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ISSN 0001 4370, Oceanology, 2010, Vol. 50, No. 3, pp. 317­326. © Pleiades Publishing, Inc., 2010. Original Russian Text © P.V. Bogorodskii, A.V. Marchenko, A.V. Pnyushkov, S.A. Ogorodov, 2010, published in Okeanologiya, 2010, Vol. 50, No. 3, pp. 345­354.

MARINE PHYSICS

Formation of Fast Ice and Its Influence on the Coastal Zone of the Arctic Seas
P. V. Bogorodskiia, A. V. Marchenko
a a, b, c, d

, A. V. Pnyushkova, and S. A. Ogorodov

e

Arctic and Antarctic Research Institute, St. Petersburg, Russia E mail: bogorodsky@aari.nw.ru b State Oceanographic Institute, Moscow, Russia c University Center in Svalbard, Longyearbyen, Norway d Prokhorov Institute of General Physics, Moscow, Russia e Moscow State University, Moscow, Russia
Received January 21, 2008; in final form, January 12, 2009

Abstract--The formation of fast ice in the costal zone of freezing seas (immobile ice) is considered on the basis of a specially developed thermodynamic model that takes into account the energy exchange in the atmo spheric boundary layer and the salinification of the water layer under the ice. The conditions at which the wind forced onshore motion of the ice under the influence of the wind stress at the ice's surface is possible are studied using the example of the Baidaratskaya Guba in the Kara Sea. DOI: 10.1134/S0001437010030033

INTRODUCTION The sea ice plays a significant role in the dynamics of the coast and the bottom of the Arctic seas. During the cold period of the year, fast ice is formed in the coastal zone: the immobile ice cover is connected to the coast whose boundary approximately coincides with the location of the 20­30 m isobaths. Its direct impact on the coastal zone is manifested in the varia tion of the dynamic conditions in the coastal zone and in the formation of specific forms of topography (fur rows, depressions, ridges, etc.) [5, 8]. The formation of fast ice starts near the coasts, where the water cool ing is faster. It also has some peculiarities related to the specific features of the ice formation in the shallow sea [3, 4]. The stable position of the fast ice is usually gained 2­3 months after the beginning of the ice for mation. During this time, the ice can brake and move. Its stable location depends on a number of causes: the existence of islands, the configuration of the coastline, the location of tidal cracks, etc. The fast ice of the Arctic seas generally consists of the ice formed in the autumn, although sometimes inclusions of second year ice and even multiyear ice are found. Depending on the geographical location and the hydrometeorological regimes of the basins, the differences in the mean multiyear fast ice thickness range from 20­30 cm in the beginning of the ice growth period to 100 cm at the end of it [3]. In the shallow depths, the ice lays on the bottom forming the foot of the fast ice. Its location is determined by the bathymetry of the coastal zone, the amplitude of the

tide, and the ice thickness. Field observations indicate that the surface of the fast ice's foot is located at the same level as the surface of the floating ice cover dur ing the period of the maximum tide; in other periods, this surface is lower than the surface of the ice foot. A few ice cracks exist between them, which play the role of elastic joints during tidal deformations of the ice. As a result of the regular impacts of the dynamic factors and the nonuniform ice cover, the ice thickness is vari able even over limited areas: the root mean square deviation is approximately 1/6 of the mean ice thick ness [3]. The fast ice foot preserves the coastal zone and the sea bottom from onshore ice motions occurring when fast ice is forced on the land [5]. Despite the exclu sively important estimates of its size in the calculations of the dynamic impact on the coast, such estimates are still lacking. In this paper, we, for the first time, try to determine the size of the overlapping between the ice cover and bottom. We also study the conditions when the ice is displaced on the shore under wind friction forcing using the example of Baidaratskaya Guba in the Kara Sea. The interest in this part of the Arctic coast is reasonable because it is determined by the key position of Baidaratskaya Guba within the project of the Yamal gas transport to the central regions of Rus sia. The upthrust of the ice on the shore can become a cause of the destructions of coastal constructions and pipelines. A thermodynamic model adjusted for the shallow water conditions was developed to calculate the characteristics of the ice formation. The model

317


318 Tb T
a

BOGORODSKII et al. Air Snow

­hs 0

mines the total heat flux to the atmosphere (the short wave radiation for the autumnal­winter period is assumed to be zero): k s T = EH , z
+

T0

z = ­hs ( t ) ,

(2)

Ice
i

h

where EH = H + LE + R; H and LE are the turbulent fluxes of the sensible and latent heat, respectively; and R is the long wave radiation balance at the surface.
Water

S h z

w

The integral aerodynamic relations are used to determine the turbulent fluxes of sensible and latent heat [6]: H = c a C a StU ( T b ­ T a ) , LE = L * c a DaU ( q b ­ q a ) , (3, b)

Bottom

Fig. 1. Scheme of the temperature distribution in the layers of snow, ice, and water. The temperature at the lower ice boundary is equal to the freezing temperature of water.

describes the variation in the ice cover thickness, the salinification of the water layer under the ice, and the components of the heat and radiation balance of the ice cover under the influence of variable atmospheric conditions. THERMODYNAMIC MODEL The necessity to take into account the bottom topography and salinity distribution in the basin, as well as the variability of the meteorological conditions, almost excludes the application of semi empiric rela tions for estimating the ice growth based on the "sum of frost degree days" [3, 4] used to calculate the thickness of the fast ice in the given conditions. A one dimensional thermodynamic model was used for this purpose. This is a spatially uniform model (in the hor izontal plane) that does not include any horizontal parameterizations. The model considers the crystalli zation of the sea water layer with thickness h assuming a constant heat flux in the entire column of the grow ing snow­ice cover [1, 6] (Fig. 1). The propagation of heat in the layers of snow and ice is described by the heat conductivity relations: (C)
s, i

where U is the wind velocity, St and Da are the coeffi cients of the heat and humidity exchange (for simplic ity, we do not take into account the influence of the stratification), L* is the specific sublimation heat, q is the specific humidity, the index is used to denote the atmospheric parameters, and the index b is used for the upper boundary of the snow. In this case, qa and qb are expressed by means of the partial pressures of the water vapor at the temperatures Ta and Tb, respectively, which, in their turn, are calculated from the empirical Magnus relation; The Brunt relation linearized with respect to (Tb ­ Ta) is used to calculate the long wave radiation. The continuity conditions of the temperature and heat flux distribution are satisfied at the interface sur face between the snow and ice: T = T = T0 ,
- +

k

i

T T ­ ks = 0, z z

+

-

z = 0 . (4, b)

The conjugation conditions (the continuity of the temperature distribution during the transition through the phase difference of the surface and thermody namic equilibrium conditions) are satisfied at the mobile surface of the phase transition: T = T = T eq ­ S w ; where ci L
- dh i T = ki , z dt - +

z = hi ( t ) ,

(5, b)

T T = k s, i , t z z 0 z hi , t > 0.

(1)

­hs z 0 ,

z = hi ( t ) ,

(6)

Here, T is the temperature; t is the time; z is the vertical coordinate; C is the heat capacity; is the density; k is the heat conductivity; h(t) is the location of the mobile interface boundary; and the indices "i" and "s" denote the ice and snow, respectively. The boundary condition is valid at the upper boundary of the growing snow­ice cover, which deter

is the heat balance (classic Stephan condition). In relations (4)­(6), L is the latent heat of the phase tran sition, the signs "­" and "+" denote the upper and lower sides of the interface boundary, and Teq are the freezing temperatures of saline and fresh water, and is the slope of the liquidus line.
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FORMATION OF FAST ICE AND ITS INFLUENCE ON THE COASTAL ZONE Va, m/s 20 15 10 5 0 0 5 10 15 20 25 30 t, days () N E Va, m/s 7 6 5 4 3 2 1 0 0 50 100 150 200 t, days (b)

319

Fig. 2. Time evolution of the wind velocity measured at Cape Harasavey during the period of October 3 to November 3, 1980 (a) and the restored wind velocity from the reanalysis of the NCEP/NCAR data at the point with coordinates 70°00N, 67°00E dur ing 210 days from the beginning of November 2004 (b). The inset in Fig. 2a shows the increase of the wind in the winter period [7].

We consider that the initial temperature and salin ity of the water are specified as T ( z, 0 ) = T
w, 0

,

S ( z, 0 ) = S

w, 0

,

z [ 0, h ] .

(7, b)

The water layer under the ice is assumed to be homogeneous due to the convective mixing caused by the complete separation of the salts during the ice for mation. The temperature of the layer is considered constant and equal to the freezing temperature at the given salinity S, which is determined from the law of dissolved salt conservation given by the equation Sw = S
w, 0

phase composition of the ice and its time variation is a disadvantage of the model (as well as any other based on the solution of Stephan's problem in the classical frontal formulation [1]). This narrows the scope of the model's application, especially at the initial stage of the ice formation when the proportion of the liquid phase in the ice is significant. The monthly mean NCEP/NCAR reanalysis data for the temperature, atmospheric pressure, relative humidity, and wind velocity from October 2004 to April 2005 for the Baidaratskaya Guba region, as the closest to the mean decadal temperature data, were used as the atmospheric forcing in the model. An example of the time evolution of the wind velocity dur ing the autumnal­winter period (October­March) based on the data of the measurements at Harasavey Cape in October 1980 and the reanalysis data is shown in Fig. 2 (the origin of the coordinates corresponds to October 1, 2004). The method of the objective analysis based on the optimal interpolation was used to solve the problem of restoring the meteorological informa tion at the nodes of the model's grid. The theoretical basis of the method is in minimization of the error functional determined within the correlation radius on the basis of the variation of the interpolation weights set [9, 10]. After the determination of the weight coefficients satisfying the condition of the error minimum, the interpolated value can be found as a linear combination of the weight coefficients and the values of the measured parameter. The analysis of the variograms showed that the calculated correlation radii for the meteorological fields appeared to be on the order of 1000 km, which agrees well with the exist ing estimates [2]. The data on the bottom topography was adopted from the one minute GEBCO depth database. The water salinities were taken from [5, 8].

h ­ h i, 0 , h ­ hi ( t )

(8)

where hi,0 is the value of the function hi(t) at time moment t = 0. The heat transport to the lower surface of the ice is not taken into account because the strati fication in the shallow water basin is considered to be zero [3, 4]. The accumulation of snow is described by the linear dependence hs = 0.3t/(210 â 24 â 3600), which is close to the in situ measurements [3]. The linearity of the temperature profiles allows us to calculate the heat flux through the snow­ice cover from the equation EH = ­ k
i

Tb ­ . hi + hs ( ki / ks )

(9)

The substitution of relations (3) and (9) into (2) results in a quadratic algebraic equation for Tb (the exponen tial dependence in the temperature range from 0 to ­45° is approximated with sufficient accuracy by a parabolic function). The determination of Tb (the largest root has a physical sense) reduces the model to an equation of the heat balance at the lower surface of the ice cover (6), which can be easily solved numeri cally. The impossibility of taking into account the
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320 hi, m 1.2 1.0 0.8 0.6 0.4 0.2 0 0 hi, m 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 January March November December February 50 100 (c) 150 () 3m

BOGORODSKII et al. hi, m 1.2 1.7 m h=1m 1.0 0.8 0.6 0.4 0.2 0 200 t, days 0 hi, m 1.4 1.2 1.0 0.8 0.6 0.4 0.2 May April 0 January March November December February May April 50 100 (d) 150 200 t, days (b)

Fig. 3. Model estimates of the variation of the ice thickness (m) at depths of 1, 1.7, and 3 m (a) and 21 m (b) during the autumnal­ winter period. The mean thickness of the ice cover measured before 1995 (solid lines) and after 1995 (the dashed lines at the Marre­Sale (c) and Ust­Kara (d) Polar stations).

FAST ICE GROWTH Numerical experiments with the model were carried out at the following ice characteristics: i = 910 kg/m3, ki = 2.24 W/(m K), L = 3.34 â 105 kJ/m3, = 0.054°C/, and L* = 2.55 â 106 J/kg; snow charac teristics: ks = 2.24 W/(m K); and air characteristics: a = 1.3 kg/m3, Cpa = 103 J/(kg K), = 0.6, = 5.67 â 10­8 W/(m2 K4), St = Da = 1.7 â 10­3, e0 = 611, a = 0.18, b = 0.25, c = 0.052, a1 = 9.5, and b1 = 265.5 K [6, 7]. The calculated ice growth from the free surface in the coastal shallow (70°00´N, 67°00´E) and central deeper (69°30´N, 66°00´E) regions of the Baidar atskaya Guba basin during a period of 210 days are shown in Figs. 3a and 3b. In the course of time, the rate of the ice formation gradually decreases due to the accumulation of snow and the ice thickness increas ing. Its growth during the first 60­70 days is approxi mately the same in both regions of the basin. The model's results agree well with the measurements both in the thickness (the mean thickness is 1.2­1.4 m and the minimum and maximum thicknesses are 1.1 and 1.7 m, respectively [3, 8]) and the transitions to the next age stages (no and young ice--gray white ice-- one year thin ice--one year thick ice). This is clearly

confirmed by the measurements near the Ural (Ust­ Kara) and Yamal (Marre­Sale) coasts (Figs. 3c and 3d). It follows from the figure that the distinguishing feature of the ice formation at shallow depths is the stabilization of the ice thickness due to the salinifica tion of the water layer under the ice and the decrease in its freezing temperature. Due to this fact, the basin cannot freeze to the bottom even theoretically at the lowest air temperatures. It is seen from Fig. 3a that, at a depth of 1 m, the stabilization of the ice's thickness caused by the salinity increase occurs if the ice thick ness is approximately 90 cm. The calculations (the results are shown in Fig. 4) demonstrate that, during the long time freezing of the shallow part of the basin with a depth of 1 m, the value of Sw can reach 315, which significantly increases the initial salinity of the seawater (25 for the coastal regions and 27.5 for the offshore regions). The high salinity of the brine in the places where the foot of the fast ice is not tightly attached to the bottom is confirmed by the data of the measurements [5, 8, 11]. In the conditions of slow water exchange, such waters are conserved for a long time in local depressions of the bottom; thus, they become a corrosion threat for the materials of con
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FORMATION OF FAST ICE AND ITS INFLUENCE ON THE COASTAL ZONE T, °C 0 ­5 ­10 ­15 Tb ­20 0 50 100 150 200 t, days T0 Ta 20 1.7 m 10 h=1m 0 0 50 100 150 200 t, days 3m () T
w

321

EH, W/m2 40 30

(b)

Fig. 4. Variations in the temperature of the interface boundaries between the snow and ice cover (a) and the heat flux through this interface (b) at depths of 1, 1.7, and 3 m in the coastal part of the basin over 210 days.

structions. If the fast ice foot has a large width and length caused by the small depth gradients and long coastline of Baidaratskaya Guba, the volumes of such waters can be sufficiently large. As the depth increases, the influence of the salinification on the ice growth gradually decreases, and, beginning from a depth of 3 m, it becomes practically the same over the entire region of the basin. The salinification of the water layer under the ice can possibly cause a porosity increase in the fast ice foot and the formation of a seasonal frozen layer in the column of the bottom ground, which, in Baidar atskaya Guba, consists generally of fine dispersed rocks of low permeability [5, 8]. Their strength char acteristics are determined mainly by the proportion of ice in the rocks (the ice content). Saline frozen ground and cold ground containing salt brines of high concen tration also have increased aggressive chemical prop erties with respect to construction materials. We note that the gaining of high salinity in the con ditions of a flat bottom is not likely due to the horizon tal mixing and advection, which are not taken into account in the one dimensional model. The amounts of reversible advective salt fluxes during the tidal oscil lations, which facilitate the inflow transport of fresh waters at the phase of the level rising and the outflow of saline waters during the level falling, do not strongly influence the intensity of the ice formation on time scales on the order of one season. Taking into account the water advection due to the residual tidal circula tion caused by the nonlinear interaction of the tide within the approach used here is difficult, because it requires the application of a fully 3D nonlinear hydro dynamic model. Figure 5 shows the time evolution of the tempera ture at the ice­water interface Ti the snow­ice inter face T0, and the air­ice interface Tb and the air tem perature Ta for the shallow water regions of the basin.
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It is seen that, for the given time evolution of the mete orological parameters, the value of Tb is usually differ ent from Ta and coincides only during approximately 30 days (from 30 to 60). In the realistic atmospheric conditions, such a coincidence is hardly possible. Approximately the same regularity is found for the increasing difference between T0 and Tb (due to the snow accumulation) in the central part of the basin. Sharp fluctuations of the air temperature Ta caused by changes in the synoptic atmospheric processes are typical for the cold time of the year. As a result of the increasing Ta, the temperature of the lower surface of the ice Ti can appear greater than the temperature of the upper surface Tb. This would cause a change in the direction of the heat flux through the ice cover EH (Fig. 5b) and hence the ice melting despite the con serving negative air temperature (see Fig. 4a). A change in the sign of the temperature gradient in the ice cover is manifested by a characteristic maximum in the time evolution of the salinity. Thus, even if the atmospheric conditions are conserved, part of the fast ice located near the coast in the shallow water would melt while the remote part would grow (see Fig. 3a). STRUCTURE OF THE FAST ICE ZONE The Baidaratskaya Guba is a large shallow gulf. Its width along the line of the projected underwater sys tem of the main Yamal­Center pipelines is 68 km, and the maximum depth is 23 m (Fig. 6) [5, 8]. The mean bottom slope angles in the coastal zone of Baidar atskaya Guba are estimated using a grid of the bathy metric data with a spatial resolution of 0.03°. Figure 7 shows the contour lines of the sea depth gradients grad = 0.0003 (a) and grad = 0.0008 (b) calculated from the relation grad = ( H / x ) + ( H / y ) , where H(x, y) is the sea depth. It is seen that the mean angles of the bottom slope in the horizontal plane in the region of the pipeline's construction are very small.
2 2


322 Sw, 300 250 200 150 100 50 0 0 50 100 150 h=1m ()

BOGORODSKII et al. Sw, 26.50 26.25 26.00 25.75 1.7 m 3m 200 t, days 25.50 25.25 25.00 0 50 100 150 200 t, days (b)

Fig. 5. Variations in the salinity () in the water layer under the ice at depths of 1, 1.7, and 3 m (a) and 21 m (b) over 210 days.

10 000 0 4 Depth, m 8
U

20 000

Distance, m 30 000

40 000

50 000

0 4 8
Y

12 16

12 16 20

20 24 Ural

24 Yamal

Fig. 6. Profile of the sea bottom in the region of an underwater pipeline based on echo soundings. U and Y are the angles of the bottom slope to the horizontal plane at the Ural and Yamal coasts, respectively.

Their values are of the order of Y = 0.001 and U = 0.0004 at the Yamal and Ural coasts, respectively. At the same time, the relief of the underwater slope is formed as a result of the wave redistribution of depos its; therefore, the angles of the bottom slope in the coastal zone quite often reach 0.01 (Fig. 8). We assume that the sea depth changes linearly with the slope angle . The surface of the fast ice's foot cor responds to the maximum sea level, while the draft of the floating ice is h (Fig. 9). In this case, at the maxi mum sea level, the length of the ice contact with the bottom in the coastal zone (the width of the fast ice's foot) is L = h cot , while, when the sea level decreases by A, the contact length of the ice with the bottom becomes L1 = (h + A)cot (Fig. 9b). The graphs of the dependence of L and L1 on the angle of the bottom slope are shown in Fig. 10 for A = 1 m and ice thick nesses of 1 and 1.5 m. Let us study the conditions at which the ice forcing on the shore under the influence of the wind friction at the surface of the ice is possible. The absolute value of

the linear wind friction force is determined by the rela tion Fa = a Ca Va l ,
2

(10)

where a = 1.3 kg/m3 is the air density, Ca = 0.002 is the friction coefficient, Va is the wind velocity, and l is the length of the wind stress accumulation. Let us assume for the estimates that l = 50 km, which approximately corresponds to the maximum width of the region occupied by the drifting ice and fast ice near one of the coasts in the region of the underwater pipeline. Let us write the balance of the forces applied to the fast ice's foot: Fa + Fg + Fn + F = 0 , (11)

where Fa = (Fa, 0) is the wind friction force applied in the horizontal direction, Fg = (0, ­wgh2cot/2) is the weight of the fast ice foot (w is water density, and g is the acceleration due to gravity), Fn = ­Fn(sin , ­cos ) is the reaction of the bottom to the fast ice foot normal to the bottom, and F = ­F(cos , sin ) is the reac
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FORMATION OF FAST ICE AND ITS INFLUENCE ON THE COASTAL ZONE °N 70.00 69.75 69.50 69.25 69.00 68.75 68.50 ()

323

66.0 °N 70.00 69.75 69.50 69.25 69.00 68.75 68.50

66.5

67.0

67.5 (b)

68.0

68.5

69.0 °E

66.0

66.5

67.0

67.5

68.0

68.5

69.0 °E

Fig. 7. Contour lines of the sea depth gradient of 0.0003 (a) and 0.0008 (b) in Baidaratskaya Guba.

tion of the bottom to the fast ice foot tangential to the bottom. We assume that the normal and tangential projec tions of the reaction force are related by the condition of dry friction F = tan F n , (12)

The relation between the wind velocity Va needed to push the fast ice on the shore and the underwater ice draft h follows from relations (11) and (12): Va = h , =
2

w g a Ca l

where is the angle of the internal friction. The coef ficient characterizes the density of the contact between the ice foot and the bottom. It is equal to = Lc/L, where Lc is the length of the actual contact of the ice foot with the bottom. We assume for the estimates that = 30° and 0.5 < < 1.
OCEANOLOGY Vol. 50 No. 3 2010

cos ( tan cos + sin ) . â 2 sin 2 ­ 2 tan sin

(13)

The dependence of the wind velocity Va on the angle of the bottom slope is shown in Fig. 11a for the ice draft h = 0.5 m and 1 m and the coefficient of the density of the fast ice foot to the bottom = 0.5 and 1. Figure 11b shows the dependence of the wind velocity Va on the ice draft h at different angles of the bottom slope


324 H, m 2 0 ­2 ­4 ­6 H, m 2 0 ­2 ­4 ­6 1.2 1.4 1.6 1.8

BOGORODSKII et al. () 2.0 2.6 2.8 3.0 3.4 L, km

2.2

2.4

3.2

(b)

67.6 67.7 67.8 67.9 68.0 68.1 68.2 68.3 68.4 68.5 68.6 68.7 L, km

Fig. 8. Bottom topography relief in the shore zone of the Ural (a) and Yamal (b) coasts.

() h Floating ice Zone of cracks Foot of the fast ice

A Linear approximation of the bottom profile (b) F z A h F x h Fg L1
a

L

Fn

L

Fig. 9. Structure of the fast ice in the coastal zone (a). Scheme for the calculations of the size of the ice contact with the sea bottom (b).

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FORMATION OF FAST ICE AND ITS INFLUENCE ON THE COASTAL ZONE L, L1, km 5 4 3 h = 1.5 m 2 1 0 h=1m 0 2 4 6 8 10 â 103

325

L L1

Fig. 10. The width of the fast ice foot at the ice draft of 1.5 m and 1 m is shown with solid lines. The width of the fast ice contact with the bottom at the sea level drop by 1 m is shown with the dashed lines for the ice draft of 1.5 m and 1 m.

lation, the width of the fast ice foot depending on the angle of the bottom slope in the direction normal to the coastline, and the fast ice draft. The width of the fast ice foot increases as the sea level drops and increases when the sea level rises. Therefore, the most favorable conditions for the ice upthrusting on the shore are formed at the maximum water level during the spring tide. At small angles of the bottom slope, the ice forcing on the shore in the region of the underwater pipeline is possible during the first month of the fast ice growth (October to the beginning of November) at winds on the order of 20 m/s and ice thickness less than 20 cm. During this period, the domination of northeastern winds with a velocity up to 20 m/s and greater indicates the greater probability of upthrusting of the ice on the Yamal coast. The character of the ice growth during the first 60­ 70 days is almost the same in the entire basin. Approx imately 35 days after the beginning of the ice forma tion, the fast ice reaches the critical thickness of 0.2 m for the ice upthrusting on the shore. A distinguishing feature of the ice formation at shallow depths (1­3 m) is the stabilization of the ice thickness, which occurs after 150 days of ice growth. It is related to the salinifi cation of the water layer under the ice. In this case, the local salinity of the sea water in the depressions of the shallow water regions of the bottom with a depth on the order of 1 m under the fast ice foot can be as high as 315, and, at depths of approximately 2­3 m, it can be within 50­100. The dense overcooled waters can significantly influence the processes of the phase transitions in the bottom ground; hence, they can influence the physical­mechanical properties. The high salinity of the water, as well as the saline ground, is hazardous for the corrosion of steel constructions. The salinification of the water layer under the ice can become a cause of the fast ice melting in the coastal shallow water regions even at conserved negative tem
(b)

( = 0.005, = 0.01) and the coefficients k = 0.5 and 1. Taking into account that the wind velocity very seldom exceeds 20 m/s [10], we find that the forcing of the ice on the shore is possible if the ice draft is less than 0.6 m at = 0.01 and for the ice draft being less than 0.4 m at = 0.005. It follows from the wind velocity variations at Cape Harasavey in October 1980 (see Fig. 2) that the actual wind velocity can sometimes reach 20 m/s, while the wind rose (in the inset) shows the dominating north eastern directions. Such winds observed in the initial period of the ice formation, in principle, can cause the upthrust of the ice on the Yamal coast. The probability of the ice upthrusting on the Ural coast is several times smaller. CONCLUSIONS The possibility of the ice cover upthrusting on the coasts of Baidaratskaya Guba is determined by the wind velocity, the distance of the wind stress accumu
() Va, m/s h=1m 50 40 30 20 10 0 0 0.2 0.4 0.6 0.8 1.0 =1 = 0.5 h = 0.5 m

Va, m/s 30 25 20 15 10 5 0 0.2
=1 = 0.005

=1 = 0.005

=1 = 0.01

= 0.5 = 0.01

0.4

0.6

0.8

h, m

Fig. 11. The wind velocity Va versus the slope angle of the sea bottom (a) and the ice draft (b). OCEANOLOGY Vol. 50 No. 3 2010


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BOGORODSKII et al. 5. A. M. Kamalov, S. A. Ogorodov, V. Yu. Biryukov, et al., "Morpholithodynamics of Shores and Floor of Baid arat Bay at the Pipeline Route Crossing," Kriosfera Zemli, No. 3, 3­14 (2006). 6. A. P. Makshtas, Thermal Balance of Arctic Ices in Winter Period (Gidrometeoizdat, Leningrad, 1984) [in Rus sian]. 7. Yu. L. Nazintsev and V. V. Panov, Phase Composition and Thermal Physical Characteristics of Sea Ice (Gidrometeoizdat, St. Petersburg, 2000) [in Russian]. 8. Natural Conditions at Baidarat Bay. The Main Results of Studies for Construction of Submerged Crossing of the System of Yamal­Center Main Gas Pipelines (GEOS, Moscow, 1997), p. 432 [in Russian]. 9. N. Cressie, Statistics for Spatial Data, Revised Edition (Wiley, New York, 1993). 10. E. H. Isaaks and R. M. Srivastava, An Introduction to Applied Geostatistics (University Press, Oxford, 1989). 11. A. V. Marchenko, S. A. Ogorodov, A. V. Shestov, and A. S. Thsvetsinsky, Ice Gouging in Baydaratskaya Bay of the Kara Sea: Field Studies and Numerical Simulations. Recent Development of Offshore Engineering in Cold Regions, POAC 07 (Dalian, China, Dalian University of Technology Press, 2007), pp. 747­759.

peratures of the air, thus providing its uniform growth far from the coasts. ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research (projects nos. 08 05 00124, 08 05 00109, and 07 05 00393). REFERENCES
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OCEANOLOGY

Vol. 50

No. 3

2010