The Elson Lagoon (Fig. 1) is the northern most coastal lagoon of the United States bounded roughly by 71°12′N, 71°23′N, 156°36′W, and 155°54′W. It is approximately a rectangle of ~8 km × 25 km (Fig. 1), with shallow water (2–3 m) in the interior and deeper channels at the passes leading to the coastal ocean and Beaufort Sea. The Elson Lagoon is oriented in the northwest-southeast direction. The axis of the lagoon is estimated to have a ~–30° angle from the true west-east direction (Fig. 1b). It is part of a larger lagoon of a flipped “L” (Fig. 1a). Along the coastal side, there is about 11 km open to the ocean between barrier islands. This larger lagoon has a length scale of ~55 km in either direction of the flipped “L” (Fig. 1a). The deepest location is at the northwestern-most channel, the Eluitkak Pass, with a maximum water depth of ~16 m and width of ~275 m. East and southeast of the Eluitkak Pass, there is a chain of islands (i.e., the Crescent, Tapkaluk, and Cooper Islands). The width of the inlet between Crescent Island and Tapkaluk Island is ~0.7 km, while that between Tapkaluk Island and Cooper Island (the Ekilukruak Entrance) is 10 times as wide: ~7.1 km. Another major inlet is at the eastern end of the lagoon (marked as B in Fig. 1a).

In this area of the Alaska Arctic, the meso-scale atmospheric high- and low-pressure systems are frequent. Cyclones and anti-cyclones have a great impact on high-latitude communities and nearshore waters (Zhang et al., 2004). During summer time, the strong Beaufort Sea high usually centers over the Chukchi Sea and Beaufort Sea. They are mostly related to the Northern Annular Mode and the Pacific-North American teleconnection pattern (Wu et al., 2014). In between these high-pressure systems are low-pressure centers or cyclones (Serreze, 1997) or fronts separating different air masses, which can be associated with storms (Vavrus, 2013). The movement of these systems over the Arctic coastal areas causes the local wind to shift between northeasterly and westerly or northwesterly. The importance of wind to the ocean circulation, exchange between the lagoons and coastal ocean, and biological responses has long been recognized. The water exchange between the Elson Lagoon and the Beaufort Sea continental shelf was studied (Okkonen, 2008) with bottom mounted current meters measuring only the near bottom currents between August and September of 2006. The study found that the near bottom velocity was correlated with the east and west winds and some aggregations of zooplankton were found at the outflow fronts.

Aimed at determining the response of flow of water in and out of the Elson Lagoon with multiple inlets to winds of meso-scale cyclonic and anti-cyclonic weather systems, we deployed a RDI 1 200 kHz Broadband Workhorse acoustic Doppler current profiler (ADCP) at the Eluitkak Pass for approximately 4.9 days between 00:00 August 19 (Day 231 from January 1) and 20:48 UTC August 23 (Day 235), 2013 . The relatively short deployment is because of the frequent severe weather conditions, rough sea state, and potential damages of occasional floating ice. This instrument was deployed at 71°21.560′N, 156°21.152′W (Fig. 1), on a relatively flat bottom at 9.6 m depth, slightly east of the deepest water (~16 m) in the main channel. The ADCP was mounted on an aluminum cross comprised of four weighted legs. The ADCP was configured to record the three components of the velocity vector at 0.5 m vertical intervals every 60 seconds. Within each of the 60-second intervals, the ADCP sampled 50 times and provided an average for the ensemble.

In addition, a HOBO U20 Titanium Water Level Logger was deployed at about 0.5 m below the surface at the northern shore of the North Salt Lagoon at 71°20.459′N, 156°37.164′W. The North Salt Lagoon is an enclosed circular lake of ~1.3 km diameter connected to the Elson Lagoon at the south-western corner of the latter (Fig. 1). The U20 recorded data at 60 second intervals. This sensor was deployed in the North Salt Lagoon between 23:33 August 19 and 13:25 UTC August 23, 2013 . The U20 pressure sensor was used together with the pressure sensor on the ADCP to derive a pressure gradient, which is expected to vary with the wind direction and magnitude. The true water level variation was resolved with an atmospheric reference logger (Bosch BMP085) several km away at 71°16.522′N, 156°38.512′W, configured to sample at 0.5 Hz with an equivalent resolution of height change of 0.25 m in the air at an averaged sea level condition, or 0.306 mm of water level change at 4°C.

Large-scale weather maps are obtained from NOAA (Fig. 2). The meteorological conditions at the ADCP deployment (00:00 UTC August 19, 2013) were dominated by a low-pressure system (cyclone) located over the Bering Strait (sea-level air pressure ~999 hPa), with a linear stationary front connecting several low-pressure centers across Alaska into western Canada in a northwest-southeast orientation (Fig. 2a). Coincident with this was another low-pressure system located over Ellesmere Island in northern Canada (sea-level air pressure ~994 hPa). A high-pressure (anti-cyclone) system was juxtaposed to the north of the study area, in between these major low-pressure systems (a 1 018 hPa sea-level air pressure contour can be seen at top of Fig. 2a—note that the contour interval is 2 hPa), generating relatively strong northeasterly winds at the Elson Lagoon (Fig. 3). The northeasterly wind peaked before August 20 (Day 232, Fig. 3c). This condition (Fig. 2b) lasted for approximately a day as the systems gradually moved to the south (Fig. 2c). As a result, the high-pressure system moved over the study area (Fig. 2c). Concurrently, as the high-pressure system moved southeastward, the stationary atmospheric front developed into a couple of cold fronts occupying the Bering Strait and Western Alaska. At 03:00 UTC on August 21 (Day 233), the center of the high-pressure moved over the Barrow area and occupied there for less than 24 h (Fig. 2c). This is confirmed by the air pressure data recorded in Barrow (Fig. 3a). During this period, the measured wind intensity at the study area was weak (Fig. 3c, Day 233). As the low-pressure originally centered over the Ellesmere Island area moved to the south on August 22 (Day 234), pushing the high-pressure system away, the study area was under the influence of a persistent northwesterly wind (Fig. 2d). This variation in wind direction is typical for the area during the summer period with cyclones and anti-cyclones passing the region, resulting in variation in dominant wind directions (e.g., northeasterly to westerly or northwesterly). The change in wind direction can result in the presence or disappearance of floating ice in the area. The circulation with the presence of ice can be more complicated but is not discussed here.

The air pressure data measured on land at intervals of 2 seconds are re-mapped to have the same time intervals of the HOBO U20 total pressure or water level data (i.e., 60 second intervals). For cross verification, we also use the air pressure data available from the nearby Barrow Airport (71.28°N, 156.79°W). The air pressure is subtracted from the total pressure measured by the HOBO sensor to calculate the water level (m), which is then de-meaned to obtain the water depth variation from the mean. The de-meaned time series is then low-pass filtered with a 30-hour sixth order Butterworth Infinite Impulse Response (IIR) filter (Emery and Thomson, 2004) which effectively removes the semi-diurnal tidal oscillations from the water level data. The 4.9 days of ADCP deployment encompassed about 9 semidiurnal tidal cycles. The averaged tidal range for that time period was about 0.2 m (Fig. 4), characteristic of a typical micro tidal system, and justifying the need to subtract the air pressure effect because of its relative significance due to the small variation of tides.

The ADCP also recorded water depth above the instrument. This water depth includes the effect of atmospheric pressure. A similar procedure is applied to remove the air pressure effect on depth measured from the ADCP. The mean value of the water level over the entire study period of ~4.9 days is then subtracted. After this, the surface elevation measured by the ADCP (ζ₁) at Eluitkak Pass and that measured by the HOBO at the North Salt Lagoon (ζ₂) are used to calculate the difference of sea level anomaly:

Because these two stations are so close (~8 km), the mean sea level of the two are essentially the same, and the difference is caused by wind effect only.

The water velocity data from the ADCP indicate a stronger along channel component than the cross-channel component, with the maximum cross channel velocity component being about 1/3 of that of the along channel component. Each component has detectable tidal signals. The velocity magnitude is generally larger near the water surface than that near the substrate, apparently because of bottom friction. The velocity at each level is also low-pass filtered by the 30-hour Butterworth filter. To avoid contaminated data near the surface due to the side-lobe effect of the transducers, the analysis of the velocity profile is restricted to below 9.36 mab (meters above bottom). The blue lines above the velocity contours in Figs 4c and d show the surface elevation measured by the ADCP’s pressure sensor excluding the air pressure effect. The low-pass filtered along channel velocity component appears to have a variation very similar to that of the pressure difference (δζ) at all levels (Fig. 4b), indicating a strong linear correlation.

To examine the statistical relationships between the wind and flow velocity, we now look at the two-dimensional momentum and continuity equations:

in which u, v, ζ, f, g, h, x, y, t, ρ, τ_ax, τ_ay, τ_bx, τ_by and p_a are the depth averaged east and north velocity, surface elevation, Coriolis parameter, gravitational acceleration, depth, east and north coordinates, time, water density, east and north wind stress components, east and north bottom stress components, and atmospheric pressure, respectively. In a rotated coordinate system, the new x-axis will be along the major axis of the lagoon (positive toward the southeast).

Each of the variables in the above equations should have a “high” frequency component (tidal or higher frequency oscillations) and the “low” frequency “subtidal” component. For example, for velocity u and v, and water elevation ζ, they can be expressed as

The subscripts H and L denote the high frequency and low frequency, respectively.

If the two frequency regimes are “far apart” (with no overlaps), either of them can be effectively filtered out by a digital filter. Thus we can apply a low-pass filter to keep only the low-frequency or the so called subtidal component (e.g., u_L, v_L, ζ_L). It can be argued that for the first order approximation, the nonlinear advective terms can be neglected for convenience. We will however keep the nonlinear stress terms. The wind-driven subtidal motion can thus be expressed as:

We can now do a quick order-of-magnitude estimate based on our data (Fig. 4). The variation in u_L, v_L is ~0.6 m/s over 3 days, while the change in ζ_L is ~0.17 m over 3 days. Consider that the lagoon has a width of ~8 km, we can estimate that $\frac{{\text{∂}{u_L}}}{{\text{∂}t}}$ and $\frac{{\text{∂}{v_L}}}{{\text{∂}t}}$ are ~2.3×10^–6 m/s², and ${{g}}\frac{{\text{∂}{\zeta _L}}}{{\text{∂}x}}$ is ~2.1×10^–4 m/s². This tells us that the local rate of change of the subtidal flow components are two orders of magnitude smaller than the subtidal pressure gradient force terms. Therefore, we can use the following approximate momentum equations:

The wind stress is

in which ${{\text{τ}}_a} = \left({{\tau _{ax}}, {\tau _{ay}}} \right)$ is the wind stress vector, ${C_{Da}}$ is the wind drag coefficient on the ocean surface, w=(w_x, w_y) is wind velocity vector, and ρ_a is the air density.

Equations (6), (7), and (8) have three unknowns (u_L, v_L, ζ_L). With proper boundary and initial conditions, a solution can be obtained for the unknowns. However, with the complicated bathymetry, coastlines, and temporally and spatially varying forcing factors, it is almost impossible to obtain an exact and general (or even a special) solution. We now seek to derive a possible relationship between the forcing (wind) and response (velocity), which can be used for a statistical regression.

Any solution for (u_L, v_L, ζ_L) can be expressed in theory by the general format:

in which the air pressure anomaly $\Delta {p_{aL}} = {p_{aL}} - {p_{aL0}}$, where p_aL0 is the background or environmental air pressure or the average air pressure at sea level. Again, the subscript L indicates a low-pass filtered quantity. Note that the Coriolis force is included for completeness. If the Coriolis effect is negligible, the format of the above solution and Eqs (12)–(14) still remain the same. Now we do a Taylor series expansion for the above equations in terms of the variables $\Delta {p_a}, {\tau _{ax}}$ and τ_ay to the first order:

All the derivatives in Eq (15), (16) and (17) are evaluated at (0, 0, 0) for $\left({\Delta {p_{aL}}, {\tau _{axL}}, {\tau _{ayL}}} \right)$. In the above equations, the wind stress terms can be further expressed by wind velocity components, i.e., for the wind stress itself, similar to the quadratic bottom friction, a Taylor series expansion (e.g., Proudman, 1953; Parker, 1984) can be used to express the stress in terms of a linear term and a higher order nonlinear term, i.e.,

where α, β, γ, δ are all constants of the Taylor series expansions. Substitute Eqs (18) and (19) into Eqs (15)–(17) and neglect the higher order terms we obtain:

These can be rewritten as:

in which, $A = {\rm{\alpha }}\frac{{\text{∂}{u_L}}}{{\text{∂}{\tau _{axL}}}}$, $B = {\rm{\beta }}\frac{{\text{∂}{u_L}}}{{\text{∂}{\tau _{axL}}}}$, $C = {\rm{\gamma }}\frac{{\text{∂}{u_L}}}{{\text{∂}{\tau _{ayL}}}}$, $D = {\rm{\delta }}\frac{{\text{∂}{u_L}}}{{\text{∂}{\tau _{ayL}}}}$, $E = \frac{{\text{∂}{u_L}}}{{\text{∂}{p_{aL}}}}$, F=u_L(0, 0, 0), $G = {\rm{\alpha }}\frac{{\text{∂}{v_L}}}{{\text{∂}{\tau _{axL}}}}$, $H = {\rm{\beta }}\frac{{\text{∂}{v_L}}}{{\text{∂}{\tau _{axL}}}}$, $I = {\rm{\gamma }}\frac{{\text{∂}{v_L}}}{{\text{∂}{\tau _{ayL}}}}$, $J = {\rm{\delta }}\frac{{\text{∂}{v_L}}}{{\text{∂}{\tau _{ayL}}}}$, $K = \frac{{\text{∂}{v_L}}}{{\text{∂}{p_{aL}}}}$, L=v_L(0, 0, 0), $M = {\rm{\alpha }}\frac{{\text{∂}{\zeta _L}}}{{\text{∂}{\tau _{axL}}}}$, $N = {\rm{\beta }}\frac{{\text{∂}{\zeta _L}}}{{\text{∂}{\tau _{axL}}}}$, $O = {\rm{\gamma }}\frac{{\text{∂}{\zeta _L}}}{{\text{∂}{\tau _{ayL}}}}$, $P = {\rm{\delta }}\frac{{\text{∂}{\zeta _L}}}{{\text{∂}{\tau _{ayL}}}}$, $Q = \frac{{\text{∂}{\zeta _L}}}{{\text{∂}{p_{aL}}}}$, R=ζ_L(0, 0, 0). It should be noted that this is not an explicit solution as the coefficients are all unknowns. However, Eqs (23), (24), and (25) suggest that the low-pass filtered velocity and elevation are linearly related to air pressure anomaly, the wind speed components, and their squares, which we will utilize in the next section for a regression analysis.

From the above discussion and derivation, the following regression equation is used:

in which u(t), W_a(t), W_c(t) are, respectively, the time series of the low-pass filtered outward component of the velocity (positive outward) at Eluitkak Pass, the along-lagoon wind velocity component (positive toward the southeast), and the cross-lagoon wind velocity component (positive toward the northeast). A, B, C, D, and E are the regression coefficients. Note that in Eq (26), we ignored the air pressure terms, which are found to be negligible compared to the wind velocity component terms. We nevertheless keep these terms in Eqs (23)–(25) in case for different applications they might be more important. The discussion can be extended to 3-D problems and Eq (26) can be applied to data at different depths.

The results indicate that the subtidal velocity is correlated to and apparently largely determined by wind velocity. When the north-northeasterly wind reaches its maximum, just prior to day 232 (August 20) (Fig. 5), the water velocity is also at a maximum, indicating a current going out of the lagoon against the wind. When the wind switches to westerly and northwesterly on Day 235 (August 23), the velocity reverses its direction. The R² values at all depths are high (all above 0.9, Table 1). The signs of the regression coefficients (A, B, C, D, and E) are all consistent at different depths. For example, A is always negative, meaning that a negative along-lagoon wind will contribute a positive outward flow at the Eluitkak pass. Likewise, C is negative, meaning a northeasterly wind will contribute a counter-wind flow (outward flow) at the pass and vice versa.

The fact that a northeasterly wind causes a northeasterly flow (out of the lagoon) through the narrower inlet verifies this idea: water in the wider openings at the eastern Elson Lagoon receive more acceleration under roughly the same wind stress due to its shallow water and broad opening; while the much narrower opening at the northwestern end receives much less forcing from the wind stress and less easier to accelerate by wind due to its much deeper water and much narrower width for the integrated wind forcing across the inlet. The barrier islands can effectively block the flow and therefore wind stress need not to be considered there for the purpose of water transport through the inlets. The larger wind forcing at the larger openings, especially the major eastern inlet (B on Fig. 1a), will tend to produce a flow in the direction of wind; only to be balanced by a return flow through the Eluitkak Pass. This can also be explained from a vorticity or torque point of view: the large wind forcing for transport in the eastern inlets than the northwestern inlet causes a “torque” similar to that discussed by Engelund (1986), Fischer (1976), and Li (2013). In other words, the wind pushes water into the lagoon from the wider openings on the eastern end, generating a higher water level on the eastern side, causing a pressure gradient induced flow to exit the lagoon through the northwestern narrow inlet, the Eluitkak Pass.

Other factors that can affect the exchange flow such as coastal current and river discharge apparently have less importance than wind in this case. This is most likely because the system is semi-enclosed by a series of barrier islands, making the integrated wind effect at the narrow tidal pass amplified. The method presented here is for ice-free conditions in the summer. With a significant presence of floating ice, the exchange flows may be affected.

The Delft3d-FLOW model is used to simulate wind-driven circulation in Elson Lagoon and Eluitkak Pass. The model domain for the Delft3D contains a 555×279 curvilinear orthogonal grid in the horizontal which extends from 154.56°W to 156.48°W and 71.25°N to 71.53°N (Fig. 6). Grid resolution varies between roughly 20 m and 2.5 km. The bathymetry data are obtained from the National Geophysical Data Center (NGDC) with the approximate spatial resolution of 90 meters (www.ngdc.noaa.gov/mgg/coastal/crm.html) and our own measurements in the Eluitkak Pass in August 2013. The time step Δt is set to 0.1 minute. The vertical discretization is based on sigma coordinate with 5 layers.

Tidal constituents at the open boundary are extracted from the US Army Corps of Engineers regional ADCIRC model (Westerink et al., 1993). The model is forced by spatially uniform and temporally variable winds obtained from the Barrow Airport station (71.28°N, 156.79°W) managed by the National Climatic Data Center (NCDC).

The numerical model reproduces tides and tidal currents consistent with the observations, especially considering the small magnitude of tides in this micro-tidal region (Fig. 7). The comparison between model results and measured current velocity time series is made at the ADCP site at 71.35°N, 156.35°W. The model captures tidal currents in and out of the inlet as well as the effect of wind. There is however some discrepancies, most likely caused by possible errors in bathymetry. This study site is remote and has no supporting facility for extensive survey operations and thus bathymetry data are very limited, both inside and outside of the lagoon. Our measurements of water depth mainly covered the channel at the Eluitkak Pass and inside the lagoon where water depth has been measured by acoustic sensors on a boat mounted ADCP or an unmanned vehicle.

To quantify the effect of various wind directions on the exchange flows through Eluitkak Pass and Elson Lagoon, we have designed and conducted a series of numerical experiments (Table 2) with this model. Considering the predominant wind conditions of the area, the experiments included easterly, northeasterly, and northwesterly winds. The wind speed is assumed in the model linearly increasing from 2 m/s to 15 m/s within 15 days for each of the three wind directions (Table 2).

Under easterly wind, the northwestern inlet (the narrow Eluitkak Pass) shows outward flows while the eastern inlets (including the wider Ekilukruak Entrance) show inward flows (near surface flows in Figs 8a and d). Under northeasterly wind, the Eluitkak Pass also has outward flows and the eastern inlets inward flows (Figs 8b and e). The outward flow through the northwestern inlet is smaller in magnitude, but still against the wind. Under northwesterly wind, the Eluitkak Pass has inward flows while the eastern inlets have outward flows (Figs 8c and f).

When the wind speed varies from 2 to 15 m/s linearly over 15 days, the water level difference between the HOBO site (Fig. 1b) and ADCP site varies. Under east wind, this water level difference (m) is positive (water level at HOBO site is higher than that at the ADCP site), consistent with an outward flow (Fig. 9a). This is confirmed by Fig. 4b of the observed water level difference. The actual magnitude from measurement is about 0.17 m between the HOBO site and ADCP site. This value is comparable to the maximum magnitude of ~0.16 from the model (Fig. 9a). The water level difference between Point A (Fig. 1b) and ADCP site is smaller for the east wind condition. For the northeast (Fig. 9b) and north winds (Fig. 9c), the water level differences are similar which are all consistent with outward flows at the Eluitkak Pass. For the northwest wind case (Fig. 9d), the water level difference between the HOBO and ADCP sites changes sign, indicating a tendency of inward flows. The water level at Point A is slightly higher than that at the ADCP site. These results from the numerical experiment are all consistent with the regression analysis using the in situ data.

In a one-dimensional channel with a closed end in the downwind direction, and under a constant wind forcing towards the closed end, the steady-state force balance would be

If the wind varies in magnitude and direction, or if the water cannot be viewed as “one-dimensional”, or if the end is not fully closed (e.g., with a narrow inlet allowing water flowing in or out), the above force balance would not hold and a local acceleration would have to be included. A two-dimensionality of motion would also invalidate the above equation. In Huang and Li (2017) however, it is shown that the above balance for subtidal variation is quite accurate even when wind is changing.

Li et al. (2018a) further investigated the adjustment of wind-driven flows and demonstrated that a change in wind will produce damped oscillations similar to the solution of:

where m, r, ω₀ are all constants, t is time, y is the dependent variable (here the water slope), and f(t) is the forcing function. The solution is a forced damped oscillation in a form like

where the first term on the right-hand side is a free damped function and the second term G a convolution between the wind stress and surface slope. The G function contains various frequencies but only the one that matches the natural oscillation frequency of the system will be significant. The fundamental seiche period of the system is defined by

where T, L, g and h are the period of seiche oscillation, the distance between two reflection points on opposite coasts, gravitational acceleration, and mean water depth, respectively. The damped seiche oscillation only lasts for 2–3 cycles, each for ~3 hours, adjusting the system to a new balance, leading to a quasi-steady state (Li et al., 2018a). Because of this quasi-steady state balance, the wind and the subtidal flow at the narrow pass are highly correlated. In comparison, Eqs (9) and (10) neglect the local accelerations because they are small in the subtidal regime. These two viewpoints give consistent conclusion that wind-driven flows in such multiple inlet lagoon system is under quasi-steady state balance even if the wind varies with time.

Using the numerical model results for the calculation between August 15 and 26, 2013, we compare the results between the numerical model and that from the quasi-steady state Eq. (27). The quantity for comparison is the water level difference, between Points A and B (Fig. 1b), and that between Points C and D—one represents the cross-lagoon water level difference (between A and B), the other represents the along-lagoon difference (between C and D). The numerical model produces cross-lagoon water level difference and that calculated from Eq. (27) are again quite consistent. The two follow each other in both magnitude and phase (Fig. 10a). The correlation coefficient of the two is 0.62. Because the wind data are noisy, there are some small magnitude random variations. After a 30-hour low-pass filtering, the correlation coefficient increases to 0.82 (Fig. 10b). The along-lagoon water level difference from the model and that calculated from Eq. (27) are also consistent. The two follow each other (Fig. 10c). The correlation coefficient of the two is about 0.55, slightly smaller than that for the cross-lagoon water level difference. After a 30-hour low-pass filtering, the two again have better correlation with a coefficient of 0.71 (Fig. 10d).

It is clear that the water level variations within the Elson Lagoon are largely wind-driven. It is quite remarkable to have such a good agreement between the modeled water level difference and that from the quasi-steady state balance. This is consistent with the recent studies in similar semi-enclosed shallow water systems with micro-tides (Huang and Li, 2017; Li et al., 2018b).

The subject of study here involves a multiple inlet lagoon system. This kind of system is different from a conventional estuary with a single opening. Wind-driven flows through a multiple inlet system has been found to be characterized by inward flows from some inlets, balanced by outward flows from other inlets, depending on the wind condition, bathymetry, depth ratios, and width ratios. It is found (Li, 2013) that when wind is perpendicular to the coast, the shallower inlet tends to have downwind flow while the deeper inlet might have an upwind flow, or at least a weaker downwind flow. In contrast, the middle inlet tends to be weakest in flow magnitude and less defined in direction. When the wind is not perpendicular to the coast with an onshore component, the outward flow usually occurs at the inlet that is farther away in the downwind direction, compensated by an inward flow in an inlet at an upwind location. These are confirmed in the present numerical model results. The counter-wind flows in the deep inlet is one example. Another example is that the middle inlet tends to have minimum flow and less defined in flow directions (Fig. 11). Under easterly wind, which is quite common in the arctic region because of the high-pressure systems in the higher latitude, strong inward flows are shown to occur at the major eastern inlet (marked with E in Fig. 11), while the flows through the middle inlet (marked with M in Fig. 11) appear to be just skimming along the coastline with a limited inward flow. We do not have data at the eastern inlets. However, the validated model provides results consistent with characteristic flow patterns in a multiple inlet lagoon.

To further examine our findings, satellite images are sought for signatures of water plumes that may indicate the exchange flows in and out of the Elson Lagoon. We have particularly searched for high-resolution images from Landsat data. We could only find two images after our 2013 field campaign. They are two orthorectified and terrain corrected Landsat-8 OLI Level 1T images in GeoTIFF format obtained from the U.S. Geological Survey (USGS) Earth Explorer portal (https://earthexplorer.usgs.gov/) for the study area on July 7, 2015 (Figs 12a-c) and July 12, 2017 (Figs 12d-f) at 22:18:29 UTC. Landsat-8 was launched on February 11, 2013 and became operational on May 30, 2013. The 30-m high spatial resolution images help to identify the patterns of inflow and outflow through the Elson Lagoon inlets. The ACOLITE (version 20170718.0) software package (https://odnature.naturalsciences.be/remsem/software-and-data/acolite) is used to make corrections for the Rayleigh scattering. On July 7, 2015, there was a high-pressure atmospheric system north of the study area over the Beaufort Sea region. The system brought a northeasterly wind over Elson Lagoon (Fig. 13a). The Landsat-8 OLI image shows that the coastal water appears to be coming into the Elson Lagoon through the wider southeastern inlets (Figs 12a and c); while a plume of turbid water can be seen going out of the Elson Lagoon from the Eluitkak Pass (Figs 12a and b). On July 12, 2017, the atmospheric system did not change much and the predominant wind over the Elson Lagoon area was easterly (Fig. 13b). The Landsat image shows again some coastal water coming into Elson Lagoon through the wider inlets (clear water on Figs 12d and f); while a plume of turbid water is seen going out of the Elson Lagoon through the Eluitkak Pass (Figs 12d and e). It can be seen from the satellite image that floating ice was edging into the lagoon (Figs 12d and f).

To further verify that the regression model results are also consistent with the satellite images and weather maps, we apply the regression coefficients for equation (26) as shown in Table 1 and use the weather data from the Barrow Airport for July-Aug. 2015 and July 2017 and calculate the near surface and near bottom along channel flows. The low-pass filtered wind components (rotated to have the along channel and cross channel components) are used in the calculation. It is found that (Fig. 14a, b) during most of the three-month period, it has outward flow through the Eluitkak Pass including at the times of the Landsat observations (July 7, 2015 and July 12, 2017). This also demonstrates the practical value of the along channel flow regression with the wind data. It is interesting to note that the results (Fig. 14) show that in about 73-80% of the time there is an outward flow of water from the Elson Lagoon to the coastal ocean from the narrow Eluitkak Pass. The strong inward flow around August 27, 2015 (Fig. 14) corresponds to the time of a severe storm with northwesterly winds.

The wind events driving the circulation and exchange flows in the Elson Lagoon are originated from synoptic scale atmospheric (high- and low-pressure) systems. The strong winds usually occur at the cold fronts separating the high-pressure systems of different air masses. The effect of frontal passages on the coastal and estuarine flows as well as related sediment transport in lower latitude regions have been more rigorously studied (e.g., Roberts et al., 1989; Walker and Hammack, 2000; Feng and Li, 2010; Li and Chen, 2014; Huang and Li, 2017; Weeks et al., 2018). As an example, Li et al. (2018b) analyzed the exchange flows through a tidal channel driven by seventy-six atmospheric fronts and concluded that the fronts provided the most significant forcing to the exchange flows with the coastal ocean. The present study provides strong evidence of similar impact of atmospheric fronts to the coastal ocean and estuaries in the high latitude arctic region. The importance of the studies on the impact to the coastal waters under such weather systems is mainly because of the repeated influence (at 3–7 d intervals) and the large scale of the weather system (~2 000–3 000 km, Li et al., 2018b). The repeated weather forcing drives the hydrodynamics and coastal erosion and sediment transport. The effect integrated over time and space will be the forcing behind the long-term impact to geomorphology, whether there is a significant climate change or not, because synoptic scale weather events are common.

In this paper, we have studied the wind-driven exchange flows in a lagoon with multiple inlets in the Arctic Elson Lagoon. Analysis is done to in situ data collected with a bottom mounted ADCP at the Eluitkak Pass of Elson Lagoon between Beaufort and Chukchi Seas in the summer of 2013. A regression analysis is conducted using the wind velocity components and the low-pass filtered subtidal velocity at various depths, after taking out the effect of the atmospheric pressure changes as a function of time. The multi-variable correlation has the basis in physics shown by the momentum equations. The regression has high R² values reaching up to 0.96. We find a strong counter-wind current at the Eluitkak Pass and provide an explanation considering the wind induced torque based on the observations which are corroborated by numerical model experiments. The asymmetric inlets work together to “amplify” the wind effect: the wider eastern inlets tend to have flows in the direction of wind while the narrow Eluitkak Pass develops counter-wind flows with a significant magnitude due to the constriction. As the flow has to go through the narrow inlet, it has a strong signal correlating with the wind stress (the amplification effect). More specifically, for example, when there is northeasterly wind, the subtidal (low-pass filtered) current at the pass moves against the wind, flowing out of the Elson Lagoon through the Eluitkak Pass. The high R² value of the regression allows a statistical prediction of wind-induced exchange flows between the Elson Lagoon and the coastal ocean through the Eluitkak Pass, given the wind vector time series (whether from weather model prediction, hindcast, or direct measurements). The calculated currents from the regression model can then be used for applications for various purposes such as larva transport or interpretation for fishery and ecological studies. As shown by the satellite images under northeasterly and easterly wind conditions, and verified by the regression predictions for July 7 , 2015 and July 12, 2017, the lagoon system with asymmetric inlets can have strong counter-wind flows through the deeper and narrower inlet. From the regression, it is estimated that during 73%–80% of the time there was an outward flow from the Elson Lagoon to the coastal ocean through the narrow Eluitkak Pass in July and August of 2015 and July 2017.

The flow through the narrow and deep northwestern inlet is consistent with the continuity requirement such that significant counter-wind current must develop for mass balance. The wind-stress applied to a system with differences in depth or width among different inlets can produce a torque that generates the circulation pattern we have discussed (flow is downwind in shallower water or wider inlet and against the wind in deeper or narrower inlet), which is consistent with the prismatic model of Engelund (1986). It is quite remarkable that the numerical model results for the water level difference can be captured by a simple one-dimensional quasi-steady state momentum balance between wind stress and surface slope induced pressure gradient force. In the Elson Lagoon, it appears that this is particularly true for the cross-lagoon momentum balance. This further confirms the findings in other micro-tidal systems (Huang and Li, 2017). Apparently, the atmospheric high- and low-pressure systems and associated cold fronts play important roles in providing the wind forcing, which drives the flows through the multiple inlet lagoon system. In contrast, the tidally-driven flows are much less important, at subtidal scales.