Modeling coastal current transport in the Gulf of Maine

Transcription

1 Deep-Sea Research II 52 (25) Modeling coastal current transport in the Gulf of Maine Robert D. Hetland a,, Richard P. Signell b a Department of Oceanography, Texas A&M University, College Station, TX, USA b NATO/SACLANT Undersea Research Centre, La Spezia, Italy Accepted 2 June 25 Available online 3 September 25 Abstract A numerical simulation of the circulation in the Gulf of Maine is compared with observations taken during the spring and summer of 1994, focusing on two distinct coastal current systems. The eastern Maine coastal current is well mixed out to approximately 5 m depth, with the influence of tidal mixing extending to 1 m depth. In contrast, the western Maine coastal current consists mainly of a surface-trapped plume emanating from the Kennebec River. Various methods of model/data comparison are discussed, ranging from qualitative comparisons of surface temperature and currents to quantitative measurements of model skill. In particular, one primary metric of comparison is the amount and distribution of fresh water carried within the coastal current systems. In both coastal current systems, fresh-water flux has an approximately self-similar structure so that measurements taken at a single mooring location may be extrapolated to estimate the entire along-shore fresh-water flux. This self-similar structure is shown to be internally consistent within the model, and results in good model/data comparisons. The model has more skill at predicting fresh-water flux than other point-to-point surface property comparisons in all cases except surface salinity in the western Maine coastal current. This suggests fresh-water flux is a robust feature in the model, and a suitable metric for gauging the model ability to reproduce the broad-scale transport of the Maine coastal current system. r 25 Published by Elsevier Ltd. Keywords: Gulf of Maine; River plumes; Buoyancy driven flow; Numerical model skill 1. Introduction Numerical models of ocean circulation are becoming a standard tool in all facets of oceanographic research; more and more they are called upon to act as the foundation for other, nonhydrodynamic models, such as ecosystem or sediment transport models. However, before the circulation model can be used effectively, the limitations Corresponding author. Tel.: ; fax: address: hetland@tamu.edu (R.D. Hetland). of the model must be clearly stated in order to ascertain if using a particular circulation model is appropriate for the overlaid application, and to estimate the errors that may cascade from the hydrodynamic model upward to the overlaid application. Clearly, any numerical model has limitations and errors. Perhaps the most obvious is the limitations of grid-scale resolution, as well as a finite domain for regional-scale models. Errors also may stem from systematically over- or underestimating mixing, or using biased initial or forcing fields. Despite such limitations, researchers have been using /$ - see front matter r 25 Published by Elsevier Ltd. doi:1.116/j.dsr

2 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) numerical models successfully for decades. We believe that this is not contradictory models may be useful despite limitations. If an application is insensitive to particular errors, a model that has those errors may still be skillful with regard to that application. However, it is clear that a model well suited for one application may be completely inappropriate for another. Therefore, estimating model skill, or in particular using skill estimates to validate a model, makes no sense without reference to an application. For example, Bogden et al. (1996) used an inverse model to estimate the inflow due to remote wind forcing along an open boundary. They note that model skill decreases with increasing model complexity (e.g., inclusion of the non-linear terms), and attribute the decline in skill to a mismatch in the actual and simulated energetic, small-scale flow features. This result seems to contradict the notion that a more complete set of physics will result in a more accurate simulation. Another possible interpretation of this result is that the spatial scales over which the comparison was performed were inappropriate for the physical processes that the inverse model was intended to estimate: the broad-scale, wind-driven flow into the domain. The small-scale features were not averaged through a large enough covariance structure, and were contaminating the skill estimate. In this paper, we examine one method of model data comparison using a particular definition of skill. We seek to quantify the ability of a regional numerical model of the Gulf of Maine to predict the fresh-water flux (FWF) in the coastal current system. The motivation is to assess the ability of the model to provide an adequate hydrodynamic basis for simulating blooms of Alexandrium fundyense, a toxic dinoflagellate found in the Gulf of Maine often associated with the buoyancy-driven coastal current system (e.g., Franks and Anderson, 1992). We presume that prediction of the broadscale features of the buoyancy-driven current, such as FWF and salinity differences between the coastal current and background waters, will lead directly to better predictions of regional A. fundyense outbreaks. Small-scale differences in, for example, the eddy field or frontal position will matter less as long as the broad-scale features are correctly simulated. The principal phenomenon of interest here is the coastal response to seasonal discharge of fresh water associated with springtime rains and melting snow. This pulse of fresh water enters the various Gulf of Maine rivers, and eventually sets up a coastally trapped, buoyancy-driven coastal current system. Because of spatial differences in tidal mixing, the Gulf of Maine has two distinct coastal current systems: the vertically well-mixed Eastern Maine Coastal Current (EMCC) and the vertically stratified Western Maine Coastal Current (WMCC). A cartoon showing the locations of these two systems is presented in Fig. 1. The EMCC extends between Grand Manan Island and Penobscot Bay, and is vertically well mixed by the tides out to approximately 1 m depth (Brooks, 1994; Lynch et al., 1997; Hetland, 1997). There is considerable horizontal salinity stratification (a proxy for density stratification), with fresher, lighter waters closer to shore. The velocity structure is similar to that proposed by Chapman and Lentz (1994), in which a region with strong, localized horizontal density gradients, combined with no flow at the bottom, create a current with uniform vertical shear with very small bottom velocities. However, it is not yet clear if the crossshore flow, or cross-shore frontal motions are consistent with the Chapman and Lentz model of a density front trapped by the bottom boundary layer. Previous modeling studies suggest that the EMCC is driven by a combination of tidal rectification, fresh-water input from the Saint Johns River, and barotropic flow from the Scotian Shelf (Brooks, 1994; Lynch et al., 1997; Hetland, 1997). In contrast, the WMCC is a surface-trapped river plume emanating from the Kennebec and Penobscot Rivers. Wind plays a large role in moving the plume on- and offshore during up- and downwelling wind events, and wind is also a primary cause of mixing in the plume (Fong and Geyer, 21; Fong et al., 1997). 2. Methods 2.1. Model description The Regional Ocean Modeling System (ROMS, Haidvogel et al., 2) was chosen for the numerical simulations in this study. ROMS uses a curvilinear horizontal C-grid, and a stretched, terrain-following vertical coordinate. The model grid size of grid is ; the horizontal grid is shown in Fig. 2. The deep waters off the continental slope are clipped to 8 m depth to limit the external/ gravity wave speed (e.g., tides).

3 2432 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) N St.Johns Grand Manan Island Bayof Fundy 44 N Merrimack WMCC Jordan Basin 42 N Wilkinson Basin Georges Basin Georges Bank 4 N 7 W 68 W 66 W 64 W 62 W Fig. 1. Gulf of Maine springtime coastal current circulation between Grand Manan Island and Cape Ann is shown, with major rivers and bathymetric features indicated. The eastern Maine coastal current (EMCC) extends from Grand Manan Island, following the 1 m isobath. Near Penobscot Bay, there is a bifurcation point, where the EMCC may continue downcoast, or be deflected offshore. The western Maine coastal current (WMCC) is more affected by the local wind stress, and may be pressed up against the coast during downwelling winds or extend 5 km or more offshore during upwelling winds. The figure is based loosely on other circulation diagrams by Bigelow (1927), Brooks (1985), and Lynch et al. (1997). The model is initialized with a regional scale climatology created by Lynch et al. (1997), which is also used to specify the tracer values along the open boundaries during integration. The climatology only contains a rudimentary coastal current system shoreward of the 1 m isobath due to scarcity of observations in that region. However, after approximately one month of integration, the coastal current system within 1 m is well defined because it is so strongly forced. Water properties deeper than 1 m change on a much longer time scale, and remain fairly steady throughout the integration. Attempts were made to modify the climatology to better represent the conditions in 1994, but these changes did not significantly alter the structure of the simulated coastal current. The model grid was designed to be large enough so that the coastal current systems were somewhat insulated from the boundaries. Lynch et al. (1997) found that information about the Gulf-scale winddriven circulation patterns, in particular the barotropic flow from the Scotian Shelf, was crucial in reproducing the coastal current system further motivation for a Gulf-wide domain. However, we did not intend to simulate the entire Gulf of Maine circulation correctly. For example, we are aware of flaws in the exchange between the deep Gulf basins and the Atlantic ocean. The model is forced with spatially uniform wind stress and surface heat flux. Values for surface forcing were specified using air temperature, air pressure, and wind from the NOAA buoy 447 (12 NM southeast of Portland at 43:53N 7:14W), a constant relative humidity of 7%, and short-wave radiation from the Woods Hole Oceanographic Institution (41:52N, 7:67W). This idealized representation of the surface forcing was considered sufficient to provide reasonable development of

4 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) o N 44 o N CPM PBM CCM JBM 42 o N 4 o N 7 o W 68 o W 66 o W 64 o W 62 o W Fig. 2. The model grid is overlaid on regional isobaths. Also shown are the four mooring locations discussed in the text: from east to west, the Cape Porpoise mooring (CPM), the Kennebec River mooring (KRM), the Jordon Basin mooring (JBM), and the eastern Maine coastal current mooring (CCM). The solid lines represent the cross-sections through which the FWF is calculated for the EMCC and WMCC. The small gray points show the location of hydrographic cross-sections used to compare with model results. seasonal stratification and wind forcing of coastal currents along the Maine coast, since the scale of synoptic weather systems is relatively large. For example, Mountain et al. (1996) showed that shortwave radiation in the Gulf has a correlation scale of several hundred kilometers, and Greenberg et al. (1997) showed that using uniform wind stress with M2 tide explains most of the remote and local wind response of the Gulf. Fresh-water discharges are prescribed from the four major rivers: the Merrimack, Kennebec- Androscoggin, Penobscot, and St. Johns rivers. Discharges from these rivers were specified using stream gauge data from the USGS 1 and from Environment Canada 2 adjusted to account for drainage area downstream of the gauge locations Time series of winds and fresh water discharges are shown in Fig. 3. To place the situation in 1994 in context to other years, 1994 was very wet, having one of the highest peak discharges on record, and had moderate upwelling persisting through most of the spring, as shown in the second panel of Fig. 3. The model includes tides using a Flather boundary condition (Flather, 1976) with tidal elevations calculated from a finite-element tidal model. M2 tidal elevation and currents were specified at the open boundary using the finite-element tidal model of Lynch and Naimie (1993). Temperature and salinity were nudged to climatological values along the boundary. Surface forcing includes heat exchange with the atmosphere, and surface wind stresses; both varied in time but were spatially constant. The model was initialized with climatological values of temperature, salinity and flow, and was integrated from March 19, 1994 through June 3, Model results were averaged over one tidal period, and stored.

5 2434 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Wind stress (m 2 s -2 ) Apr May Jun Jul River transport m 3 s -1 τ dt Apr May Jun Jul St. Johns Kennebec-Androscoggin Penobscot Merrimack 1-Apr May Jun Jul-1994 Fig. 3. Wind and river forcing used in the numerical simulation is shown. The upper panel shows the along-shore winds (relative to the majority of the Maine coast, with positive wind stress, t, rotated 55 to the right of north). The middle panel shows integrated along-shore wind stress for four different years (see, for example, Blanton and Atkinson, 1983). In this figure, a positive slope represents net upwelling winds, a negative slope means net downwelling. Winds in 1994 are generally upwelling favorable throughout the spring, punctuated by a few downwelling events in May. The lower panel shows the fresh-water discharge for the four rivers included in the model simulation Data Moored measurements In the Eastern Gulf of Maine two moorings were deployed. The eastern Maine coastal current mooring (CCM) was deployed within the eastern Maine coastal current at about 1 m depth from April 3 to June 4, The Jordon Basin mooring (JBM) was deployed at the northwestern corner of the Jordan Basin at a depth of about 2 m from April 2 to May 7, Both moorings were equipped with downward-looking acoustic Doppler current profilers and three temperature/salinity sensors spread over the mooring line; at the CCM, temperature and salinity were measured at 5, 4, and 8 m depth. Four moorings were deployed in the western Gulf of Maine from February 17 to October 13, 1994 field program, but only two are discussed in this paper. The Cape Porpoise mooring (CPM) deployed offshore of Cape Porpoise in approximately 5 m of water with current meters and temperature/ salinity sensors at 5 and 27 m depth. The Kennebec River mooring (KRM) was deployed in about 8 m of water offshore of the Kennebec River with current meters and temperature/salinity sensors at 5, 27, and 5 m depth Hydrography In the eastern Gulf of Maine, a single hydrographic cruise was conducted from 26 to 29 April In the western Gulf of Maine, three large-scale hydrographic surveys were conducted throughout the spring and summer of 1994, with additional surveys conducted along the Cape Porpoise transect. In this paper, the focus is on two transects, shown in Fig. 2, along with the corresponding

6 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) transect used from the model for comparison. We chose these lines because they both cross mooring locations where time series of along-shore FWF is estimated. Other transects, not shown, also have been used in the hydrographic estimates of FWF Other data Advanced Very High Resolution Radiometry (AVHRR) sea-surface temperature images are available from the NOAA CoastWatch program. 3 Five Satellite tracked drifters were released in the eastern Gulf of Maine during the hydrographic cruise, drogued at either 1 or 4 m depth. The drogue depth seemed to make very little difference in the behavior of the drifters, in that both types of drifter were carried into the coastal current system, and both types were entrained into the Jordan Basin Gyre Definitions Fresh-water flux (FWF) FWF is calculated by multiplying the fresh-water fraction, ðs s Þ=s, times the velocity, v, and integrating over some plane, A, so that ZZ FWF ¼ A s s s v da, (1) where da is directed perpendicular to the area through which the flux is being calculated, s is the salinity, and s is a reference salinity. The definition of the reference salinity is not always straightforward, and the particular choices are discussed in more detail below. In this paper, we are primarily concerned with the local FWF, following the freshwater input into the system from local rivers, so the reference salinity is chosen accordingly Model skill Model skill is defined in this paper as P N i¼1 skill ¼ 1 ðd i L½m i ŠÞ 2 P N i¼1 ðd i c i Þ 2, (2) where d i are the available measurements, and L½m i Š is a row vector of the model results in which m i is transformed by the linear operator L to match the measurements (see Bennett, 22), and c i is a vector of climatological, or background values. The final term in the definition of skill can be interpreted the model error variance normalized by the data 3 variance, where the data variance is relative to the climatology. Thus, a perfect model (d i ¼ L½m i Š) has a skill of one, as long as the data contain significant departures from the climatology (i.e. the denominator is non-zero). If the model simply returns the initial best guess of climatology (m i ¼ c i ), the skill is zero. Note that an energetic model that disagrees with the data may have negative skill. Also, because the time series are not detrended, differences in the mean values will contribute to the error variance, and reduce the skill. The definition of skill has not been standardized, differing primarily in the denominator of the final term. This term represents a proxy for the true variance of the observed field. Ideally, this number would be specified before the skill calculation, and in some cases where long time series are available, a good a priori estimate may be found using measurements outside of the time frame of the numerical simulation. However, given our relatively short, solitary time series, care must be taken in estimating the data variance. We choose to estimate the variance by referencing the data to the climatology, as opposed to a data mean. By referencing the time series to climatology, we avoid the possibility that the mean is biased by the strong events that are apparent in the measurement time series. That is, we assume that the climatology is a better estimate of the true mean state of the system than a simple mean of the relatively short time series. 3. Results A variety of model/data comparisons were performed. Comparisons between modeled and measured properties in the EMCC and WMCC range from qualitative (sea-surface temperature and salinity cross-sections) to quantitative (estimates of model skill), and are described below, with each region examined separately. Although the focus of this paper is quantitative skill assessment, a qualitative understanding of the flow field is important in identifying potential weak elements of the prediction Eastern Maine coastal current (EMCC) The development of the EMCC in 1994 was studied by Hetland (1997), who noted that there was a transition in the along-shore current strength associated with a homogenization of the water

7 2436 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) column on around May 6. The mean along-shore currents nearly double after this date, increasing from.12 to :22 m s 1. This transition will be a focal point of the analysis below. Both the character of the flow before and after the event, and the timing of the transition are important in correctly predicting the along-shore fresh-water transport Sea-surface temperature Two relatively cloud-free AVHRR images of seasurface temperature were available on May 3 and 11 (Fig. 4), straddling the transition date May 6. On May 3, a plume of cold water is seen to be traveling down the coast from Grand Manan island; the core of the current is just about to impact a mooring located within the coastal current. On May 11, the cold jet has already hit the CCM, and a cold filament has squirted offshore. The influence of this filament is seen in surface currents measured at a mooring located on the northern rim of the Jordan Basin, as well as in satellite-tracked drifter paths. This filament is discussed in more detail by Pettigrew et al. (1998). Comparisons with AVHRR imagery (Fig. 4) show that, although the details are different, the model produces a cold coastal jet with surface filaments flowing offshore from the EMCC that is qualitatively similar to what is seen in the satellite imagery. These jets may be important mechanism for transporting fresh water from the EMCC offshore, so it is important that numerical simulations reproduce these features at least statistically correct. Because of the non-linear nature of the flow, we do not expect to reproduce these features exactly Salinity cross section The EMCC is well mixed within 5 m depth, and the influence of tidal mixing extends to approximately 1 m depth. Observed and modeled salinity cross-sections are shown in Fig. 5. The comparison shows that the measured extent of tidal mixing front occurs at about the same place in the model, approximately 1 m depth. However, absolute values of salinity are off by a constant value; the model is approximately :2 psu saltier than observations. This is due to an initial condition that is not representative of the true initial state. Climatological values of salinity may not be representative of a particular year. Because of the timescales of salinity changes in the deep basins within the Gulf are seasonal, or longer, errors in the initial condition will persist throughout a simulation covering only one or two seasons. Mountain (23) shows that the average salinity over the Mid-Atlantic Bight can change by over 1 psu, and similar changes might be expected in the Gulf of Maine Moored salinity and current time series Point-to-point comparisons of moored salinity and current time series at the CCM are calculated by finding the nearest grid cell to the measurement location. The model results are not averaged over neighboring points because the EMCC jet is fairly narrow at the mooring location. Using a spatial covariance structure as a weighted spatial average may bias the measurements toward waters that are not within the EMCC jet. Comparisons of salinity time series at the CCM are shown in Fig. 6. The comparison indicates that the model is much more stratified than observations. Also, while in mid-may, in the observed salinity time series the water column stratifies and then mixes (partially) again, the model predicts that the water column remains stratified until mid-june (bottom panel in Fig. 6). Much of the variability in stratification in the observations most likely has to do with the position of the EMCC front. The water column will stratify as the front moves onshore, and destratify as the front moves offshore. There is some evidence in the model that on- and offshore motions of the EMCC front are responsible for changes in stratification at the mooring location. Further inshore, at the 5 m isobath, the model does stratify temporarily, then destratifies in a manner similar to the observations (not shown). Here, the peak surface-to-bottom stratification is similar in magnitude to the observed surface-tobottom (5 8 m) stratification at the CCM (about 1:1 psu), but the modeled peak in stratification at the 5 m depth is delayed by 5 days because the flow inshore of the EMCC jet is weaker. Comparisons of velocity time series (Fig. 7) show that model results generally are within the envelope of variability for observations. Measured mean surface currents in the EMCC were :16 :8; modeled currents over the same time frame are :18 :4. The modeled currents have consistently much less variance than observed currents; both along- and cross-shore; observed currents have two to three times more variance as modeled currents throughout the water column (not shown). This is a typical problem with coastal ocean models that do not reproduce the smaller scale turbulent flow field often observed in satellite images. As resolution

8 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Fig. 4. Modeled surface temperature (upper panels) and AVHRR satellite-derived sea surface temperature images (lower panels) from May 3 and May 11, 1994 show a cold jet protruding from the EMCC. The jet has not yet developed in the satellite image on May 3. The jet is most pronounced in both the model and observations on May 11, and is circled in both images. The colormap is arbitrary, chosen to highlight the features of the flow, with darker colors representing colder water. The AVHRR images also show near-surface moored current measurements (the straight lines attached to crosshaired circles), and drifter tracks (the curvy lines). The flow at the inshore mooring on May 3 is.9, :23 m s 1 on May 11. The solid lines in the drifter tracks show two days prior and after the time of the image, with a circle marking the time of the image; dashed lines continue the tracks to 1 days after the image date. The offshore mooring was cut between the SST image dates, and the dashed line represents the average flow between May 6 and 7, the last two days of the current record. increases, these features become part of the simulated solution, and the simulated variance becomes closer to the observed variance (e.g., Marchesiello et al., 23). In early May, the modeled currents are relatively steady, and follow the peak measured velocities, indicating that perhaps the EMCC jet is more stationary in the model. Some of the measured

9 2438 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Data 1 15 Depth (m) Depth (m) Model Data 2 Data FWF ( 1 3 m 3 s 1 ) at the CCM Latitude Model Depth (m) x FWF (m 3 s 1 ) Fig. 5. A comparison of measured and modeled salinity structure across the EMCC. The bold isohalines represent the reference salinity used for calculations of FWF from measurements and the model. The position of the stations, and the line of the cross-section in the model, is shown in Fig. 2. The data cross-section shows the locations of the hydrographic casts (vertical lines). The model cross-section shows the cross-shore structure of the mean FWF as determined by the model (shading); the vertical line shows the location of the FWF profile. The panel to the left shows a comparison of the vertical structure of the predicted and measured FWF at the CCM. Note that the measured profile is extrapolated from salinity time series at 5, 4, and 8 m depth by assuming constant vertical shear and salinity stratification. variability may have to do with meandering of jet associated with the EMCC tidal mixed front; however, there is only slight evidence for this in the T-S time series (not shown). Another explanation is that the flow within the EMCC pulses in response to upstream variability; for example, windforced continental shelf waves propagating into the region from the Scotian Shelf Fresh-water flux time series In the model, a time series of FWF was calculated through a plane near the hydrographic cross-section (Fig. 5, located at the bold line in Fig. 2) using a reference salinity of 32:6 psu. The reference salinity was chosen as the isohaline intersecting the 1 m isobath (i.e., the saltiest water at the CCM location, Fig. 2). The same criterion was also used to set the reference salinity in the observational estimates of EMCC FWF, described below, although the actual values are different because of differences in the climatology used to initialize the model and the actual distribution of salinity in This choice of reference salinity gave values of FWF similar in magnitude to the inputs of fresh water from the St. John River in all cases. The calculation was set up such that salinity values higher than the reference value do not contribute to the FWF. The mean cross-sectional structure of the EMCC FWF is shown in Fig. 5, along a hydrographic section crossing the CCM position. The model predicts that most of the FWF occurs in the upper 2 m, and is horizontally centered about the CCM. A comparison of the vertical profile of FWF at the CCM location, however, indicates that the model

10 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Fig. 6. The upper panel shows a time series of salinity measured at three depths and is compared to model predictions. The lower panel shows the measured and modeled surface-to-bottom salinity difference. Climatological values are also shown in both panels for reference. over-predicts the local FWF by about a factor of 2 (Fig. 5, left panel). Given that the measurements show a less-stratified water column at this location as compared to that predicted by the model, and that the model has stronger crossshore salinity gradients, it seems that the modeled EMCC is narrower than observed. However, in the discussion section, it is explained how changes in width of the EMCC will not significantly alter the FWF. As a test of the systematic errors in assuming a self-similar structure to arrive at the observed estimates of FWF, the self-similarity of the modeled FWF is examined. We hypothesize that the modeled FWF has a self-similar structure, in that measurements at a single profile of velocity and salinity are representative of the entire FWF carried by the EMCC. That is, an estimate of FWF from a vertical profile (say, from a mooring) can be used to estimate the entire cross-sectional FWF by multiplying the profile derived estimate by a constant. FWF calculated across the entire cross-section is compared to the FWF calculated at the CCM multiplied by a constant value, 16; 55 m 2, calculated such that the two FWF time series would have the same mean. A comparison of the point and entire cross-sectional estimates of FWF is shown in Fig. 8. The ratio of FWF calculated from the profile vs. the entire cross-section has a standard deviation of 18% of the mean.

11 244 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) EMCC mooring along-shore currents Speed (m s -1 ) /1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Speed (m s -1 ) EMCC mooring cross-shore currents Climatology Data Model -.2 4/1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Fig. 7. Observed and modeled along-shore (upper panel) and cross-shore (lower panel) currents at the EMCC mooring are compared. Positive currents are upstream (against the Kelvin wave propagation direction) and offshore. Fresh water flux FWF mooring / FWF xsec1.5 Cross-section estimate Point estimate 4/1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Fig. 8. Comparison of EMCC FWF calculated from a profile vs. an entire cross-section. The upper panel shows the filtered (one week) FWF for a single profile and the entire cross-section of the FWF. The profile estimate of FWF was normalized by an area, such that the mean of both FWF estimates is identical. The bottom panel gives the ratio between these two estimates. A value of one would mean the two FWF estimates are identical. Higher values indicate that the point estimate is greater, lower values mean that the cross-sectional estimate is greater.

12 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Observed FWF carried by the EMCC was estimated from observations by multiplying the vertically integrated profile of FWF at the CCM by the constant representing the cross-sectional area of the FWF calculated above. The results are compared with numerical estimates of the FWF in Fig. 9. The reference salinity for the observational estimate is 32.4 (see Fig. 5). FWF was also estimated from a number of other cross-sections taken during the hydrographic cruise using geostrophic currents with v ¼ set at the sea floor, and again using a reference salinity of The hydrographic estimates of FWF agree with both the FWF estimated from the moored measurements and calculated from the model. The model correctly simulates the magnitude and timing of the boxcar-like response present in the observational FWF estimates; the model reproduces the sudden increase in FWF observed on May 6, as well as the sudden decrease on May 27. More specifically, the model has a skill of.94 at reproducing the observed FWF estimate for timescales of 7 days and longer; model skill is discussed in more detail in the discussion section Western Maine Coastal Current (WMCC) Geyer et al. (24) discuss observations of the WMCC taken during the spring and early summer of 1993 and They hypothesize that the alongshore FWF may be extrapolated from surface measurements at a single mooring, with deeper measurements upstream to estimate background flow and salinity. Below, this hypothesis is examined within the context of the model Salinity cross-sections and near-surface salinity Salinity cross-sections and near-surface salinity measured during a number of hydrographic cruises are compared with model results. Salinity crosssections show that, although there is reasonable agreement below about 5 m depth, the model predicts fresher and more stratified near-surface waters than suggested by the observations. In part, this may be due to the fact that the upper few meters of the water column is not always accurately measured using standard CTD techniques. Also, there is considerable stratification between the upper two cells in the model; the uppermost cell may be up to 2 psu fresher than the underlying cell. Maps of surface salinity (Fig. 1) show that the model predicts a pool of fresh water offshore from the Kennebec River estuary that is not present in observations. This pool comes from river discharge blown offshore in the early part of the model simulation in April. The model does not sufficiently mix this fresh water, resulting in a persistent, St. Johns river discharge Climatological FWF estimate Coastal Current Mooring FWF estimate ROMS FWF estimate Hydro cruise FWF estimate Fresh water transport (m 3 s -1 ) /1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Fig. 9. Simulated and observed FWF, and ancillary quantities are shown for the EMCC. Methods of calculation are explained in the text.

13 2442 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Fig. 1. The upper panels show observed and modeled cross-sections of salinity along the Cape Porpoise line on May 3 and May 1, the average date of each cross-section. Lower panels show comparisons of modeled and observed near-surface salinity (at 3 m depth) on May 3 and May 11, 1994, the average date of each survey. Observations are indicated by filled circles using the same color scale used to plot the simulated fields. surface-trapped pool of fresh water that is still present when downwelling first occurs in early May (see Fig. 3). This persistent stratification is a well-known problem in the Mellor- Yamada turbulence closure. In general, mixing in river plumes, which are highly stratified and usually only a few meters thick, is poorly understood.

14 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Moored salinity and current time series Salinity time-series measurements (Fig. 11, lower panels) show good agreement between observations and model predictions after the plume has had time to develop. Although the waters near the Kennebec outflow are freshened by the mean presence of the plume in the climatology, a well-defined plume is not present in the initial condition (climatology), but forms after the model has been started. The simulated plume grows to contact the CPM location in early May. The large increase in FWF occurs about a week after the Kennebec river inflow reaches the CPM. The model remains slightly saltier than the observations, about :5 psu, which is not surprising given that the background water in the model is about 1: psu saltier than that measured. Again, this is due to slightly saltier conditions in the climatology than were present in Current time-series observations (Fig. 12) reveal that the model is generally within the envelope of variability seen in the observations. Downcoast flow (in the Kelvin wave propagation direction) appears to be related with onshore flow, as expected for a wind-influenced buoyant plume, but this trend is not statistically significant Fresh-water flux time series Plume cross-sectional area was estimated in the model by comparing the FWF at a single point to that calculated over an entire cross-section (Fig. 13). Fresh water transport (1 3 m 3 s -1 ) All upstream rivers Climatology Data - Mooring Data - Hydrography Model Plume salinity (S p ) Climatology Data - Mooring ROMS Ref. salinity (S ) Climatology Data - Mooring ROMS 4/1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 7/1/94 7/15/94 Fig. 11. The upper panel shows FWF estimated from salinity and current observations, and from the model in the WMCC. The center panel shows the measured and modeled plume salinity (CPM, at 5 m depth), and the bottom panel shows the measured and modeled reference salinity (KRM, at 5 m depth).

15 2444 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) Geyer et al. (24) used a nearly identical method to extrapolate point measurements of FWF to a crosssectional estimate of FWF. The cross-sectional area of the plume stays nearly constant, and the pointestimate and cross-sectional estimate of FWF agree to within a factor of 2 when the FWF is high (over.4 WMCC mooring along-shore currents Speed (m s -1 ) /1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Speed (m s -1 ) WMCC mooring cross-shore currents Climatology Data Model -.4 4/1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 Fig. 12. Observed and modeled along-shore (upper panel) and cross-shore (lower panel) currents at the Cape Porpoise mooring are compared. Positive currents are upstream (against the Kelvin wave propagation direction) and offshore. Fresh water flux FWF point / FWF line Cross-section estimate Point estimate 3/15/94 4/1/94 4/15/94 5/1/94 5/15/94 6/1/94 6/15/94 7/1/94 Fig. 13. Comparison of WMCC FWF calculated from a profile vs. an entire cross-section. The upper panel shows the filtered (one week) FWF for each case; the bottom panel gives the ratio between these two estimates. The ratio is only shown for values of FWF over 1 m 3 s 1. The presentation is identical to that shown in Fig. 8.

16 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) m 3 s 1 ). The total WMCC FWF (Fig. 11, top panel) was estimated from observations by extrapolating the point FWF measurement, assuming the same constant cross-sectional area as calculated within the internal model point/cross-section comparison. 4. Discussion 4.1. Model skill Estimates of model skill for various point-topoint surface property comparisons and estimated FWF are presented in Table 1. Surprisingly, the FWF calculated within the EMCC, a bulk property of the flow field, is relatively skillful despite negative skill in nearly all of the point-to-point comparisons. Skill at estimating the FWF in the WMCC is also relatively high, at least for time periods of more than one week, but here the highest skill is the comparison between modeled and observed seasurface salinity. One explanation for the high skill in predicting FWF is that it depends on the product, or covariance, of along-shore velocity and salinity. For example, imagine that the velocity and salinity are both oscillatory functions. Simulated time series of both these properties could be individually out of phase with observations, while the product of the two time series is in phase. This results in lower skill for the individual time series, and higher skill for the product. This difference in skill might be expected if small-scale eddies are a significant fraction of the FWF. It is not yet clear that high skill in reproducing FWF will result in better simulations of A. fundyense or other plankton in the Maine coastal current. Based on the calculations of model skill, we Table 1 Model skill is calculated for surface values of along-shore currents and salinity EMCC WMCC 33 h 7 day 33 h 7 day Along-shore surface currents Cross-shore surface currents Surface salinity Fresh-water flux Time series were filtered with either a tidal filter (33-h cutoff), or a seven-day boxcar filter to remove weather-band variability. expect that broad features of A. fundyense blooms could be simulated with high skill, but the details of the population distribution with less skill. This may translate into the ability to predict the presence of A. fundyense regionally, but not the ability to predict the exact location of affected regions along the coast Conceptual models of self-similar fresh water flux In the model, it is comparatively straightforward to extract the time series of some large-scale process. In contrast, a point measurement requires a conceptual model of the process to extrapolate information at to an entire cross-section. The conceptual model is essentially a covariance structure based on simple physical processes. Unfortunately, skill measured using a conceptual model to extrapolate measurements to a larger scale now depends not just on the model s ability to represent the flow field, but also on the ability of the conceptual model to extrapolate the measurements. When using this method of model assessment, the numerical model and conceptual model of the circulation field are tightly linked. Predictions of FWF may be expected to have a high skill because fresh water is conserved in the model calculation. However, there are many potential sources for errors that could degrade the FWF prediction. The primary error in FWF calculations is the reference salinity, as the fresh-water fraction is defined relative to this quantity. There may also be errors in the predicted FWF because of model errors. In the case of the EMCC, the model may over- or under-predict the cross-frontal FWF. In the case of the WMCC, too much mixing in the model may destroy the coherency of the plume, so that the fresh water of the plume becomes entrained into the background flow. The fact that the model maintains skill at predicting FWF despite these compounding potential errors means that the simulated dominant dynamical balances integrated over each of the coastal current legs must be mostly correct. More fundamentally, the underlying dynamics that cause the two coastal current systems to be selfsimilar must be understood in order to quantify the errors in the assumption, as well as to predict if and when the assumption will break down. The causes of self-similar FWF, distinct in each leg of the coastal-current system, are discussed below.

17 2446 ARTICLE IN PRESS R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) EMCC The EMCC is a bottom-trapped flow, controlled in part by topography and tidal mixing. As noted by Yankovsky and Chapman (1997), the transport carried by a bottom-trapped front, at its equilibrium position across the shelf, is dependent only on the height of the front and the density difference across the front. The transport is carried within the frontal region, rather than across the entire shelf, similar to the FWF shown in Fig. 5. This simple model may be modified to examine the fresh-water transport carried by the EMCC. Suppose the EMCC may be characterized as a discrete front of height H and width W with a density difference, Dr, and an associated salinity difference, DS, across the front (see Fig. 14). Assume the cross-shore density gradients are constant, so that the vertical shear will also be constant. Similar to Yankovsky and Chapman, it will be assumed that the front is positioned such that the flow near the bottom is essentially zero. The fresh water carried by this front will be Z Z W FWF EMCC u s s dx dz s H ¼ g H 2 4f Ds s ¼ gbh2 4f r Ds 2 s, ð3þ where g gdr=r is the reduced gravity. There is a quadratic relationship between FWF and the salinity difference cross the front if a linear relationship between salinity and density is assumed (Dr ¼ bds). Note that the total FWF does not depend on the width of the front. The FWF is modulated by the cross-shore position (in particular, the local depth H) and the near-shore salinity (assuming the offshore salinity remains relatively constant). However, the local FWF measured at a point will depend on the width of the front; halving the frontal width will double the local FWF. Thus, the measured FWF at any point within the EMCC front will be proportional to the total, integrated EMCC FWF as long as the front maintains its geometry and position over the shelf. Extrapolating point measurements of FWF to estimates of total along-shore FWF is equivalent to assuming that the front maintains a constant width throughout the analysis period. Chapman (2) extends the basic theory proposed by Yankovsky and Chapman (1997) to include ambient vertical stratification. Ambient vertical stratification acts to reduce the trapping isobath, but the solution is qualitatively similar. Chapman s results suggest that the reference density to use is that near the base of the front, in a similar position to the reference salinity used in this paper to estimate the FWF. The fact that the observed frontal width is wider than the modeled frontal width will not affect the W (ρ ο ρ) v(z) (S o - S) H (ρ o ) (S o ) Fig. 14. A diagram of the EMCC front based on the conceptual model of a bottom-trapped front described by Yankovsky and Chapman (1997). Note that the isopycnals do not extend from the bottom to the surface, but rather veer into the stratified offshore waters. The Yankovsky and Chapman model will still be valid with arbitrary vertical stratification superimposed on the horizontal stratification responsible for the bottom-trapped jet (Chapman, 2). The assumption of self-similar FWF requires that the vertical structure remains constant (or constantly proportional) across the width of the jet. Compare with Fig. 5.

18 R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (25) extrapolated estimated of FWF as long as both the observed and modeled frontal width remains constant. The good agreement between the modeled total FWF and the FWF extrapolated from moored measurements suggests that both the real and simulated EMCC width are indeed approximately constant, unless there are compensating errors in temporal variations of the FWF and frontal width. Moreover, because the FWF relies on the product of the velocity and salinity anomaly, the observed and modeled FWF may be the same even if the salinity and velocity time series differ. An analogy to this would be getting the turbulent flux of a property correct without correctly reproducing the eddy field. To correctly simulate the effect of the eddy field, the statistics of turbulent field must be reproduced or the turbulent flux may be parameterized. In the case of FWF, the details of the frontal position and small-scale energetic features may incorrect. However, we reproduce these features statistically in a way that, on average, they create a FWF similar to the observed FWF. This may explain why the model had relatively high skill in predicting FWF despite the lower skill in predicting either salinity or along-shore velocity WMCC The WMCC is a surface-trapped plume that is strongly influenced by the local along-shore wind stress. The plume may be stretched offshore, to the point where it may loose contact with the coast, during upwelling winds; during downwelling, the plume is pressed up against the coast (see Fig. 15). The along-shore fresh water transport is similarly influenced by the local along-shore wind stress: downcoast transport of fresh water is generally enhanced during downwelling and suppressed during upwelling. The correlation between along-shore winds and FWF is given by the regression FWF ¼ 3: :8 1 4 t (r 2 ¼ :44), where positive t is an upwelling wind stress. The regression implies that in the absence of wind, the FWF is still around 35 m 3 s 1, and an upwelling wind stress of :5 1 4 m 2 s 2 will block downcoast transport of fresh water. For energetic flows within the plume, with a mean speed of :3 m s 1 or more and salinities between 24 and 28 psu, the flow was moderately slab-like: the standard deviation about the mean flow speed in the plume was 3 4%. For less energetic flows, the standard deviation was 4 6% of the mean flow speed, owing to stronger advection of momentum and tracers in the plume that break the Ekman balance between wind stress and surface layer flow. The stronger flow events are associated to strong wind events, indicating that the wind-driven plume is generally slab-like. The largest potential for error in the self-similar assumption will be when there are no measurements within the plume. Because the plume changes W downwelled W upwelled (ρ ο ρ) (S o - S) V upwelled H upwelled V downwelled (ρ ο ) (S o ) H downwelled Fig. 15. A diagram of the WMCC front shows how the plume is moved on- and off-shore by downwelling and upwelling winds. The assumption of self-similar FWF requires that the velocity within the plume is constant throughout the cross-sectional area, which remains constant (i.e., H downwelled W downwelled ¼ H upwelled W upwelled ). Compare with Fig. 1.