Characterizing storm water dispersion and dilution from small coastal streams

Abstract

Characterizing the dispersion and dilution of storm water from small coastal creeks is important for understanding the importance of land-derived subsidies to nearby ecosystems and the management of anthropogenic pollutants. In Southern California, creek runoff is episodic, intense, and short-lived while the plumes are buoyant, all of which make the field sampling of freshwater plumes challenging. Numerical modeling offers a viable way to characterize these systems. The dilution and dispersion of freshwater from two creeks that discharge into the Santa Barbara Channel, California is investigated using Regional Ocean Modeling System (ROMS) simulations with a horizontal resolution of 100 m. Tight coupling is found among precipitation, hydrologic discharge, wind forcing, and submesoscale flow structures which all contribute to plume evolution. During flooding, plumes are narrow and attached to the coast, due to downwelling/onshore wind forcing and intense vorticity filaments lying parallel to the shelf. As the storm passes, the winds typically shift to offshore/upwelling favorable conditions and the plume is advected offshore which enhances its dilution. Plumes reach the bottom nearshore while they form thin layers a few meters thick offshore. Dilution field of passive tracers released with the runoff is strongly anisotropic with stronger cross-shelf gradients than along-shelf. Dispersion analysis of statistical moments of the passive tracer distribution results in scale-dependent diffusivities consistent with the particle-pair analysis of Romero et al. (2013). Model validation, the roles of submesoscale processes, and wind forcing on plume evolution and application to ecological issues and marine resource management are discussed.

Key Points

• Tight coupling among precipitation, discharge, winds, and currents contribute to plume evolution
• Plume dilution is strongly anisotropic with stronger cross-shelf gradients than along-shelf
• Statistical dispersion analysis of runoff tracer results in scale-dependent relative diffusivities

1 Introduction

Knowledge of transport and dilution from freshwater runoff is important for understanding of coastal ecosystems and the proper management of pollutants. For example, in Southern California freshwater plumes from creek runoff have the potential to deliver significant amounts of terrestrially derived materials, including anthropogenic pollutants, to coastal ecosystems [e.g., Ackerman and Schiff, 2003; Ahn et al., 2005]. Southern California coastal waters are important economically providing approximately 9 billion U.S. Dollars per year from recreational activities which can be significantly affected by pollution from small-scale river and creek runoff [e.g., Bay et al., 2003]. Nevertheless, little is known about transport and dilution of the small-scale yet societally important coastal plumes.

In contrast to large-scale river plumes, runoff from small coastal creeks in semiarid environments like Southern California is difficult to sample with traditional oceanographic instrumentation because it is highly episodic and the events are often short-lived, with peak discharge generally occurring during storms. In situ sampling from a manned vessel is only possible after peak discharge periods when the winds and seas are relatively calm. Washburn et al. [2003] collected shipboard measurements of freshwater plumes in Santa Monica Bay, providing a rough characterization of the spatial structure and evolution of the plumes due to limited temporal resolution. Warrick et al. [2007] present results of a large-scale coordinated study of two discharge events for the eight largest river systems in southern California. Unfortunately, this study only provides a rough characterization of the dispersion and fate of the terrestrially discharged waters due to severe in situ sampling constraints. Moored observations require dense arrays to resolve the spatial structure of the plume's dilution and dispersion and often do not sample the upper layers where much of the buoyant plume will be found [e.g., Geyer et al., 2000; McPhee-Shaw et al., 2007]. Remotely sensed ocean color as well as synthetic aperture radar imagery have also been used to detect freshwater plumes but again with limited temporal resolution [e.g., Mertes and Warrick, 2001; Otero and Siegel, 2004; DiGiacomo et al., 2004; Warrick et al., 2004b; Nezlin et al., 2008] and do not provide information about the vertical structure of the freshwater plumes. Numerical simulation provides an alternative way to study the dispersion and dilution of freshwater plumes.

Many factors affect the dynamics of freshwater plumes, including Earth's rotation, surface winds, currents, waves, tides, background stratification, coastal geometry, and bathymetry and the time course of the discharge itself. Large-scale plumes affected by rotation without external forcing remain attached to the coast and propagate to the right (in the northern hemisphere) of the freshwater source [Garvine, 1995]. In contrast, unforced small freshwater plumes not significantly affected by rotation will spread radially away from the source [Horner-Devine et al., 2015]. The shelf slope modulates the cross-shelf extent of freshwater plumes with lower bathymetric slopes corresponding to farther cross-shelf extent of the plume [Garvine, 1999].

Surface wind forcing plays an important role on freshwater plume evolution. Field observations by Fong et al. [1997] showed that freshwater plumes are strongly influenced by wind forcing with downwelling leading to narrower and thicker plumes, whereas upwelling winds result in a seaward expansion of the plume and thinner layers as noted in modeling studies [Whitney and Garvine, 2005; Choi and Wilkin, 2007; Moffat and Lentz, 2012]. Lentz and Largier [2006] also described narrower plumes with moderate downwelling winds. However during strong downwelling, wind-induced vertical mixing resulted in a wider plume near the bottom. Recently, Jurisa and Chant [2013] showed that offshore winds result in offshore plume detachment from the coast for large-scale, steady plumes while Kniskern et al. [2011] showed coherence of river discharge with wind and wave forcing for the U.S. West Coast. Coastal topography may also be an important factor in plume dispersion. Just as bays can limit horizontal dispersion of material [Mestres et al., 2006; Romero et al., 2013], headlands can significantly influence the dispersion of freshwater plumes [Warrick et al., 2004; Warrick and Stevens, 2011]. Similarly, tides can be important near complex topography enabling separation of freshwater plumes from the coast [Li and Rong, 2012].

Numerical ocean models are useful tools for improving our understanding of freshwater plumes. However most studies consider runoff into a quiescent ocean or a background ambient flow [e.g., Fong and Geyer, 2001, 2002, Cole and Hetland, 2015] as opposed to the turbulent ocean that characterizes the nearshore coastal ocean. To the best of our understanding, no study has focused upon the dispersion and dilution characteristics of small coastal streams into a turbulent ocean. Other studies simulating realistic runoff focused on larger coastal discharges, for example the work by MacCready et al. [2009] on the Columbia River in the northwest Pacific.

This study presents results from realistic three-dimensional numerical simulations of creek runoff in the Santa Barbara Channel (SBC), California into a fully developed submesoscale turbulent flow field with a horizontal resolution of 100 m. Here submesoscale processes are defined as those with spatial scales ranging between 100's of m to 10 km where geostrophic balance is not as dominant. The SBC is characterized by complex coastal circulation including basin-scale flows that are both locally and remotely wind-forced, mesoscale eddies, enhanced submesoscale activity due to coastal topographic and island wakes, fronts, and eddies [e.g., Harms and Winant, 1998; Dong et al., 2007; Washburn et al., 2011; Romero et al., 2013]. The present study focuses on characterizing freshwater plume dispersion and dilution near the Mohawk Kelp Forest a key field site for the Santa Barbara Coastal Long-Term Ecological Research (SBC LTER) program [e.g., McPhee-Shaw et al., 2007; Reed et al., 2008]. The numerical model is described in section 2, and the numerical experiments are introduced section 3. Model output analysis and results are presented in section 4, which are discussed and summarized in sections 5, and 6, respectively.

2 Numerical Model

The Regional Ocean Modeling System (ROMS) was configured with a series of one-way nested domains (L0, L1, L2, and L3 at horizontal resolutions of 5 km, 1 km, 275 or 250 m, and 100 m, respectively) following Buijsman et al. [2012] and Uchiyama et al. [2014]. Supporting information Figure S1 shows the nested domains used. The innermost domain (L3) covers the entire SBC including the Northern Channel Islands to properly account for island wake eddies (Figure 1b). This study focused on two wet seasons: (1) winter 2004/2005 and (2) winter 2007/2008 (Figure 2a).

Figure 1

(a) Area/volume of analysis (shading gray area) over Mohawk Kelp Forest (yellow star). Contours show the water depth. The mouths of Arroyo Burro and Mission Creek are shown with solid yellow circle and triangle, respectively. (b) The Santa Barbara Channel, including the inner most domain (L3) in cyan, and the corresponding box around the zoom area. (c) Zoom of the land mask near SB including the point sources (red circles) and the grid points (black dots) where horizontal tracer diffusion was enabled during strong discharge. The black-dotted line shows the control volume used for passive tracer budget balance (see discussion section).

Figure 2

Measured hydrographs in UTC time. (a) Hydrograph at Mission Creek between 1 January 2002 and 1 January 2009. The shaded areas in Figure 2a correspond to winters 2004/2005 and 2007/2008 shown in plots (b) and (c), respectively. The red and blue lines correspond to Arroyo Burro (AB) and Mission creek (MC), respectively. Shaded areas in Figures 2b and 2c indicate the periods of analysis.

The vertical grid is in sigma coordinates with 40 (L0-L2) or 32 (L3) levels with vertical grid cell refinement near the surface and the bottom. The model bathymetry consists of the global product (SRTM30_PLUS) by Becker et al. [2009] with a resolution of 30 arc seconds and the higher-resolution (3 s) product from the National Oceanic and Atmospheric Administration/National Geophysical Data Center (NOAA/NGDC) coastal relief data set. The bathymetry data were interpolated on the model grid and smoothed such that the slope between adjacent grid points is less than or equal to 0.2.

The largest domain (L0) was spun up for 15 years with climatology for both initial and boundary conditions, and surface fluxes. Subsequently L0 was run from 1996 through 2004 with realistic surfaces fluxes and boundary conditions from Simple Ocean Data Assimilation (SODA) reanalysis data [Carton and Giese, 2008], including surface heat relaxation toward monthly average sea surface temperature (SST) and surface salinity relaxation toward climatology [Killworth et al., 2000]. The L0 domain was forced with QuikSCAT-ECMWF blended winds.

Tides were introduced at the boundary of L1 computed using 10 tidal constituents (i.e., M₂, S₂, N₂, K₂, K₁, O₁, P₁, Q₁, M_f, and M_m) from TOPEX/POSEIDON satellite altimeter data inverted by Egbert et al. [1994]. This study's model implementation differs from that by Buijsman et al. [2012] only for the two innermost domains (L2 and L3) with surface temperature relaxation toward monthly average SST from Moderate-Resolution Imaging Spectroradiometer (MODIS) [Kahru et al., 2012]. L2 and L3 domains were forced with surface fluxes, including momentum, evaporation, precipitation, and solar heating from the Weather Research Forecast model (WRF) [Skamarock et al., 2008] with a horizontal resolution of 6 km. Sponge layers were used to minimize edge effects due to the one-way nesting [Mason et al., 2010] and were set to a width of about 5% of the longest side of each domain. For details of model initialization, spin-up and nesting, the reader may refer to Buijsman et al. [2012] and Uchiyama et al. [2014].

Subgrid-scale vertical mixing is parameterized with K-profile parameterization [Large et al., 1994], including a bottom boundary layer for coastal applications [Durski and Haidvogel, 2004]. The bottom roughness length was set to 10⁻² m and bottom drag coefficient bounded between 10⁻⁴ and 10⁻². The horizontal viscosity and diffusivity were neglected except near creeks during strong discharge as described below. Runoff was modeled as multiple point sources following Uchiyama et al. [2014]. During our initial simulations, numerical issues were found for large discharge rates near the point sources (i.e., negative salinities). These issues were alleviated by implementing horizontal mixing near the point sources (blacks dots in Figure 1c) with a diffusion coefficient K = min(0.6 d_i(t), K_max) for d_i(t) > 1 m³ s⁻¹, with d_i(t) corresponding to the discharge per point source and K_max varying between 2 and 3.5 m² s⁻¹ as needed. The values of K_max were determined iteratively by slowly increasing K_max until obtaining positive salinity values during intense runoff. This approach is not expected to impact our results since our focus is on the plume's mid and far field dilution and dispersion, particularly because momentum inputs from the river are neglected. The Froude number, F_e = u/(h g Δρ/ρ)^1/2, calculated during the largest discharge events near the point sources was ∼0.15, where u is the discharge current (discharge divided by the cross-sectional area of the point sources), g is gravity, and Δρ/ρ is the density difference between the plume and the background normalized by the background density. For F_e ≪ 1, there is not jet-like near-field region affecting the mid and far-fields [Horner-Devine et al., 2015].

Coastal plumes emanating from Arroyo Burro (AB) creek and Mission Creek (MC) were selected because of their proximity to Mohawk Kelp Forest (Figures 1a and 1c). The inner-shelf off AB is steeper than that at MC as shown in Figure 1a. Moreover, AB is situated in an area of larger eddy kinetic energy when compared to MC as AB is close to a headland and MC is in an embayment [Romero et al., 2013]. Both creeks discharge nearly simultaneously and during large discharge events MC will discharge approximately twice the freshwater as AB (Figure 2). To achieve similar discharge fluxes per source grid point, the number of point sources for MC (6) is twice that used for AB (3). Each array of point sources was positioned along the coast, centered at the mouth location (red dots in Figure 1c). The input discharge data is based on freshwater discharge measurements at each creek [Melack, 2012a, 2012b, 2012c]. The scalar discharge from point sources includes measured salinity (freshwater), temperature, and nitrate concentration (time varying), including two passive tracers (or dyes) for each creek of constant concentration (equal to 1). This allows characterization of dilution and dispersion per creek, in contrast to freshwater fraction, which is influenced by rain and other processes. Three-dimensional flow and tracer fields were averaged over hourly intervals and saved offline for post processing and analysis.

3 Experiments

Numerical simulations were carried out for the two rainy seasons: winters 2004/2005 and 2007/2008 (hereafter referred to as W04-05 and W07-08, respectively), with the largest runoff events observed between 2002 and 2009 (Figure 2a). W04-05 had the most runoff with four significant events and maximum discharge reaching 80 and 35 m³/s at MC and AB, respectively, during the flood event on 10 January 2005. The W07-08 had three significant runoff events with maximum discharge of 35 and 12 m³/s at MC and AB, respectively. Model output analysis was carried out over periods shown in the shaded areas in Figures 2b and 2c. For some events, the analysis period includes more than one discharge peak. A total of seven periods of analysis were selected: four for W04-05 and three for W07-08.

The runoff analysis was focused over an area that extends 5 km offshore and ±7.5 km along-shore off Mohawk Kelp Forest, which is shown with gray shading in Figure 1a. Table 1 characterizes the total discharge volume, D, wind, and oceanographic conditions for each storm event computed over the analysis area. Discharge duration, T_d, was calculated according to

(1)

where d(t) is the hourly discharge rate, with t₁ and t₂ corresponding to the limits for each analysis period with significant runoff, where t₁ is the onset of discharge and t₂ is calculated iteratively such that t₂-t₁ ≈ 2 T_d. The choice of t₂ allowed ensemble averaging of spatial distributions of runoff events with different duration. Values of T_d range from 0.6 and 4.2 days. The eddy kinetic energy (half of the surface current variance) varies between 0.3 × 10⁻² and 2.1 × 10⁻² m²/s², and flow anisotropy, defined as the ratio of the flow variance along-shelf over the cross-shelf variance, ranges from 1.2 to 3.5 (Table 1). Mean currents are small (< 22 cm/s) and are generally oriented along-shelf flowing toward the west. Mean winds are also small, oriented to the west, with large variability, particularly in the along-shelf direction (roughly east to west). In general, events with larger wind variability correspond to periods with larger mean currents and eddy kinetic energy.

Table 1. Summary of the Runoff Events Including: Total Discharge, Discharge Duration, Eddy Kinetic Energy at the Surface, Anisotropy, Mean Surface Currents, and Mean Winds (± Standard Deviation)a

Event #	D (m^3 × 10^6)	Td (days)	EKE (m^2/s^2 × 10^−2)	Anisotropy	Mean Currents		Along-Shelf Winds		Cross-Shelf Winds
					Ua (cm/s)	Uc (cm/s)	Mean (m/s)	rms (m/s)	Mean (ms/)	rms (m/s)
W04-05
1	1.0	3.9	0.7	2.5	−6.1	−0.6	−1.4	8.5	−1.7	6.0
2	3.4	3.2	1.3	3.5	−6.7	−1.0	−0.7	10.9	−3.6	7.8
3	1.6	4.2	1.2	1.9	−11.3	2.7	−1.2	9.3	−2.9	6.0
4	0.3	0.6	0.3	2.6	6.5	−2.0	1.0	3.8	−2.7	4.8
W07-08
1	0.2	0.6	1.6	1.2	−13.6	−3.4	−5.5	8.7	−1.2	5.7
2	0.4	0.9	1.4	1.6	−13.4	−0.5	−2.0	9.8	−4.1	6.9
3	1.2	2.9	2.1	2.3	−22.5	−2.0	−5.2	14.4	−3.7	7.6

• ^a The surface current and wind statistics were computed over the control volume shown in Figure 2 for a period of twice the discharge duration starting at the beginning of flooding. W04-05 and W07 are shown on the top and bottom, respectively. Positive along-shelf currents are on average due east and positive cross-shelf currents are offshore.

4 Results

4.1 Horizontal and Vertical Plume Distribution

The numerical simulations of SBC freshwater runoff produce plumes that are generally attached to the coast during flooding periods, followed by offshore advection by winds and stirring by background currents. Plumes reach the bottom within 1 km from the coast, and detach from the bottom offshore. Figure 3 shows an example of the time evolution of combined passive tracer from both creeks at four different times from the New Year's Eve/Day event of W04-05 (Figure 2b), which is broadly consistent with the other events simulated. A clear correspondence between the winds, hydrological discharge, and plume evolution is observed. During flooding periods, winds are strong, oriented toward the north-northwest, and freshwater plumes are narrow (Figure 3a). This is followed by weaker winds and surface plumes that extend farther offshore (Figure 3b). Subsequently offshore winds induce detachment of the plume from the coast (Figure 3c) and background currents actively stir the plume (Figures 3c and 3d). Two days after peak flooding (Figure 3d), the maximum concentration is of order 1% of the discharged value. Differences between AB and MC include: (1) the discharge from MC is larger than that of AB, (2) the currents are much stronger off AB when compared to MC, (3) coastline orientation (southwest facing at AB versus southeast facing at MC), (4) the plume is narrower off AB than MC, (5) during flooding plumes are advected due west off AB and east off MC due to the wind direction relative to the shore orientation, and (6) the presence of a breakwater just a few hundred meters west of MC (Figure 1b).

Figure 3

Evolution of plumes during the first storm of W04-05 at four different times: 31 December 12:00, 1 January 8:00, 2 January 04:00, and 2 January 15:00 (UTC) shown from left to right. (a–d) Surface passive tracer concentration (log base 10). The black vectors show surface currents. AB and MC are shown with yellow circle and triangle, respectively. The inset shows the hydrographs and corresponding instantaneous discharge rates from AB (circle) and MC (triangle). The blue text and arrows show the forcing wind speed and direction averaged over the area of the ocean shown. The gray-dashed lines labeled s1, s2, and s3 show the position of the vertical cross-shelf sections shown in plots (e–h), (i–l), and (m–p), respectively.

The gray-dashed lines s1, s2, and s3 in Figures 3a–3d show the location of the corresponding vertical cross sections of combined dye concentration (Figures 3e–3h, 3i–3l, and 3m–3p, respectively). At early times, during flooding, plumes at AB and Mohawk Kelp Forest are vertically mixed, reaching the bottom, with the upper and lower boundary layer fully overlapped, which are shown with light green and pink lines for the upper and lower layer, respectively. This is followed by offshore advection producing thin layers near the surface while the upper and bottom boundary layers separate. As the plumes are advected offshore, their vertical thickness grows. In contrast, the plumes off MC exhibit thin layers near the surface at all times with areas where the upper and lower boundary layers are separated. These layers are wider and thicker than those off AB.

The evolution of plume in time is further analyzed from cross-shelf position of the plume with respect to the winds and background surface currents. The mean cross-shelf position of the passive tracer distribution over the area of analysis, X_c(z,t), can be calculated according to

(2)

where c(x,y,z,t) is the passive tracer concentration anomaly from the background mean, x and y correspond to the cross and along-shelf distances and z is depth. Negative anomalies were neglected when computing equation 2 to minimize contributions from previous events. Similarly, the mean cross-shelf position of freshwater can be calculated according to equation 2 by replacing the tracer concentration anomaly with freshwater fraction FW = (S_r − S)/S_r, where S is the simulated salinity value and S_r is a reference salinity value calculated as the maximum salinity value over the volume of analysis at each hourly field. Again, FW values below the mean background were neglected in applying equation 2. Computations of the mean cross-shelf plume position near the surface (z = −1 m) give generally consistent values for both passive tracer and density, except when FW values are small.

Tight coupling is observed in Figure 4 between precipitation in the AB watershed [Melack, 2015] and the combined discharge records from MC and AB with 1 h time lag between peak values. The time evolution of the mean cross-shelf position of the passive tracer and freshwater are shown in gray and green color, respectively in Figure 4b. Both cross-shelf centroid representations track each other well. During the flooding period, the winds blow toward the northwest (see Figure 4c) and the mean cross-shelf position of the plume is less than ½ km from the shore. Subsequently the winds relax and the plume widens cross-shelf. Finally as the winds accelerate and shift toward the south/southeast, the plumes penetrate further offshore with a mean position reaching 2 km. The mean surface currents are variable and generally due west during flooding (Figure 4c). Mean currents are generally weak and show diurnal and semidiurnal modulation consistent with the tidal forcing. The tight coupling between precipitation and discharge, the cross-shelf position of the plume, and the progression of discharge during downwelling/onshore favorable winds followed by upwelling/offshore winds exemplifies the seven storm water discharge events examined (Figure 4 and supporting information Figures S2–S8).

Figure 4

(a) Time series of discharge, (b) mean cross-shelf frontal position, (c) wind vectors, and (d) currents during the first significant discharge event W04-05. Figure 4a Hydrographs from AB and MC combined (blue line), and precipitation record (magenta) measured within AB watershed at Santa Barbara Cater Water treatment plant. Figure 4b Mean cross-shelf position of freshwater (green) and combined passive tracers (gray) from both AB and MC. The thin vertical lines indicate the times from Figures 3a–3d. Figure 4c Feather plot of surface winds averaged over the control volume. Figure 4d Surface currents averaged over the control volume. The black and red lines correspond to the cross and along-shelf (approximately eastward) components, respectively.

4.2 Plume Dilution Statistics

The ROMS results enable the characterization of the expectations for the near surface passive tracer concentration. Probability density functions (pdfs) were calculated from the near surface passive tracer concentration field over each runoff period and then ensemble averaged. This was calculated using a logarithmic discretization of the concentration field with ΔC/C = 1.08 and 180 values between 10⁻⁶ and 1. Ensemble averages of pdfs within the volume of analysis at two different cross-shelf bins from both passive tracers combined are shown in Figures 5a and 5c, for 0 < x < 500 m and 2 km < x < 4 km, respectively. The blue, green, red, and cyan lines show W04-05 runoff events 1-4, respectively. Pdfs show strong spatial dependence with longer tails closest to shore. The maximum concentration closest to shore is 1, corresponding to the input passive tracer concentration (Figure 5a). In contrast the offshore bin shows maximum concentrations an order of magnitude smaller (Figure 5c).

Figure 5

Probability density functions (a, c) and exceedance probability distributions (b, d) of passive tracer concentration C within the control volume at two different cross-shelf bins: (a and b) 0 < x < ½ km and (c and d) 2 < x < 4. The blue, green, red, and light blue lines show the four main runoff events for W04-05.

To assess the probability that a given threshold concentration is exceeded, we calculate the exceedance probability (EP) from the pdfs according to

(3)

Figures 5b and 5d show EP distributions corresponding to the averaging bins closest (0 < x < 500 m) and farthest from the shore (2 km < x < 4 km), respectively. The probability of exceeding threshold concentrations C_T = 0.1 varies between 40% and 80% over all events within 500 m from the shore (Figure 5b) whereas offshore EP values are ∼0 for a C_T value of 0.1 (Figure 5d). Offshore EP values (Figure 5d) are greater than 90% for C_T ≈ 0.0001, which is two orders of magnitude smaller than that for the nearshore bin. Thus tracer concentration expectations exhibit a strong cross-shelf dependence.

Passive tracer concentration statistics are also analyzed spatially in two dimensions, treating tracers from each source independently. Pdfs of near surface tracer concentration where combined through ensemble averages with an arbitrary grid in (x,y) space of higher-resolution closest to the source (creek mouth). Figures 6a and 6e show EP distributions for AB with larger values close to the source and exhibit anisotropic patterns with stronger gradients cross-shelf than along-shelf. Similarly, both EP distributions show along-shelf asymmetry with higher values west of the point source discharge location. As expected, cross-shelf values of EP(x,y;C_T) are smaller for larger values of C_T (Figures 6a and 6e). For C_T = 0.1 the largest probability values reach 70% within 500 m from the creek. In contrast at low concentration values for C_T = 0.0001, EP values reach 100% ∼2 km offshore.

Figure 6

Average spatial distributions of exceedance probability (EP) and cumulative time of exceedance (T_x) as function of the cross (x) and along-shelf distance (y) for different surface tracer concentration thresholds (C_T) at Arroyo Burro (a, b, e, f) and Mission Creek (c, d, g, h). C_T = 10⁻¹ and 10⁻⁴, in Figures 6a–6d and 6e–6h, respectively. The data were averaged over all runoff events for both seasons. y =0 corresponds to mean location of the point sources. The spatial bins in (x,y) space where chosen arbitrarily with coarser resolution away from the creek to improve the robustness of the statistics due to the strong spatial dependence relative to the point source.

The corresponding EP(x,y;C_T) distributions for MC are shown in Figures 6c and 6g. The distributions from MC are qualitatively similar to those from AB, exhibiting anisotropic spatial dependence with decreasing probabilities with increasing distance from the creek, particularly in the cross-shelf direction. However, MC distributions exhibit a reduced degree of anisotropy when compared to AB. The reduction in anisotropy is consistent with MC's relatively weaker background flow and weaker shelf slope, which results in a wider plume in the cross-shelf direction. At high concentrations, the distribution shows along-shelf asymmetry in opposite direction relative to that of AB, with larger EP values towards the west. This is likely due to the different shoreline orientations (southwest versus southeast facing) relative to the prevailing northwestward winds during flooding and the presence of the breakwater just a few hundred meters west of MC (Figure 1c). At low C_T values, the EP(x,y) distributions at MC are approximately symmetric along-shelf. Statistical distributions for intermediate C_T values exhibit qualitatively similar spatial patterns (supporting information Figure S9).

The second statistical metric considered is the normalized cumulative time T_x that a point near the surface exceeds a threshold concentration, C_T, or

(4)

where H(C(x,y,z = 0,t)-C_T) is equal to one when the concentration is greater than the threshold value and zero otherwise. The normalized cumulative time of exceedance T_x is bounded between 0 and 1 and a T_x value of 0.5 implies that 50% of the time the surface concentration exceeds the threshold concentration. For consistency with the EP analysis, data were ensemble averaged over all runoff events.

T_x(x,y;C_T) distributions in Figure 6 exhibit similar patterns to those previously identified in the EP distributions, including: (1) strong spatial dependence with rapid decay away from the creek particularly cross-shelf (anisotropic), and (2) along-shelf asymmetry is westward for AB even at low values of C_T and opposite close to shore for high concentrations (C_T = 0.1) only at MC. However, the degree of anisotropy (cross-shelf gradients relative to those along-shelf) is qualitatively more pronounced for T_x when compared EP, particularly at low tracer concentrations. For C_T values of 0.1, the peak values of T_x, located within 500 m of the source, reach values of 25 and 50%, for AB and MC, respectively. Peak values increase for decreasing tracer concentrations reaching 80% and 100% for C_T = 0.0001, for AB and MC, respectively, within 500 m from the shore.

4.3 Plume Dispersion Statistics

Statistics of horizontal dispersion of passive tracer were calculated for each creek separately from the horizontal moments of the vertically integrated dye concentrations fields

(5)

where h(x) is the bottom depth and η(x) is the sea surface elevation. The mean position of the vertically integrated dye distribution, C′(x,t), is defined in two dimensions according to

(6)

with mean square width

(7)

where i = x,y correspond to the cross and along-shelf direction, respectively. Components of horizontal relative diffusivity can be calculated from time derivative of mean square width as given by

(8)

Equations 6-8 were calculated within the volume of analysis and over areas with concentration values greater than 0.01 and 0.1 to avoid contamination from low background values. The lower concentration threshold resulted in larger σ_i values. The relative diffusivities where averaged as a function of σ_i over all runoff periods, neglecting negative values of κ_i. The resulting mean relative diffusivities, κ_i, versus spatial scales, σ_i, are shown in Figure 7. Values of κ_i are proportional to σ_i² for root-mean-square widths between 100 m and 2 km and proportional to σ_i^4/3at larger scales, except for AB along-shelf with κ₂ ∝ σ₂^4/3 over all scales. Fitting both models to data from AB give k_a= 16 ± 2 σ_a^4/3 for 100 m < σ_a < 20 km and k_c = 14 ± 2 σ_c² for 100 m < σ_c < 2 km, and fits to MC data yield for 100 m < σ_i=a,b < 2 km, k_a = 23 ± 3 σ_a² and k_c = 13 ± 3 σ_c² and for σ_i=a,b > 2 km, k_i=a,b = 14 ± 3 σ_i^4/3. κ_i ∝ σ_i² is dimensionally consistent with two-dimensional enstrophy cascade suggesting nonlocal dispersion and mixing due to eddies of larger scale. κ_i ∝ σ_i^4/3 is consistent with dispersion and mixing due to turbulence or horizontal shear. The scale-dependent diffusivities from the dye patches agree qualitatively well with the particle-pair dispersion statistics by Romero et al. [2013], shown as the light red and light blue lines, corresponding the along and cross-shelf directions, respectively.

Figure 7

Relative diffusivity (κ) as a function of root-mean-square dye patch width (σ) from horizontal moments of vertically integrated passive tracer fields discharged at AB and MC, shown in plots (a) and (b), respectively. The red and blue lines correspond the along and cross-shelf direction, respectively, with error bars corresponding to the 95% confidence interval. The dashed black and gray lines are reference power laws of σ² and σ^4/3, respectively. The light red and blue lines correspond to the two-particle dispersion results in the along and cross-shelf direction from Romero et al. [2013] for particle trajectories with centroids within 2 km from the shore in SBC west and SBC east, shown in Figures 7a and 7b, respectively.

5 Discussion

The dispersion and dilution of creek runoff plumes have been investigated using high-resolution ROMS simulations during two rainy seasons from two creeks. The results showed plumes attached to the coast with plumes reaching the bottom near shore and forming thin surface layers a few meters thick offshore. The dilution field had strong anisotropic spatial dependence with large cross-shelf gradients. Plume evolution is tightly coupled to both the wind forcing and the hydrological cycle. Below we compare the results to available in situ observations, discuss the influences of wind forcing and submesoscale processes, address the relative importance of vertical versus horizontal transport processes, and address applications of these results to ecological problems relevant to the SBC LTER program.

5.1 Validation

Previous studies have shown that ROMS simulations with proper boundary conditions result in coastal circulation patterns that are statistically consistent with observations. For example Dong et al. [2009] showed good agreement between observed and modeled currents averaged over multiple years in SBC. Buijsman et al. [2012] showed good agreement between ROMS and observations at diurnal and semidiurnal frequencies, including sea level and vertical profiles of currents and temperature at several locations in Southern California. Without data assimilation, instantaneous comparisons between ROMS results and observations are not particularly meaningful because of intrinsic variability in the modeled winds and currents. Notwithstanding, we compare ROMS solutions with available salinity measurements collected nearshore during one of the simulated runoff events of W04-05.

Field observations of freshwater creek runoff with traditional oceanographic instrumentation are challenging. Creek runoff is flashy and short in duration; moreover conditions are often not safe for small boat sampling. In 2005, in situ measurements were collected with a hand-lowered conductivity, temperature, depth (CTD) sensor from a small boat off AB. CTD measurements were collected with a Sea Bird Electronics 19plus V2 SeaCAT profiler and were collected just after peak discharge. Figure 8a shows the locations of the CTD samples (open circles; numbered in sequence) collected between 20:00 and 23:00 (UTC) on 10 January 2005. Because of the rough sampling conditions, personnel were not able to equilibrate the CTD to in situ conditions (C. Nelson, personal communication, 2015), which resulted in large down versus upcast hysteresis. The upcasts were deemed more realistic and will be used here, although data quality issues likely remain.

Figure 8

(a) CTD casts (white circles) collected off AB (gray circle) on 10 January 2005 between 21:21 and 23:03 UTC. (b) Average measured FW profiles (thick circles in plot a) at different water depths with the red, green, and blue lines corresponding to water depths h=6, 17, and 68 m, respectively. (c) Representative model profiles at similar water depths off AB at an instance with similar near surface FW values in shallow water.

The available salinity profiles captured freshwater signals particularly near the surface within a few meters from the surface. Determinations of freshwater fraction, FW, were averaged in three groups over adjacent CTD casts at water depths of 6 (casts 1–5), 17 (10–14), and 68 m (17–19), shown as red, green, and blue lines, respectively, in Figure 8b. The horizontal bars correspond to standard error determinations. At depths below 1 m from the surface, there is a trend of increasing FW with decreasing water depth or cross-shelf distance. However, near the sea surface, mean FW values are similar for all the groups.

Representative model FW profiles (Figure 8c) show similar maximum FW fractions and cross-shelf trends compared with the observations (Figure 8b). However, there are consistent differences between the model and the observations: the modeled FW profiles do not penetrate as deep as the observations, and the model shows much smaller FW values at depth. A likely factor contributing to these differences is that in the ROMS simulations only the AB and MC watersheds are supplying freshwater to the SBC. The AB and MC watersheds combined provide only about 2% of the total mean discharge per year to the SBC [Warrick, 2002] (J. Warrick, personal communication, 2015). As only the AB and MC watersheds are considered in this modeling study, the water column structure that the modeled plumes are discharging into may differ from the actual case. Further, rain inputs may also contribute to the freshwater signals observed and the choice of subgrid-scale vertical mixing parameterization may also have a role in these discrepancies [Hetland, 2005]. Thus, the lack of correspondence of aspects of the ROMS results is not totally unexpected.

The present ROMS simulations do not include wave-current interactions, which may also have important influences on the evolution of storm water plumes. For example, surface waves over the inner-shelf may induce vertical mixing due to wave breaking and Langmuir circulation and advect buoyant plumes onshore. Also, surf zone effects may result in complex flows and cross-shelf exchanges of tracers with the inner-shelf [Hally-Rosendahl et al., 2014]. Future modeling work should incorporate surface wave effects [e.g., McWilliams et al., 2004; Uchiyama et al., 2010; Kumar et al., 2015], including surf zone effects at the next level of nesting with higher horizontal resolution.

5.2 Contributions of Winds and Submesoscale Flows to Plume Dilution and Dispersion

Analysis of modeled creek runoff showed that the evolution of freshwater plumes was linked to the correlation between the wind forcing and the hydrological cycle. During flooding, winds are strong due west (downwelling) and onshore resulting in narrow freshwater plumes. After flooding, winds may decay, subsequently flowing offshore and/or slightly due east (upwelling), resulting in offshore penetration of the plume.

Wind direction is clearly important to plume dispersion. To better understand the effects of different wind regimes, we carried out a statistical analysis with Lagrangian particles releases at AB and MC under different wind regimes. Particle trajectories were released every 3 h and were tracked for up to 1 day following procedures in Romero et al. [2013] and used to compute two-dimensional pdfs as a function of time after release for three wind regimes: northwestward winds, southeastward winds, and calm conditions (see examples in supporting information Figure S10). The ensemble pdfs centroid location and widths for particle releases from AB are shown in Figures 9a and 9b and 9c and 9d, respectively, as a function of time. Results from releases at MC are qualitatively similar and are not shown. The cross-shelf centroid of the particle field (Figure 9a) moves offshore much faster during southeastward winds than under calm or northwestward wind conditions reaching 3 km after one day. The mean along-shelf position (Figure 9b) remains constant at the release location under calm conditions, and shifts to the west and east when the winds blow to the NW and SE, respectively, with largest displacement for the former (i.e., 10 km versus 5 km after 1 day). The width of the distributions (Figures 9c and 9d) is similar under northwestward winds and calm conditions. However under southeastward winds, the width of the distribution increases most rapidly in both the cross and along-shelf direction. These results are consistent with the analysis freshwater plume evolution and illustrate the important role of wind direction in plume dispersion.

Figure 9

Moments of particle density distributions as a function of time from release. Mean positions along and cross-shelf are shown in (a) and (b), with corresponding root-mean-square widths in (c) and (d), respectively. The blue, red, and gray lines correspond to periods during northwestward winds, southeastward winds, and calm conditions, respectively.

The presently observed progression of discharge and wind shifts differs from a recent analysis of plume discharge from a nearby watershed, the Santa Clara River [Kniskern et al., 2011]. These authors found downwelling winds prior to peak discharge (as opposed to during flooding) followed by upwelling winds. However the Santa Clara River watershed is much larger than AB or MC and it takes longer for the discharge to reach the ocean from when a storm passes. Figure 4a shows the precipitation record from a station within AB watershed (magenta) together with the discharge record from AB and MC combined (blue), which peaks 1 h after peak precipitation. The tight relationship between rain and discharge demonstrates the flashy nature of the small coastal watersheds that discharge into the SBC.

Submesoscale processes also have important impacts on plume evolution. During flooding, strong winds induce strong westward flow and horizontal shear, which frequently results in strong alongshore filaments of large relative vorticity that can trap freshwater runoff against the coastline. Filament structures with large vorticity are ubiquitous and have a tendency trace the nearby coastline [Romero et al., 2013]. After peak flooding, freshwater plumes dilute rapidly, typically within a day, due to the combined action of offshore advection by winds, stirring by submesoscale currents, and vertical mixing. An intense submesoscale filament structure located between 3 and 5 km from the shore with an alongshore length of >10 km is seen during peak flooding from the 2005 New Year's Day storm (Figures 10a, 10e, and 10i). Absolute values of ζ/f along this filament exceed 5 and its location corresponds with a strong density front (not shown), strong downwelling velocity (> 5 m/day), and large straining rates, illustrating that this feature is acting as a transport barrier. As wind forcing decays, the freshwater plume expands offshore and strong correspondences between the locations of the freshwater tracer front and the relative vorticity filaments and intense downwelling features are observed (Figured 10b, 10f, and 10j and for subsequent times as well). Also notice the flow convergence at the freshwater fronts in Figure 10b consistent with O'Donnell et al. [1998]. Subsequently, the freshwater plume dilutes rapidly while being stirred by background submesoscale currents (Figures 10c and 10d), which are identified from the spatial correspondence between features of the magnitude of the passive scalar gradient with those of the vorticity and vertical velocity fields.

Figure 10

Evolution of (a–d) the magnitude of surface passive tracer concentration gradient (log base 10), (e–h) relative vorticity ζ = u_y-v_x normalized by f, and (i–l) vertical velocity fluctuations with the spatial mean subtracted, with each plot corresponding to time shown in Figures 4a–4d, respectively.

Fresh water inputs also have influences on submesoscale dynamics. Pdfs of surface relative vorticity and vertical velocity anomaly with and without significant FW (defined as regions where passive tracer concentrations are > 0.005) illustrate marked differences in their levels of submesoscale activity. Figure 11a shows the pdfs of ζ/f with for C < 0.005 calculated at two different offshore bins, 0 < x < 1 km and 2 km < x < 3 km, which are shown in the solid red and blue lines, respectively. The variance increases toward the shore and the skewness is reduced from 2.4 to −0.4. Similarly the pdfs of in Figure 11b show a trend of increasing variance toward the shore while the skewness increases −1.8 to −1.3. Positive skewness for vorticity and negative for vertical velocity is characteristic of submesoscale frontal dynamics [Capet et al., 2008a, 2008b]. The increase in vorticity variance and reduced skewness nearshore can be attributed to the presence of the boundary and the mean along-shore flow due west. Pdfs calculated for the nearshore areas affected by the plume (C > 0.005) are shown in Figure 11 with solid circles (corresponding pdfs for the offshore bin did not show significant differences). The variance and skewness of the normalized vorticity pdfs increase in the presence of freshwater runoff illustrating the dynamical impacts of the buoyancy gradients imposed by the freshwater inputs. Similarly the vertical velocity variance increases and the skewness decreases with significant FW, showing much larger downwelling velocities consistent with the convergence at freshwater fronts [e.g., O'Donnell et al., 1998]. The increase of vorticity variance with significant FW is presumably associated with frontal instabilities created by the horizontal buoyancy gradients from the freshwater inputs.

Figure 11

Probability density functions of surface ζ/f (a) and ω′ (b) calculated over the control area within 1 km from the shore (red lines) and for 2 < x < 3 km (blue) combining both simulated seasons. Data with low passive tracer concentrations C < 0.005 (C>0.005) are show with thick lines (solid circles).

Thus both wind forcing and submesoscale processes have important implications for the dispersion and dilution of freshwater plumes. Both processes contribute to trapping plumes nearshore during flooding resulting in large concentrations nearshore and strong cross-shelf gradients. After flooding, offshore expansion of the plumes due to cross-shelf pressure gradients and offshore wind forcing, accompanied by stirring by submesoscale currents that are also enhanced by the freshwater buoyancy gradients, results in their rapid dilution. Consequently, expected probability distributions of passive tracer at high concentrations, which occur at early stages of the runoff event, are more anisotropic than those for low tracer concentrations from later stages of the event.

5.3 Vertical Versus Horizontal Transport

The relative importance between horizontal and vertical fluxes is assessed by budgeting the changes in passive tracer concentration within a control volume. The area covered by the volume is shown with a black-dashed line in Figure 1a covering both creeks and the headland region in between and its depth is 3 m from the surface based on the minimum water depth of the model of 1.5 m the typical tide amplitude of 1 m. The budget terms are

(9)

where is the passive tracer field integrated over the control volume, Q is the input of tracer from the streams, and F represents the outward fluxes given by

(10)

The first and second terms correspond to the horizontal and vertical advective fluxes, respectively, and the third term corresponds to the flux due to vertical mixing. All terms were calculated directly from saved model output over each runoff event, except for the vertical mixing term, which was calculated as the residual of the budget. All terms in the tracer control budget are significant, with vertical mixing (outward flux) nearly in balance with the vertical advection (inward flux) due to restratification (supporting information Table S1). Consequently the net vertical fluxes (advective plus vertical mixing) are typically smaller than the net horizontal fluxes. For example, the average budget over the entire first runoff event (9 day average) gives a ratio of net vertical over horizontal fluxes of 0.4 and 0.3 for AB and MC, respectively (supporting information Table S1).

The size of the control volume has a bearing on the relative importance of vertical versus horizontal transport. If the control volume is deepened from −3 m to −10 m, the ratio of net vertical to horizontal flux decreases to 0.1 and 0.03 for AB and MC, respectively, implying that vertical fluxes are nearly negligible. Conversely if we increase the cross-shelf extent of the control volume by 2 km farther offshore, the ratios of vertical to horizontal transport increase to order 1. Therefore, horizontal transport processes as opposed to vertical dominate the evolution of tracer near the surface and within a few kilometers from the creek. This budget analysis with a control volume does not imply that horizontal advection is diluting the tracer; instead passive tracer is advected out of the box.

5.4 Application to Ecological Problems and Marine Resource Management

The ecological and resource management impacts of land-to-ocean discharges can be quantified knowing the dose-response relationship for a tracer. The simplest example of a dose-response relationship is a lethal threshold above which the organism in question perishes. Determination of the exceedance probability (Figure 6) of a discharged contaminant concentration provides a straightforward way of assessing the risks of exposure to lethal levels of a contaminant. For example, freshwater discharges from coastal streams can contain human pathogens that lead to gastrointestinal illnesses. Thresholds have been established for fecal indicator bacterial abundances below which recreational exposure is considered safe. For marine waters, enterococci is a useful bacterial indicator for human pathogens and the U.S. EPA has set geometric mean recreational water quality criteria for enterococci of 30 colony forming units (cfu) per 100 mL [U.S. Environmental Protection Agency (U.S. EPA), 2012]. Measurements of fecal indicator bacteria in the AB and MC watersheds during storms found enterococci abundances of ∼10,000 most probable number (MPN)/100 mL [Sercu et al., 2011; MPN units approximate cfu units at high abundances; U.S. EPA, 2014]. Thus, recreational exposure to coastally discharged pathogens from these watersheds are potentially dangerous if the dilution of storm water is less than ∼300-fold, corresponding to a C_T value of ∼0.003. At a dilution factor of 100 (C_T = 0.01; supporting information Figure S9), storm water from these two creeks would create substantial risks to human health (exceedance probabilities ≥0.5) at public beaches within roughly 4 km of the two creek mouths. Further for the affected sites, fractional exceedance times are ≥0.5 illustrating that these water quality thresholds will be surpassed at least half of the time during storm water events. Please note that these rough risk estimates do not account for any processes that would alter the abundance of the indicator bacterial abundances or their pathogenicity.

Coastal creeks may be an important source of beneficial ecological subsidies to nearby kelp forests providing nitrate nutrients for the growth of giant kelp populations [e.g., McPhee-Shaw et al., 2007; Brzezinski et al., 2013]. Minimum nitrate concentrations supporting the net growth in giant kelp are ∼1 µM [Zimmerman and Kremer, 1984] while a recent analysis of giant kelp biogeographical patterns demonstrates enhancements in giant kelp canopy growth for nitrate concentrations in excess of 6 µM [Bell et al., 2015]. Ambient nitrate concentrations at the Mohawk kelp forest which is located between MC and AB vary from ∼0.2 to ∼20 μM [McPhee-Shaw et al., 2007; Brzezinski et al., 2013]. Concentrations of nitrate in coastal creek storm water discharges will vary with many factors (cf., runoff intensity, land use and nutrient cycling within the watershed, poor wastewater infrastructure, etc.). During peak storm flow, nitrate concentrations from Mission Creek and Arroyo Burro Creek can be as high as 300 µM while storm-weighted mean nitrate concentrations for the two creeks are 68 and 92 µM for MC and AB, respectively [Goodridge and Melack, 2012]. A value of 100 µM is assumed here to be a good estimate of storm flow nitrate concentration. Determinations of the exceedance probability above a normalized threshold concentration C_T of 0.1 indicate that storm water nitrate concentrations in excess of 10 µM (10% of 100 µM) will be found within ∼2 km of the two creek mouths (Figures 6a and 6c). The AB creek is close enough to the Mohawk Kelp Forest (Figure 1a) to provide ecologically significant amounts of nutrients from storm water runoff. However their annual contribution of storm water nitrate to kelp forests will likely be small due to the episodic nature stream discharges [e.g., McPhee-Shaw et al., 2007; Brzezinski et al., 2013].

Dose-response relationships are often much more complicated than a simple threshold response. For example, organismal growth rates will have a saturating relationship with substrate concentration where there will be no added response to additional substrate concentrations. Further, organisms typically will have physiological temperature limitations that make a range of thermal conditions optimal for growth and reproduction. Consideration of nonlinear dose-response relationships requires the integration of exposure, here the contaminant concentration, with the nonlinear dose-response relationship. In principle, this calculation is straightforward yet it requires knowledge of the dose-response relationship and the space-time variability of the contaminant concentration.

6 Conclusions

This study presents high-resolution simulations of freshwater plume dispersion and dilution from two creeks in the Santa Barbara Channel. Plume evolution responds to coupled changes in precipitation, creek discharge, and wind forcing modulated by the background currents. Within 1 km from the shore, plumes reach the bottom; while further offshore, plumes detach forming thin, near-surface layers a few meters deep. Freshwater plumes are found within ½–2 km from the shore, with narrower extent during flooding times when the winds blow to the north/northwest and long filaments of large relative vorticity develop helping trap freshwaters nearshore. After flooding winds decay and change direction to the south/southeast, and the freshwater front moves offshore. Freshwater fronts expand cross-shelf exhibiting significant surface convergence with sharp downwelling filaments that correlate with areas of large vorticity and straining rate. Finally, advection of freshwater due to wind forcing and stirring due to background submesoscale flow results in fast mixing and dilution of the freshwater plume after flooding. Differences between the two creeks simulated are likely due to differences in coast orientation relative to the winds and the presence of the breakwater just east of MC. Moreover, plumes are narrower at AB compared to MC, where the shelf is less steep, and the background flow is less energetic.

Statistical analysis of surface passive tracer concentration from runoff showed strong spatial dependence with high concentrations only within about 1 km of the mouth. Statistical distribution of the exceedance probability and normalized time of exceedance are highly anisotropic with sharp cross-shelf gradients. At a few kilometers from the shore, maximum tracer concentrations drop by several orders of magnitude. The results suggest that AB storm water can be a significant, yet intermittent, source of nutrients to nearby kelp ecosystems due its proximity to the kelp communities. In contrast, both creeks likely create a risk to human health during flooding and a few days after due to expectations of poor water quality and the proximity of these creeks to public beaches.

The calculations performed here address the freshwater dispersion from two small coastal streams discharging into the Santa Barbara Channel. This begs the question whether one can assess the impacts of storm water inputs from small coastal streams without conducting computationally intensive high-resolution ROMS simulations. The plume dispersion statistics showed good qualitative agreement with particle-pair dispersion statistics (Figure 7). Romero et al. [2013] used particle-pair statistics to develop a coastal dispersion parameterization that accounts for spatial inhomogeneities (bays versus headlands), distance from the shore and anisotropy in energetics. The Romero et al. [2013] parameterization can be applied to model plume dispersion and dilution for other sites using a two-dimensional advection-diffusion model. Such approach would be suitable for practical applications and more computationally tractable than high-resolution ROMS simulations.

Acknowledgments

This study was supported by the Santa Barbara Coastal Long Term Ecological Research (SBC LTER) program (NSF OCE-0620276 and OCE-1232779), and used computer resources provided by NCAR's Computational and Information Systems Lab (CISL) and the Extreme Science and Engineering Discovery Environment (XSEDE). The authors would like to thank Libe Washburn, Dan Reed, John Melack, and Blair Goodridge for discussions and would like to acknowledge the efforts of Libe Washburn and SBC LTER technicians Clint Nelson and David Salazar for collecting in situ observations in very difficult conditions. The data used are listed in SBC LTER repository at http://sbc.lternet.edu//data/.