It is known that salinity anomaly under a polynya reaches and remains an equilibrium value S* after termination of its initial increase associated with brine rejection at the surface. In this paper, we investigate effect of along-shore (downwelling-favorable) wind on the equilibrium salinity anomaly by idealized numerical calculations and scale-based estimates. Numerical calculations showed that high saline water beneath polynya is advected downstream by wind-driven circulations over the shelf besides baroclinically developed eddies, which consequently induces a decrease in S* beneath polynya. The downwelling-favorable wind generates an offshore overturning flow through lower layers, referred to as Ekman Compensation Flow (ECF), which causes a great offshore salinity flux, as well as an along-shore current. We also constructed an equation for estimation of S* from the viewpoint of salinity budget over the polynya region, in which lateral salinity fluxes caused by ECF, along-shore wind-driven current and baroclinic eddies, are scaled. The solution S* was also verified by a series of numerical calculations. Furthermore, we investigated the effects of along-shore wind on dense water generation beneath the Okhotsk coastal polynyas. We conducted simplified numerical experiments assuming the Okhotsk situation, in which Fs and offshore width b of polynya are predicted by a thermodynamic polynya model with ECMWF meteorological variables. The simulated salinity shows a good agreement with the direct measurements. The theoretical estimates for S* was also applied to two Okhotsk polynyas, northwestern polynya (NWP) and northern polynya (NP). In conclusion, we found that the along-shore wind causes greater salinity decrease in NP than in NWP, whose variations substantially depend on the Aleutian Low activity.
 In the Sea of Okhotsk, strong and cold outbreaks from northern Eurasia cause the growth of coastal polynyas in pack ice and a large amount of sea ice production [Martin et al., 1998; Gladyshev et al., 2000; Ohshima et al., 2003]. Figure 1 (left) shows a typical feature over the Okhotsk northern shelves, where two large polynyas can be seen. We refer to these polynyas as the northwestern polynya (NWP) and the northern polynya (NP). Accompanied by the intensive ice production, cold, oxygen-rich DSW is formed over the shelf. The DSW is transported to the southern part of the Okhotsk Sea and forms Okhotsk Sea Intermediate Water by a confluence with the Soya Warm Current Water [Watanabe and Wakatsuchi, 1998; Itoh et al., 2003; Gladyshev et al., 2003]. Subsequently, it is diapycnally mixed with the East Kamchatka Water around the Kuril Island, contributing to the Oyashio Current Water. Thus the DSW formed over the Okhotsk northern shelves is believed to be a ventilation source of the North Pacific Intermediate Water [Talley, 1991; Yasuda, 1997]. Consequently, the DSW also brings out signals of climate change occurring in the Okhotsk Sea to the entire North Pacific. Itoh  has reported rapid warming of the Okhotsk intermediate water based on historical data since the 1950s. Nakanowatari et al.  noted that the warming of the Okhotsk Sea is greatest in the North Pacific intermediate layer, and it spreads out in the subarctic gyre. They also suggest decreasing of the sea ice formation in the Okhotsk Sea, mainly in NWP, as the most likely cause of the warming. The total amount of DSW production could also be changed by formation and modification processes, e.g., tidal mixing or entrainment/detrainment, even with the same amount of ice production [Nakamura et al., 2006]. Therefore it is important to investigate the detailed processes of the DSW formation over the northern shelf regions in the Sea of Okhotsk.
Shcherbina et al.  presented direct measurements of DSW formation during 1999/2000 winter using two bottom moorings over the northwestern shelf in the Okhotsk Sea. A steady, near-linear salinity increase was observed in the inshore mooring over a month. The total salinity increase was 0.83 PSU in 35 days, corresponding to a potential density increase of 0.68 kgm−3. Shcherbina et al. [2004b] estimated the DSW export based on the moored velocity, and highlighted the importance of the along-shelf advection to the observed salinity change. Simizu and Ohshima [2002 and 2006] simulated remarkable along-shore coastal currents over the northwestern shelf by a barotropic numerical model. They interpreted the mechanism as so-called arrested topographic waves driven by the along-shore wind stress [Csanady, 1987]. Therefore the effects of the along-shore wind needs to be further discussed in terms of DSW formation over the Okhotsk shelves.
 Generally, it is known that baroclinic eddies, developed at the edge of coastal polynya, effectively disperse the density anomaly through the cross-shore salinity transport, causing an equilibrium state in salinity after the near-linear increase [Gawarkiewicz and Chapman, 1995; Chapman and Gawarkiewicz, 1997; Chapman, 1999; Tanaka and Akitomo, 2000]. On the other hand, Chapman  investigated contribution of ambient currents with different along-shore velocities to the lateral DSW discharge and its influences on the total amount of DSW production, using an idealized numerical model. He found that although there are almost no significant changes in the total DSW production, the ambient current advects the dense water downstream, and consequently reduces the equilibrium salinity anomaly. Since the along-shore wind also yields a cross-shore Ekman current and its compensation flow [Ikeda, 1985; Carmack and Chapman, 2003; Yang, 2006], the dense water advected by the cross-shore circulation should be included in the lateral salinity flux from the polynya region for better estimation in addition to the effects of the along-shore current discussed by Chapman .
 In this study, we investigate the effects of along-shore wind stress on DSW formation, including the effect of the offshore salinity flux by Ekman transport. First, we conduct idealized experiments with simplified bathymetry, resembling the northern Okhotsk shelves. Second, we construct a theoretical equation to estimate the equilibrium salinity anomaly where lateral salinity fluxes are scaled from a perspective of salinity budget over the polynya region. The analytically derived salinity estimates are compared with the idealized numerical experiments forced by surface salinity flux and along-shore wind stress fixed in time. In order to understand oceanic responses governed by time-dependent wind stress, the oceanic model is also forced by isolated wind event and periodically oscillating wind stress. Additionally, the along-shore wind effects are investigated over the Okhotsk polynyas, in which the numerical model is forced by realistic wind stress obtained from ECMWF data and buoyancy forcing based on the surface heat budget there. Here the wind effect is examined independently for NWP and NP. Since dominant wind directions with respect to the coastline are different between these polynyas, we may be able to examine variety of oceanic responses by studying these Okhotsk polynyas.
 This paper is organized as follows: section 2 describes the model configurations. In section 3, the equations for the equilibrium salinity anomaly are derived in terms of salinity budget within polynya region. The numerical results are described in section 4. In section 5, we give the results of numerical calculations where time-dependent wind is applied. In section 6, the effects of along-shore wind are investigated over the Okhotsk coastal polynyas, in which the surface wind stress and salinity flux are calculated by a thermodynamical polynya model. Section 7 describes our conclusion.
2. Model Description
 The numerical model used in this study is the Princeton Ocean Model described by Blumberg and Mellor . The model is a free surface, primitive equation model that uses hydrostatic and Boussinesq approximations for incompressible fluid. The three-dimensional equations for conservation of mass, momentum, potential temperature, and salinity are solved using a finite differencing scheme, coupled with an equation of state. A level 2.5 turbulent closure scheme is embedded in the model to provide vertical mixing parameters. Horizontal viscosity and diffusivity coefficients are calculated by the Smagorinsky diffusion formula [Smagorinsky, 1963].
2.1. Model Domain
 The model domain is idealized for a continental shelf such as the Okhotsk northern shelves (right in Figure 1), having very gentle offshore slope and long coastline. A schematic diagram of the model is presented in Figure 2. The study uses a right-handed coordinate system where positive x is offshore, positive y is westward, and positive z is upward. The model spans 400 km along-shore and 200 km offshore for standard experiments. The bottom topography is described as H(x, y) = (H0 + 0.001y) where Lx is 400 km, so that the shelf gently deepens southward with a constant slope of 0.001 except for the regions adjacent to the eastern and western boundaries, and its shallowest depth H0 is 30 m at y = 0. H also varies moderately along the x direction near the eastern and western boundaries. Basic analyses were conducted within an elongated “analysis domain” adjacent to the northern boundary, depicted in Figure 2, with an offshore width of 10 km and along-shore length of ℓ = 300 km. The western part of the model (300 km < x < 400 km in Figure 2) was not included in the present analysis in order to avoid complicated processes in the western boundary region. The east end of the analysis domain is attached to the eastern boundary of the basin to assure no salinity influx from the boundary. Since the analysis region is narrow and the slope is gentle, the zonal topographic variation do not induce serious influence to the results.
 In this study, we required a numerical model with a high resolution in vertical and horizontal directions to efficiently represent the eddies and some features within the boundary layers. A baroclinic Rossby radius R is estimated to be 3.8–7.7 km for a typical depth of = 50 m and the buoyancy frequency N = 1–2 × 10−2 s−1 suggested by the observations over the Okhotsk northern shelves [Shcherbina et al., 2003]. Thus the horizontal grid size of 2 km resolves the oceanic phenomena with a scale of deformation radius [see also Gawarkiewicz and Chapman, 1995]. Vertical resolutions are provided by 21 sigma levels; the spacing is 0.5% of the water column near the bottom, and 8% in the surface and interior.
 Each calculation begins from the rest. The model ocean initially has a homogeneous structure (potential temperature −1.8°C and salinity 32.5 PSU) in all experiments. The Coriolis parameter f is set at 1.3 × 10−4 s−1 and is uniform throughout the study.
2.2. Boundary Conditions
 The bottom frictional stress (τbx, τby) is determined by matching velocities with the logarithmic law of the wall [for detail description, see Blumberg and Mellor, 1987], given by
where ub and vb are corresponding velocities in the grid nearest the bottom, KM the vertical eddy diffusivity of the turbulent momentum mixing, and h the bottom depth. The drag coefficient CD in equations (1) and (2) is determined by
where κ = 0.4 is the von Kármán's coefficient, Δz is the vertical grid spacing nearest the bottom, and z0 = 1 cm is the roughness height. The model adopts half-slip boundary conditions for the lateral sidewalls, in which the velocity along the coast is set at one half of the nearest grid value and the normal velocity component is zero. On the sidewalls and bottom, the normal gradients of temperature and salinity are set to be zero so that there are no advective and diffusive heat, salt and mass fluxes across these boundaries.
 The surface salinity flux Fs is applied at time t = 0 within the shaded area of Figure 2, which represents the effect of brine rejection in a coastal polynya. The offshore length b, in which the salinity flux is supplied at the ocean surface, is held fixed at b = 10 km in numerical calculations of section 4, the scale suggested by analytical polynya models [e.g., Pease, 1987; Maqueda and Willmott, 2000]. In section 4, Fs is fixed in time where standard value of Fs = 1.0 × 10−5 PSU m s−1 is used; this is smaller than fluxes during individual events but represents a similar total flux averaged over events. In section 6, b and Fs are variable in time, which are predicted four times every day for NP and NWP based on the ECMWF meteorological data (See the section for the detail).
 The oceanic model is also forced by wind stress = (τax, τay) at the surface. In all calculations, the wind stress is applied only in the along-shelf direction, namely,
where Ua = (Ua, Va) is the surface wind speed, ρa = 1.2 kg m−3 is the air density, Ca = 2.0 × 10−3 is the air drag coefficient. In section 4, Ua is held fixed in time, although it varies from 0 to 13 m s−1 among the various cases, while in section 5, Ua is variable with time (see the section for detail). We emphasize Va = 0 in these sections. In section 6, ∣Ua∣ is calculated with use of Va, based on the ECMWF 10-m wind over the Okhotsk polynyas, keeping τay in zero.
 The along-shore wind speed Ua(y) also varies in the y direction (Figure 2, right), given by
where Ua0 is magnitude of the along-shore wind, corresponding to its maximum at y = 0, and Ly = 200 km. Ua varies only 0.3% over the polynya (0 < y < 10 km), and therefore the wind stress can be regarded as nearly uniform in the coastal region.
3. Scale-Based Analysis for Equilibrium Salinity Anomaly
 In this section, we derive scaling estimation for equilibrium salinity anomaly S* in terms of both the surface salinity flux Fs and the along-shelf wind velocity Ua.
 First, we consider salinity budget within a rectangular box adjacent to a straight coastal boundary as in Figure 2. The fact that the surface salinity input should balance with the sum of lateral salinity anomaly export yields
where Txeddy = dydz, Txwind = dydz, Tyeddy = dxdz and Tywind = dxdz, where the over bar and prime denote the mean and perturbation components respectively, s denotes salinity anomaly deviated from the initial value, and u and v denote along-shore and cross-shore current velocities, respectively.
3.1. No Wind Case
 Here we discuss a case where no wind-forcing is applied at the surface, in which the surface salinity flux should be balanced with the perturbation salinity flux due to baroclinic eddies (i.e., Txwind and Tywind = 0). Therefore, equation (6) reduces to
The eddy-induced salinity flux is larger in the downslope direction, so that the ratio between the terms on the right-hand side (RHS) in equation (7) becomes
Since in the present study we consider coastal polynyas of which along-coast length is much greater than the cross-shore extent (i.e., ℓ/b ≫ 1) as shown in Figure 2, equation (7) can be further reduced to
This simply becomes
where H is the depth of the water column at y = b.
 In the present study, we adopted a scaling of Visbeck et al. [1996, hereinafter V96] by assuming that the forcing has a sharp transition from the outer region. V96 gave an expression for the lateral density flux caused by baroclinic eddies, in which the lateral flux is related to the depth-averaged density anomaly within a disc where the buoyancy flux is uniformly imposed at the surface. Their idea is applicable to the present problem by modifying the notation as follows
where Seddy is the equilibrium salinity anomaly determined by the baroclinic eddies, N is the Brunt-Väisälä frequency, and ξ is an empirical constant. Seddy is also considered as a salinity difference across the front. Assuming that there is no discontinuity in density across the front at the base of the polynya, Seddy may be given by
where ρ is the density of oceanic water, g is the acceleration of gravity, and β is the seawater haline contraction coefficient, where β = 7.9 × 10−4 PSU−1 for T = −1.8°C and S = 32.5 PSU.
 Combining equations (10), (11) and (12) yields a solution of the equilibrium salinity anomaly, in the absence of the wind effects, given by
 According to equation (13), the equilibrium salinity anomaly increases proportional to Fs2/3 as discussed in V96, while Chapman and Gawarkiewicz [1997, hereinafter CG97] presented another solution in that Seddy follows a curve of Fs1/2. CG97 argued that the scaling of V96 may not be suitable for such polynya problems because of the presence of coastal boundary and choice of horizontal length scale for the density front. Thus we verify the scaling of V96 adopted here, by comparing it with numerical results and superimposed by the curve of CG97 (Figure 3, left). As a result, we found the solution derived in V96 may be more appropriate to the configuration of this study, although the both curves are not so different in this parameter range with each other. We infer this is because we assume the discontinuous buoyancy forcing at the polynya edge, that is, uniform within the region and vanishing outside the forcing region, instead of being gradually reduced through the forcing decaying region. Therefore the baroclinic Rossby radius is the only possible horizontal length scale for the front. If the forcing has the decaying region larger than the Rossby radius, the parameterization discussed by CG97 should be better.
 In order to determine ξ′, additional experiments were conducted with different salinity fluxes of Fs = 0.5, 1.0, 2.0 and 3.0 × 10−5 PSU m s−1, in which no wind-forcing is applied and Seddy is evaluated as an average within the analysis box at day 30. ξ′ is then chosen so that Seddy becomes consistent with the estimation from RHS of equation (13). As a result, we obtain ξ′ ≈ 3.2; this value is close to the value of γ = 3.9 used in V96 despite difference of the model configuration.
V96 also suggests an estimation of depth-averaged velocity associated with baroclinic eddies Veddy, which can be applied to this problem, given by
where ζ is a constant, which is evaluated based on the numerical calculations. According to the no-wind calculations with Fs varying between 0.5 × 10−5 and 3.0 × 10−5 PSU m s−1, we obtain ζ = 0.8 ± 0.2 from equation (14) by assuming that magnitude of eddy field velocity ∣u′∣ = = 4.4 ± 2.1 cm−1, averaged in the analysis box at day 30, is equal to Veddy. Thus we adopt ζ = 0.8 for the estimation below.
3.2. Case Under Wind Effects
 Next, we introduce salinity fluxes related to the wind-induced circulation and also construct a prediction equation for the equilibrium salinity anomaly S*.
Equation (19) indicates that the wind-influenced salinity anomaly S* tends to decrease as the wind-induced currents Vwind and Uwind become strong relative to Veddy. The aspect ratio b/ℓ, seen in RHS of equation (19), represents the effects of polynya shape. Therefore for the long coastal polynya, such as NWP and NP in this study, the along-shelf current may have less contribution than the across-shore current to the salinity decrease beneath the polynya. On the other hand, if b/ℓ increases, the contribution of the along-shore current becomes greater in determining S*. The estimation equation (19) will be verified in section 4 by compared with numerical results.
3.3. Parameterizations of Wind-Generated Current Velocity Scales
 The wind-induced velocities Vwind and Uwind are scaled below to complete the estimation of S*.
3.3.1. Ekman Compensation Flow (ECF)
Ikeda  simulated overturning flow via the lower layer under such downwelling-favorable wind situation, which is expected to transport a large amount of salinity from under polynya. We refer to this offshore-oriented overturning flow as the Ekman Compensation Flow (or ECF).
 First, the offshore volume transport due to the ECF (Figure 5) is parameterized. The downwelling-favorable wind considered here generates the onshore surface Ekman volume transport (=−τa/ρwf), which accompanies a volume input into the polynya region but no net salinity anomaly transport. In contrast, ECF compensates the volume transport due to the surface Ekman flow through the offshore drainage via the lower layers, which accompanies large salinity anomaly transport out of the polynya region. The offshore volume transport due to ECF is expressed, defining the offshore current velocity VECF instead of Vwind, by
opposing to the onshore Ekman transport at the surface.
3.3.2. Along-Shelf Current
 For the estimate of the wind-driven along-shelf current Uwind, we adopt frictionally adjusted flow [Csanady, 1978; Whitney and Garvine, 2005], in which the simplest momentum balance between along-shelf wind stress and bottom stress (i.e., τax = τbx) is assumed. To obtain the Uwind estimate, both the surface and the bottom stress are represented by quadratic drag laws. For these scaling purposes, only along-shelf components of the winds (Ua) and depth-averaged current (Uwind) are considered:
where CDa is the bottom friction coefficient for the depth-averaged velocity. If we assume that the along-shelf wind stress balances with the bottom stress solely, combining equations (21) and (22) yields a simple expression for the frictionally adjusted current, given by
This linear relationship between current and wind velocity is supported by observations at the Delaware inner shelf [Garvine, 1991] and Scotian shelf [Sandstorm, 1980].
The present model's CD around polynya is evaluated as ∼0.02 from equation (3), which corresponds to CDa ∼4.4 × 10−3. Consequently, we adopt Uwind/Ua = 0.018 in later estimates of the along-shore current.
 The results of scale-based estimates are depicted in Figure 3 (right), superimposed by numerical plots that are averaged vertically at the western boundary of the analysis box at day 15. The estimate (23) for the wind-induced current velocity embraces the simulated velocity well when Ua < 10 m s−1, while it is slightly underestimated for Ua > 10 m s−1. This underestimate for large Ua may be associated with the weak stratification due to vertical mixing under the polynya and the substantial wind-forcing at the surface, which generate thick boundary layer [Weatherly and Martin, 1978]. It is therefore considered that the entire water column is affected by viscosity and then Uw is decelerated from the theoretical estimate of equation (23). In the case of Sea of Okhotsk, surface wind typically blows with a magnitude less than 10 m s−1 (e.g., Figure 10), so we apply the parameterization of equation (23) in the present study.
4. Results of Numerical Experiments
4.1. Effects of Winds on DSW
 In this section, results of numerical calculations are presented, focused on the roles of along-shore wind on the salinity anomaly around the polynya. Bottom salinity distributions for Ua = 0, 5 and 9 m s−1 are depicted in Figure 4.
 In contrast, in the case of Ua = 5 m s−1, the eddy activities are somewhat moderated, and high-salinity water with ΔS > 0.5 PSU is carried away to the west of the polynya (Figure 4b). Consequently, the salinity anomaly reduces by approximately 0.2 PSU around the coast compared with that of Ua = 0. This is basically due to the large amount of salinity advection induced by wind-driven circulations. Chapman  discussed the similar decrease in density anomaly caused by coastal advection, in which along-shore ambient current is directly imposed instead of being driven by along-shelf wind. In the present study, however, fluid particle near the bottom travels to the offshore direction due to the ECF as well as the downwind (i.e., westward) direction. This is an essential difference from Chapman . In the case of Ua = 9 m s−1, the salinity anomaly decreases further and becomes as small as 0.2 PSU around the coastal region (Figure 4c). In this case, the eddy activity furthermore attenuates compared to the case of Ua = 5 m s−1.
Figure 5a represents a vertical section of salinity anomaly and stream function for Ua = 0, corresponding to Figure 4a. Salinity anomaly is averaged in the along-shelf direction in the analysis box (i.e., 0 km < x < 300 km). The stream function is defined as = − and = , where w is the vertical velocity and the over bar denotes the average with respect to the x direction. In the cross-shore range of 0 < y < 25 km, where ΔS is the highest over the shelf, the isopycnal surfaces stand nearly upright, while they are relatively relaxed near the front which may be a result of geostrophic adjustment and associated with the generation of baroclinic eddies. Consequently, the relaxation of the surrounding isopycnal surfaces enhances the density stratification, and leads to the release of potential energy and further eddy generation.
Figure 5b shows the vertical section of the stream function ϕ when Ua = 9 m s−1 (corresponding to Figure 4c), where the contour interval of the stream function is four times greater than those of Figure 5a. Onshore Ekman current occurs approximately within 10 m from the surface due to the easterly winds and then is blocked at the northern boundary, yielding strong downwelling in a very narrow coastal region. The surface Ekman flow then overturns and flows out to the offshore direction as the Ekman compensation flow through the internal and bottom layers, accompanied with great salinity export from the polynya region. The ECF substantially restrains salinity increase beneath the polynya, by which salinity flux across the front is scaled in the previous section. In addition, Figure 5 shows that the ECF forcibly relaxes the isopycnal surface near the front, implying that it is indirectly responsible for the eddy attenuation seen in Figures 4b and 4c.
Figure 6 depicts the time evolution of ΔS, averaged within a volume of the analysis box (Figure 2). The salinity anomaly evolves in time with some common features regardless of the variation of Ua; at the initial stage it linearly increases with time, then breaks away from the linear increase, and finally approaches a quasisteady value S* which depends on Ua. The initial salinity increase coincides with a simple estimate given by ΔS(t) = Fst/H, where Fs = 1.0 × 10−5 PSU m s−1, H = 35 m and t denotes time, implying that the surface salinity input is used for the salinity rise of the entire water column through the vertical mixing from surface to bottom until the density front develops enough and eddies facilitate lateral advection [Chapman and Gawarkiewicz, 1997]. After the initial linear increase ceases, salinity anomaly still fluctuates with time when Ua is small (≤5 m s−1), while for the cases of Ua ≥ 7 m s−1, it is relatively stable with time. Moreover, we also emphasize that the equilibrium value S* varies with Ua, which tends to decrease as Ua increases, in particular, when Ua > 5 m s−1. The time required to reach quasisteady state also decreases with increasing Ua. This is similar to the results of Chapman , who showed a decrease in equilibration time with increasing ambient current velocity.
4.2. Equilibrium Salinity Anomaly
 The theoretical estimate (19) for the equilibrium salinity anomaly is verified by comparing numerical calculations with different Ua applied (Figure 7). The simulated salinity anomalies, depicted in Figure 7, are averaged within the analysis box at day 60, when ΔS already achieves the equilibrium S* for all cases (Figure 6). For the comparison, we substituted Ua0 in equation (5) into Ua in equation (19), where Ua(y) is almost uniform in the analysis box as mentioned (Figure 2). According to the numerical calculations, the influence of wind is small for Ua < 3 m s−1, while S* rapidly decreases with increasing Ua in the range of 3 < Ua < 9 m s−1, and then it becomes close to S* = 0.2 PSU with less dependence on Ua again. The theoretically derived curve reproduces numerical results well for Ua ≤ 11 m s−1, while it slightly underestimates the results for Ua ≥ 13 m s−1. The theoretical estimation assumes that the eddy transport is independent of winds, but this assumption does not seem to influence the results greatly as in Figure 7.
5. Effects of Time-Dependent Wind Forcing
 So far, we have focused on the oceanic responses to steady wind-forcing. Here the response governed by time-dependent wind is discussed. In all experiments, the wind stress starts to be imposed after the surface salinity flux gets in balance with the eddies (i.e., day 25). Note that we still consider the situation that only westward wind blows near the surface, say, keeping τax > 0 and τay = 0.
 First, we describe the salinity response when isolated wind event suddenly happens and lasts for a week (Figure 8). According to Figure 8, salinity beneath the polynya keeps decreasing with a constant rate of −0.02 PSU day−1 for a time period of T1. After the termination of wind-forcing, the salinity linearly increases with the same rate of (∼0.015 PSU day−1) as before the wind stress starts. Consequently, it takes a restoration time of T2 ∼ 10 days to recover to Seddy.
 Next, we present results of the numerical calculations forced by oscillating wind stress (Figure 8b), given by
where U0 is the amplitude of wind speed being 9 m s−1, ω is the frequency of wind-forcing, written as ω = using time period Tp of oscillation. In this experiment, Tp varies from 10 to 30 days at intervals of 10 days. When Tp = 10 days, salinity beneath polynya decreases by 0.13 PSU in 5 days (Figure 8, bottom right). Afterward, it gradually increases having a periodic oscillation with an amplitude of 0.06 PSU; it takes more than 50 days to recover to the original level of Seddy. For longer period cases, salinity shows greater decreases of 0.2 PSU for the initial half period from day 25. It nevertheless recovers to Seddy within each oscillation period. In consequence, the maximum salinity anomaly may not be reduced severely unless the westward wind events happen as often as once every 10 days.
 In conclusion, the results presented in this section indicate that the salinity anomaly continues to decrease as long as wind blows over the polynya, but it tends to restore immediately after the termination of the wind. However, if such wind events with a certain duration time continuously happen without sufficient time interval to restore, severe restraint of salinity anomaly is expected over the shelf.
6. Application to Coastal Polynyas in the Sea of Okhotsk
 In this section, we consider along-shore wind influences on the salinity beneath the Okhotsk coastal polynyas. We perform numerical calculations with simplified bathymetry imitating the Okhotsk northern shelves (Figure 1c) and apply the theoretical estimates derived in section 3 for NWP and NP, based on the ECMWF meteorological data. Surface salt flux Fs and offshore width b of polynya are predicted by a thermodynamical polynya model developed by Pease .
6.1. Thermodynamical Polynya Model
 The analytical polynya model [Pease, 1987], referred to as “Pease model”, gives the offshore extent of the wind-generated coastal polynya, based on the balance between the advection of sea ice away from the coast and the area-averaged production rate of new ice. The Pease model was applied for numerous arctic polynyas [Winsor and Björk, 2000] and used to provide the forcing parameters for an oceanic model by Chapman . In this section, the Pease model is used to obtain Fs and b for periods between January to March in 1999 (Figure 17) and 2000 (Figure 10), which are evaluated independently for NWP and NP from each meteorological variables averaged within (135–142°E, 55–59°N) and (147–153°E, 59–60°N), respectively (Figure 9).
 At first, the surface salt input Fs into the underlying water, representing the brine rejection, is calculated based on the production rate of ice over the polynya by
where ρice = 920 kg m−3 is the ice density, So and Si are ocean surface and ice-inside salinity in PSU, respectively. The difference So − Si represents the total amount of rejected salt per 1000 mass units of water, and is set at So − Si = 0.69 So [Martin et al., 1998]. The freezing rate Pi can be estimated from bulk parameterization for the vertical heat flux at the air-sea interface, given by
where Lf = 3.34 × 105 J kg−1 is the latent heat of freezing for salt water, and Qld, Qlu are the downward and upward long wave radiation, respectively, Qs is the sensible heat flux. Following Pease , Qlu is assumed constant and equal to 301 W m−2 because the surface water is always near freezing point at Tw = −1.8; Qld = σea(273°C + Ta)4, where σ = 5.67 × 10−8 W m−2 °C−4 is the Stefan-Boltzmann constant, ea = 0.95 is the effective emissivity for the air, and Ta is the air temperature in; and Qs = ρaChCp∣Ua∣(Ta − Tw), where ρa = 1.3 kg m s−3 is the air density, Ch = 0.002 is the sensible heat coefficient, Cp = 1004 J−1 kg−1 is the specific heat of air. In equation (28), heat fluxes due to the solar radiation Qr and the evaporation Qe are neglected because Qr is nearly zero at the high latitudes during winter and Qe is smaller than the uncertainty in Qs. Substituting into equations (27) and (28) yields
After equation (29), the surface salinity flux depends on both, the air temperature and the magnitude of wind speed, so that Ta and ∣Ua∣ basically control the salinity flux at the surface. Note that the Fs is calculated with use of Va through ∣Ua∣ = .
 The offshore extent b is determined by a competition between ice formation within open water area and offshore ice advection, such as
where Vi is the advection rate of the solidified ice from the shore, and hi = 0.1 m is the collection depth of newly formed frazil ice. Since ice response to wind-forcing depends on its thickness, the deviation angle from surface wind direction is less than 10° for ice thinner than 1 m in thickness [Leppäranta, 2005]. Therefore since the consolidated ice surrounding the polynya is at most 0.5 m thick in the Sea of Okhotsk [Toyota et al., 2004], the offshore ice velocity Vi is simply estimated as a product of the offshore component of surface wind speed Va and a wind factor Na:
where Na = is the so-called Nansen number, where ρw and Cw are the water density and the drag coefficient for ice-water interface, respectively. For the consolidated new ice observed around polynya, the ratio Ca/Cw becomes approximately 0.8 [Wadhams, 2000], and gives Na ≈ 0.03; this value is utilized by numerous analytical studies on polynya problems [e.g., Pease, 1987; Biggs et al., 2000; Morales Maqueda et al., 2004] and also verified by observation in Bering Sea [Reynolds et al., 1985].
 Although the offshore movement of ice may somewhat modify the cross-shore transport induced by along-shore stress [Tilburg, 2003], τay = 0 is used in the numerical calculations for the sake of simplicity.
6.2. Meteorological Conditions and Characteristics of the Okhotsk Coastal Polynyas
 At first, the meteorological characteristics of the Okhotsk coastal polynyas are presented. Sea level pressure (SLP) and wind vectors at 10 m height (averaged between January to March during 1998–2002) are drawn in Figure 9. In principle, the SLP contours coincide with the direction of geostrophic wind, and then the surface wind deviates leftward from the geostrophic wind due to friction effect. The contour of SLP intersects with the coast line at an angle of 20° to 30° over NWP, while SLP is almost parallel to the coast over NP. Consequently, the SLP distribution over NWP yields wind stress nearly perpendicular to the coast line. In contrast, the 10 m wind traverses the coast at an angle of around 45° over NP [Martin et al., 1998].
Figure 10 shows time series of parameters Ua, Va, Fs, b and Fsb, where Fs and b are calculated by the Pease model described above. From Figure 10a, westward wind speed (i.e., Ua > 0) is greater over NP than NWP throughout the period, which are on average 1.2 and 3.0 m s−1 for NWP and NP, respectively. According to Figure 10c, there is no significant difference in Fs between NWP and NP. For both polynyas, Fs reaches the maximum of 4 × 10−5 PSU m s−1 during days 10–32 (corresponding to the calendar days of 10 January and 1 February), and subsequently it gradually reduces to less than 2.0 × 10−5 PSU m s−1 after day 70. On the other hand, there is considerable difference in the offshore width b (Figure 10d). In NP, the width is less than 10 km, except for periods of days 35–50 and days 70–80 when it is ranging from 15 km to 20 km. In NWP, the polynya intermittently closes in early January and, as a result, the width is very small until day 10 as noted in Shcherbina et al. . NWP then widely expands offshore in which the width reaches 25 km at around day 70. Thus there is approximately 4 km difference in b between NWP and NP on average. This is mainly attributed to the difference of offshore ice advection by wind, because the movement of newly formed thin ice directly follows the surface wind as shown in (p4). Eventually, the total brine rejection, proportional to Fsb, is greater in NWP than in NP; the difference reaches a factor of two from day 10 to day 35 (Figure 10e).
 In this study, the total ice production per unit length of the coastline is estimated as 0.95 km2 and 0.65 km2 in NWP and NP, respectively. Considering the length of the coastal line, the total ice production formed in each coastal polynya is 52.2 km3 in NWP and 34.1 km3 in NP. Comparing the estimates of ice production with those in the previous studies (Table 1), Martin et al.  estimated cumulative ice production of 103 km3 and 34 km3 for NWP and NP, respectively, by an SSM/I algorithm. Gladyshev et al.  estimated the respective ice productions in NWP and NP of 166 km3 and 38 km3 in 1996, and 88 km3 and 21 km3 in 1997. Our result is lower than the both studies regarding ice production in NWP, while it is consistent in NP. It may be because our estimates, based on the Pease model, do not consider outer thin ice regions but inner open water region. Martin et al.  estimated offshore width of the thin ice region of 66 km for NWP, which is about four times larger than the value of b evaluated in this study. However, ice production rate decreases rapidly as ice thickness increases, so that cumulative ice production becomes similar to the value evaluated over an area of the open water [Maykut, 1986]. The ice production during December is not included in this study, which may be another reason for the underestimation of ice production.
6.3. Effects of Along-Shore Wind on Okhotsk Coastal Polynyas
 Here we examine the influences of the along-shore wind on the salinity beneath the Okhotsk coastal polynyas, focusing on the differences between NWP and NP.
 First, to mimic the Okhotsk northern shelves (right in Figure 1), we carry out a numerical calculation of which western and eastern half regions (Figure 11) are respectively forced by the NWP and NP forcing parameters (Figure 10), and then compare the result with direct measurements by Shcherbina et al. . Figure 12 displays time evolution of the simulated bottom salinity as well as the schematically drawn observed salinity. Precisely, the measurement location is not right under the polynya (right in Figure 1) and therefore the modeled salinity anomaly is the one advected by eddies and/or mean currents. The simulated value is taken at the location marked in Figure 11, which approximately corresponds to the observation location (Figure 1, right, triangle). According to Shcherbina et al. , the bottom salinity began to increase on 20th January which may be related to the late ice production as mentioned above. The simulated salinity increase starts at day 25, which approximately coincides with the measurements (Figure 12). Additionally, the model reproduces well the characteristic feature of the linear increase in the salinity. The observed salinity increases by 0.8 PSU for 35 days, while the model simulates a similar increase of 0.8 PSU for 30 days. Hence despite its simplicity, our model reproduces the observed salinity well, and therefore it is sufficient for addressing the DSW formation beneath the Okhotsk coastal polynyas.
 Next, two kinds of numerical calculations are conducted to reveal the influence of along-shore wind in each polynya; one is forced by both τa and Fs (Case Ua), while the other is forced only by Fs (Case Fs), where τa and Fs are obtained from ECMWF data and the Pease model as well as b is, during the 2000 winter. In order to examine the wind effect on the respective polynyas, the along-shore distance is set at 400 km in the calculations (bathymetry shown in Figure 2), similar to the coastal length for the both polynyas [Martin et al., 1998] (see also Figure 1). Figure 13 shows salinity evolution (averaged within 10 km from the coast) beneath NWP and NP from January to March in 2000. According to Figure 13, the difference between Case Ua and Case Fs is greater in NP than that in NWP. In NWP, the difference is evaluated as 0.03 PSU based on equation (19). The estimation approximately corresponds with the simulated difference, although the latter temporarily reaches 0.1 PSU around day 50 (Figure 13a). In contrast, in NP, the theoretical estimates of salinity difference is about 0.08 PSU (Figure 13b), which is greater than that of NWP and corresponds well with the numerical results. These results imply that the reduction of the equilibrium salinity by the along-shore wind is more significant in NP than NWP.
 We further quantify the wind effect in each polynya based on the theoretical estimates derived in section 3. Figure 14 displays a scatterplot between Ua and Fsb for both NWP and NP, superimposed by contours of normalized salinity decrease (≡1 − ). According to Figure 14, Fsb in NWP ranges mainly from 0.2 to 0.5 PSU m2 s−1, while Ua concentrates to a range less than 2 m s−1 in NWP. On the other hand, in NP, Fsb is relatively small ranging from 0.1 to 0.3 PSU m2 s−1, while Ua is broadly distributed from 1 to 6 m s−1, which is typically larger than in NWP. Judging from the theoretical estimates, the along-shore wind reduces salinity on average (squares) by 12% of the eddy-induced anomaly Seddy, but only 3% in NWP.
Figure 15 shows the interannual variability in the estimated salinity reduction ΔS(=Seddy − S*) for NWP and NP between 1978 and 2002. Here ΔS is even greater for NP than NWP for all years, similar to Figure 14. Figure 15 also suggests an increase in ΔS for NP in a recent decade; it is relatively small until 1993, around 0.03 PSU, while it steeply increases reaching greater than 0.1 PSU in 1999. If ΔS for NP is compared with SLP difference (dashed curve in Figure 15) between positions A and B in Figure 9, we can find a good correlation between them (0.74 and 0.52 for NP and NWP, respectively; both significant at over 95%). That is, the SLP gradient across NP drives the easterly wind over NP, which consequently induces the salinity decrease beneath NP through ECF and the coastal jet. Figure 15b shows SLP anomaly averaged between January to March in 1999, when the greatest salinity decrease occurs. From Figure 15, negative SLP anomaly is seen in the center of the basin and resultantly strengthens the SLP gradient across NP, because the Aleutian Low extends to the inside of the Sea of Okhotsk. It is suggested that the interannual variations of the wind effects on the dense water formation would be associated with the Aleutian Low activity.
6.4. Remarkable Salinity Decrease Due to a Low Pressure System
 Finally, we discuss a remarkable salinity decrease simulated in the late January of 1999 (Figure 16), in which the model was forced by parameters in Figure 17 in the similar manner to Figure 13, i.e., with the coastline of 400 km in length. In NWP, the salinity drastically decreases for around 10 days (from January 20 to 30) by 0.6 PSU and 0.4 PSU for Case Ua (NWP) and Case Fs (NWP), respectively. Similar reduction in salinity is simulated in NP as well. The salinity evolution resembles the oceanic response to the single wind event shown in Figure 8 (left), where the salinity rapidly decreases while the wind blows and then gradually recovers to Seddy. According to the SLP evolution in Figure 18, the low pressure system developed in the Japan Sea, which then moved to the northern part of the Sakhalin Island accompanied with strong along-shore wind over the polynyas. Therefore it is interpreted that the remarkable salinity decrease seen in Case Ua was caused by the along-shelf wind through the mechanism discussed above. In Case Fs, however, considerable salinity decrease still occurs even though no along-shore wind is applied. It is found that the low pressure system yields the onshore wind component (Figure 18) as well, particularly over NWP, which closes the polynyas by advecting the consolidated ice onshore as shown by equation (31). Indeed, the SSM/I sea ice data, following the method of Kimura and Wakatsuchi , shows a rapid increase in ice concentration over the polynyas from January 24 to 27 (N. Kimura, Personal Communication). It is inferred therefore that the onshore advection of the consolidated ice existing outside of the polynya temporarily interrupts the ice production within the polynyas (shaded Figures 17b and 17c). Hence the salinity decrease of Case Fs is partly attributed to the temporal cease of the surface salinity flux. Furthermore, salinity reduction becomes more sensitive to the along-shore wind as Fsb becomes small (see Figure 14). Therefore we suggest that the salinity decrease should be enhanced through the joint effects between the strong along-shore wind and the temporal cease of the surface salinity flux during such an event.
 In this paper, effects of along-shore (downwelling-favorable) wind on equilibrium salinity anomaly S* were investigated by idealized numerical calculations and scale-based estimates. Numerical calculations showed that high saline water beneath polynya is advected downstream by wind-driven circulations over the shelf besides baroclinically developed eddies, which consequently induces a decrease in S* beneath polynya. Downwelling-favorable wind generates offshore overturning flow through the lower layers (ECF) as well as along-shore current, in which the former compensates the volume input due to the onshore surface Ekman current and generates a great salinity flux to the offshore direction. The equilibrium anomaly was also represented as a function of along-shore wind Ua and surface salinity flux Fs from the theoretical viewpoint of salinity budget over the polynya region, in which lateral salinity flux caused by ECF, along-shore wind-driven current and baroclinic eddies, are scaled. The solution S* was also verified by a series of numerical calculations. In addition, salinity response beneath polynya governed by time-dependent wind-forcing was examined numerically. The calculations suggested that the maximum salinity beneath polynya may not be reduced severely unless the westward wind events happen as often as once every 10 days.
 Furthermore, we investigated the effects of along-shore wind on DSW generation beneath the Okhotsk coastal polynyas. We conducted simplified numerical experiments assuming the Okhotsk situation, in which Fs and offshore width b of polynya are predicted by the Pease model based on ECMWF meteorological parameters. The simulated salinity shows a good agreement with the direct measurement of Shcherbina et al. . The theoretical estimates for S* are applied to two Okhotsk polynyas, NWP and NP. It is found that along-shore wind causes greater salinity decrease in NP than in NWP throughout the period between 1978 and 2002. We also suggest that the wind influence on DSW greatly varies depending on the Aleutian Low activity. It is worth noting that NP is located upstream from NWP. Therefore DSW formed in NWP is likely to be affected indirectly by winds through the DSW formation upstream in NP.
Shcherbina et al. [2004b] tried to reproduce the observed salinity around NWP based on an advective approach, in which an inertial current was artificially constructed over the northern part of Sea of Okhotsk based on the moored current measurements. As a result, the estimated salinity was at maximum 20% greater than the observed, although the linear-increase and the subsequent transition to the equilibrium state in salinity were reproduced well. They discussed that the overestimation in salinity may be responsible for considering no lateral salinity flux due to the baroclinic eddies. Shcherbina et al. [2004a] showed that an abrupt increase in kinetic energy occurred at the inshore mooring immediately after the termination of the linear increase in salinity. They suggested that the stratification process by the baroclinic instability was completed on that timing, and therefore the tidally induced internal waves were excited easily on the enhanced pycnocline. According to our estimate, since the typical along-shore wind is smaller than 5 m s−1 for NWP, the eddy salinity flux should be dominant there.
 The present paper focused on the effect of the downwelling favorable wind over polynyas. Indeed, seaward monsoon wind during winter typically deviates to such a direction on average because of the Coriolis force. However, the reversed upwelling-favorable wind could produce extensive coastal polynyas beyond 100 km wide, discussed by Kawaguchi , which results in changing the salinity input at the surface. Moreover, the upwelling due to the westerly wind provides a large amount of nutrient-rich water into the surface layer and therefore facilitates the primary production over the continental shelf, as discussed over the Chukchi shelf [Carmack and Chapman, 2003]. Therefore the effects of the upwelling favorable wind merit further exploration and future efforts.
 We thank the anonymous reviewers for their constructive and useful suggestions for improving this paper, particularly on the scaling for the lateral salinity advection. We also thank Dr. S. J. Marsland of CSIRO for his valuable comments and advice on this study. The AVHRR image was provided by Kitami Institute of Technology. The numerical experiments were performed on Pan-Okhotsk information System of ILTS, Hokkaido University. This work has been supported by grant-in-aid of Ministry of Education, Culture, Sport, Science and Technology and the Sasagawa Scientific Research grant from the Japan Science Society. English was proofread by Tak Ikeda and Mika Mäkela.