a. Cross-shore variation in ice drift

Cross-correlation of ice-drift records for different offshore distances indicates that 1) in the cross-shore direction, alongshore drift is highly correlated (r² ∼ 0.96– 0.97), slightly better than cross-shore drift (r² ∼ 0.82– 0.86), and 2) ice-drift velocity is maximum at the most remote radar distance (16 km offshore) and gradually decreases with proximity to the coast. For alongshore motions, drift speeds decrease relative to the most offshore (16 km) site by 1% at 12 km, 3% at 8 km, and 8% at 4 km; for cross-shore motions, corresponding decreases are 13%, 18%, and 23%, respectively.

According to cross-spectral analysis (not shown for sake of brevity), alongshore ice-drift motions have high cross-shore coherence, steady near-zero cross-shore phase difference, and unity admittance for frequencies as high as 2.0–3.0 cycles per day (cpd) (i.e., for periods as short as 8–12 h). The energetic alongshore ice drift associated with diurnal and wind-driven currents (with frequencies less than 0.25–0.30 cpd) is nearly uniform across the shelf. Cross-shore drift currents also exhibit high cross-shore coherence and zero phase lag for frequencies as high as 1.2 cpd (periods as short as 20 h), but even at these frequencies, admittances become smaller with proximity to the coast. Admittance also decreases with decreasing frequency, indicating stronger boundary effects for long-period motions.

b. Time scales of ice-drift variability

We used spectral analysis to estimate the relative importance of various frequency components of ice-drift motions on the Sakhalin shelf. To improve the spectral estimates and increase the number of degrees of freedom ν, the time series records were divided into 1024-h overlapping segments, and each segment was weighted using a Kaiser–Bessel window prior to application of the Fourier transform (Emery and Thomson 2003). The results of the separate analysis of the cross-shore (u) and alongshore (υ) components for the 1993 ice-drift data are presented in Fig. 5. The main findings are as follows:

1. The alongshore (north–south) component of drift dominates at all frequencies, especially at tidal and subtidal frequencies.

2. There are strong spectral peaks at the northern stations CL and OD due to diurnal (K₁, O₁) tidal motions, whereas at southern station KM, the diurnal peak is weak.

3. Semidiurnal (M₂) sea-ice oscillations are negligible at all sites. The only M₂ peak is observed in the alongshore motions at radar station KM (Fig. 5).

4. In contrast to other high-frequency ice-drift observations (cf. Thorndike 1986; Padman and Kottmeier 2000; Heil and Hibler 2002), no inertial oscillations were found in the observed spectra of ice drift at radar stations CL, OD, and KM. Apparently, rotary inertial oscillations of ice in these areas (periods of about 15 h) are suppressed by the coastal boundary.

5. Spectra in the subtidal (low frequency) band are dominated by motions at approximately 5- and 12-day periods at all three radar stations. Spectra also suggest the existence of 21-day oscillations on the shelf. This latter peak is absent in Fig. 3 because of insufficient spectral resolution, but can be identified in higher-resolution spectra. The 5-, 12-, and 21-day ice-drift oscillations also are present in local wind spectra (not shown), suggesting that the shelf motions are atmospherically induced.

Current-meter time series have durations of only 3– 5 weeks and so cannot be used to examine low-frequency oscillations. The spectral frequency resolution also is much less than for the longer-duration ice-drift series. However, the general features of these spectra are the same in that alongshore currents prevail at all frequencies, diurnal tidal motions are dominant, subtidal motions are significant, and semidiurnal tidal peaks are negligible.

Guided by the peaks and gaps in the ice-drift spectra, we partitioned the total velocity variance (σ²₀) into four frequency bands (f) (Table 2): low frequency (LF), f < 0.8 cpd; diurnal (D), f ≈ 0.8–1.4 cpd; semidiurnal (SD), f ≈ 1.5–2.3 cpd; and high frequency (HF), f > 2.3 cpd. Here,

View Expanded

is the total variance of ice-drift motion for a given coastal radar or current-meter station (n) for a specified frequency band Δf. According to our variance partitioning, diurnal ice motion in 1993 at the north-central stations CL and OD accounted for 66%–77% of total variance and had 20–25 times the energy of diurnal motion at the southern station KM, and it was correspondingly stronger than the semidiurnal ice-drift motion at all stations. Low-frequency ice-drift motion accounted for 15%–25% of the total variance, except at site KM where it accounted for more than 91% of the variance. Semidiurnal and high-frequency ice motions together accounted for only 5%–8% of the total variance at all sites. Approximately 92%–94% of total variance was associated with alongshore motion (last column of Table 2).

The variance partitioning for the summer current-meter velocities at station Ombinskaya is similar to that for the ice-drift data, except that diurnal tidal currents are even more pronounced (accounting for 92% of the total energy), while low-frequency (subtidal) currents account for only 3%. Semidiurnal currents remain negligible (2.4%). In contrast to cross-shore ice-drift motion, cross-shore currents are relatively strong and account for almost 21% of the total variance (as compared with only 6%–8% for cross-shore ice-drift motion).

c. Effects of ice concentration on ice drift

Comparison of the 1993 ice drift at CRS Odoptu with the 1988 currents for nearby station Omb indicates that the current variance (2434 cm² s⁻²) is about 1.5 times the ice-drift variance (1616 cm² s⁻²). This difference is mainly due to differences in diurnal motions (variances of 2242 and 1073 cm² s⁻², respectively), which may be related to the prominent 18.6-yr nodal cycle in the diurnal tides. An analysis for extreme historical tides reveals that maximum diurnal tides on the northeastern shelf of Sakhalin Island occurred in 1968– 69, 1987–88, and will occur every 18.6 yr thereafter. During 1993, diurnal tides were approximately 20% weaker than in 1988, and so the diurnal variance in 1988 was presumably 1.45 times that in 1993. However, this still does not explain the factor of 2.1 difference in ice-drift variance between the two years. We therefore conclude that the difference is related to physical differences between the actual tidal currents and the ice-drift response to these currents arising from the anomalously high ice concentration observed in the Sea of Okhotsk in 1993 (cf. Preller and Hogan 1998). Both observations and numerical models indicate that internal ice stresses associated with high ice concentrations can significantly dampen tidal motions (Fissel and Tang 1991; Geiger et al. 1998; Heil and Hibler 2002).

We have compared the 1993 and 1994 ice-drift data at CRS Odoptu to characterize the importance of ice concentrations on ice drift. The 1994 concentrations on the northeastern shelf of Sakhalin Island were low as compared with 1993 (50%–70% and 80%–90%, respectively) (Preller and Hogan 1998). Accordingly, the 1994 ice-drift variance was about 1.5 times the 1993 variance, and this difference was associated with the much stronger diurnal ice drift in 1994 (Table 2). The ratio between the diurnal current variance at site Omb in 1988 (2242 cm² s⁻²) and the diurnal ice-drift variance at site OD in 1994 (1609 cm² s⁻²) is about 1.4, which is very close to the theoretical ratio for 1988–1994 for diurnal tides modified by the 18.6-yr nodal cycle. We therefore conclude that tidal ice drift in 1994 was relatively free, while that in 1993 was damped by high ice concentrations.

Because both the ice-drift and current-meter records indicate that over 92% of the total energy is in diurnal and low-frequency bands, the remaining analysis will focus on these two types of motions. Dominance of these two forms of ice motion is apparently typical for high latitudes (cf. Padman et al. 1992; Padman and Kottmeier 2000).

a. Tidal observations and analysis

Our harmonic analyses of the ice-drift and current tidal motions are based on the least squares method, with subsequent calculation of current ellipse parameters from component amplitudes and phases (cf. Pugh 1987). The major diurnal (K₁ and O₁) and major semidiurnal (M₂) constituents are presented in Table 3. Other semidiurnal harmonics, as well as the computed monthly (Mm), fortnightly (Mf and Msf), and high-frequency (e.g., MK₃, MO₃, M₄) tidal harmonics, are not significant. The residual ice-drift series (obtained by removing the estimated tides) were then further examined for wind-induced ice drift (see section 4). We used the residual spectral energies for diurnal and semidiurnal frequency bands (Fig. 5; Table 2) to estimate possible errors in tidal amplitudes (ε_H) and phases (ε_G) (Pugh 1987):

View Expanded

where σ²_Δω is the nontidal residual variance in the averaging frequency band Δω, T is the length of the time series, and H is the amplitude of the tidal constituent (Pugh 1987). Estimated ε_H values for the K₁ and O₁ harmonics range from 2.7–3.0 cm s⁻¹ (CL and OD) to 0.8–0.9 cm s⁻¹ (KM and Omb), while for the M₂ constituent, values range from 0.4 cm s⁻¹ (KM) to 1.2 cm s⁻¹ (Omb). The K₁ and O₁ phase errors (ε_G) for the alongshore component (υ) were 1.2° for Omb, 3.4°–4.5° for CL and OD, and 10°–18° for KM. For M₂ the phase errors were 73° (CL), 80° (OD), 8.5° (KM), and 17° (Omb). Amplitudes of cross-shore (u) motions are a factor of 15–20 times smaller than those of alongshore motions, and so the respective phase errors for the u components are 15–20 times those for the υ components. Results from harmonic analysis of the ice records (Table 3) are consistent with numerical tidal models for the Sea of Okhotsk (Suzuki and Kanari 1986; Kowalik and Polyakov 1998; Nakamura et al. 2000), which produce strong diurnal currents near the northern end of Sakhalin Island (Cape Yelizavety) and weakening diurnal currents to the south (Fig. 6).

Ellipses of tidal ice drift for the major diurnal constituents, K₁ and O₁, are similar for stations CL and OD (Table 3). Moreover, the ice-drift ellipses are in general agreement with the respective ellipses for tidal currents measured at nearby current-meter station Omb. In both datasets, ellipses are clockwise and their axes stretched along the Sakhalin coastline. The slight difference in ellipse orientation between ice drift and currents is apparently related to local changes in coastline orientation. Maximum K₁ and O₁ currents at the current-meter station Omb were about 40–50 and 35–40 cm s⁻¹, respectively, similar to those for the 1994 ice-drift motions. Other measurements of tidal currents in this region (cf. Rabinovich and Zhukov 1984; Popudribko et al. 1998; Putov and Shevchenko 1998) agree closely with the 1994 ice-drift measurements and with the results of the numerical modeling by Kowalik and Polyakov (1998). However, the 1993 tidal diurnal ice-drift motions were approximately 30%–35% weaker than those observed in 1994 and those predicted numerically by Kowalik and Polyakov (1998; Tables 2 and 3; Fig. 6).

Spectra of the 1993 alongshore (υ) ice drift (Fig. 5) obtained after subtraction of estimated mean tidal ice drift show significant diurnal peaks in the residual ice motion. Residual motions account for 25.6% of the total diurnal variance of 1685 cm² s⁻² at CL and for 22.6% of the total variance of 1073 cm² s⁻² at OD (Table 2). In contrast, the 1994 residual diurnal ice drift was considerably smaller: only 6.3% of 1609 cm² s⁻² at OD. For comparison, the residual diurnal currents at station Omb were negligible and account for only 0.3% of 2242 cm² s⁻². Results indicate the regular deterministic character of diurnal currents on the Sakhalin Island shelf during ice-free periods and the less regular, partly random behavior of diurnal ice-drift motions during ice-covered periods. These irregularities were less pronounced in 1994 when compared with 1993 because of the lower ice concentrations in 1994.

In the cross-shore direction, the K₁ and O₁ ellipses are quite similar (not shown for sake of brevity), suggestive of high-quality and reliable ice-drift data. Ellipses are flat and elongated along the coastline [e.g., at CRS Odoptu the azimuths of the major axes are between 347.8° (degrees true) and 350.6° for K₁ and between 346.4° and 348.6° for O₁] and all have clockwise rotation. Tidal ice-drift amplitudes at CRS Odoptu gradually increase seaward from 28.4 (at S1) to 34.4 cm s⁻¹ (at S4) for K₁ and from 27.5 to 31.5 cm s⁻¹ for O₁. Presumably, this seaward increase in amplitude is due to reduced coastal and bottom friction, which, in turn, arise from the effects of land-fast ice and internal ice stress within an ice-drift boundary layer (cf. Thorndike and Colony 1982; Overland and Pease 1988). A typical width of land-fast ice in the study region is 2–3 km (cf. Tambovsky et al. 2001). The tidal ice-drift motions within the near-coastal boundary layer were found to have significant temporal variations. For example, at the 16-km distance (S4) at site OD, the K₁ amplitudes varied with time from 24 to 40 cm s⁻¹, and the O₁ amplitudes varied from 27 to 38 cm s⁻¹. These temporal variations are well correlated for different offshore distances and for different constituents (Fig. 7). Comparison of tidal amplitude distributions with 1993 satellite images of ice on the Sakhalin shelf (Martin et al. 1998; Preller and Hogan 1998), as well as with the coastal visual observations made during the radar ice measurements (Tambovsky et al. 2001), indicates that minimum tidal ice-drift amplitudes (in particular, those in April 1993) occurred during periods of the highest ice concentrations (>85%–90%) in this region. Maximum tidal amplitudes were associated with periods of lowest ice concentrations (<50%–60%). This suggests that in May when the ice began to melt and the ice-covered area decreased the ice drift became free and tidal motions became as intensive as in summer (summer tidal amplitudes at station Omb are indicated in Fig. 7 by a dashed line).

b. Alongshore tidal variations

To examine the spatial variations in diurnal tidal motion along the Sakhalin coast, we combined the ice-drift data for 1993 and 1994 and the data from 32 current-meter moorings on the northeastern shelf of Sakhalin Island. The current measurements were made in different years and different seasons. Despite the different observation dates, the computed tidal constants are in good agreement, indicating the stable predominantly barotropic character of diurnal tides in this region. Plots of the alongshore current amplitudes and phases for the K₁ and O₁ constituents are presented in Fig. 8. Large errors for cross-shore phases and relative amplitudes, which are 15–20 times those for the alongshore component (see section 3a) prevent us from the constructing corresponding plots for the cross-shore motions. Figure 8 is consistent with the results in Fig. 6 and has the same specific features, namely,

1. a zone of large-amplitude K₁ tidal currents bordering the northeastern end of Sakhalin Island,

2. an abrupt southward decrease in K₁ tidal velocities beginning around 51.5°N latitude,

3. a zone of minimum currents at approximately 51.0°– 51.2°N latitude, and

4. evidence (from the alongshore K₁ phase change) for southward propagation of the K₁ tidal wave along the coast of Sakhalin.

c. Modeling diurnal shelf waves

Rabinovich and Zhukov (1984) were the first to suggest that strong diurnal currents on the northeastern shelf of Sakhalin Island are produced by tidally generated, coastally trapped shelf waves. Because diurnal shelf waves are formed through the joint effect of earth's rotation and shelf topography rather than gravity, their energy is predominantly kinetic, so these waves produce negligible sea level variations but significant tidal currents (LeBlond and Mysak 1978; Mysak 1980). Southward propagation of diurnal tidal motions along the northeastern coast of Sakhalin Island is consistent with the theoretical direction of shelf waves (cf. Mysak 1980; Crawford and Thomson 1984). A least squares analysis using the observed phases of the diurnal currents gives wave phase speeds c = 4.0 m s⁻¹ for K₁, and c = 4.2 m s⁻¹ for O₁ (Fig. 8a). Ice-drift phases at stations CL and OD are in good agreement with current-meter phases and phase speed estimates, while the KM phases are outliers. Slightly different phase speeds for the two diurnal constituents (which is evidence for wave dispersion) are in good agreement with theoretical estimates of phase speed of diurnal shelf waves for the central part of the northeastern Sakhalin shelf (3.9 m s⁻¹ for K₁ and 4.3 m s⁻¹ for O₁) presented by Rabinovich and Zhukov (1984). Similar values were obtained by Kowalik and Polyakov (1998) based on their barotropic numerical model of the Okhotsk Sea tides, specifically, c = 3.35 m s⁻¹ (K₁) and c = 3.70 m s⁻¹ (O₁) for the central part of the northeastern shelf of Sakhalin Island.

Current amplitudes (Fig. 8b) have a complicated alongshore structure. On the northern part of the shelf (from 54.4° to 51.8°N), amplitudes of alongshore diurnal currents remain strong, approximately 35–50 cm s⁻¹ for K₁ and 30–40 cm s⁻¹ for O₁. However, in the vicinity of Nabil Bay (51.8°N), the K₁ and O₁ amplitudes drop abruptly, with diurnal currents in the region 51.3°– 50.3°N having speeds of only a few centimeters per second. The numerical simulations by Kowalik and Polyakov (1998) show a similar alongshore current structure with strong diurnal currents on the northern shelf attenuating rapidly southward, reaching minimum velocities in the vicinity of 50.5°–51.5°N (Fig. 6). Using trajectory data from 20 surface Argos drifters in the Sea of Okhotsk (August–September 1999), Ohshima et al. (2002) also found strong diurnal tidal currents over the shelf shallower than 200 m north of 51.5°N, but weak diurnal currents south of 51.5°N. The area of broken ice in the satellite image presented in Fig. 2 also closely coincides with the zone of strong computed diurnal tidal currents (Fig. 6) located north of 51.5°N.

The model by Rabinovich and Zhukov (1984) accounts for the phase behavior of the currents (Fig. 8a) but not the amplitude variations (Fig. 8b). An alternate model, which was successfully applied by Foreman and Thomson (1997) to the Pacific shelf of Vancouver Island, involves frictional attenuation of diurnal shelf waves. According to this model, friction and scattering can cause the amplitudes of the alongshore diurnal currents υ to decay exponentially, such that υ (y) ∼ exp(−δy), where y is the distance from the source area, and δ is the decay coefficient. [Numerical results of Kowalik and Polykov (1998) indicate that the source area of diurnal shelf waves on the northeastern shelf of Sakhalin Island is Cape Yelizavety, the northernmost end of the island.] However, for the Sakhalin coast the observed alongshore velocity changes are not accurately described by an exponential decay (see Fig. 8b). We, therefore, conclude that the southward amplitude decay arises not from friction and scattering but from alongshore changes in the cross-shore shelf topography, which are the key factors influencing shelf waves (cf. Mysak 1980; Crawford and Thomson 1984). The model by Rabinovich and Zhukov (1984) did not take these changes into account; all calculations were made for one cross-shelf profile (∼53°N). Consequently, for the present model, we undertook several numerical calculations to determine if current amplitude variations, in particular the abrupt drop in current amplitudes in the central part of the northeastern Sakhalin shelf, could be due to the rapid change in topography along this part of the shelf (Fig. 9a).

The linearized, barotropic long-wave equations for alongshore propagating free waves of angular frequency ω and wavenumber k in a rotating coordinate system yield the following equation for the cross-shore structure of the sea level displacement ζ(x) (LeBlond and Mysak 1978):

View Expanded

with boundary conditions

View Expanded

Here, x and y are the offshore (eastward) and alongshore (northward) directions, respectively; h = h(x) is the depth (uniform alongshore); and ′ ≡ d/dx. For subinertial frequencies (ω < f), (3)–(4) describe two types of trapped coastal waves: gravity-dominated Kelvin waves and quasigeostrophic continental shelf waves (LeBlond and Mysak 1978). Kelvin waves generate large sea level oscillations with relatively weak shelf currents, whereas shelf waves generate strong shelf currents with small sea level oscillations (Mysak 1980; Yefimov and Rabinovich 1980). Shelf waves of diurnal period have been shown to be responsible for strong diurnal currents on the northeastern shelf of Sakhalin Island (Rabinovich and Zhukov 1984; Suzuki and Kanari 1986; Kowalik and Polyakov 1998; Nakamura et al. 2000).

Rabinovich and Zhukov (1984) solved (3) and (4) using the initial parameter method with a steplike approximation to the shelf depth profile. Here, we have used the Brink and Chapman (1987, hereinafter BC87) algorithms, which better approximate the depth profiles and shelf wave dispersion curves. We applied the BC87 algorithms for 15 different cross-shore depth profiles along the northwestern coast of Sakhalin Island (Fig. 9a). Although the numerical integration scheme assumes uniform alongshore topography, one can compute changes in the shelf wave structure and parameters along the island from dispersion curves for different profiles (cf. Crawford and Thomson 1984). Shelf waves exist only on the negative side of the dispersion diagrams (Fig. 9b), indicating that the waves propagate southward on the Okhotsk shelf of Sakhalin Island with the coast on their right.

Computed dispersion curves (Fig. 9) are similar for the entire coast. However, the maximum allowable frequency for first-mode waves differs significantly for the different depth profiles (lines 1–15). Similarly, the wavelengths/phase speeds of the K₁ and O₁ shelf waves differ along the coast. The wider shelf along the northernmost part (line 1) and the central part of the northeastern coast of the island (lines 8 and 9) support longer-wavelength, more rapidly propagating shelf waves, while the narrower shelf between these two areas (lines 2–5) supports shorter and slower shelf waves. Maximum first-mode shelf wave frequencies depend on the depth contrast between the coastal shelf and the open ocean. Frequencies are normally higher for well-defined shallow shelves and steep slopes and lower for smooth gentle shelves and slopes. For the area seaward of CRS Komvro (lines 13–15), computed dispersion curves for first-mode shelf waves are below the frequency threshold for diurnal tides (Fig. 9b). Presumably, it is for this reason that diurnal tidal currents are negligible in this region (Figs. 6 and 8b). Ohshima et al. (2002) came to a similar conclusion based on the shelf wave dispersion relations for the averaged bathymetry north and south of 51.5°N. According to these authors, first-mode diurnal shelf waves can only exist north of 51.5°N.

Figure 10 shows the alongshore variation in the maximum frequency of the first-mode shelf wave and the corresponding phase speeds of this mode for the K₁ and O₁ tidal frequencies. There is close agreement between the alongshore zone of permitted diurnal shelf waves (Fig. 10a) and the zone of significant diurnal currents (Fig. 8b). On the basis of these results, we identify three distinct regions of diurnal tidal current behavior along the northeastern shelf of Sakhalin Island (these regions are marked by straight lines in Fig. 8b):

1. 54.5° to 51.5°N: a region of strong diurnal currents, with gradual north-to-south decrease in amplitude,

2. 51.5° to 51.3°N: a region in which there is an abrupt drop in diurnal current amplitude, and

3. 51.3° to <50.5°N: a region of weak diurnal currents.

As indicated by Figs. 9b and 10a, the first region is a zone of strong diurnal shelf waves, the second is a transition zone composed of evanescent diurnal shelf waves (maximum frequency drops below the threshold frequency), and the third is a forbidden zone for diurnal shelf waves. Although we lack observational data south of 50.5°N and have not computed shelf wave modes for higher latitudes, the upturn of the southern end of the curve in Fig. 10a suggests a possible area for diurnal shelf waves, and associated strong diurnal currents, south of our study region. Numerical computations of tidal currents for the Sakhalin shelf by Kowalik and Polyakov (1998) support this possibility (cf. Fig. 6).

Several details are worth noting. For example, both the numerical modeling of tides in the Sea of Okhotsk by Kowalik and Polyakov (1998) (Fig. 6) and our estimates of the observed K₁ tidal currents (Fig. 8b) suggest a local minimum in K₁ coastal currents around 53.5°N. According to the numerical calculations, the maximum frequency of the first-mode waves has a local minimum in this area (Fig. 10a), dropping below the threshold frequency for K₁ waves but not for O₁ waves. As a result, K₁ currents become weaker but O₁ currents remain about the same as currents to the north (Fig. 8b). As indicated by Fig. 10b, the predicted phase speeds of K₁ and O₁ shelf waves (about 3.4 and 3.8 m s⁻¹, respectively) are slightly less than the observed speeds of 4.0 and 4.2 m s⁻¹ (Fig. 8a), consistent with the influence of stratification upon these waves (cf. Crawford and Thomson 1984). In all our computations, the second-mode shelf waves have frequencies far below diurnal tidal frequencies (Fig. 9b) and are not expected to contribute to diurnal tidal currents on the northeastern shelf of Sakhalin Island.

d. Diurnal tidal currents and ice behavior

Satellite imagery suggests a possible linkage between ice concentration and tidal currents. As indicated by Fig. 2, the area of broken ice closely coincides with the zone of strong diurnal tidal currents associated with diurnal shelf waves (see Fig. 6). The relatively small wavelength scales (∼300 km) of these waves means that diurnal tidal currents in the vicinity of CL and in the area southward of OD (∼150 km separation) are roughly one-half of a wavelength apart and therefore flow in opposite directions at any given stage of a diurnal cycle (Fig. 11). Southward tidal drift at site CL corresponds to northward drift at the southern areas, and vice versa. During a rising tide, tidal currents in the northern and southern areas are directed toward one other (Fig. 11a), causing convergence of the sea ice. Twelve hours later, during a falling tide, current vectors are directed away from one other (Fig. 11b), causing divergence of the sea ice. This convergence–divergence action is focused at approximately 53°15′N and appears to be a possible cause for the ice cracking and hummocking observed in Fig. 2. Almost the same area of broken ice on the northeastern shelf of Sakhalin Island is clearly visible in satellite images of 24 March 1979 and 5 April 1979 (Figs. 4b,c in Wakatsuchi and Martin 1990). Moreover, in the image of 24 February 1979 (Fig. 4a in Wakatsuchi and Martin 1990), this zone totally coincides with the zone of the “Sakhalin polynya” commonly observed in this zone (cf. Martin et al. 1998). So, we assume that intensive shelf-wave-induced tidal currents not only contribute to ice breaking but also maintain the ice opening and polynya formation.

The intensity of this process presumably depends on the speed of the tidal currents. Maximum diurnal tides and associated currents normally occur when the lunar declination is greatest (“tropical tides”), while minimum diurnal motions occur when the declination is close to zero (“equatorial tides”) (Fig. 12). Fortnightly modulation of diurnal tides has a period of 13.61 days (≡1/2 of the “nodical month”) (Pugh 1987). In terms of the tidal constituents, fortnightly nodical modulation is associated with the superposition of K₁ and O₁ diurnal harmonics: maximum diurnal tidal sea levels and currents occur when the K₁ and O₁ are in phase and minimum when they are out of phase. This fortnightly modulation of tidal currents affects wind-forced ice drift (see section 4) on the Sakhalin shelf. During the period of equatorial tidal currents, if air temperature is sufficiently low and winds are not too strong, the sea ice can freeze into an extensive cohesive mass that would not respond to the local wind. Such a situation occurred on 6–11 April 1993 at site OD; tidal currents at the time of a near-zero lunar declination were weak, air temperature was low, and the ice froze in place. As a result, the correlation coefficient between the alongshore wind and ice drift dropped to near zero (Fig. 12). This observation is in agreement with theoretical results of Hibler (1986) for an idealized one-dimensional system with and without plastic ice interaction (his Fig. 6). More specifically, for times of strong ice interaction, there is a threshold wind speed of about 4.5 m s⁻¹ below which the ice does not move (unlike the case for free ice). However, once this threshold wind speed is exceeded, the ice begins to move quickly and, for increasing wind speed, ice flow velocity begins to rapidly approach that for free ice.

We remark here that the ice did not stop moving during two other periods of equatorial tides (22–26 March and 19–22 April 1993) because of strong winds and high air temperatures, respectively. In general, strong tropical diurnal tidal currents are likely to contribute to ice breaking and formation of free ice, while weak equatorial tidal currents likely result in an increase in ice compactness. The resulting feedback interaction between tidal currents and ice could significantly affect both processes.

a. Formulation of a wind–ice drift relationship

Another factor influencing ice-drift parameters is nonlinearity. McPhee (1982, 2002) examined various nonlinear sea-ice boundary layer formulations and showed that a quadratic relationship between wind and ice-drift better accounts for wind-induced motions at high wind speeds. Hibler (1986) suggests a nearly linear relation between the wind speed and ice drift for all but very low speeds, with a resulting greater sensitivity of the turning angle to the wind speed. This means that, in general, both a₀ and θ₀ are functions of the wind speed, |V|, although in the open ocean, they are expected to be invariant to the wind direction, φ. The latter assumption becomes invalid near the coast. Fissel and Tang (1991) used model (6) to examine the ice-drift response to wind forcing over the northern Newfoundland shelf and found α₀ varies from 0.026 to 0.054 and θ₀ from 10° to 63°. Although the model was originally formulated for the open ocean, Fissel and Tang (1991) established that proximity to the coast and direction of the wind relative to the coastline are the major factors influencing variability in wind factor and turning angle. Similarly, Overland and Pease (1988) indicated a strongly anisotropic response of the ice drift to the wind near coastal boundaries.

For the region under study, the influence of the coast and direction of the local wind relative to the orientation of the coast become crucial. Model (6) does not take these effects into consideration. Therefore, to account for the low-frequency ice drift on the northwestern shelf of Sakhalin Island, we applied a two-dimensional regression model based on the regional wind. Such models are widely used in oceanography and meteorology for analysis and prediction of ocean currents and other vector processes (cf. Emery and Thomson 2001). Specifically,

utτVtτEt(7)

where

View Expanded

a_ij are the regression (response) coefficients linking the cross-shore (u) and alongshore (υ) components of ice drift with the corresponding components (U, V) of wind velocity and random noise components (ε_u, ε_υ), and τ is the time lag between wind forcing and ice-drift response.

In the terminology of McNutt and Overland (2003), we have focused on “coherent scale” ice motions, that is, those motions having spatial scales of roughly 75– 300 km and temporal scales of approximately 3–7 days. To examine the ice-drift response to the wind, we first low-pass filtered simultaneous series of wind and residual (detided) ice velocities to remove fluctuations with frequencies ≥1 cpd. The resulting low-frequency local wind and ice velocities were highly correlated. Table 4 presents mean cross-correlation and regression coefficients (averaged over the entire observational period) for CRSs Komvro (1993) and Odoptu (1993 and 1994). Comparative results are shown for two offshore ice observation distances: 4 km (S1) for both sites, 12 km (S3) for Komvro, and 16 km (S4) for Odoptu. The results obtained for different stations and distances are in good agreement. The best results (maximum explained variance) were obtained for zero lag (τ = 0), when there is no time delay between wind forcing (input) and ice-drift response (output). The explained variance for the wind-drift regression is R²(σ²₀ − σ²_res)/σ²₀ ≈ 0.55–0.75, where σ²₀ = σ²_u + σ²_υ is the initial, and σ²_res is the residual variance of the low-frequency ice drift (Table 4). Thus, 55%–75% of the total energy in low-frequency ice-drift motions is determined by the wind through the relatively simple model (7). In most cases, R² values for the remote offshore observational areas (S3 and S4) are greater than for observational areas closest to shore (S1), where ice drift is more strongly influenced by the coast.

There are several factors that may be responsible for the unexplained variance (25%–45%) between wind and ice drift. First, this variance could, of course, be reduced by increasing the number of regression coefficients a_ij(τ_k), that is, by using more than one value for the time lag, τ_k, k = 1, 2, …. For example, Geiger et al. (1998) found 90% coherence between the modeled atmospheric field and the ice motions for the Wedell Sea. In this case, coherence can be viewed as an estimate of the correlation integrated over a range of time lags (cf. Emery and Thomson 2001). However, it is known that multilag regression models are less stable and reliable. A second factor that may be responsible for the unexplained variances is nonlinearity (cf. McPhee 1982, 1986, 2002; Hibler 1986). To determine possible effects of nonlinear input, we undertook several calculations using wind stress (i.e., quadratic wind velocity) as the input function in (6). Surprisingly, the results were worse than with wind velocity alone (R² was approximately 10% smaller), probably because of local characteristics of the wind and ice fields in this region. The residual variance also could be associated with time variations of the mean flow on the Sakhalin shelf (cf. Preller and Hogan 1998). Last, an important factor influencing ice drift, and probably responsible for unexplained variance, is the ice concentration and rheology (see section 5). As noted by Hibler (1986), because the force on the ice is given by the gradient of the ice stress, the ice motions may give the impression of free-ice drift in response to the winds whereas, in fact, ice stresses may be high and undergoing intense nonlinear interaction.

As was mentioned above, model (6) is described by two parameters: wind factor and turning angle, both independent on wind direction. In contrast, the four regression coefficients, a_ij in model (7)–(8), define the “response ellipse,” which is traced by the tip of the current velocity response vector during one complete rotation of the uniform unity wind vector (Table 4). For an isotropic (open ocean) response, the response ellipse is circular. Each response ellipse is described by four invariant parameters: the semimajor, A_max, and semiminor, A_min, ellipse axes (the maximum and minimum current responses); the orientation of the semimajor axis, θ_max; and the direction of the “effective wind” (producing maximum current response), φ_max (see the appendix for details). At this point it is worth noting the similarity between the response ellipses and ice stress or deformation ellipses (cf. Mellor 1986; Hibler 1986, Geiger et al. 1998; Richter-Menge et al. 2002). Although the processes leading to these two elliptical structures may be related, investigation of any dynamical relationship is nontrivial and beyond the scope of the present study.

Derived response ellipses are presented in Fig. 13. As with tidal ellipses (insets in Fig. 6), all response ellipses are oriented along the coastline. The marked flatness of the response ellipses indicates that the ice reaction to the wind is strongly anisotropic: Ice response in the alongshore direction is much greater than in the cross-shore direction [3.0–6.0 and 0.2–1.5 (cm s⁻¹)/(m s⁻¹), respectively]. The alongshore values of the response coefficients (i.e., the wind factor) are similar to those obtained by Fissel and Tang (1991) for the Newfoundland shelf [2.6–5.4 (cm s⁻¹)/(m s⁻¹)], but significantly greater than those estimated by Thorndike and Colony (1982) for the Arctic Ocean [1.5–1.8 (cm s⁻¹)/(m s⁻¹)]. Response ellipses for the remote offshore observational areas (S3, S4) are from 50% (KM) to 15%–20% (OD) greater than for the areas closest to shore (S1). As in the Nansen– Ekman theory, ice-drift vectors are mainly directed to the right of the wind direction. Thus, even winds blowing cross-shore can generate alongshore ice drift. Vectors of maximum ice drift are typically directed 20°–40° clockwise to the “effective wind” direction, close to the theoretical Nansen–Ekman angle of 28° for the open ocean and findings by Thorndike and Colony (1982), Fissel and Tang (1991), and Stern and Moritz (2002). However, in contrast to the Nansen–Ekman theory, turning angles of the ice drift and the wind vectors are highly nonuniform. In particular, for closely meridional winds, ice motions are directed counterclockwise to the wind vector (Fig. 13).

The response ellipses for radar sites KM and OD for 1993 are quite similar; in both cases, the ellipses are almost flat and have similar angles of the ice drift relative to the wind vectors (pairs of thick and thin arrows isolated in the four quadrants of Fig. 13). However, the KM ellipse is about 1.5 times as long, suggesting that wind-induced alongshore ice drift in the vicinity of site KM is 1.5 times that in the vicinity of site OD. This explains why the variance of low-frequency ice-drift motions at KM is more than 2 times that at OD (Table 2). This difference may be related to the relatively gently deepening continental shelf and slope seaward of site KM (line 13 in Fig. 9c). The relatively shallow depths in this region appear to support the formation of intense, wind-induced, low-frequency currents. We assume that wind-induced currents are stronger in this region because momentum transferred from the wind to the currents is distributed over a thinner portion of the water column.

Although model (7)–(8) is clearly an oversimplification, it is consistent with our attempt to characterize the dominant low-frequency mechanisms forcing spatial and temporal variability in ice drift on the Sakhalin shelf. In general, higher-order models are likely needed, especially for regions undergoing marked deformation and shear. McPhee (1986, 2002) and Hibler (1986) also emphasize the considerable effects attributed to ice–water boundary layers, ice rheology, and other dynamical factors.

b. Time variation of ice drift

The main features of the ice-drift response ellipses (orientation, shape, and turning angles) at two different sites (KM and OD) computed for the same year (1993) are similar (Fig. 13). In contrast, the response ellipses at the same site (OD) but for two different years (1993 and 1994) are significantly different. The 1994 ellipses for both the nearshore (S1) and offshore (S4) distances are more circular, suggesting a stronger cross-shore wind response when compared with 1993. Also, turning angles between the direction of the wind and ice drift in 1994 were smaller when compared with those for 1993. We assume that these differences arise from the higher ice concentration in 1993 when compared with 1994.

To estimate the influence of ice concentration on wind-induced ice drift, we divided the 1993 data into four 20-day segments and examined these segments separately. The four time segments were characterized by markedly different ice type and concentration (Tambovsky et al. 2001): 1) the first period (centered on 21 March) had an ice concentration of approximately 80%– 90% with the ice field consisting of large and small broken floes; 2) the second period (centered on 9 April) had the highest ice concentration (95%–100%), consisting of large ice fields; 3) the third period (centered on 27 April) consisted of gradually melting ice, with reduced concentration (60%–80%) and diminished flow sizes; and 4) the last period (centered on 13 May) was associated with intensive ice melting, during which time the ice concentration reduced to 40%–50% and the ice mostly had the character of shuga. The computed response ellipses (Fig. 14) demonstrate significant temporal changes in the ice-drift response to the wind, apparently reflecting the corresponding changes in ice features. During the period of the highest ice concentration (the second period), the response ellipses became almost flat, indicating that the ice-drift response was almost rectilinear (alongshore). Even the magnitude of the alongshore response (major ellipse axis) was smaller during this period in comparison with the others. During the early spring (the first period), and especially during the third period, the response ellipses became larger and more circular, indicating the presence of more intensified cross-shore ice motions. Last, during the late spring (the fourth period) the response ellipses changed from flat to oval. Apparently, the last period corresponds to a time of free-ice drift, while other periods reflect a strong interaction between the internal ice stress and the coast. This effect was maximum during the second period. These results are in good agreement with theoretical studies on the influence of ice stress on ice motions and are consistent with Hibler (1986): “The most obvious effect of the ice stress is to change the ice drift direction and magnitude from the free drift case.”

To examine variations over time in the low-frequency winds and associated ice-drift motions, we used a multiple filter technique (MFT) similar to wavelet analysis (cf. Emery and Thomson 2001; Rabinovich and Thomson 2001). For this analysis, we selected simultaneous low-frequency series of wind and offshore (16 km) ice drift at CRS OD from 12 March to 22 May 1993 and focused on the frequency band from 0.03 to 0.6 cpd (periods from approximately 33 to 1.7 days). The f–t diagrams (Fig. 15b) reveal a very close similarity between time variations in the alongshore wind (V) and alongshore ice drift (υ). Close agreement of these motions is observed in both frequency and time, with the main energy bands centered at periods of 10–11, 5, and 2.5 days. It is evident from these plots that time– frequency variations in the alongshore wind are the primary cause of the ice-drift velocity fluctuations.

Variations in the cross-shore component of the wind and coincident ice motions were poorly correlated for about two-thirds of the observational period. The situation changed dramatically after yearday 120 (30 April 1993) when variations in the wind velocity and ice drift became similar in both the frequency and time domains (Fig. 15a). A possible cause for this change is that, by the end of April, the ice cover had begun to break into smaller ice floes and to melt, creating larger areas of open water, allowing the ice pack to more easily respond to the cross-shore wind component. These results are consistent with the results from the response ellipses shown in Fig. 14. Thus, during high ice concentrations (when the sea ice is most extensive and internally cohesive), the ice drift is almost entirely alongshore and highly correlated with the respective component of the wind stress. However, in late spring, when sea ice becomes broken and patchy (i.e., free), it responds to both the cross-shore and alongshore components of the wind.