relative

to the continental shelf are in broad agreement with the available observations, it is clear that other

aspects of the reversed currents (particularly their vertical structure) is not completely realistic.

This reflects the present level of skill of the eddy form stress parameterization, particularly the

assumption of a depth-independent form stress.

Although the addition of an eddy form stress parameterization can possibly be claimed to

improve the overall oceanic simulation, it has little effect on the ice dynamics in experiment C4.

Figure 32 shows the monthly mean sea ice thicknesses obtained in C4. (Cf, Figure 19, taken

from C3.) Minor differences in sea ice thickness can be seen in most months; however, the overall

patterns are largely unchanged. In these simulations, if not in the real world, sea ice dynamics is

most intimately tied to atmospheric wind stress forcing, and thermodynamic exchanges across the

atmosphere/ice/ocean boundaries. Neither of these exchanges appears to be strongly influenced in

these simulations by the addition of parameterized eddy form stress.

A final three-year simulation (C5) was conducted to assess sensitivity to a more realistic specification of inflow through the Bering Strait. Prior experiments treated the inflow as uniform in time,

with a value of 0.8 Sverdrups. Following Coachman and Aagaard [12], a better approximation is

to vary the transport as a function of the surface wind component towards 192 degrees True. In

C.S, transport through the Bering Strait was allowed to vary in time in response to the imposed

atmospheric winds, as prescribed by Coachman and Aagaard.

Figure 31 shows the monthly mean streamfunction fields for experiment C5. Monthly mean

inflow through the Bering Strait (roughly proportional to the number of streamfunction contour

lines which ~manate from the Bering Strait) is seen to vary substantially throughout the year, by

as much as 50%. Stronger than average inflows during 1983 are observed to occur in June, July,

August, September and December; weaker than average fluxes into the Western Arctic are shown

in January, February, March, October and November. The fluxes in each of these months differs

from the mean by at least 25% (one contour level out offour), signifying substantial inter-monthly

59
'., "

CON~OUR FROM -5400000 TO -200000 BY 200000

Figure 26: Eddy-induced streamfunction. Contour interval is 0.2 Sv

60
• I

I '

I

,-- I '

I •

, I

"

- .......- - ,-'

Figure 27: Eddy-induced velocity vectors

61

. t' -

, I , t'

. I '

. I - I I I I

----"

0.311E+00

MAXIMUM VECTOR
June

Figure 28: Streamfunction from eddy form stress experiment. Contour interval is 0.2 Sv

62
September

Figure 28: cant.

63

October
lJllll1 I>< X

}<x

ImJfJ

\{

January February

"

June

-0.105 -0.075 -0.045 -0.015 0.015 0.045 0.075 0.105 0.135

,\tImJII

\11

March Apr i 1

May

Figure 29: Transects of the monthly mean along-shore current from the eddy form stress experiment

in m/s. Positive is towards the west and is shown with hashing

64
October

July August

September

November

I

I

'~ I

IlJlllll: I

'~I I

I

I

I

I

I

December

x

-0.285 -0.255 -0.225 -0.'95 -0.1b5 -0.135 -0.105 -0.075 -0.045 -0.015 0.015 0.045 0.075 0.105 0135

Figure 29: cant.

65
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~~~ :: :: ; :. : : : ; :::::::::: ~~~~ ~::: : : : . .: ;: :: :; :: ; ::;: ::: ~~~~ : : : : : : : ::; ::; ::: ; : : ::: ~~X\,'" , __ , i • , , I , , I I I

~~~~ : : :: ::- : : : : : : :::; ; ::::; :: ~~~~~ ::::::: : ; ; :; ; :: :: ::: ~~~~~~ ~~ ~:::: : ::': :: :; ; ; ; ; ; ; ; :: \~~~~~~~~~~:::::::;::::;:;;:;:: : ~~~~~~~~~~~~~:::::::;;::;::;:::: : '~~~~~~ ~~ ~~:::: :-::::::: : =: : : ; ; : ; :

~~~~~~~~~~~~:::::::::::::::;;: . \\\,''"'''~''~~~---.-~~~~I'' ..

~~~~~~~~~:~::::::::::::;:::. "\"\"""------~~#~.# .. ,\""\,""----~--~---.. Y ,\"\"~,~,-,----~--_ .. \,,""~"'-----~--­ ,\\\,""~----~~ .. lll'~..... ,. 1111 I' .-" , I I I ..•.•.

till. • •.••

1111 oR ••••

l' 1 I,'
August

0.20 0.30 0.40 0.50 0.60

Figure 30: cont.

67

0.70
variability in the influx through the Bering Strait.

Given the intensity of the wind-driven component of the Beaufort Gyre, which typically exceeds

the volume flux through the Bering Strait by an order of magnitude, it is not likely that this timedependence in the Bering Strait inflow will have a large effect on the mean properties of the Beaufort

Gyre. This expectation is borne out by the monthly mean streamfunction fields (Figure 31) which

differ little from their counterparts in the central experiment (Figure 11). The largest qualitative

gyre-scale change in transport pattern occurs in June; above-average inflow through the Bering

Strait is seen to form a strong coastal flow along the coast of Siberia which is absent in the control

run.

Since the gyre-scale patterns of circulation are not strongly influenced by Bering Strait inflow

variability, associated changes in the monthly mean ice fields also undergo only minor changes.

Figure 32, for instance, shows the monthly mean ice thickness fields for experiment C5. Overall

patterns of monthly mean ice thickness are largely unaffected by the improved parameterization of

Bering Strait inflow (cf, Fig. 19).

Despite the insensitivity of the mean ice properties to these changes in model formulation, it

should be no surprise that the trajectories of individual ice floes (floats) are themselves extremely

sensitive to such changes, since even small velocity perturbations will influence float dispersion.

Figure 33 shows the simulated trajectories of drifting buoys obtained for experiment C.5. Substantial

changes in the float movements are indicated in both the Beaufort and Chukchi Seas (cf, Fig. 20).

Overall agreement with observed drifter motion does not appear to be improved (though we would

need to conduct an appropriate statistical analysis of the modeled and observed float locations in

order to confirm this visual impression). The float results of C5 do however confirm the inherent

sensitivity of drifter dispersion estimates to model formulation choices. Much further work along

these lines needs to be done.

68
Figure 31: Streamfunction from variable Bering Strait transport experiment. Contour interval is

0.2 Sv

69
-_.- -- --_.-.---.-:::::.-....

Figure 31: cant.

70
0.25 0.75 1.2 1.8 2.2 2.8 3.2 3.8 4.2 4.8

Figure 32: Ice thickness in meters from the variable Bering Strait transport experiment

71
••••••_f~,I.i!rj'!'4tt:l~n,·,i!.;<l;!.i,>u'l I I

0.25 0.75 1.2 1.8 2.2 2.8 3.2 3.8 4.2 4.8

Figure 32: cant.

72
Jr-----~~#1

Figure 33: Drifting buoy trajectories from the variable Bering Strait transport experiment. The

red tracks are from the buoys released by Roger Colony's group while the black tracks are those

made by model buoys. The model buoys have a + every ten days. The three model buoys that

go through Bering Strait were placed there after leaving via the northern boundary and have no

corresponding real buoys.
6 Overall Assessment and Desirable Improvements

The results of model simulation C3 are consistent with the large-scale circulation features of the

Western Arctic. In particular, the Beaufort Gyre and its seasonal variability in the sense and

amplitude of its circulation are reproduced to the extent of our ability to quantify them in the

target year of 1983. Local reversal of the climatological circulation along the continental shelf (the

Beaufort Undercurrent) is not reproduced at the resolution of the current study. Incorporation

of the Eby and Holloway eddy form stress parameterization improves the degree of skill in the

Undercurrent region, though to an unknown degree. Clearly, simulations at enhanced resolution

(perhaps 4 or more times finer than presently employed) are necessary.

The bulk properties of the ice distribution observed during 1983-including ice concentration

and thickness and its seasonal growth and retreat-are reproduced well by the coupled model to

the degree that available observations allow model evaluation. Some systematic tendency for fasterthan-observed melting in the spring and summer months is seen in the model along the Siberian

continental shelf. The regional reasons for this disagreement are unclear, but may lie within the

limitations of the present model formulation-discussed further below.

The poorest model performance is seen in the comparison between the model-inferred ice floe

("float") trajectories and the observed trajectories of surface floats released in the Arctic in 1983.

Mean motion of the simulated drifters is comparable to those observed; however, there is little

agreement between individual sets of trajectories. The apparent. inability of the present coupled

system to reproduce the detailed motions of individual floats is likely a consequence (at least) of

the heavily smoothed atmospheric wind stresses used in the present study (Kozo and Robe, [28]).

Though the bulk properties of the ocean/ice circulation are retained in the smoothed atmospheric

products, local Lagrangian flow properties are clearly influenced by spatial and temporal filtering

of the wind forces. It is suggested that further study be instituted of the influence of using higher

resolution wind products.

Enhanced simulation skill, particularly as it relates to local properties such as the detailed

dynamics of the Beaufort Undercurrent and the individual trajectories of ice floes and surface

drifters, will require improvements to the coupled model and its inputs. Improvements in several

areas are desirable, as follows:

• Ocean/Ice Dynamics:

1. Relocate or remove the cross-basin open boundary to reduce or eliminate sensitivity to

poorly known ice boundary conditions. The most desirable way to go about this would

be to include the entire Arctic, perhaps with decreased resolution in the far field to

maintain economy.

2. Modify or replace the ice model. There are (at least) two known problems with the Hibler

ice model dynamics. The first is the treatment of the "pressure gradient" terms. The

pressure gradient is meant to represent the resistance of ice to horizontal convergence

once the ice is sufficiently dense (near 100% ice coverage). The problem is that the term

is always on, whether or not the ice is converging. The other problem is that there is

an implicit assumption that the ice is isotropic, or that the gridspacing is much greater

than the size of the individual floes. This is not a valid assumption for gridspacings less

than 100 km, since floes can be as large as 20 km across. We are in contact with several

investigators-including Carol Pease, Jim Overland and Max Coon-who are working

on these problems.

• Thermo,dynamics:

1. Improve the mixed layer formulation in the oceanic component of the coupled model

to allow more realistic thermodynamic exchanges across the ice/ocean boundary. New

74
formulations of the oceanic mixed layer component of our model hierarchy are presently

being implemented.

2. Improve ice thermodynamics. Current formulations have the problem that they grow

ice at the sides of the leads rather than covering the leads. This causes more heat to

be lost through the remaining open water. Doug Martinson of Lamont-Doherty Earth

Observatory is exploring alternative formulations.

3. Add river inflow. In the spring, there is a large flux of fresh water into the Arctic,

along the Siberian coast and at the MacKenzie river mouth in Canada, with likely local

consequences for ice break-up and melting. Prof. Jim Miller of Rutgers University has

access to these river inputs, and has agreed to make them available for future use.

• Numerical Parameters and Methods:

1. Decrease horizontal resolution. A minimum grid resolution of 5 km is desirable, at least

in the region(s) of maximum interest.

2. Replace the pseudo-ADI elliptic solver in the ice model. The linear openings in the ice

are disturbingly straight and aligned with the model coordinate system, and are likely

an artifact of the elliptic solver which performs line relaxation in the x-direction to solve

the u equation, followed by line relaxations in the y-direction to solve the v equation.

We are hoping that Paul Budgell and his colleagues will make some progress in this

direction, but they may find that the equations become ill- behaved for sufficiently fine

resolution or large numbers of gridpoints.

75
References

[IJ K. Aagaard. The beaufort undercurrent. In P.W. Barnes, D.M. Schell, and E. Reimnitz,

editors, The Alaskan Beaufort Sea: Ecosystems and Environments, pages 47-71. Academic

Press, Orlando, Florida, 1984.

[2J K. Aagaard. A synthesis of arctic ocean circulation. Rapp. P.- V. Reun. Cons. Int. Explor.

Mer, 188:11-22,1989.

[3] K. Aagaard and E. C. Carmack. The role of sea ice and other freshwater in the arctic circulation. J. Geophys. Res., 94:14,485-14,498, 1989.

[4] K. Aagaard, J. H. Swift, and E. C. Carmack. Thermohaline circulation in the arctic mediterranean seas. J. Geophys. Res., 90:4833-4846, 1985.

[5] G. Bjork. A one-dimensional time-dependent model for the vertical stratification of the upper

arctic ocean. J. Phys. Oceanogr., 19:52-67, 1989.

[6] G. Bjork. On the response of the equilibrium thickness distribution of sea ice to ice export,

mechanical deformation, and thermal forcing with application to the arctic ocean. J. Geophys.

Res., 97:11,287-11,298, 1992.

[7J A. F. Blumberg and G. L. Mellor. A description of a three-dimensional coastal ocean circulation

model. In N. Heaps, editor, Three-Dimensional Coastal Ocean Models. American Geophysical

Union, Washington, D.C., 1987.

[8] R. H. Bourke and R. P. Garrett. Sea ice thickness distribution in the arctic ocean. Cold Reg.

Sci. Tech.,. 13:259-280,1987.

.[9] P. B. Brasseur. A variational inverse method for the reconstruction of general circulation fields

in the northern bering sea. J. Geophys. Res., 96:4891-4907, 1991.

[10] W. J. Campbell, J. P. Gloersen, E. G. Josberger, O. M. Johannessen, P. S. Guest, N. M.

Mognard, R. Shuchman, B. A. Burns, N. Lannelongue, and K. L. Davidson. Variations of

mesoscale and large-scale sea ice morphology in the 1984 marginal ice zone experiment as

observed by microwave remote sensing. J. Geophys. Res., 92:6805-6824, 1987.

[11]. L. K. Coachman and K. Aagaard. On the water exchange through bering strait. Limnology

and Oceanography, 11:44-59, 1966.

[12J L. K. Coachman and K. Aagaard. Transports through bering strait: annual and interannual

variability. J. Geophys. Res., 93:15,535-15,539, 1988.

[13] 1. K. Coachman, K. Aagaard, and R.B. Tripp. Bering Strait: The Regional Physical Oceanography. University of Washington Press, Seattle, 1975.

[14] R. Colony and 1. Rigor. Arctic ocean buoy program data report for 1 january 1990-31 december

1990. Technical Report APL-UW TM 10-91, Appl. Phys. Lab., Univ. of Wash., Seattle, May

1991.

[15J R. Colony and A. S. Thorndike. An estimate of the mean field of ice motion. J. Geophys. Res.,

89:10,623-10,626,1984.

[16J R. R. Dickson, J. Meincke, S.-A. Malmberg, and A. J. Lee. The great "salinity anomaly" in

the northern north atlantic, 1968-1982. Prog. Oceanogr., 20:103-151, 1988.

76
[17] M. Eby and G. Holloway. Sensitivity of a large scale ocean model to a parameterization of

topographic stress. J. Phys. Oceanogr., 24:2577-2588, 1994.

[18] G. H. Fleming. Development of a large-scale coupled sea-ice model for interannual simulac

tions of ice cover in the arctic. Technical Report NDS-68-89-009, Naval Postgraduate School,

Monterey, California, 1989.

[19] G. H. Fleming and A. J. Semtner, Jr. A numerical study of interannual ocean forcing on arctic

ice. J. Geophys. Res., 96:4589-4603, 1991.

[20] D. Haidvogel, J. Wilkin, and R. Young. A semi-spectral primitive equation ocean circulation

model using vertical sigma and orthogonal curvilinear horizontal coordinates. J. Compo Phys.,

94:151-184, 1991.

[21] S. Hakkinen. An arctic source for the great salinity anomaly: a simulation of the arctic

ice-ocean system for 1955-1975. J. Geophys. Res., 98:16,397-16,410, 1993.

[22} K. S. Hedstrom. Technical manual for a coupled sea-ice/ocean circulation model (version 1).

Technical report, Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick,

NJ, April 1994. OCS Study MMS 94-0020.

[23] W. D. Hibler, III. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., 9:815-846,

1979.

[24] W. D. Hibler, III. Documentation for a two-level dynamic thermodynamic sea ice model.

Technical report, USACRREL, Hanover, NH, 1980. Special Report 80-8.

[25] W. D: Hibler, III. Modeling a variable thickness sea ice cover. Mon. Wea. Rev., 108:1943-1973,

1980.

[26] W. D. Hibler, III and K. Bryan. A diagnostic ice-ocean model. J. Phys. Oceanogr., 17:987-

1015, 1987.

[27] L. Kantha and G. L. Mellor. A two-dimensional coupled ice-ocean model of the bering sea

marginal ice zone. J. Geophys. Res., 94:10,921-10,935, 1989.

[28] T. L. Kozo and R, Q. Robe. Modeling winds and open-water buoy drift along the eastern

beaufort sea coast, including the effects of the brooks range. jgr, 91:13011-13032, 1986.

[29] P. Lemke. A coupled one-dimensional sea ice-ocean model. J. Geophys. Res., 92:13,164-13,172,

1987.

[30] P. Lemke and T. O. Manley. The seasonal variation of the mixed layer and the pycnocline

under polar sea ice. J. Geophys. Res., 89:6494-6504, 1984.

[31] G. L. Mellor and 1. Kantha. An ice-ocean coupled model. J. Geophys. Res., 94:10,937-10,954,

1989.

[32] G. L. Mellor and T. Yamada. A hierarchy of turbulence closure models for planetary boundary

layers. J. Atmos. Sci., 31:1791-1806, 1974.

[33] J. E. Overland and A.T. Roach. Northward flow in the bering and chukchi seas. J. Geophys.

Res., 92:7097-7105, 1987.

[34] C. L. Parkinson. Interannual variability of the spatial distribution of sea ice in the north polar

region. J. Geophys. Res., 96:4791-4801, 1991.

77
[35] S. Piacsek, R. Allard, and A. Warn-Varnas. Studies of the arctic ice cover and upper ocean

with a coupled ice-ocean model. J. Geophys. Res., 96:4631-4650, 1991.

[36] D. M. Pollard, L. Batteen, and Han Y.-J. Development of a simple upper-ocean and sea ice

model. J. Geophys. Res., 13:754-768,1983.

[37] A. J. Semtner, Jr. A model for the thermodynamic growth of sea ice in numerical investigations

of climate. J. Phys. Oceanogr., 6:379-389, 1976.

[38] A. J. Semtner, Jr. Numerical simulation of the arctic ocean circulation. J. Phys. Oceanogr.,

6:409-425, 1976.

[39] A. J. Semtner, Jr. A numerical study of sea ice and ocean circulation in the arctic. J. Phys.

Oceanogr., 17:1077-1099,1987.

[40] M. Spaulding, T. Isaji, D. Mendelsohn, and A. C. Turner. Numerical simulation of wind driven

flow through the bering strait. J. Phys. Oceanogr., 17:1799-1816, 1987.

[41] A. Stigebrandt. The north pacific: A global-scale estuary. J. Phys. Oceanogr., 14:464-470,

1984.

[42] A. S. Thorndike, D. A. Rothrock, G. A. Maykut, and R. Colony. The thickness distribution

of sea ice. J. Geophys. Res., 80(33):4501-4513, 1975.

[43] A. S. Threshnikov and G. 1. Baranov. Water circulation in the arctic basin. Technical report,

Israel Program for Scientific Translations Ltd., 1973.

[44] J. E. Walsh, W. D. Hibler, III, and B. Ross. Numerical simulation of northern hemisphere sea

ice variability, 1951-1980. J. Geophys. Res., 90:4847-4865, 1985.

[45] J. E. Walsh and C. M. Johnson. An analysis of arctic sea ice fluctuations. J. Phys. Oceanogr.,

9:580-591, 1979.

[46] W. B. White and N. E. Clark. On the development of blocking ridge activity over the central

north pacific. J. Atmos. Sci., 32:489-502, 1975.

[47] J. Wilkin and K. Hedstrom. User's manual for an orthogonal curvilinear grid-generation

package. Institute for Naval Oceanography, 1991.

78