Tidal ice dynamics in the area of Svalbard and Frans Josef Land N . E . DMITRIEV, A. Y U . PROSHUTINSKY, T . B . L 0 Y N I N G and T. VlNJE * Dmitriev, N . E . , Proshutinsky, A . Yu., L ~ y n i n g , T.B. & Vinje. T. 1991: Tidal ice dynamics in the arca of Svalbard and Frans Josef Land. Polar Research 9(2), 193-205. This study is part of the Soviet-Norwegian Oceanographic Programme (SNOP) on ice and water dynamics in the region between Svalbard and Frans Josef Land. The effects of the movements of water and ice on the ice regime are discussed. Due to the scarcity of data, numerical hydrodynamical simulations are used. The tidal ice drift is visualized on satellite images as elliptically shaped traces in the ice fields formed by grounded icebergs. These traces are a result of the joint action of tides. wind and permanent currents. N . E . Dmitriev and A . Yu. Proshutinsky, Arctic and Antarctic Scienr$c Research Institute. Bering st. 38. St. Petersburg 199226, U . S . S . R . ; T. B . Lmyning and T . Vinje. Norsk Polarinstitutt, P.O. Box 158, N-1330 Oslo Lufrhaun, Norway. Introduction This study is part of the Soviet-Norwegian Oceanographic Programme (SNOP) on ice and water dynamics in the region between Svalbard and Frans Josef Land. The effects of the move- ments of water and ice on the ice regime are discussed. Due to the scarcity of data, numerical hydrodynamical simulations are used. The tidal ice drift is visualized on satellite images (Figs. 1 and 2 ) as elliptically-shaped traces in the ice fields formed by grounded icebergs. The length, form and orientation of the elliptic axis make it possible to determine some important parameters which can accordingly be used for the calibration of the mathematical models. Two different methods have previously been used for tidal ice drift estimation. Zubov (1945) and Legenkov (1968) assumed the ice motion to be determined by the surface currents only. They calculated deformation in the ice cover t o specify the regional and temporal change of the ice con- centration. Kagan (1968), Kheysin & Ivchenko (1973), Kowalik (1981), and Timokhov & Khey- sin (1987) took into account the additional effects of the ice cover and formulated a coupled model. Kagan (1968) considered a three-layer model with near-bottom and near-ice boundary layers, and a central layer where the turbulence was neglected. The lack of knowledge of frictional forces in the central layer prevent us from using this model for studies in the Arctic oceans where the frequency of the major tide-generating force M2 is equal or very close to the inertial frequency. Kowalik (1981) offered a non-linear two- dimensional model, which was based on shallow water theory and coupled with a non-linear ice- model. His model took into account the internal shear in the ice cover. This model has been used in this study to simulate the tides and the cor- responding ice drift. The ice and weather conditions, the area cov- ered by satellite images, and the area covered by the model are all shown in Fig. 3. The model The horizontal momentum equation for the water, according to shallow water theory and with the tide producing forces included, is + Am’V’U - The continuity equation on the integral form is - -m2div (:H), a6 at _ - The equation of the ice motion is - dUi + 2fi x Ui = -mgVE+: TI + F, dt P ( 3 ) 194 N . E. Dmitriev el al. Ftg. / Satcllitc imagc of ice bituatioo on 21 M a y 198X. and the equation for the ice concentration is U . U , are the horizontal velocity vectors of water t is the time variable. C is the horizontal del operator, H is the depth; H = D + t. where D is the equi- librium depth of the ocean: is the displacement of the sea surface from its equilibrium position, and ice, is the equilibrium tide: (I is a Coefficient which takes into account the effects of increased water mass o n the solid earth. i.e. depression d u e t o higher sea level and uplift d u e t o tide producing forces (the changes of the phases a r e neglected). ( Y = 1 is used in the model simulation. is a reduction coefficient, which parametrizes the effect of tidal forces o n a n elastic e a r t h . /3 = 0.69 is used in t h e model simulation. F, is the internal ice friction (forces of interaction between ice floes), m is a scale coefficient for the set approximating the Arctic Ocean o n t h e stereographic pro- jection map. For o u r m a p m = l.Oon the North The tidal ice dynamics 195 Fig. 2 Satcllite imagc of ice situation on 1 June 1988. Pole, m = 1.017at latitude 75"Nand m = 1.072 at latitude 60"N. pw is the density of water, p i s the surface density of the ice cover where p = plh, S , p,, h, and S, are the density, thickness and concentration of the sea ice respectively; A is the coefficient of the horizontal eddy viscosity , R is the angular velocity of the earth's rotation, g is the magnitude of acceleration due to gravity. The bottom and ice-water stress vectors Tb and T, can be expressed by ~b = KbpwUIUI, T, = K,pJU - u,I(u - u,) (5) where Kb and K, are bottom and ice-water friction coefficients. The equation for the internal ice friction is F, = qV*U, + yVdivU, - VP. (6) = (nK,divUi if divUi 2 0 if divU, < 0 (7) Where q and y are the coefficients of bulk and shear viscosity in the ice cover with units in cm2/s, P is the pressure due to the ice compression, K, is the coefficient of compression. We borrowed the Fi from the studies of Rothrock (1975) and Kowalik (1981). 196 N . E. Dmitrieu et al. 80’ 20. 40 0” 75 * I I 20 O 40- = region corresponding to satellite photos, Figs. 1 and 2. -1 01 0 - = isobars, mbr. The tidal ice dynamics 197 T h e model parameters used for the simulation are A = 55555 m grid size, Kb = 2 . 6 . bottom friction drag coefficient, Ki = 5 . 5 . ice-water friction drag coefficient. A = 10". D m2/s. hi = 250 cm average ice thickness value in the Arctic Basin, hi = 450 cm average ice thickness value in the Canadian sector, hi = 140 cm average ice thickness value in the marginal seas, r ] = l o x coefficient of bulk viscosity, y = l o 8 coefficient of shear viscosity, K, = 10 r ] coefficient of compression. Polyakov & Proshutinsky (1988) obtained root- mean-square errors for the values of the tidal amplitudes and phases, using observed harmonic constants for 94 stations located on the coast and islands of the Arctic oceans. These values are 0.054m, 0.023m. 0.013m and 0.014m from amplitudes of the waves M2. S2, K 1 and 0 1 . respectively. T h e standard deviations for the phases a r e 26, 28, 28, 30 degrees, respectively. There is a lack of tidal observations in the region of Spitsbergen and Frans Josef Land. Most sta- tions are situated in the narrow bays or straits far from the open ocean. O n e station. located in the strait between Nordaustlandet and Kvitaya (Aagard e t al. 1983) provides data o n bottom pressure and current records (Tables 1 and 2 ) . Apparently, the observed harmonic constants for most of the stations do not reflect the real process of spreading of the tidal waves in the ocean (Figs. 4 and 5). T h e tidal currents in the Fram Strait (Table 1) are assumed to be more representative and they are in closer correspondence with the calculated values. We observe many features in our cotidal charts (Figs. 4 and 5) of waves M2 and K 1 common t o those obtained by Gjevik & Straume (1989). T h e main differences are related t o the displacement of the amphidromic point of the M2 wave near Franz Josef Land and Novaja Zenilja. Our charts indicate that these points are in the open sea (two grid steps from the coast) while the charts of Gjevik & Straurne (1989) indicate a location on the coast. The differences are d u e to different grid implimentation. The study of Polyakov & Proshutinsky (1988) shows that the Barents S e a is a good resonater of the semidiurnal oscillations. Small differences in Boundary and initial conditions At the coasts ( G , ) we have used a no-slip condition, i.e. zero velocities, along t h e coastlines U l G , = 0, U i l G l = 0 (8) Along the open boundary (G2) t h e vector of the average velocity must b e known as a function of position and time. Let U = (u, v) and U, = (ui, y ) then U(X, Y, t)lc2 = A,cos(wt - I),) u(x, y , f)lG2 = cOs(wt - w v ) (9) u,(x, y , t)/G, = '"1 cos(wt - w u , ) u,(x, y , t)lGz = A v ~ cos(wt - I ) v , ) with the following condition, which means that the water mass and masses of ice a r e conserved in the basin: u, = u sin q + u cos cq. u,, = u, sin a1 + v, cos (Y, where n is a normal t o t h e open boundary, w is a frequency of the tidal wave, V,, I),,, I),,, I)v, are the phases of water and ice velocity and A,, A,, A,,, A,, a r e the amplitudes of ice and water velocities, respectively, (Y, is the angle between the n and X-axis and d G is an infinitesimal seg- ment of G Z . W e assumed the system to be initially at rest, U ( X , y . 0) = 0, U , ( X , y, 0) = 0, z(x, y, 0) = 0 at t = 0 (10) and the ice concentration t o be S(x, y, 0) = 0.9 a t t = 0. (11) Results In the numerical simulations reported below, we have used the boundary values for A,, I)", A,,, I),,, obtained by Polyakov & Proshutinsky (1988). Equations 1 t o 4 were approximated by a Lax-Wendroff semi-implicit, central-difference scheme, modified by Tee (1976). Fig. 3. Ice and meteorological situation i n the region on 21.05.88 ( A ) and 01.06.88 (B). 198 N . E . Dmitrieo et al. Tublr 1 . Tidal ellipse parameters in the Fram Strait. Abbre\ations: Mod = model results: obs = observations: res = our results. Model results are from Gjevik (19%)). observations ( F I . F?. F3I arc from Aagard et a l . (1985). and (F4) is from Aagard et al. (1983) * indicates upper current recordcr; * * indicates near bottom current recorder. The geographical positions of the stations FI. F2. F3 and F4 are +en i n Tablc 3. Station Consistuent Major scmiaxis Minor semiaxis cmils cm/s Mod Obs Res Mod Obs Res F1 M? K I F2 M? K I F.7 M? K1 F1 M2 F1 K I F4 S2 F4 01 3.3 2 . 5 1.5 1.1 3.6 2 . 5 I .3 1 . 2 2 . 5 2 . 5 I ? I .4 8.6 3.6 1.3 0.9 3.5 1.6 0.5 0.3 3.3 1.7 2.8 1 6 2.4 1 . 5 7 9 1.3 3.2 0.5 0.2 0.4 0.4 0.2 0 . 2 0.2 0.3 0.3 0.2 0.2 0.1 0.1 2.2 2.4 0.1 0.2 1.3 0.7 0.2 0.0 0.6 0.3 0.4 0.0 0.4 0.1 3.4 0.1 1.1 0.3 Table 7 . Tidal ellipse parameters in the Fram Strait. Ahbrevations: Mod = model results; obs = observations; res = our results. Model results are from Gjevik (1990). observations ( F I . F2. F3) are from Aagard et al. (1985). and (F4) is from Aagard et al. (1983). Azimuth = oricntation in degrees of major axis from north. positive eastward. Rotation: positive (+) = anticyclonic; negative ( - ) = cyclonic. * indicates upper current recorder: * * indicates near bottom current recorder. Station Consistuent Azimuth degree Rotation Mod 0 bs Res Mod Ohs Res F1 M2 K I F2 MZ K I F3 M2 K1 F4 M? F4 K I F3 S? F4 01 I 3 18 - 1 1 - 37 10 14 I 19 I6 8 3 - 6 -6 - 12 - 14 - 27 -1s 5 1 - 57 ~ 68 10 ~ 14 0 I5 17 6 -8 15 12 I0 + - + + + + Table i Geographical positions of the stations the approximation of depths of coastline between the different models may therefore lead to con- Station La t Lon siderable differences in the cotidal charts. The calculated tidal ice drift (Figs. 6 and 7) F1 78"59'N Y15'E shows maximum velocities to the south of Spits- F2 79"W'N 4"Z5'E bergen, at depths from 5 0 m to 100m. The vel- ocity of the semidiurnal ice drift is in this area about 30 cm/s. The ice velocities caused by the Station Coordinates 3"18'E 30a00,E F3 78% ' N F4 80"OO'N 0 75 ' a 75 ' The tidal ice dynamics 0' 20 L O 60 ' 80 ' 80 * 0' 40' 20' 40 a ~- - tidal wave phases - - = tidal wave amplitude l8 at the stations , 34 = phaselamplitude observed 99 30° 50 ' 80' 60' f i g . 4 Phases and aniphtudcs of the M2 ( A ) and S2 (B) tidal waves. Zero phase corresponds to the lunar time at the Greenwich Meridian. Phases are in degrees, amplitudes i n cm. 63 152 = phase/amplitude observed by pressure recorder 200 N . E . Dmitriev et al. 0' 75 ' 0 75 20' 80' 0" 20" 60' 20 75' 40" __ = tidal wave phases -- = tdal wave amplitude -2z = phase/arnplitude observed at the stations Frg .i Phd5r.s and 'trnplitudcs of the K I ( A ) and 01 ( 8 ) tlddl @go = phaselamplitude observed w a e 5 4mplitudes a r e in cm ' by pressure recorder :0 i0 * 80' 60' The tidal ice dynamics 201 9 1p 2p 3p y c*/s Fig. 6 . Principal axis of M2 (A) and S2 (B) tidal ice motion ellipse 202 N . E . Dmitrieu et al. , ‘ - ’ \ I I,--+- / - - ‘ I / f I I # , I I ‘ I - I - I I - 1 ’ I I I c 0 10 20 30 40 c”/s - Fig. 7 . Prlnctpal axis of the K l ( A ) and 01 ( B ) tidal ice motion ellipse 203 The tidal ice dynamics \ I I I I / I 01.06.88 0 3 6 9krn Fig. 8. Trajectories of ice motions. a) = observed data where A corresponds to Fig. 1 and B corresonds to Fig. 2. b) = calciilated results, where ice velocities and the sum of the harmonic tidal wave components M2, S2. K1 and 01 have been used. c) = calculated results as b) plus the influence of wind and permanent currents. 204 N . E. Dmitrieu e t a / . 30 20 40 0 -10 -a -3( 4 0 30 20 10 0 -10 - 2c - 3c - 4 0 h o u r s - EVENT 11. Fip. Y. The dnergcncc of t h c ice velocities f o r the situation o n ? I Ma! lYX8 (Event 1 ) and f o r the situation on 1 June 19x8 ( E i e n t I ! ) diurnal K1 wave are greater or equal to the effects of the semidiurnal S? wave. The intensification of the semidurnal ice drift is noticeahle in the area between Frans Josef Land and Spitsbergen. The velocities of the net diurnal ice drift is. however. relatively small and possibly directed northwards between Spitsbergen and Frans Josef Land. T h e main direction of the maxi- mum ice drift deviates from 8 to 30 degrees from the main direction of t h e maximum water vel- ocities in the region. Now let us discuss the correspondence between the calculated ice drift a n d t h e observed drift (Figs. 1 and 2 ) . We will then analyse the character of the ice drift and specify t h e ice and nieteoro- logical conditions. The tidal ice dynamics 205 The sign of the divergence changes from positive t o negative with a variable period from 4 t o 16 hours. T h e channels in the ice cover can exist only when the divergence is positive. If the divergence is negative, the channels will b e closed. Intensive freezing may prevent t h e channels from closing, but this is unlikely t o occur in May and June, the months when the satellite pictures where taken. It would be valuable t o analyse similar satellite pictures from t h e winter (freezing) season. Accordingly, performed simulations may at least qualitatively explain the formation of the regu- larly formed channels in t h e ice cover caused by grounded icebergs. O n 21 May (Fig. 1) the ice concentration was 9-10/10. T h e ice border was well-defined and the ice was in a compressive condition because of normal directed, on-ice winds. In this situation, apparently, there were no discernible wind- induced movements of the ice cover. T h e orien- tation of the most elliptical trajectory was parallel to the ice border. T h e average length of the major axis was 5.8 km and the minor axis about 3.9 km. The trajectories of the ice drift were unclosed with a small distance from the beginning to the end of the track. If we assume that the semidiurnal tidal icedrift prevailed in this region, then the average permanent current velocity must have been equal t o 4 c m / s and directed t o the west. This current may be related with the general anticyclonic circulation of t h e seawater around Spitsbergen. Fig. 8A and B show (a) observed trajectory, (b) calculated trajectory with only the tidal forces included in the model, and (c) cal- culated trajectory with tidal forces, the wind and permanent current included. T h e model cal- culations a r e carried out for two tidal periods. This explains why there are two loops in the model results (Fig. 8 A ( b ) , B(b), and B(c)) and not in the observations (Fig. 8 A ( a ) and B(a)). T h e trajectories a r e obtained by using current hourly values from the model calculations t o cal- culate the particle displacement. Nilsen e t al. (1990) employed a simular procedure, using cur- rent measurements averaged over a period of 30 minutes. Fig. 8A reveals that good correspondence between the model calculation and observations is obtained by using all tidal waves together with the wind and the permanent current influence. Modelled ice drift trajectories for 1 June are shown in Fig. 8 B(b) and (c). T h e wind and ice conditions a t this date differ from the event discussed above. T h e concentration of ice is about 7-Y/10 and the wind blows in a southwesterly direction, coinciding with the direction of the permanent current. T h e trajectories of the ice movements are therefore elorigated. T h e major axis is now about 15 k m , which corresponds well with the observed trajectories (Fig. 8 B(a)). The consequence of the joint action of tides, wind and permanent current creates the periodic formation of loops. T h e twice diurnal divergence and compression (Fig. 9) may explain why the tracks of ice movement live for only 12-13 hours. References Aagard. K.. Foldvik. A., G a m m e l s r ~ d , T . & Vinje, T . 1983: One-year records of current and bottom pressure in the strait between Nordaustlandet and Kvitoya, Svalhard. 198C-1981. Polar Research 1(2), 107-113. Aagard. K., Darnall. L . , Foldvik. A. 6t T ~ r r e s e n , T . 1985: Fram Strait current measurement5 1984-1985. Report no. 63. Dept. of Oceanography, University of Bergen. Gjevik, B. 1990: Model simulations of tidcs and shelf waves along the sbelvcs of the Norwegian-Greenland-Barents sea. I n Davies. A . M. (cd.): Modelling Marine Systems, ool. I CRC Press Inc. Gjevik, B. & Staume. T. 1989: Model simulations of the M and K tide in the Nordic Seas and the Arctic Ocean. Tellus 41A. 73-96. Kagan. B. A . 1968: Hydrodynamical tidal mouementc. in the sea. Hydrometeoizdat. 219 pp. (in Russian). Kheysin. D . E. & Ivchenko. B. 0. 1973: A numerical model of tidal ice drift with thc interaction between flocs. I z o . Arad. Sci. USSR: Atmosplteric and Oceanic Plfvsics 9, 42&429 (in Russian). Kowalik. Z . 1981: A study of the M2 tide in the ice-covered Arctic Ocean. Modelling. Identification and Control 2. 201- 223. Legenkov, A . P. 1968: On the definition of ice concentration. dispertion and compaction using tidal currenta. A A RI lssue 285, 215-222 (in Russian). Nilsen. J. H . , McClimans. T. A. & L0vis 1990: Rift drift in floe flow: ice-berg wakes in Arctic Sea ice. Continental Shelf Research l O ( 1 ) . 81-86. Polyakov, I. V. & Proshutinsky, A . Yu. 1988: Periods of the eigcnoscillations of sea level i n the Arctic Ocean. Mereor- ologia and Hvdrologia 11. 91-100 (in Russian). Rothrock, D . A . 1975: The mechanical behaviour of pack ice. A n n . Reu. of Earth and planetary Sci. 3. 317-342. Tee. K. T. 1976: Tide-induced residual current, a 2-D nonlinear numerical tidal model. Journal of Marine Research 34. 603- 628. Timokhov, L. A . & Kheysin, D. E. 1987: Dvnamics ofrhe sea ice. Hydrometoizdat. Leningrad. 271 pp. (in Russian). Zuhov. N . N. 1945: Arctic ice. Izd. Glavsevmorputi. Moscow. 350 pp. (imRussian).