The wind-driven formation of cross-shelf sediment plumes in a large lake

Abstract

Wind-driven turbidity plumes frequently occur in the western arm of Lake Superior and may represent a significant cross shelf transport mechanism for sediment, nutrient and biota. Here we characterize a plume that formed in late April 2016 using observations from in situ sensors and remote sensing imagery, and estimate the volume of cross shelf transport using both the observations and an idealized analytical model of plume formation. The steady-state, barotropic model is used to determine a relationship between the intensity and duration of a wind event and the volume of water transported from nearshore to offshore during the event. The model transport is the result of nearshore flow in the direction of the wind and a pressure-gradient-driven counter flow in the deeper offshore waters, consistent with observations. The volume of offshore transport associated with the 2016 plume is estimated by both methods to have been on the order of 10¹⁰ m³. Analysis of similar events from 2008–2016 shows a strong relationship between specific wind impulse and plume volume. Differences in the intensity and duration of individual events as well as ice cover, which prevents plume formation, lead to interannual variability of offshore transport ranging over an order of magnitude and illustrates how wind-driven processes may contribute to interannual variability of ecosystem functioning.

Introduction

Coastal waters are characterized by cross-shelf gradients in chemical, biological and physical parameters due to inputs from the surrounding watershed and hydrodynamic constraints that favor transport aligned with bathymetry (Brink 2016). Cross-shelf transport processes redistribute dissolved and particulate matter across the gradients, affecting nearshore and pelagic ecosystems (Rao and Schwab 2007). Here we focus on transport that occurs in southwestern Lake Superior following multi-day wind events in which the wind blows steadily from the northeast, down the axis of the western portion of the lake (hereafter the western arm). These events occur primarily in spring, prior to the formation of the seasonal thermocline, when the water column is isothermal near freshwater’s temperature of maximum density. In the days following the wind events, sediment plumes extending tens of kilometers offshore are visible from shore and in satellite imagery (Fig. 1). We hypothesize the volume of transport represented by the plumes is directly related to the magnitude of the northeast wind forcing and constitutes an important cross-shelf transport mechanism, increasing the rate at which sedimentary, biological and chemical constituents move from nearshore to offshore ecosystems (Sierzsen et al. 2014, Yurista et al. 2016).

Fig. 1.

MODIS Terra imagery of Lake Superior's western arm, April 27, 2016. (a) Lake Superior coastline; box indicates location of the western arm, arrow indicates the Apostle Islands (AI). (b) True color image shows sediment plume discussed in the text; (A) nearshore buoy 45027; (B) offshore buoy 45028 and vertical profiler; (C) Nemadji River and meteorological station Superior, WI.; (D) meteorological station DULM5; (E) meteorological station DLH; (F) transect occupied by underwater glider. (c) Lake surface temperature. (d) Band 1 reflectance; gray lines indicate water depth, contour interval is 50 m. True color MODIS imagery from University of Wisconsin. MODIS SST from Ocean Color Group. MODIS band 1 reflectance from LP-DAAC.

We draw a distinction between the wind-driven plumes we will consider here and plumes of river and estuarine water that deliver land-based nutrients, sediment and pollutants from the surrounding landscape to coastal areas (Jiang and Xia 2016; Jameel et al. 2018). River and estuarine plumes vary in size according to changes in river discharge (Nezlin and DiGiacomo 2005; Zhang et al. 2016), and additional forces including wind, tides and buoyancy contribute to their dispersal. Plumes of large rivers typically veer to the right (left) in the Northern (Southern) Hemisphere due to the Earth’s rotation and hug the coast (Masse and Murthy 1992; Jiang and Xia 2016). Nutrients contained in river plumes promote phytoplankton growth and species composition (Johengen et al. 2008; Grosse et al. 2010), and contribute to enhanced fishery production (Grimes 2001; Smith and Simpkins 2018) and nursery habitat (Reichert et al. 2010). Pollutants from urban watersheds discharged in stormwater plumes can threaten sensitive coastal ecosystems and water sources (Lahet and Stramski 2010; Petus et al. 2014). In contrast, internal loading processes including coastal erosion and resuspension contribute to turbidity in wind-driven plumes (Lee et al. 2007; Niu et al. 2018) and their size is a function of the wind forcing as well as basin morphology relative to wind direction (Schwab et al. 2006). Their impact on coastal ecosystems is a function of their size as well as ambient nearshore water quality and character of the eroded/resuspended sediment (Eadie et al. 2002). High winds can homogenize the water column increasing availability of dissolved oxygen for the remineralization of the resuspended sediment, affecting coastal oxygen dynamics (Moriarty et al. 2017).

Early investigations of wind-driven coastal circulation in the Great Lakes include Rao and Murty (1970), who used an analytical model with realistic bathymetry and shoreline data to model Lake Ontario’s circulation during non-stratified conditions. A steady, moderate wind from the west resulted in a two cell circulation pattern with coastal currents along the north and south coast aligned with the wind, and offshore current in the deeper central basin opposed to wind. Csanady (1973) presented a more general solution based on an idealized, elongate lake basin with parallel sides and variable bathymetry. The response to imposed wind stress consisted of the same double-gyre circulation predicted by Rao and Murty (1970), with higher velocity currents occurring in the coastal zone, and weaker return flow in the deeper central basin. The geometry of the flow was directly related to the cross-basin depth distribution, with transports in the direction of the wind where depth was less than the average basin depth, and in the opposite direction where depth was greater than the average (Csanady 1973). Griffin and Middleton (1987) investigated the effect of variable coastal bathymetry, and found the double-gyre flow pattern weakened as the minimum coastal depth increased, which reduced alongshore transports.

A number of observational studies (e.g. Eadie et al. 2002; Lohrenz et al. 2004) investigated the impacts of episodic wind-driven coastal transport in Lake Michigan. The transport occurs when wind and waves associated with late winter storms (Schwab et al. 2006) resuspend and redistribute sediments from the west side of the southern part of the lake to the east. Whereas a significant motivation for these analytical and observational studies is quantifying the wind-driven alongshore transport and its impact, our primary focus is the volume of offshore transport that occurs in a plume event.

The primary novel contribution of this paper is the development of a simple dynamical relationship between the volume of cross shore transport associated with the plume and the intensity and duration of a wind event during ice free, unstratified conditions. This model will not only develop intuition about how the system functions, but provide useful quantitative estimates of plume volume. We focus initially on a single large event that occurred in 2016 when several observational platforms were operational. The suite of sensing platforms provided us with a unique opportunity to characterize the plume from a number of different perspectives, as well as spatial and temporal scales. We then compare the estimate to satellite and autonomous glider observations of the plume’s surface and subsurface extent. Finally, we analyze meteorological data and satellite imagery of several similar events since 2008 to place the 2016 event into historical context and evaluate the interannual variability of cross shore transport. The emphasis in this paper is on the volume of water transported offshore, rather than on the source, transport, or fate of sediments carried with that water. In this case, sediment is simply a visible proxy for water that has recently been in the nearshore. Since these events occur as a result of high winds, it is unlikely that they could happen without some observable sediment load.

Setting and Methods

Setting

The western arm of Lake Superior, here taken to be the portion of the lake west of the Apostle Islands (Fig. 1a), consists of a deep channel along the north (Minnesota) shore, reaching depths of roughly 200 m, and a broad, gentle shelf along the south (Wisconsin) shore (Fig. 1d). The surrounding region is home to roughly 45% the total population within the lake’s watershed and includes the port cities of Duluth, Minnesota and Superior, Wisconsin, which are located within the natural harbor formed by the estuary of the St. Louis River. Development of the ports resulted in water quality declines in the estuary and adjacent waters of Lake Superior during the early and mid 20^th century (Bellinger et al. 2016). Besides the St Louis River estuary, the western arm also includes numerous embayments and coastal wetlands that provide nursery habitat for a variety of fish species (Trebitz et al. 2005).

In contrast to the erosion-resistant bedrock that characterizes most of the lake’s watershed, the western arm’s southern shoreline and surrounding landscape is composed of easily eroded glacial lacustrine clay (Halfman and Johnson 1989). Coastal erosion and resuspension (Sydor 1979) result in western arm turbidity levels (Yousef et al. 2017) and sedimentation rates (Corcoran et al. 2018) being among the highest lakewide. The largest tributary along the clay-rich southern shore is the Nemadji River (Fig. 1b), which drains an area of 1088 km², and has a mean discharge of 36 m³ s⁻¹ and typical maximum discharge of 98 m³ s⁻¹ during the month of April (https://waterdata.usgs.gov/nwis/) when the large sediment plumes occur.

Meteorological data

We used over-lake meteorological data recorded at two locations in Lake Superior’s western arm during the navigation season (Fig. 1b). National Data Buoy Center (NDBC) 45027, hereafter the ‘nearshore’ buoy, was anchored at 46° 51.6'N, 91° 55.8'W in 52 m of water, and NDBC 45028, hereafter the ‘offshore’ buoy, at 46° 48.6'N 91° 50.4'W, also in 52 m of water. In 2016, the buoys were deployed on April 14 and recovered on October 25. Instruments deployed on each buoy record air temperature, relative humidity, barometric pressure, wind velocity, and downward shortwave radiation. In addition, rainfall is measured at the nearshore buoy and wave data are collected at the offshore buoy. Thermistor strings suspended from the buoys record water temperature every 10 minutes at depths of 1, 3, 5, 10, 15, 20, 25, 30, 35 and 40 m.

The National Oceanic and Atmospheric Administration (NOAA) and the National Weather Service (NWS) have several automated meteorological stations positioned around the western arm of Lake Superior (ndbc.noaa.gov). To place the 2016 event in historical context, we analyzed wind data for the months of March, April and May between 2008 and 2016 to find the magnitude and duration of similar events. We used wind data from station DULM5, located at the far end of the western arm (Fig. 1b). The wind data were nominally recorded at 6 minute intervals, although there were numerous gaps in the time series over the period studied. For gaps that were less than five hours we used linear interpolation to fill in missing data. Longer data gaps were excluded from the analysis. Wind stress was estimated from wind speed and direction using standard bulk flux algorithms (Fairall et al. 1996) assuming an anemometer height of 7.1m (ndbc.noaa.gov).

We evaluated the contribution of Nemadji River discharge to plume size using two metrics. For the April 2016 event, river discharge is available from the United States Geological Survey (USGS) online at https://nwis.waterdata.usgs.gov/wi/ for the Nemadji River South of Superior, Wisconsin (station id 04024430). Data is recorded every 15 minutes and reported in cubic feet per second. The USGS deploys sensors seasonally and discharge data was unavailable for events in additional years. Therefore, for historical analysis we obtained daily precipitation data available at https://www.ncdc.noaa.gov/cdo-web/ for the Superior, Wisconsin NWS station (Fig. 1b). To characterize variability in Nemadji River discharge we used the accumulated rainfall for the five days previous to the date of MODIS imagery. Four of the days in the Superior, WI precipitation record were missing data and for those we used data recorded at station DLH, located 20 kilometers northwest of the Superior station (Fig. 1b).

Profiler data

A WETLabs moored profiler was anchored adjacent to the offshore meteorological buoy from 14 April to 30 June 2016. The profiler was outfitted with batteries that allowed for multiple profiles during which it traveled from the bottom to the surface on its tether at a prescribed interval, which for this deployment was 36 hours (midnight and noon, every other day). During each trip to the surface, water temperature, optical backscatter, and a variety of other parameters (which are not considered here) were measured at roughly 1 Hz, with an ascent speed of approximately 20 cm s⁻¹, for a vertical resolution of approximately 0.2 m.

Glider data

Between May 3 and May 13, a Teledyne Webb Research G1 autonomous underwater glider “Gichigami” was deployed in the western arm and made 13 crossings from the northern shore to the southern shore at a distance of approximately 25 km from the far southwestern end (Fig. 1b). The glider was outfitted with an un-pumped Seabird CTD and a WetLabs Ecopuck triplet configured to measure chlorophyll-a fluorescence, colored dissolved organic matter (CDOM) fluorescence, and optical backscatter at 700 nm. Data were acquired continuously at the maximum sampling frequency of one Hz throughout the deployment. The glider continuously profiled from the surface to 5m above the bottom and back to the surface with vertical speeds of ±0.1 m s⁻¹, while making forward progress of 0.25 m s⁻¹, resulting in a “zig-zag” path, and very high data density in both the horizontal and vertical. A single 25 km-long transect crossing the lake took 22 hours and consisted of approximately 200 profiles. Due to the fixed dive/climb angle, the horizontal resolution was typically on the order of twice the water depth. For example, if the water depth was 50m, a single dive or climb horizontally traversed approximately 100m. Further details of glider operation can be found in Austin (2013).

MODIS data

We used MODerate resolution Imaging Spectroradiometer (MODIS) imagery to make order of magnitude estimates of the surface area of sediment plumes in the western arm. The MODIS sensor is deployed on the two NASA Earth Observing System (EOS) satellites Terra and Aqua, which are in sun-synchronous orbit, potentially providing two views each day, depending on cloud cover. The frequency of MODIS imagery increases the number of usable images relative to other remote sensing platforms with higher spatial resolution but lower frequency (e.g. Landsat, Sentinel), and makes it possible to track the development of features such as sediment plumes over daily time scales (Miller and McKee 2004; Moreno-Madrinan et al. 2010; Zhang et al. 2016).

The MODIS sensor collects energy reflected by the surface of the earth in 36 spectral bands at nominal spatial resolutions of 250 m (bands 1 and 2), 500 m (bands 3–7) and 1000 m (bands 8–36). We estimated the spatial extent of sediment plumes using the band one (620–670 nm) land surface reflectance data in the level 2 products MOD09GQ (Terra) and MYD09GQ (Aqua), available from the Land Processes Distributed Active Archive Center (LP-DAAC) (https://lpdaac.usgs.gov). The land surface reflectance products have been widely used to characterize turbidity levels in estuarine (Doxaran et al. 2009), coastal (Moreno-Madrinan et al. 2010; Constantin et al. 2017) and inland (Zhang et al. 2016) waters and are a suitable alternative to MODIS ocean color products designed for open water applications (Feng et al. 2018). We selected dates for analysis by visually inspecting MODIS true color imagery (http://ge.ssec.wisc.edu/modis-today/) within three days of significant wind events to find dates with cloud free and ice free conditions in the western arm. We selected either Terra or Aqua imagery for analysis based on a qualitative comparison of the pixel quality information included with each reflectance product (Vermote et al. 2011). For dates when the quality of Terra and Aqua imagery was equal, the Terra image was used. For the 2016 event when in-situ sensors were deployed, we also obtained MODIS 1 km resolution lake surface temperatures from the NASA Ocean Color Group (https://oceancolor.gsfc.nasa.gov).

Reflectance is the unitless ratio of reflected to incident radiation, and varies from 0.0 (no reflectance) to 1.0 (all incident light is reflected). Values reported in the MODIS level 2 products are scaled by a factor of 10000, and range between -100 to 16000. After correcting for the scaling factor, values below 0 and greater than 1 may occur due to the atmospheric correction algorithm (Vermote et al. 2011); we converted negative values to zero and values greater than one to one so that all values were between 0 and 1. A minimum reflectance threshold characterizing the plume periphery was determined manually, by visual comparison with MODIS true color imagery of the same scene (Fig. 1). Based on the visual comparison, a minimum reflectance threshold of 0.15 was used to distinguish plume-impacted from plume-free areas (Fig. 1d, Supplemental material Fig. S1). Our results were not qualitatively sensitive to small (< .005) changes in this threshold value, and the same value was used for all reflectance imagery (Supplemental material Fig. S2).

We estimated the fraction of nearshore water contained within the plumes using a linear mixing model with nearshore water characterized by reflectance value of one, and offshore water characterized by reflectance less than the threshold. The volume of nearshore water contained in the plumes was estimated using

$$V=\int r_p{z}_{p}dA$$ (1)

where r_p is the pixel reflectance and z_p is the water depth at the pixel location. Our estimate assumes that the sediment concentration is, to first order, vertically uniform, and that the sediment in the plumes acts as a tracer for nearshore water, remaining in suspension over the time the plume forms and the MODIS imagery was acquired. Although reflectance may vary independently of suspended load due to changes in the optical properties of the sediment, sediment size, or variation in concentration of CDOM (Moreno-Madrinan et al. 2010), we expect these factors to have minor effect on our results because the primary contribution to the reflectance signal in each of the events is assumed to be clay eroded from coastal areas (Yousef et al. 2017). CDOM levels are assumed to be relatively constant, and most strongly affect reflectance at shorter wavelengths than the red part of the spectrum covered by the band 1 products (620–670 nm). These assumptions may not be valid for plumes associated with large runoff events, for example “mega-rain” flood events associated with summer thunderstorm systems (Minor et al. 2014; Cooney et al. 2018). These are likely to include sediments with a wider range of sizes and optical properties as well as higher CDOM concentrations.

Analytical solution

A simplified analytical approach can be used to develop intuition about the processes involved in the formation and propagation of the plume. This solution allows us to make an order of magnitude estimate of the velocity of the plume as well as the volume of water transported offshore. Our approach is similar to early work of Csanady (1973) or Griffin and Middleton (1987) who developed analytical theories for this geometry, especially focusing on the development of narrow coastal ‘jets’ driven in the same direction as the wind. Here we will develop a similar analytical model to characterize the oppositely directed flow in the central channel, and compare it to the observations of the plume. We extend previous results by computing the offshore flux of water as well as the total offshore volume during a wind event.

We begin with the shallow water equations (Pond and Pickard 1983) in order to solve for the vertically averaged two-dimensional circulation. We assume the water column is unstratified, which is typical for the spring, and assume the response is vertically uniform. We will solve for the steady-state response to wind being blown along the axis of a semi-infinite channel that is capped at one end (Fig. 2). We orient the x-axis centrally along the channel, and define the channel width as 2L, so that the channel walls are at y = ±L. We will solve far enough from the channel cap that any flow distortion from the presence of the cap is negligible, and there are no appreciable along-channel gradients in the flow field. We define the bottom bathymetry as H(y), a function strictly of the cross-channel position. Far from the end of the channel, the flow does not vary along-channel. If, then, $\frac{du}{dx}=0$, continuity requires that $\frac{dv}{dy}=0$, and since the cross-channel velocity must be zero on the boundaries, the cross-channel velocity must be zero throughout the flow. The vertically integrated shallow water momentum equation in the x-direction is

$$H\frac{du}{dt}-fvH=-gH\frac{d\eta }{dx}+\frac{{\tau }^{sfc}}{\rho }-\frac{{\tau }^{bot}}{\rho }$$ (2)

where u and v are the depth-averaged along-channel and cross-channel velocity, respectively,f is the Coriolis parameter, g is gravitational acceleration, η the displacement of the free surface, τ^sfc the imposed wind stress along the axis of the channel, and τ^bot the bottom drag. Assuming a steady state (so that $\frac{d}{dt}=0$), and noting that v=0 throughout the flow, yields

$$\mathrm{0}=-gH\frac{d\eta }{dx}+\frac{{\tau }^{sfc}}{\rho }-\frac{{\tau }^{bot}}{\rho }$$ (3)

where H is the water depth. This can be further simplified by parameterizing the bottom stress as:

$$\frac{{\tau }^{bot}}{\rho }=ru$$ (4)

Where r has been estimated to be on the order of 5×10⁻⁴ m s⁻¹. (Beardsley et al. 1977), which yields

$$\mathrm{0}=-gH\frac{d\eta }{dx}+\frac{{\tau }^{sfc}}{\rho }-ru$$ (5)

The solution could be improved by distinguishing the vertically averaged velocity, as used here, from the near-bottom velocity; however, assuming they are proportional, this will not qualitatively change the solution. Next, we will make the assumption that, to first order, the surface level gradient is proportional to the alongshore wind stress. This is reasonable, since the system is linear, we might expect the setup to be linearly proportional to the wind stress. Specifically, we assume that

$$\frac{d\eta }{dx}=b\frac{{\tau }^{sfc}}{\rho }$$ (6)

Where b is a proportionality constant, the value of which is not yet known, but we will show is constrained by volume conservation. The solution becomes

$$\mathrm{0}=-gHb\frac{{\tau }^{sfc}}{\rho }+\frac{{\tau }^{sfc}}{\rho }-ru$$ (7)

Or, solving for u:

$$u=r^{-1}(1-gH(y)b)\frac{{\tau }^{sfc}}{\rho }$$ (8)

Now, we can place a constraint on the solution by noting that the transport through this section at steady state must be zero:

$$\underset{-L}{\overset{L}{\int }}u(y)H(y)dy=\mathrm{0}$$ (9)

Substituting (8) into the integral yields

$$\underset{-L}{\overset{L}{\int }}{r}^{-\mathrm{1}}\mathrm{(}\mathrm{1}-gH\mathrm{(}y\mathrm{)}b\mathrm{)}\frac{{\tau }^{sfc}}{\rho }H\mathrm{(}y\mathrm{)}dy=\mathrm{0}$$ (10)

We can then solve for b, yielding

$$b=\frac{\underset{-L}{\overset{L}{\int }}H(y)dy}{g\underset{-L}{\overset{L}{\int }}H{\left(y\right)}^{2}dy}$$ (11)

At this stage, the integrals can be solved numerically for an arbitrary bathymetric distribution H(y), and from this b can be uniquely determined.

Fig. 2.

Schematic figure of analytical model setting. The along-channel dimension is x, and the cross-channel dimension is y, with the sides of the channel at y=±L. Bottom bathymetry is designated H(y). The wind stress τ is entirely in the along-channel direction.

For a typical distribution of bathymetry (shallow near the coast, deeper in the center), the solution for the along channel velocity u(y) is going to have two zero crossings, between which transport will be into the open lake. Integrating between these zero crossings will yield the instantaneous flux:

$$q=\underset{y_1}{\overset{y_2}{\int }}{r}^{-\mathrm{1}}\mathrm{(}\mathrm{1}-gH\mathrm{(}y\mathrm{)}b\mathrm{)}\frac{{\tau }^{sfc}}{\rho }H\mathrm{(}y\mathrm{)}dy$$ (12)

where y₁ and y₂ are the zero-crossings of the along-channel velocity field, and q [m³s⁻¹] represents the instantaneous flux.

If we assume that the system is constantly adjusting to a varying surface wind stress, then we can write the total offshore transport of coastal waters during a wind event to be:

$$Q=\underset{t_1}{\overset{t_2}{\int }}q\mathrm{(}t\mathrm{)}dt=\underset{t_1}{\overset{t_2}{\int }}\underset{y_1}{\overset{y_2}{\int }}{r}^{-\mathrm{1}}\mathrm{(}\mathrm{1}-gH\mathrm{(}y\mathrm{)}b\mathrm{)}\frac{{\tau }^{sfc}\left(t\right)}{\rho }H\mathrm{(}y\mathrm{)}dydt$$ (13)

Where t₁ and t₂ are the start and end times of a wind event, and Q [m³] represents the total volume transported offshore during an event. Note that the only part of this solution that is time-dependent is the surface wind stress. We can therefore re-write the total transport as:

$$Q=\mathrm{[}\underset{y_1}{\overset{y_2}{\int }}\mathrm{(}\rho r{\mathrm{)}}^{-\mathrm{1}}\mathrm{(}\mathrm{1}-gH\mathrm{(}y\mathrm{)}b\mathrm{)}H\mathrm{(}y\mathrm{)}dy\mathrm{]}\left[\underset{t_1}{\overset{t_2}{\int }}{\tau }^{sfc}\mathrm{(}t\mathrm{)}dt\mathrm{\right]}$$ (14)

For convenience, we can re-write this as

$$Q=\mathrm{[}\underset{y_1}{\overset{y_2}{\int }}\mathrm{(}\rho r{\mathrm{)}}^{-\mathrm{1}}\mathrm{(}\mathrm{1}-gH\mathrm{(}y\mathrm{)}b\mathrm{)}H\mathrm{(}y\mathrm{)}dy\mathrm{]}I$$ (15)

where

$$I=\underset{t_1}{\overset{t_2}{\int }}{\tau }^{sfc}\mathrm{(}t\mathrm{)}dt$$ (16)

is the specific impulse of a given wind event. The first portion of the solution is entirely a function of lake morphology and the second integral represents the specific impulse applied to the lake during a single wind event, suggesting that the volume of water displaced during an event is a function of both the duration and intensity of the event. In reality, there is transient behavior, but we should expect that to first order transport and specific impulse are roughly proportional.

As an example that can be solved in closed form, and to illustrate the role of bathymetry on transport, we will solve for a parabolic distribution of depth

$$H\mathrm{(}y\mathrm{)}=H_{\mathrm{0}}(\mathrm{1}-\frac{y^{\mathrm{2}}}{L^{\mathrm{2}}})$$ (17)

which is zero at the boundaries y = ±L, and has depth H₀ in the center of the channel. Evaluating (11) using this yields b = $\frac{5}{4}$(gH₀)⁻¹. Putting this back into (8) yields

$$u=\frac{r^{-1}}{4}\frac{{\tau }^{sfc}}{\rho }(5\frac{y^2}{L^2}-1)$$ (18)

This solution shows that in shallow water (close to the coasts), the along-channel flow is going to be in the direction of the wind stress, whereas in deeper water, in this specific case, between $y=\pm \frac{1}{\sqrt{5}}L$, the flow will be in the opposite direction of the wind stress. The wind acts uniformly across the channel on the surface of the water, whereas the along-channel pressure gradient works throughout the water column. Where the water is shallow, the wind stress will dominate the force balance, and where the water is deep, the pressure gradient dominates (Fig. 3), driving the return flow. The magnitude of setup as a function of wind stress can be determined as well, yielding

$$\frac{d\eta }{dx}=\frac{\mathrm{5}}{\mathrm{4}}\mathrm{(}g{H}_{\mathrm{0}}{\mathrm{)}}^{-\mathrm{1}}\frac{{\tau }^{sf\mathrm{c}}}{\rho }$$ (19)

This is consistent with the tendency that for a given wind stress, setup tends to be greater in shallow lakes than in deep ones (i.e. large setup in Erie happens periodically, whereas setup in Superior is relatively small (e.g. Trebitz 2006)).

Fig. 3.

Conceptual diagram of the resulting flow. Surface wind stress from the northeast acts uniformly across the surface of the water and dominates flow in shallow areas. An opposing pressure gradient works throughout the water column and dominates flow in deeper areas, driving the plume offshore.

We can evaluate these expressions with values characteristic of the western arm of Lake Superior to estimate typical transport magnitudes. We set H₀ = 50 m, L = 10 km, and tau = 0.2 N m⁻². In this particular case, the steady state velocity in the center of the channel should be

$$u=\frac{r^{-1}}{4}\frac{{\tau }^{sf\mathrm{c}}}{\rho }(-1)=-\frac{{(5\times {10}^{-4}m{s}^{-1})}^{-1}}{4}\frac{0.2{Nm}^{-2}}{1000{kgm}^{-3}}=0.10m{s}^{-1}$$ (20)

Over two days, this would result in a displacement of roughly 20 km, consistent with remote sensing imagery (Fig. 1). In this case, evaluating the integral for just the region of offshore flow yields an analytical result of

$$q=\underset{-L/\sqrt{5}}{\overset{L/\sqrt{5}}{\int }}u\mathrm{(}y\mathrm{)}H\mathrm{(}y\mathrm{)}dy=-\frac{8}{25\sqrt{5}}\frac{H_{0}L}{r}\frac{{\tau }^{SFC}}{\rho }$$ (21)

Which, for the example here, evaluates to roughly 3×10⁴ m³ s⁻¹. If this transport took place steadily over two days, that would result in a total transport of

$$Q=\int qdt=\mathrm{(}\mathrm{3}\mathrm{\times }\mathrm{1}{\mathrm{0}}^{\mathrm{4}}{m}^{\mathrm{3}}{s}^{-\mathrm{1}}\mathrm{)}\mathrm{(}\mathrm{172800}s\mathrm{)}=\mathrm{5}\mathrm{\times }\mathrm{1}{\mathrm{0}}^{\mathrm{9}}{m}^{\mathrm{3}}$$

To put this in perspective, the volume of the western arm of Lake Superior (west of the Apostle Islands) is roughly 6 × 10¹¹ m³, so the event transports amounts to roughly 1% of the total volume of the western arm.

Results and discussion

A cloud free MODIS visible band image from data acquired by the Terra spacecraft on April 27, 2016 shows that a sediment-laden plume extended over 18 km offshore in the western arm of Lake Superior, to the offshore buoy and profiler (Fig. 1b). Lake surface temperature (Fig. 1c) from the same overpass shows the central area of plume was warmer than the surrounding offshore waters. Band 1 reflectance (Fig. 1d) shows a sharp gradient between the area affected by the plume, where reflectance was high, and the surrounding offshore waters where reflectance was low.

The plume formed during a wind event which began on 23 April, reached its peak on 25 April and persisted through 29 April (Fig. 4a). Wind speeds were over 12 m s⁻¹, from the northeast, with gusts over 17 m s⁻¹. Subsurface observations of optical backscatter (Fig. 4b) and temperature (Fig. 4c) recorded by instruments on the vertical profiler show that the warmer, sediment laden water visible in the MODIS images extended throughout the water column. In winter and early spring, Lake Superior’s surface temperatures are colder than 4 °C, the temperature of maximum density for freshwater (hereafter T_md). The springtime increase in surface heat flux warms shallow areas more quickly, causing them to stratify earlier than deeper areas. The coincident high backscatter level and warming supports our hypothesis that the source of the sediment plume is advection of warm, turbid nearshore water, and is not simply local resuspension of sediments in situ, which would not warm the water column. The thermistor data (Fig. 4c) also indicate that conditions at the offshore buoy were isothermal during the event, and seasonal stratification began in late June.

Fig. 4.

Observations from meteorological station DULM5, offshore buoy 45028 and vertical profiler. (a) Magnitude of the southwest-northeast component of wind stress observed at DULM5; Positive values indicate wind from the southwest; the shaded region corresponds to the 2016 wind event discussed in the text. (b) Vertical profiler observations of optical backscatter. (c) Water temperature at offshore buoy 45028; 1 meter depth (light gray), 5 meters depth (dark gray), and 40 meters depth (black).

Glider observations from May 4 (Fig. 5), several days after the main wind event, show conditions were close to vertically isothermal across most of the western arm. The warmest temperatures were in the shallower southern end of the transect (Fig. 5a). Due to the steepness of the north shore bathymetry it is difficult to get the glider close to shore safely at the northern end of the transect. At approximately 16 km from the southern shore, surface temperatures had not yet warmed to T_md and the water column was stratified as in winter, with colder surface layer above a bottom layer which is still below T_md. The presence of high sediment concentrations likely further stabilizes the water column at this location.

Fig. 5.

Glider observations of (a) temperature, (b) optical backscatter, (c) CDOM fluorescence, and (d) chlorophyll; from the transect completed between May 04, 22:34 GMT and May 05, 15:52 GMT.

High backscatter values (Fig. 5b) throughout the water column shows the glider crossed through the plume between 5 and 11 km from southern end of the transect. The maximum detection limit of the backscatter sensor (5.8 × 10⁻³ m⁻¹ sr⁻¹) is exceeded within the central plume, and variability above this value is unresolved. The concentration of CDOM is also higher within the plume (Fig. 5c); values are within the detection range of the sensor and extend vertically through the entire water column. In general, CDOM concentrations are higher in nearshore areas (Stephens and Minor 2010), and elevated CDOM levels within the plume are additional evidence for a nearshore source. The highest values of chlorophyll-a fluorescence were found in the warmer, shallower southern end of the transect (Fig. 5d), typical for springtime (Auer and Bub 2004). Low levels of surface chlorophyll-a at 5 km and 20 km are due to daytime quenching effects (Falkowski and Kolber 1995; Sackmann et al. 2008), rather than low chlorophyll concentration.

For this event, we can numerically estimate the value of b from equation (11) for a realistic cross-lake bathymetry profile, and use measured winds to estimate the total transport. Choosing a cross section of the western arm as shown in Fig. 6, we find a value of b=5 × 10⁴ s²m⁻². Applying this value to (15) and integrating over the duration of the late April 2016 NE wind event (Fig. 4a), we find a specific wind impulse of roughly 6 × 10⁴ N s m⁻² and an offshore transport volume of 4 × 10¹⁰ m³, roughly 10 percent of the volume of the western arm. If we assume that the plume water has an average sediment concentration of 20 mg l⁻¹ (Halfman and Johnson 1989), this corresponds to an offshore transport of 8 × 10⁸ kg of sediment, comparable to estimates discussed in Stortz et al. (1976). Peak discharge of the Nemadji River over the period of the wind event was 147 m³ s⁻¹, and total discharge was less than 4 × 10⁴ m³ (Supplemental material Fig. S3), suggesting a minor contribution of river discharge to the sediment plume visible in the MODIS imagery. This is consistent with (Sydor 1979) who found that the principle sources of turbidity in the western arm are wave driven coastal erosion of clay banks and resuspension, and similar to findings of Niu et al. (2018), who found the contribution of resuspension to the size of high-turbidity areas in western Lake Erie exceeded the contribution from river loading.

Fig. 6.

Cross channel bathymetry and velocity distribution. Circulation in the shallower nearshore areas is aligned with the wind stress. An oppositely directed flow occurs in the deeper channel, driven by an offshore-directed pressure gradient force.

Historical analysis

The proportionality between specific impulse and displaced volume (15) can be explored by comparing wind impulses to remote sensing imagery, using sediment as a proxy for nearshore water being transported into the open lake. Wind events are identified by finding periods when the NE-SW component of the wind stress estimated at DULM5 stayed consistently negative (blowing to the SW) for more than 24 hours. The wind stress is then integrated over the period in question to generate the wind impulse, as in (16).

Over the 9 year period of interest (2008–2016), there were 47 events during the months of March, April, and May in which the wind blew primarily to the southwest, and during which the total impulse was greater than 1×10⁴N s m⁻² (Fig. 7). This is roughly equivalent to a 15 kt wind blowing for a day. Visual inspection of MODIS visual band imagery indicated 22 of the events had cloud free conditions over the western arm. Of those, 10 were ice-free in the nearshore area of the western arm (Fig. 1, Fig. 8). Maximum ice cover in Lake Superior occurs in early March (Wang et al. 2012), and events in that month were affected by ice cover in four of the ten years surveyed. The events omitted due to ice cover included all six events in 2014, a year when ice cover persisted until May (Supplemental material Fig. S4) (Clites et al. 2014), four events in March of 2009, another year with extensive ice cover (Wang et al. 2010), one event in March of 2008 and one in March of 2013.

Fig. 7.

Magnitude of specific impulse for significant (>1 × 10⁴ N s m⁻²) NE wind events in the western arm of Lake Superior for months of March, April and May, 2008–2016. The date corresponding to peak wind stress is plotted, dates of the largest wind events are labeled. Crosses indicate events with ice-free conditions. Asterisks indicate events that occurred when significant ice cover prevented plume formation. Circled ice-free events had cloud-free MODIS imagery within three days and were used in the MODIS band 1 reflectance analysis.

Fig. 8.

MODIS band 1 reflectance imagery used in the plume volume analysis. Dates of image acquisition are shown. The first cloud-free image within three days of the corresponding wind event was used. The image from April 27, 2016 discussed in the text is shown as Fig. 1d.

Fig. 9a shows plume area for the selected events is strongly correlated with the specific impulse. In contrast, no correlation is observed between accumulated rainfall during the five days prior to MODIS image acquisition and plume area (Fig. 9b), supporting the hypothesis that for the large wind events considered here, the size of the visible plume is controlled by the wind forcing. Fig. 10 shows plume volumes range over an order of magnitude, with the April 2016 event being one of the largest during the period of interest. The slope of the best fit line, 2 × 10⁵ m³ (N s m⁻²)⁻¹ on the same order of magnitude as the analytical prediction value of 7 × 10⁵ m³ (N s m⁻²)⁻¹. The quantitative disagreement is not surprising given the crude nature of both the analytical model and the method used to estimate the volume of the plume and with further refinement of both the comparison should improve. This suggests that during the ice free spring season, wind impulse is a useful predictor of the volume displaced offshore in plume events and allows us to estimate the total volume displaced offshore each year given the measured wind stress alone.

Fig. 9.

Correlation between plume area in MODIS imagery and (a) specific impulse of northeast wind events and (b) accumulated rainfall. Dates correspond to MODIS imagery.

Fig. 10.

Volume of nearshore water transported offshore in a plume event versus the magnitude of NE wind impulse. Plume volume was calculated from cloud-free and ice-free MODIS band 1 reflectance imagery acquired within 3 days of the wind event. Specific NE wind impulse was calculated from station DULM5 wind records. Dates correspond to MODIS imagery.

Applying the wind stress-plume volume relationship from the image analysis to the ice free events reveals a significant amount of interannual variability in the total amount of nearshore water transported offshore in a given spring (Fig. 11). There are some years, such as 2011, with multiple large events, and other years, such as 2013, with no major events. In some cases, a single event might be larger than the sum of another year’s total. This raises the prospect that interannual variability in processes in the open lake, which are often thought of in the context of thermal variability (Magnuson et al. 1997; Cline et al. 2013), might also be, to an extent, a function of the wind field and the frequency and intensity of this particular kind of wind event.

Fig. 11.

Cross shore transport by wind-driven plumes in the western arm of Lake Superior during March, April and May, 2008–2016. The volume of individual plume events was calculated using the wind records from station DULM5 and the relationship determined in Fig. 10 between NE wind impulse and plume volume. Dates of the largest wind events are indicated.