Wind and melt driven circulation in a marginal sea ice edge frontal system: a numerical model

Continental Shelf Research, Vol. 1, No. 1, pp. 49 to 98, 1982. Printed in Great Britain.

0278~.343/82/010049-50 $03.00/0 :~ 1982 Pergamon Press Ltd.

Wind and melt driven circulation in a marginal sea ice edge frontal system: a numerical model* H. J. NIEBAUERt

(Received 4 September 1981; accepted 8 January 1982) A b s t r a e t - - A seasonal ice edge zone is a unique frontal system with an air-ice-sea interface. This paper is a report on the numerical results from a quasi-three dimensional,time dependent, non-linear numerical model of circulation at a continental shelf-seasonal ice edge zone. The purpose of the experiments is to model the hydrography and circulation, includingupwelling,baroclinic geostrophic flow, and inertial oscillations, at the ice edge with emphasis on examining the driving forces of wind and melting ice. It is suggested that the non-linear acceleration terms and vertical density diffusion terms are negligible and that the horizontal density diffusion terms are of secondary importance within the time and space scales of the experiments.The vertical eddy viscosity terms are important in a spin-up time scale and for Ekman transport and a bottom Ekman layer. The effects of the horizontal eddy viscosity terms are observable (a long-icejet is diffused away from the ice edge) by the end (72 h) of the model runs. Model results are compared with available oceanographic and meteorological data for verification. The observed and modeled features of melt water induced water column stability, frontal structure, and ice edge upwellingare briefly discussed relative to observed ice edge primary production. Because the model is relatively general in nature, it is readily applicable to other seasonal or marginal ice edge zones in either hemisphere.

INTRODUCTION HIGH latitude seas are often partially covered with sea ice (frozen seawater with thickness ca. meters) either fixed to land masses (fast ice) or floating unattached (pack ice). The sea ice edges are intensive oceanic frontal systems since there are large horizontal density gradients at the surface caused by the change in phase of water from liquid to solid. However, melting and freezing at ice edges generate additional density gradients in seawater. The gradients are both vertical and horizontal. Ice, edge frontal structure is also attributed to ice edge upwelling due to wind-driven Ekman transport (BUCKLEY et al., 1979; ALEXANDER and N1EBAUER. 1981). In these two studies, hydrographic structure, observed in the Atlantic and Bering Sea ice edge zones, respectively, is thought to be due to upwelling driven by winds associated with synoptic scale (ca. days) weather systems. This paper is a theoretical consideration of the wind and melt-water driven circulation and hydrographic structure at marginal sea ice edges through the use of a computer model. GAMMELSRI~D, MARK and ROED (1975) consider analytic linear, homogeneous, time dependent, and steady-state models of wind-driven upwelling near an ice edge. They find that. in the steady-state mode, the ice-covered region is similar to a coast. In the time-dependent * Institute of Marine Science, Contribution No. 446, University of Alaska, Fairbanks, AK 99701, U.S.A. ÷ Institute of Marine Science, University of Alaska, Fairbanks, AK 99701, U.S.A. 49

50

H . J . NIEBAUER

mode, friction (which is proportional to the along-ice geostrophic velocity) determines a time scale of 10 days for the onset of the upwelling process. CLAaKE (1978) considers an analytic linear model of quasi-geostrophic water motion near sea ice edges. The ocean is stratified (2 layers) with the sea ice thinner than the surface Ekman layer. He finds that the stationary ice sheet prevents the water beneath it from 'feeling' wind stress so that the boundary layer currents and upwelling are due to local forcing functions (i.e., the curl of the wind stress at the ice edge). He finds time and length scales for these phenomena to be in the order of one day and 10 km (the latter is the baroclinic Rossby radius of deformation). This study is an extension of the previous modeling efforts in that a quasi-three dimensional, time dependent, non-linear numerical model is used to simulate hydrography and circulation, including melting and upwelling, in a seasonal ice edge zone overlying a continental shelf. The model is multi-layered with separate equations for the advection and diffusion of salinity and temperature to allow more detail in examining the structure of the velocity and density fields in time and space. Inter-layer friction (vertical eddy viscosity) i~ included as well as horizontal eddy viscosity and diffusion, vertical diffusion, a timc dependent wind stress field, under-ice friction, baroclinic geostrophic flow, and inertial oscillations. The main purpose of the experiments is to examine the effects of the driving forces of wind and melting on the density and velocity fields. Model results are compared with available oceanographic and meteorological data for verification. The model, being relatively general in nature, is applicable to other seasonal or marginal ice zones in either hemisphere. THE M O D E L

The model is a modified version of a cross-sectional time-dependent finite difference numerical model developed by BENNETT (1973. 1974) to study wind-driven circulation in Lake Ontario. The model has also been used by NmSAUER (1980a) to study wind-driven circulation in a continental shelf-silled fjord coupled system. The variables of the model are as follows: X

Y Z t

u(x, z, t) v(x, z, t) w(x, z, t) f g p p z ~ ( x , z, t) "tz~ (x, z, t) Ax Az At /'(x, z, t)

coordinate normal to ice front coordinate parallel to ice front vertical coordinate time x-component of velocity (normal to ice front) y-component of velocity (parallel to ice front) z-component of velocity (vertical) Coriolis parameter gravitational acceleration density of water pressure

x-component of vertical shear stress y-component of vertical shear stress horizontal grid separation (2 km) vertical grid separation (7 m) time step (600 s) temperature (°C)

Wind and melt driven circulation

S(x, z, t) Nz(z, t) K:. r, K:. s Nx Kx. r, Kx, s

51

salinity (x 10 -3) vertical eddy viscosity vertical eddy diffusivity of heat and salt (1.0 and 5 . 0 c m 2 s L) horizontal eddy viscosity (106 cm 2 s -~) horizontal eddy diffusivity of heat and salt (104 and 105 cm 2 s

i).

The equations of the model are as follows: 3u 3u --+u--+w--Ùt 3x

Ou

Ov Ov --+u--+W 3t 3x

3v

3T --

3t

bS --+ 3t

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+ Kxl.--

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(4)

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3z

= 0

(5)

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3z

9g

p = o(S, T).

(6)

(7)

Equation (7) represents an equation for density taken from Cox, MCCARTNEY and CULKIN ( 1970). In its present form, the model includes non-linear terms, friction, stratification, and topography but assumes no along-ice propagation or advection. The latter implies that the along-ice direction is modeled as infinitely long. Parameters (currents, salinity, etc.) can vary in time but not in space along this axis so that, for example, propagating edge or shelf waves are filtered out. Tilting of the sea surface and associated transport are allowed in the along-ice direction. The tilt and transport can vary in time but not in space, hence the term 'half a dimension'; i.e., because u, v, and p are independent of y and because of the hydrostatic assumption, the along-ice pressure gradient, Op/Oy, is a function of time only and is barotropic. In the numerical scheme all but the diffusion terms are calculated by a 'leap frog' centered time-difference method essentially the same as that of BRYAN and Cox (1968). The diffusion terms are forward differenced in time while the spatial derivations are evaluated by centered differences. This scheme gives conservation of mass, momentum, and energy as used with the flux form of the equations. The pressure gradient terms in equations (l) and (2) are computed diagnostically from the hydrostatic equation and mass balance constraints. [See BENNEI-r (1973) Appendix B for further details.1 The no-slip condition is applied to the bottom and closed end of the basin, while at the surface and bottom the vertical velocity is zero. Heat and salt fluxes are specified at the boundaries with temperature and salinity predicted one-half grid space interior. Wind stress

52

H . J . NIEBAUER

(xz.~, xzy at z = O) is specified at the surface, while below the surface vertical shear stresses are computed using: ~U z,~ = p N : ( z ,

t) • -~z

"~:, -

t) • - ~3z

(8,~

21' pN,(z,

One vertical grid space above the bottom of the basin, shear stresses are computed

(U!

from:

~:~--: p • 0.002 lu: ~ v21 ~. u

~ 10i

z:~-~ p • 0 . 0 0 2 l U 2 + ~,'21~. t'.

(11~

The ice cover is parameterized (i.e., not thermodynamic) as a non-moving rigid lid with wind stress identically zero over the ice. The no-slip condition is not applied at the under-ice surface as this computationally requires the first non-zero velocity grid point to be 10.5 m beneath the ice, which is physically unrealistic. An under-ice boundary friction coupling is applied using equations (10) and (11) to generate shear stresses at the first grid point under the ice. The hydrostatic, Boussinesq, and rigid lid approximations are invoked. The first two approximations are straightforward, but the third requires some justification. The rigid lid assumption eliminates surface waves and tides which increases the efficiency of the mcxtcl markedly since the largest time step consistent with computational stability that can be used in this case is now: (Az) At~ ..... 2A,

4h

rather than the C o u r a n t - F r e i d r i c k s - L e w y stability criterion Ax At ~< ~ h

60 s,

where h is the depth of the basin. A time step of 4 h is probably too large here as it is the same order o f magnitude as the time scale associated with Coriolis-type dynamics ( f - ' to 2nf ' or approximately 2 to 12 h in this case). Solutions to the equations are generated on a grid overlayed on a rectangular basin, 66 km wide by 120 m deep and infinitely long (e.g., Fig. 1). The iced-over end of the basin is closed while the ocean end of the shelf is open with a radiative boundary condition. The initial condi tions are u = v = w = 0 at t = 0. The water is isothermal with only a salinity gradient to affect density. This is a reasonable simplifying assumption li.e., p = p (S)I to make in high latitude cold water situations. The surface vertical eddy viscosity value of 100 cm 2 s -~ is a reasonable estimate for a wind stress of 1 dyn cm 2. The vertical eddy viscosity decreases with depth to 10 cm" s ' at 80 m as a function of Z 2. Below 80 m, N : = 10 cm z s '. The vertical eddy viscosity is also set equal to 10 cm 2 s ' when the wind stress goes to zero. This vertical distribution is arbitrary yet reasonable. Varying the N~ profile primarily varies the Ekman depth which is not critical to these experiments but does dictate a spin-up time scale as will be shown. The relatively low

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Fig. I. Vertical and horizontal circulation perpendicular (a, d, g) and horizontal circulation parallel (b, e, h) to ice sheet, and associated salinity structure (c, f, i) for a 1.0 dyn cm -2 wind stress applied to open water next to the ice edge. Wind is parallel to ice edge. Circulation and salinity photographs of data are shown 12 h (a, b, c) and 36 h (d, e, 0 after wind stress is applied and 36 h after the wind stress is removed (g, h, i). (Note speed scale changes in b, e, h.)

values of the vertical and horizontal eddy diffusivities were chosen to illuminate the advective character of the circulation and to smooth the solutions. The horizontal eddy viscosity (106 cm 2 s -l) is in the range of those used in the modeling of coastal upwelling dynamics by HAMILTON and RATTRAY(1978) that will allow the formation of a baroclinic geostrophic ice edge jet. EXPERIMENTS

The experiments are performed in two basic groups that differ only in initial hydrographic conditions. In the first group the density (salinity) initial conditions are a linear increase with depth with no horizontal density gradients. For the second set of experiments there is lower salinity melt water structure in the vicinity of the ice with associated increased vertical and horizontal density gradients. Estimates of the initial vertical density (salinity) gradient are taken from ALEXANDERand NIEBAUER(1981) for the eastern Bering Sea shelf. The two groups of experiments are similar in that a simple time series of wind stress derived from observations of ALEXANDER and NIEBAUER (1981) is used to model a passing storm to force the model. That is, a uniform wind stress of 1 dyn cm-2 is applied for 36 h and then

58

H.J. NIEBAUER

turned off for 36 h. Within each of the two basic groups, experiments are performed with this wind directed along, normal to, and at a 45 ° angle to the ice edge.

Experiments without melting ice Wind parallel to ice edge. Figure 1 shows the circulation and salinity structure after 12 and 36 h of being driven by a I dyn cm 2 model wind stress (~8 m s -~ or 16 kn), and 36 h after the wind is turned off. The wind flowing parallel to the ice edge with the ice to the left is straightforward with maximum off-ice and along-ice velocities concentrated at the surface near the ice. The circulation perpendicular to the ice edge at 12 h is concentrated within ---30 m of the surface with strong upweUing at the ice edge (Fig. la). There is a hint of flo~ along the bottom. By 36 h (Fig. ld) the circulation involves the cross-section seaward of the ice edge and the layer of no horizontal flow has deepened to ,-,25 m. Flow in a bottom Ekman layer is now relatively intense. At 36 h the wind is turned off and the system is allowed to collapse. By 72 h after the start of the experiment (36 h with no wind) the flow has reversed (Fig. lg) but the bottom Ekman layer still persists even when the flow directly above it is in the opposite direction. Maximum ice edge upweUing is shown in the salinity structure at 36 h with the 31.55 × 1 0 isohaline breaking the surface (Fig. If). By 36 h after the wind is turned off (Fig. li). the domed structure persists but has spread laterally and sunk slightly. The along-ice flows at 12 and 36 h (Figs lb, e) are similar, with relatively strong surface wind-driven flow seaward of the ice edge, a surface jet at the ice edge, a slight surface counter current just iceward of the ice edge, and zero flow under the ice. The ice edge jet and under-ice counter flow are attributed to geostrophic balance of the horizontal pressure gradient generated by the domed (upwelled) salinity structure. An interesting feature of the along-ice circulation is the sharply reduced along-ice float at about 10 m below the surface (Figs ib, e). This is attributed to Coriolis force turning the strong off-ice flow (Figs la, d from 0 to 10 m) to the right against the wind-driven along-ice flow. Thus, at the surface, the wind stress dominates the Coriolis force, while just below the surface the effect of Coriolis force becomes more important. Below the Ekman layer the Coriolis force associated with the on-ice flow (Fig. ld) and the wind-driven flow are in the same direction so that by 36 h the deep along-ice flow is about 10 cm s J. The sharply reduced along-ice flow at 10-m depth at 12 and 36 h is replaced by a broader, deeper, and smaller magnitude reduced flow 36 h after the wind stops (Fig. lh). The less intense along-ice flow is associated with the more widespread, reduced flow in Fig. lg. The slightly stronger flow at the bottom (Fig. I h) is due to the bottom Ekman layer augmenting the along-ice flow. The 72-h time series of depth-dependent along-ice velocity structure from grid points m open water 6 km away from the ice (Fig. 2a), at the ice edge (Fig. 2b), and 4 km under the ice (Fig. 2c) are used to illustrate the time dependence of the circulation. The most striking featurc is the change in phase and sometimes direction of the surface currents and those at depth in undergoing inertial oscillation. The change in phase with depth is related to the continuity constraint perpendicular to the ice edge. The off-ice surface Ekman flow requires on-ice flow at depth and vice versa. The cross-ice continuity and the vertical eddy viscosity (which con trols the Ekman depth) separate the water column into a two-layer system, which oscillates at the inertial period with upper and lower layers 180 ° out of phase. Strong wind-driven surface flow occurs in open water at 6 km from the ice edge (Fig. 2a). All velocities are positive here (i.e., flowing parallel to the ice edge with the ice to the left). At the ice edge (Fig. 2b) an initially negative surface flow is associated with the tilting upwelled salinity (density) surfaces.

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Later, after the wind stops, positive flow is illustrated apparently associated with the strong along-ice flow as the upwelling collapses. Under the ice, (Fig. 2c) there is reduced surface flow due to isolation from the wind and under-ice friction. The surface current is negative initially. due to the influence of the tilting isohalines. After the wind stops, the flow oscillates at the inertial period about zero. The magnitude of the bottom flow gradually becomes stronger positively due to the effect of the bottom Ekman layer. An 18-h long time series of 3-hourly observations of the ice edge circulation, from 36 to 51 h into the experiment (Fig. 3), shows the inertial oscillations corresponding to those tn Fig. 2. It is obvious that, just as in the collection and analysis of data in the field, sampling the numerical model data fields must be done carefully to avoid aliasing. For example, the flow fields at 36 and 39 h, only 3 h apart, are different. A related point is that the impulse starting and stopping of the forcing function (wind) excites inertial oscillations which then tend to die out.

Wind perpendicular to ice edge. The case for a 1 dyn cm -2 wind blowing off the ice sheet (Fig. 4) is not as straightforward as for the wind blowing parallel to the ice. For example, as long as the wind is blowing, the cross-section flow is concentrated within the upper 25 to 30 m (Figs 4a, d). In the previous case, by 36 h, almost the entire cross-section was in motion (Fig. l d). With the wind blowing office, the circulation is closed in the upper layers with upweiling at the ice edge. However, the upweUing is not as intense nor as deep as in the along-ice wind case. This is further illustrated by the salinity cross-sections (Figs 4c, f, i) which show that the

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upward advection of salt is not as intense, nor does it come from as deep, nor is the domed structure as wide as that shown in Fig. l from the previous experiment. The reasons for the reduced upwelling are explained below. There is no bottom Ekman layer as in the previous experiment. The along-ice flow (Figs 4b, e, h) is also markedly different from that of the previous case (Fig. l). The surface along-ice flow for the first 36 h is in the opposite direction of the previous case, to the right of the off-ice wind, with the ice to the right of the water flow. The flow, which is concentrated in the upper 10 m and is approximately the same magnitude as in the previous experiment, is surface wind-driven Ekman transport. Coriolis force then generates an on-ice surface transport associated with the along-ice flow that opposes, but is less than the winddriven off-ice transport. Thus, the off-ice surface transport is less than that of the previous experiment (Figs la, d), hence less upwelling. (In the along-ice experiment the two off-ice transports are in the same direction.) Notice also that the net off-ice transport at the surface is less than the on-ice flow just beneath (Figs 4a,d). An along-ice current in the opposite direction to the surface flow, for the first 36 h, at --,10 to 30 m (Figs 4b, e) is apparently being driven by the effect of Coriolis force on the relatively strong on-ice flow at 10 to 30 m (Figs 4a, d). This counter current has lessened in magnitude and diffused downward by 36 h (Fig. 4e). There is a hint of a weak jet parallel to the ice edge associated with the weak horizontal salinity gradient generated by the upwelling. As before, at 36 h into the experiment the wind is turned off and the upweUing is allowed to collapse. Now nearly the entire water column seaward of the ice edge is in motion. However,

72

H . J . NIEBAUER

if only the single photograph (Figs 4g, h, i) is considered, an aliased view of the circulation is presented. To illustrate this point for the off-ice wind case, a time series of 3-hourly photographs of the flow field is presented (Fig. 5) for 0 to 15 h after the wind stops (36 to 51 h into the experiment). The sections perpendicular to the ice are not shown because they are similar to Fig. 3b except for the absence of a bottom Ekman layer. As in the previous case (Fig. 3) inertial oscillations are apparent with surface flow ~180 ° out of phase with flow at depth. The flow patterns are more exaggerated due to the smaller magnitude currents on the same size plot compared with Fig. 3 (e.g., the ice edge jet in Fig. 5 at 45 h). Wind 45 ° to ice edge. The final experiment in the series is a combination of the previous two with a 1 dyn cm-2 wind blowing along and across the ice (to give a 1.4 dyn cm-2 wind blowing 45 ° off the ice edge). It is not too surprising then that the velocity fields are com posites of the previous experiments. Most of the cross-sectional flow at 12 h (Fig. 6a) is con centrated in the upper 30 m as with the off-ice wind (Figs 4a, b) but maximum velocities are in the surface layer as with the along-ice wind (Figs la, b). The stronger off-ice surface flow is due to the combination of an off-ice component of the wind plus an off-ice component of the Ekman transport due to along-ice wind. By 36 h, the entire cross-section is in motion with a bottom Ekman layer (Fig. 6d) as with the along-ice wind (Fig ld). By 72 h (Fig. 6g) the circulation is dominated by inertial oscillations in the cross-ice section although a bottom Ekman layer persists. The along-ice velocity field (Figs 6b, e, h) is also a composite of the previous fields. The surface velocity reduction is similar to the off-ice wind case except that the surface flow at ~ ) to 25 km is near zero at 12 h (Fig. 6b) and a positive 2 to 5 cm s -m at 36 h. The slight decrease in speed at ~10 m, the ice edge jet, and under-ice counter jet are similar to the along-ice experiment as is the speed increase at depths greater than 20 to 30 m. By 72 h, the along-ice flow bears more resemblance to the first experiment (Fig. lh) than to the second (Fig. 4h). This is due to the influence of the stronger, wind-driven along-ice flow and to the stronger horizontal salinity gradients normal to the ice (compare, e.g., Fig. 6i with Fig. 4i) supporting stronger along-ice geostrophic flow. Finally, ice edge upwelling is strongest for the wind blowing at a 45 ° angle with the ice edge (cf. Figs 1, 4, 6). This result agrees qualitatively with that of HIDAKA(1954) and O'BRIEN and HURLBURT(1972), who found the optimum angle between wind and a solid coast to be 5 to 30 ° offshore to generate maximum coastal upwelling. An additional comparison of the three experiments is presented in 72 h progressive vector diagrams (Fig. 7) from a point 2 km off the ice in open water. The flow is about 45 o to the right of the wind vector for the first 36 h of all three experiments. Evidence of inertial oscillations are present in all three data sets. After the wind vanishes, the flow is generally along-ice. with ice to the left, driven by the geostrophic balance between the cross-ice salinity gradient and Coriolis force. In the first and third experiments the along-ice flow is strong enough for the cross-ice inertial oscillations to be superimposed on the strong along-ice flow. In the second experiment, the along and off-ice velocities are similar so that nearly complete ine~rtialcircles occur with some along-ice drift. The point is that off-ice Ekman transport is a~f~ore effective mechanism for converting the kinetic energy of wind into potential energy for drawing denser water higher in the water column than is off-ice wind stress. When the wind ceases in alongice wind stress, the increased potential energy is converted back into kinetic energy via the geostrophic balance. Thus, any episode of ice edge upwelling (or downwelling) with a component of the wind parallel to the ice edge will produce stronger and more persistent along-ice flow than will an equivalent wind perpendicular to the ice edge. This is consistent with

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Wind and melt driven circulation

81

CSANADe'S (1981) suggestion that offshore (off-ice) wind does cause upwelling but that the flow pattern so generated is not in equilibrium without the wind acting. Thus, at least in theory, upwelling driven by longshore (along-ice) winds is longer-lived than is upwelling driven by offshore (office) winds.

Experiments with melting ice Figure 8 shows velocity and salinity initial condition fields for the second series of experiments. These fields were generated by melting ice parametrically (i.e., not thermodynamically) to lower the surface salinity from 31.5 x 10 -3 in open water to 30.9 x 10 -3 under the ice. This sets up ice edge frontal structure in the salinity field. The weak velocity structure associated with the frontal system is helical in nature (Figs 8a, b). Given these initial conditions, the wind conditions used in the previous experiments are repeated. Basically, there are few differences in the velocity fields in comparing experiments 1 to 3 (Figs 1 to 6) with the melted ice experiments and so the figures are not shown. The sole exception is a slightly intensified along-ice 'jet' associated with ice salinity front due to the melting. The magnitude of the flow is not great due to the shallowness of the frontal feature in the salinity field (e.g., Fig. 8). However, there are obvious differences in the salinity fields (Fig. 9) due to the lower salinity melt water at and under the ice. The lower salinity surface water is advected office in the upwelling process. The higher salinity water beneath it is upweiled at the ice edge and intercepts this 'lid' of less saline water (Fig. 9). The ice edge salinity upwelling structure is thus capped to some degree. DISCUSSION

A consideration of time and space scales and non-dimensional numbers is relevant to a discussion of the relative importance of the various terms in the equations of the numerical model. For example, the Rossby number is a non-dimensional ratio of non-linear terms to the Coriolis term, Ro = u f -~ L -l, w h e r e f i s the Coriolis parameter and u and L are speed and length scales. When Ro is less than unity, the non-linear accelerations (the second and third terms in equations 1 and 2) can be neglected. Calculations of Ro from the model results here are generally less than 0.1. Therefore, the non-linear accelerations are probably not required to understand the dynamics of the wind and melt driven ice edge phenomena presented here. The same is probably true of the second and third terms in equations (3) and (4) except in the presence of strong upwelling as occurs near the ice edge where the w 3s/3z term cannot be neglected. The shortest relevant time scale i s f -~ (,-,2.2 h) over which Ekman transport nearly reaches its mean value. This is usually short compared with the phenomena of interest, although that may not be true in water more shallow than the 120 m considered here. More appropriate to this study is a spin-up time scale E ~ f -~, where Ev = vertical Ekman number = N j - ~ h '2. This gives an estimate of the length of time it takes for horizontal momentum to (eddy) diffuse to the bottom. Alternatively, for model forcing times in the order of or greater than spin-up times, as in the present case, a bottom Ekman layer will form (provided a bottom no-slip or friction condition is properly specified) and its effect must be considered. In the present study, Nz varies from 100 cm 2 s -~ at the surface to 10 cm 2 s -~ at depth which gives estimates of 0.8 to 2.4 days. These estimates bracket the 1.5-day period of wind forcing used in the model. Consequently, Figs 1, 3, and 6 show a pronounced and persistent bottom Ekman layer. Field

82

H.J. NIEBAUER

data are not yet available to verify this bottom Ekman layer. However, the calculations do suggest that the fifth terms in equations (1) and (2) should be retained in this theory. The terms must, of course, be retained for the classical Ekman transport type upweiling. Associated with the spin-up time scale is a length scale, the Rossby radius of deformation, hNf -1, where N = (gl)p/~zp-r) ~, about 7 km in this case. In the model results, the majority of the variation in currents, both along and cross ice, and hydrography, due both to melting and upweiling, does occur within a Rossby radius of deformation of the ice edge. Time and space scales for which horizontal diffusion becomes important are h 2N~-2K;t and hK~N~. The time scale estimate is ~55 days which suggests that horizontal diffusion of salinity (density) is not important within the time frame of these experiments. However, for N: = 10 and 100 cm 2 s -a, the length scales are ~ 1 2 - 4 km suggesting that horizontal diffusion may be important as these estimates are similar to the Rossby radius of deformation. A Prandtl number, o = N~Kf 1, of 10 has been assumed for these experiments. If we can assume that the ratio of kinematic viscosity to kinematic diffusion is approximately the same as eddy viscosity to eddy diffusion, then this calculated value falls between the 7 and 13 range quoted for seawater (FOFONOFF, 1962). The point is that if horizontal diffusion of density is important, then both horizontal fluxes of momentum and density are important at these scales, but because of the assumed Prandtl number, Nx is an order of magnitude greater than Ks. Thus, the diffusion scales of the ice edge jet are dominated by N~. HAMILTON and RAvrxAY (1978) point out that high values of N~ cause a jet to be diffused away from a coast (ice edge) even though the isopycnals are still upwarped at the coast (ice edge). The horizontal o.

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Wind and melt driven circulation

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eddy viscosity of 106 c m 2 s-~ was chosen here to allow the initial formation of a baroclinic geostrophic ice edge jet yet provide stability to the solutions. However, note that by 3 days into the experiment, or 36 h after the wind ceases, the ice edge jet which initially formed (Figs I b. e, 6b, e) has diffused away (Figs lh, 6h) even though there is still a relatively strong horizontal salinity (density) gradient (Figs li, 6i). There is as yet no verifying evidence, either for or against an ice edge jet although, as will be shown later, there is evidence of ice edge frontal structure that may give rise to a jet. It is clear that more verifying data must be collected before the model can be fine tuned. Much of the discussion of the experiments in the preceding section centered about inertial oscillations (Figs 2, 3, 5), especially after the wind died (Figs 3, 5). These figures may give the impression that inertial oscillations are the dominant motion. However, Fig. 7 brings the relative importance of geostrophic, Ekman, and inertial oscillations into the proper perspective. In all experiments except the last 36 h of the wind blowing directly off-ice, inertial oscillations play a small role compared with geostrophic and wind-driven Ekman motion. Inertial oscilla tions are only dominant after the wind stops where there is almost no horizontal pressure gradient at the ice edge (compare, e.g., Figs li and 5i with 4i). In this case (i.e., Fig. 40, the local acceleration terms are almost entirely balanced by the Coriolis terms (first and last terms in equations 1 and 2) with some slight along-ice drift.

89

Wind and melt driven circulation

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H . J . NIEBAUER

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Wind and melt driven circulation

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Fig. 10. Temperature (a), saSnity (b), density (c), chlorophyll a (d), and nitrate (e) cross sections taken from the eastern Bering Sea showing the relationships among ice edge melting, ice edge upwelling, and concentrations of chlorophyll a and nutrients for 1975. (After ALEXAI~DER and NIEBAUEIL 1981.)

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M A R C H • A P R I L 1976

93

W i n d a n d melt driven c i r c u l a t i o n

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MARCH -APRIL 1976 1976.

200

94

H . J . NIEBAUER

The inertial oscillations are probably a realistic phenomenon at the ice edge but their contribution to the total flow field is often almost non-existent because of relatively strong mean flow and/or tidal flow. For example, KINDER and SCHUMACHER(198 l) analyzed direct current measurements over the southeastern Bering Sea shelf and came to the conclusion that over the shelf most of the horizontal kinetic energy was tidal, varying from 90% of the total in the coastal shelf region to 60% on the outer shelf. This broad, relatively shallow shelf is unique in that the mean flow for a large portion of the region is not energetic at 0 to 29% of the relative energy. However, inertial frequency energy makes up only 0 to 1% of the total over all the shelf regimes over all seasons. Some (qualitative) verification of the hydrographic model data is possible due to a few collected hydrographic sections through the marginal ice zones in the Bering Sea. Examples of the phenomena of increased vertical density gradients due to less dense ice melt water at and under the ice edge in the upper 30 m and the associated frontal structure within 10 km of the ice edge are shown in Figs 10a to c and 1 la to c. The model hydrographic structure (Fig. 9) is in at least qualitative agreement with these cross-sections. MARSHALL(1957), McRoY and GOERING (1974), and ALEXANDER and COONEV (1978) have hypothesized that the observed high spring primary productivity near the retreating Bering Sea ice edge is due in part to increased water column stability resulting from the low salinity melt water. ALEXANDERand NIEaAUER (1981) also find that the spring ice edge bloom is similar to a classic spring bloom, but is intensified in time and space by the influence of the melting ice edge on the physical structure of the water column (i.e., increased vertical stability) and the marked change in light regime as the ice breaks up. Alexander and Niebauer also suggest the intense phytoplankton bloom during the ice-retreat period accounts for a significant proportion of the annual primary productivity over the Bering Sea shelf. This production probably exceeds the water column demand for particulates during the bloom, and a large amount of the material falls to the sea bed, as in most shelf systems with seasonal pulses in primary production (WALSH el al., 1978). However, the system differs, for example, from the ice-free New York Bight (WALSH et aL, 1978) in that the sea ice attenuates mixing and wind stirring, thereby increasing the effect of water column stability in enhancing the phytoplankton bloom, but probably limiting nutrient replenishment from below. While increased stratification at ice edges and its implications have been reported and discussed, less is known about ice edge upwelling. BUCKLEr et al. (1979) have observed winddriven upwelling along the edge of the ice pack in the Arctic Ocean north of Spitsbergen. They suggest that ice edge upwelling may be important in bottom water formation, in determining the world's climate, and in determining biological productivity in ice edge zones (ice edge upwelling is probably not important to bottom water formation in the Bering Sea as no bottom water is formed in the North Pacific-Bering Sea). ALEXANDERand NIEBAUER(1981) have reported multiple occurrences of wind-driven ice edge upwelling in the Bering Sea (Figs i0 and l l). They hypothesize that the surfacing of the isopleths (especially salinity and density) that forms frontal structure seaward of the ice edge is due, at least in part, to melting ice, but is also due to surface divergence and upwelling at the ice edge caused by wind-driven off-ice Ekman transport. They further suggest that the hydrographic structure farther off-ice (i.e., doming of the isopleths from the surface to 30 to 80 m ,,~ 25 km seaward of the ice, and still farther off-ice, the decrease in water density with distance offshore) support ice edge upwelling. There is a qualitative agreement between the hypothesized wind-driven upwelling in the vicinity of Stas 27 to 30 in Fig. 10, Stas 194 to 200 in Fig. 11, and the model results in Fig. 9. The upwelling may increase the supply of nutrients to the ice edge zone resulting in an

Wind and melt driven circulation

95

increase in primary production. Local maxima in chlorophyll a concentrations are shown (Fig. 10d) associated with the denser upwelling water (Fig. 10c) in the order of 25 to 50 km off the ice edge. While similarities exist between the model results and the hydrographic data, there are some problems and differences. The model assumption that is most difficult to defend in the experiments is a stationary ice cover. The ice modeled here represents the thin (compared to the Ekman depth) marginal ice zone that seasonally covers a shelf. However, the seasonal ice cover on continental shelves is often mobile. For example, M c N u r r (1981) has shown that the pack ice over large portions of the eastern Bering Sea shelf can be advected at speeds up to at least 1 kn (-,-50 cm s-~). This is five times greater than the water speeds generated in the modeling experiments. Ice traveling this fast can generate surface shear stress magnitudes several times those associated with the model winds because ice-sea shear stress coupling is at least an order of magnitude greater than the air-sea coupling (e.g., McPHEE, 1975). For example, ice moving at 0.34 kn (17 cm s -~) generates about 1 dyn cm 2 of stress which is approximately equivalent to that generated by 16 kn (800 cm s-~) of wind. This suggests that wind-driven ice may, at times, be important in driving circulation at an ice edge. This model, at present, does not simulate this situation. However, the ice--water stress vectors are approximately in the same direction as the wind-water stress vectors so that, at least qualitatively, the modeled ice edge upwelling hydrographic structure and circulation are probably correct. In addition, under-ice shear stresses are computed according to equations (10) and (I 1). MCPHEE (1975) suggests drag coefficients (0.002 in equations 10 and 11) should be 0.0034 for a typical ice-sea interface. For the under-ice speeds generated in this study ( ~ I cm s-~), the stress magnitudes are in the order of 10 -3 dyn cm 2--three orders of magnitude less than the wind stress assumed for this study. A related point is that the baroclinic radius of deformation is the horizontal (off-ice) length scale for ice edge upwelling. However, wind-driven ice may over-run or be blown away from the ice edge upwelling structure and distort the space relationships between the ice and water column features. BUCKLEY et al. (1979) observed that the ice edge in the North Atlantic around Spitsbergen moved several baroclinic radii of deformation in a few days, while NIEBAUER (l 980b) reports significant movement of the Bering Sea ice edge on similar time scales. This may help explain why BUCKLEY et al. (1979) and ALEXANDER and NIEBAUER (198 i) find that calculated baroclinic radii of deformation underestimate the width of ice edge upwelling regions in their respective data. However, the maximum calculated baroclinic radius for the model results is in the order of 7 km. Figure 9 shows that the spatial relationship between the model ice edge and upwelling structure is represented by this length scale, providing the ice edge is held fixed in time and space. Upwelling circulation and hydrographic structure at an ice edge can extend well under the ice as opposed to being constrained by a solid coast. To quantitatively analyze these differences the increase in potential energy was calculated for experiments with identical wind magnitude and duration and identical hydrographic initial conditions. The increase in potential energy was identical in the ice edge and solid coast upwelling experiments for the wind blowing at 45 ° to the ice edge or solid coast. However, Table l shows that modeled upwelling along a solid coast is nearly twice as efficient in bringing more saline (dense) water to the surface as the similar (identical wind stress) case for an ice edge. This result is similar to that of CLARKE (1978). Thus, the hydrographic structure at the ice edge was approximately twice as wide but half as high as for the solid coast. As the wind shifts farther off-ice (Table 1), the difference becomes more pronounced. Thus, given identical wind vector, ice edge upwelling

96

ft. J. NIEBAUER

appears to be half as effective in bringing nutrient-rich water into the photic zone as along a solid coast. This may be important in places like the Bering Sea shelf where the more nutrient rich Bering Sea source water that is warmer and more saline then the shelf water is found at depths greater than or equal to ~90 m (compare Figs 10 and 11). The less effective ice edge upwelling may not be able to draw this water high enough in the water column to aid the primary production, given the observed duration of wind. A final observation is that the ice edge upweUing phenomena reported here, in BUCKLEYe/ al. (1979) and ALEXANDER and NIEBAUER (1981), are probably different in terms of time scales than is the seasonal upweUing in the eastern boundary regions of the world's ocean although the physics is similar. In the latter case, the driving force is longshore wind associated with the permanent, though seasonally varying, large-scale atmospheric gyres or high pressure systems such as the North Pacific High. The upwelling process is modified by individual storms, but the wind, when integrated over time, drives coastal upwelling with time scales in the order of months. For the ice edge upwelling the driving force is also wind, but wind associated with the passage of synoptic time-scale storm systems. Moreover, at least for the Bering Sea, there is no large-scale pressure system generating winds conductive to upwelling. The storms seem to pass right through the ice edge so that direction frequency plots (BROWER et al., 1977) show no preferred wind direction, hence no long-term ice edge upweiling. More work is needed to discern whether the winds associated with these passing storms occur often enough for enhanced primary production due to ice edge upwelling to be important. SUMMARY AND C O N C L U S I O N S

Seasonal ice edge zones are unique marine environments in which at least three physical water column structural features (melt water induced water column stability, frontal structure. and ice edge upwelling) often associated with high oceanic primary production can occur simultaneously. In this paper a quasi-three dimensional, time dependent, non-linear numerical model is used to simulate these hydrographic and circulation features in a seasonal ice edge zone overlying a continental shelf. It is suggested that the non-linear acceleration terms and the vertical density diffusion terms are negligible while the horizontal density terms are of secondary importance within the time and space scales of the experiments. The vertical eddy viscosity terms are important in a spin-up time scale and for Ekman transport and a bottom Ekman layer. The effects of the horizontal eddy viscosity terms are observable (a long-ice jet is diffused away from the ice edge) by the end (72 h) of the model runs. The ice cover is parameterized as a non-moving rigid lid which may be the source of some errors in the study. The purpose of the study is to examine the driving forces of wind and melting ice.

Table I.

Surface salinity rise measured at a solid boundary after 36 h o f modeled upwelling driven by a 1.0 dyn cm-2 wind

Solid boundary Angle of wind to solid boundary Maximum rise in surface salinity × 10 -3) at solid boundary

Ice

Ice

Ice

Coast

0° (Parallel) 0.06

45 °

90 ° (Perpendicular) 0.05

45 °

0.08

O. 14

Wind and melt driven circulation

97

The results of the modeling are presented in two basic groups of experiments; one group with melting ice and one group without. The experiments are conducted with wind stress applied along, across, and at 45 o to the ice edge for 36 h. The wind is always conducive to upwelling with the ice either to the left of the wind or the wind blowing off the ice. After 36 h the wind stress is removed and the system is allowed to relax for an additional 36 h. With the wind parallel to the ice, maximum off-ice and along-ice velocities are concentrated at the surface near the ice with upwelling at the ice edge. This upwelling is not as effective as that constrained by a solid coast because the circulation can extend well under the ice. There is relatively strong surface flow parallel to the ice seaward of the ice edge, a surface jet at the ice edge, a slight counter current just iceward of the ice edge, and zero flow under the ice. There is also sharply reduced along-ice flow just beneath the surface in open water which is attributed to the influence of Coriolis force on the off-ice Ekman transport. A relatively strong and persistent bottom Ekman flow also forms. The flow patterns are not as straightforward for the wind perpendicular to the ice edge. The surface wind-driven along-ice flow is in the opposite direction of the previous experiment, to the right of the off-ice wind (i.e., an Ekman transport), with the ice to the right of the water flow. This flow, in turn, retards the off-ice surface transport due to Coriolis force turning the along-ice flow to the right, toward the ice edge. Thus, the ice edge upwelling is not as strong as in the previous case. The reduced upwelling results in reduced horizontal cross-ice pressure gradients which lead to reduced along-ice flow via the geostrophic balance. No bottom Ekman layer is formed in this experiment. A third set of experiments are conducted with the wind at a 45 ° angle off the ice edge. The flow patterns are a combination of the previous two experiments with the upwelling the strongest of all three experiments. The wind-driven experiments are repeated with the addition of ice edge frontal structure initial conditions generated by melt water. There are few differences in any of the flow fields when compared with the previous experiments, but there are obvious differences in the salinity fields. The lower salinity surface water is advected off-ice in the upwelling process and acts like a lid to the higher salinity water being upwelled from below. The model data are compared with available ice edge hydrographic cross-sections and at least qualitative agreement is found in the physical structural features of melt water induced water column stability, ice edge frontal structure, and wind-driven ice edge upwelling. These phenomenon are discussed relative to their role in increasing ice edge primary production.

Acknowledgements- -1 wish to thank VERA ALFXANDER and JAMES J. O'BRIEN for their contribution to this paper. The two anonymous reviewers' comments greatly improved the manuscript. This research was supported by the National Science Foundation, Divisions of Polar Programs, Grant DPP 76-23340 A02 (PROBES), and Ocean Sciences. Grant O C E 80-24058, and by the State of Alaska through the Institute of Marine Science, University of Alaska, Fairbanks. This paper is dedicated to Dr. WAt,TI-:R O. DI~'ING. REFERENCES AL.bXANDER V. and T. CO()NEY (1978) Bering Sea ice edge ecosystem study: nutrient cycling and organic matter transfer. In: Annual Reports, Environmental Assessment of the Alaskan Continental Shelf (OCS). At,V;XANDER V. and H.J. NIEBAUER (1981) Oceanography of the Eastern Bering Sea Ice Edge Zone in Spring. Limnolog3' and Oceanography, 26, 1111 - I 125. BEN~E'rl J. R. (1973) On the dynamics of wind-driven lake currents. Ph.D. Thesis, University of Wisconsin, Madison, 85 pp.

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