Linking Hydrodynamic Complexity to Delta Smelt (Hypomesus transpacificus) Distribution in the San Francisco Estuary, USA

Long-term fish sampling data from the San Francisco Estuary were combined with detailed threedimensional hydrodynamic modeling to investigate the relationship between historical fish catch and hydrodynamic complexity. Delta Smelt catch data at 45 stations from the Fall Midwater Trawl (FMWT) survey in the vicinity of Suisun Bay were used to develop a quantitative catch-based station index. This index was used to rank stations based on historical Delta Smelt catch. The correlations between historical Delta Smelt catch and 35 quantitative metrics of environmental complexity were evaluated at each station. Eight metrics of environmental conditions were derived from FMWT data and 27 metrics were derived from model predictions at each FMWT station. To relate the station index to conceptual models of Delta Smelt habitat, the metrics were used to predict the station ranking based on the quantified environmental conditions. Salinity, current speed, and turbidity metrics were used to predict the relative ranking of each station for Delta Smelt catch. Including a measure of the current speed at each station improved predictions of the historical ranking for Delta Smelt catch relative to similar predictions made using only salinity and turbidity. Current speed was also found to be a better predictor of historical Delta Smelt catch than water depth. The quantitative approach developed using the FMWT data was validated using the Delta Smelt catch data from the San Francisco Bay Study. Complexity metrics in Suisun Bay were evaluated during 2010 and 2011. This analysis indicated that a key to historical Delta Smelt catch is the overlap of low salinity, low maximum velocity, and low Secchi depth regions. This overlap occurred in Suisun Bay during 2011, and may have contributed to higher Delta Smelt abundance in 2011 than in 2010 when the favorable ranges of the metrics did not overlap in Suisun Bay.


INTRODUCTION
proposed a conceptual model of estuarine habitats as a dynamic aquatic regime overlaying a stationary bathymetric framework that captures much of the physical and habitat complexity of estuaries. River flows and tidal forcing shift the dynamic environment across the stationary base to produce varying environmental conditions for biological organisms. For each species, the overlap of the dynamic and stationary environments affects feeding, predation, survival, growth, and density. For each life stage of each species, there will be different optimal overlaps of stationary and dynamic conditions. In estuaries, salinity is generally the dynamic element that most strongly drives species distribution and composition along with biomass, density, and species richness (e.g., Elliot and Dewailly 1995;Thiel et al. 1995;Marshall and Elliot 1998). The role of temperature, dissolved oxygen, turbidity, and hydrodynamics in structuring fish communities in estuaries varies more from estuary to estuary than the role of salinity (e.g., Elliott and Dewailly 1995;Marshall and Elliott 1998; Barletta et al. 2005). The stationary bathymetric aspects of an estuary can provide both shallow habitats of low velocity and high productivity (e.g., Neves et al. 2013) and deep channels where visual predators are at a disadvantage (e.g., Brabrand and Faafeng 1993). Moyle et al. (2010) note that "a vast ecological literature documents the significant roles of habitat complexity and variability in promoting abundance, diversity, and persistence in a wide array of ecosystems." For pelagic organisms such as the Delta Smelt (Hypomesus transpacificus) of the San Francisco Estuary (estuary), habitat complexity is largely synonymous with hydrodynamic complexity. The food, competitors, and predators of pelagic organisms occur in association with complex hydrodynamic features that vary at all spatial and temporal scales (e.g., at very large scale see Trenkel et al. 2014; at intermediate scales Govoni and Grimes 1992;Bakun 2006;Kai and Marsac 2010;Hood et al 1999; and at smaller scales Thiel et al. 1995;Menendez et al. 2012). Even in laboratory studies, hydrodynamic complexity affects the feeding efficiency of small fish on copepods (Lee et al. 2010).
The principal scientists of the Interagency Ecological Program (a consortium of the nine state and federal agencies doing science in the estuary) identified a primary need to "develop a method of measuring 'hydrodynamic complexity'" (Brown et al. 2014). However, there is currently no established method to quantify hydrodynamic complexity, defined by Brown et al. (2014) as habitat heterogeneity that provides a large array of habitat types for Delta Smelt to use for resting, feeding, and other activities. Brown et al. (2014) note that there remains much uncertainty about the interaction of hydrodynamics with stationary habitat components in Suisun Bay and their combined effects on other dynamic habitat components including turbidity, contaminants, and biota.
The estuary encompasses San Francisco Bay (Central Bay and South Bay), San Pablo Bay, Suisun Bay, and the Sacramento-San Joaquin Delta (Figure 1, inset). The largest sources of freshwater to the estuary are the Sacramento River and the San Joaquin River. The mixing of this freshwater with the saline water from the Pacific Ocean results in an estuary-wide salinity gradient, with salinity varying from more than 30 psu near the Golden Gate to less than 0.1 psu in the Sacramento River. The salinity gradient varies strongly on tidal, seasonal, and annual time scales. The estuary is bathymetrically and hydrodynamically complex; broad shoals are bisected by a network of deeper channels. We focused on the easternmost embayment, Suisun Bay, comprising two relatively flat and shallow sub-embayments: Grizzly Bay and Honker Bay (Figure 1). During fall, the Low Salinity Zone (LSZ), the portion of the estuary with salinity between 0.5 and 6 psu, is often in the vicinity of Suisun Bay (MacWilliams et al. 2015). Although there is a net westward water flow through Suisun Bay resulting from the freshwater outflow from the Delta, the currents within Suisun Bay are primarily driven by the interaction of the semidiurnal tides with a complicated bathymetry (Cheng and Gartner 1984).
Delta Smelt are endemic to the estuary and have declined in abundance, resulting in their listing as a threatened species in 1993 under both the California Endangered Species Act and the federal Endangered Species Act. Efforts to protect Delta Smelt have been contentious and primarily focused on water management and anthropogenic effects on water 3 MARCH 2016 http://dx.doi.org/10.15447/sfews.2016v14iss1art3 quality. Considerable planning has been done to reduce the effect of current water management and to restore the habitats relied upon by Delta Smelt and other species of concern (BDCP 2014; Resources Agency 2012). However, further defining the physical parameters of Delta Smelt habitat is essential for the success of future management actions and habitat restoration efforts (Baxter et al. 2015). To date, descriptions of the physical habitat used by Delta Smelt have relied on concurrent (or nearly so) measures of the salinity, temperature, and turbidity where they have been captured (Moyle et al. 1992;Aasen 1999;Nobriga et al. 2005;Brown and May 2006;Feyrer et al. 2007). Numerical modeling tools now allow estimation of the detailed hydrodynamic conditions throughout the estuary, and analysis of fish catch data with variables that cannot be easily measured in a field setting.
Delta Smelt are caught most often in shallow open water with low salinity, high turbidity, and moderate temperatures (Moyle et al. 1992;Sommer and Mejia 2013). Suisun Bay has historically been a good location for catching Delta Smelt because it has low salinity, high turbidity, and broad shallow areas (Moyle et al. 1992;Merz et al. 2011 found that salinity and turbidity explained about one quarter of the variance in the distribution of Delta Smelt extending from San Francisco Bay through the Delta. Fish catch data shows more frequent Delta Smelt catches in shallow water (Moyle et al. 1992), but it is unknown if Delta Smelt are simply seeking out shallow water or if other environmental conditions lead to more frequent catches in the shallower areas of Suisun Bay.
Recent studies have combined three-dimensional (3-D) numerical modeling and observational data to improve understanding of variation in fish catch in long-term surveys of fish abundances in the estuary (e.g., Kimmerer et al. 2009Kimmerer et al. , 2013. However, these studies have generally evaluated associations using the annual abundance index for the whole estuary as the response variable. This study took a more granular approach, and analyzed the specific environmental conditions at each individual station in the vicinity of Suisun Bay that have historically resulted in Delta Smelt catch. Using a quantitative approach, we evaluated how the interaction of salinity, turbidity, and hydrodynamics affected the likelihood of catching Delta Smelt at a given site. We focused on the physical characteristics of places where Delta Smelt have been caught in accord with the Peterson (2003) conceptual model. This approach avoids the complexities of incorporating predator-prey dynamics (e.g., Walters and Juanes 1993;Essington and Hansson 2004) into habitat descriptions. Our goal was to determine the extent to which the historical fish catch data are correlated with specific quantified environmental conditions, and whether these correlations can be used to improve the monitoring and prediction of fish abundance. This study investigated the spatial distribution of both observed and model-predicted variables that may explain why some stations have historically had both more frequent and higher fall Delta Smelt catches than other stations. This approach builds on earlier work and established hypotheses by investigating the following questions:

Fall Midwater Trawl Survey
The California Department of Fish and Wildlife's (CDFW) Fall Midwater Trawl (FMWT) began in 1967 and has sampled every year except 1974 and 1979 (Stevens and Miller 1983;Feyrer et al. 2007;CDFW 2014 The FMWT was designed to index the year-to-year relative abundance of Striped Bass (Morone saxatilis, Stevens and Miller 1983). However, all captured species are identified and measured and the FMWT has become a long-term indicator of population trajectories for several small, pelagic fish, including Delta Smelt (Moyle et al. 1992;Sommer et al. 2007). Although Delta Smelt are caught westward of Suisun Bay in the spring and summer, the majority are caught east of Carquinez Strait (Bennett 2005). To span the extent of the LSZ during the fall period, we used all available survey data from 1967 to 2012 at the 45 FMWT stations in the vicinity of Suisun Bay ( Figure 1, Table 1).

San Francisco Bay Study
The San Francisco Bay Study (Bay Study) began monthly otter and midwater trawl sampling in January 1980 (Armor and Herrgesell 1985;Baxter et al. 1999). Bay Study sampling stations span the entire estuary. We used the 10 Bay Study stations in the vicinity of Suisun Bay for the years from 1980 to 2012 ( Figure 1). We restricted our analysis to the Bay Study midwater trawl surveys from the months of September through December for comparison with FMWT results. The Bay Study gear and procedures are essentially identical to those of the FMWT.

UnTRIM Bay-Delta Model
UnTRIM is a 3-D hydrodynamic numerical model that solves the Navier-Stokes equations on an unstructured horizontal grid and z-level vertical grid. The governing equations are discretized using a finite difference -finite volume algorithm. The governing equations, numerical discretization, and numerical properties of UnTRIM are described in Casulli (1999),  Casulli and Walters (2000), and Casulli andZanolli (2002, 2005).
The UnTRIM hydrodynamic model has been implemented in the San Francisco Bay and Sacramento-San Joaquin Delta to simulate tides, inflows and water diversions, water surface elevations, 3-D velocities, and salinity throughout the Bay-Delta system (MacWilliams et al. 2015). The UnTRIM Bay-Delta model spans the entire estuary, from the Pacific Ocean through the Sacramento River and San Joaquin River ( Figure 2). Model boundary conditions included tides at the Pacific Ocean, freshwater inflows to San Francisco Bay and the Sacramento-San Joaquin Delta, and water diversions at six locations in the Delta. Nine control structures were implemented in the model, and the Delta Island Consumptive Use (DICU) model (CDWR 1995) was used to represent agricultural diversions and return flows within the Delta (Figure 2). Spatially and temporally varying wind, evaporation, and precipitation were included based on weather stations around San Francisco Bay and the Sacramento-San Joaquin Delta. We used a two-equation turbulence closure model, choosing parameter values of the generic length-scale equation from Warner et al. (2005) to yield the k-ε closure (Umlauf and Burchard 2003).

Calculation of the Historical Delta Smelt Catch Station Index
We used the FMWT Delta Smelt catch data to rank stations based on their relative historical Delta Smelt catch. We developed a quantitative catch-based station index, SI C . This index takes into account that a single Delta Smelt catch in a tow is currently a success (presence vs. absence) and weights a catch of multiple fish higher than a catch of a single fish.
The SI C was based on the percent of FMWT tows during the 1967-2012 period in which a Delta Smelt was caught, and the total number of Delta Smelt the FMWT caught at each station ( Figure 4A). The percent of FMWT tows with a catch and the total number of Delta Smelt caught were then normalized to produce a value between 0 and 1, and a station index based on the historical Delta Smelt catch (SI C ) was calculated as The resulting value of SI C at each station was between 0 and 1, with higher values of SI C indicating that the station historically had more consistent and/ or higher Delta Smelt catches and lower values of SI C indicating less frequent and/or lower Delta Smelt catches. We then divided the 45 stations used in this analysis into four quartiles based on the value of SI C , with 12 stations included in the lowest quartile and 11 stations in each of the other three quartiles. We identified the quartile of stations with the highest SI C values as 'good' stations and the lower quartile were identified as 'poor.' We refer to the middle two quartiles collectively as 'medium' stations.

Complexity Metrics
We used 35 environmental variables as "complexity metrics" that quantified either the average or the variability of historical conditions at each station, with each representing a portion of the hydrodynamic complexity surrounding stations in Suisun Bay. We derived eight of these variables from the environmental data collected as part of the FMWT surveys. We calculated the remaining 27 variables from the UnTRIM Bay-Delta model predictions to characterize surface and bottom salinities, surface and bottom velocities, vertical and horizontal gradients in salinity and velocity, and local bathymetry for each FMWT station (Table 2). We chose the 35 complexity metrics a priori to the analysis based on published literature that described Delta Smelt distribution and related hypotheses of Delta Smelt in the fall (Moyle et al. 1992;Aasen 1999;Bennett 2005;Feyrer et al. 2007;Sommer and Meija 2013;Brown et al. 2014).
We calculated the complexity metrics derived from the FMWT observation data as the average value at a given station over the full record of historical data. The results from the UnTRIM Bay-Delta model were the model-derived complexity metrics from September through December of 2011, and included maximum or minimum values, mean values, Root-Mean-Square (RMS) values, and standard deviation. Complexity metrics derived from the model predictions included both vertical 1-D metrics based only on the model grid cell that included the established geographic FMWT station location, and 2-D metrics that were based on model predictions within a 550-m diameter circle centered at each station location. Based on the FMWT sampling protocol, 550 m roughly corresponds to the target distance travelled in each tow. Lastly, two modeled complexity metrics were based on the amount of time a variable was within a specific range. These two metrics were the percent of time the salinity at a specific location was within the LSZ-defined here as between 0.5 and 6.0 psu-and the percent of time the depth-averaged salinity at a specific location was less than 6 psu.

Prediction of the Station Index Using Complexity Metrics
We calculated the correlation between each of the complexity metrics and SI C , and identified the complexity metrics with the highest correlation (either positive or negative) to SI C (Table 2). A moving-average best-fit line with seven points was used to relate specific values of each complexity metric to individual predictions of the station index. This moving-average approach provided a best-fit line that both followed the data and could be easily used to predict a station index from the quantified complexity metrics. Seven averaging points resulted in lines that followed the data well but did not lead to an excessive number of line segments. The individual station index predictions from the selected metrics were then combined to predict SI C . We developed a simple equation from a combination of the station indices predicted from the individual salinity, velocity, and turbidity metrics to predict a station index: where SI H is the predicted station index at a given location based on the environmental conditions; C 1 , C 2 , and C 3 are coefficients with values between 0 and 1; S is a station index predicted using the bestfit line between a single salinity metric and SI C ; V is a station index predicted using the best-fit line between a single velocity metric and SI C ; and T is a turbidity metric. The equation was based on previous literature indicating that salinity and turbidity strongly influence the location of Delta Smelt Sommer and Mejia 2013), but also includes a term based on the hydrodynamics. We developed the form of the equation to allow for different weighting of each of the three complexity metrics. We constrained the values of C such that C 1 + C 2 = 1.0, and C 3 was between 0 to 1, to ensure that all values of SI H were between 0 and 1.
10 VOLUME 14, ISSUE 1, ARTICLE 3 Table 2 The complexity metrics calculated from the model predictions and the FMWT data and the correlation of the metric to the catchbased station index, SI C . 1-D or 2-D indicates whether the metric was calculated based on 1-D values at the station or 2-D values in space around the station, and r is the correlation coefficient between the metric and SI C . Unless otherwise noted, the metrics are mean values. We first predicted SI H using only a salinity metric to determine how much of the variability in the station index could be predicted using only salinity. This was accomplished by setting C 1 and C 3 to 1 and C 2 to 0 in Equation 2. We then combined the salinity and the turbidity metrics to predict SI H to determine if the addition of turbidity improved the accuracy of the predictions. This was accomplished by specifying C 1 = 1, C 2 = 0 and setting C 3 by minimizing the rootmean-squared difference (RMSD) between SI C and SI H . We combined the salinity, turbidity, and velocity metrics to predict SI H , with C 1 , C 2 , C 3 , and cutoff specified to minimize the RMSD between SI C and SI H .
Using Equation 2, we computed a value of SI H at every location within the model domain. We used a weighted average of the turbidity metric based on the distance of each horizontal model grid cell from the two closest FMWT stations to interpolate the value of the observed turbidity metric in each horizontal (2-D) model grid cell. We then used these values of SI H to produce a 2-D map of the spatial distribution of SI H , which allows the quantitative analysis developed at the FMWT stations to be applied spatially throughout the study region.

Influence of the Location of Individual Tows on SI H
We investigated differences between the value of SI H at the spatial mid-point of each individual tow during 2010 and 2011, and the value of SI H at the established geographic station location to assess whether the conditions at the exact location of individual tows may have influenced Delta Smelt catch on a tow-by-tow basis in 2010 and 2011. Differences between the conditions at the midpoint of individual tows and the conditions at the established geographic station location could cause tows to be in environmentally different areas than the established geographic station location. Such differences would increase variability in predictions of Delta Smelt catch relative to the variability based on the average conditions at the geographic station location, since the conditions sampled in each tow would vary depending on where the tow occurred relative to the established geographic station location.

Validation of Approach Using Bay Study Data
Using Equation 1, we calculated SI C from the Bay Study midwater trawl catch data for Delta Smelt at each of the 10 Bay Study stations. We also calculated SI H for each Bay Study station with Equation 2, using the same three metrics, coefficients, and turbidity cutoff as determined from the FMWT data set. We then compared the values of SI H and SI C based on the Bay Study data to determine if the coefficients fit using the FMWT data also applied to the Bay Study data.

Analysis of Interannual Variability
We examined interannual variability in the individual complexity metrics and in SI H relative to average historical conditions by comparing the values from fall 2010, when the outflow from the Delta was low, and fall 2011, when the outflow was higher and salinities were lower. We compared the different spatial distributions of SI H in Suisun Bay between these 2 years to provide insight into how different environmental conditions in Suisun Bay during 2 different years influenced the likelihood of Delta Smelt catch.

Calculation of the Historical Delta Smelt Catch Station Index
The relationship between the percent of historical tows in which a Delta Smelt was caught and the total number of Delta Smelt caught showed a consistent positive trend ( Figure 4A). The trend shown in Figure 4A was generally reproduced when we examined the FMWT data by decade from 1967 through 2012; however, the scatter about the trend increased when the analysis time period was shortened. We normalized the percent of FMWT tows with a catch and the total number of Delta Smelt caught at each station based on the values calculated for station 519 ( Figure 4A). FMWT Stations 703 and 606 were not included in the normalization to prevent skewing of the normalization based on the high number of Delta Smelt caught at these two stations ( Figure 4A). We gave FMWT Stations 703 and 606 a SI C value of 1.0 (the same value calculated for Station 519). The distribution of values of SI C between the four quartiles is shown in Figure 4B. The 12 VOLUME 14, ISSUE 1, ARTICLE 3 value of SI C showed a general west-to-east increase in the catch-based station index, yet also showed substantial small-scale spatial variability within the larger west-to-east trend ( Figure 4C). For example, neither the clusters of 'good' and 'medium' stations around the bathymetric gradients near the western side of Grizzly Bay (601 through 604) and Honker Bay (504, 505, 517, and 518), nor the distribution in SI C between the stations on the Sacramento River and the San Joaquin River (701, 703, 801, and 802) can be explained based on the west-to-east salinity gradient ( Figure 4C).

Complexity Metrics
The metrics based on salinity, both from the 2011 model predictions and the FMWT survey data, were consistently the most highly correlated with SI C ( Figure 5, Table 2), with the observed and predicted surface salinity metrics very similar ( Figure 5). Since the salinity metrics were highly correlated to each other, only the salinity metric with the highest correlation to SI C was selected for further analysis.
Of the salinity metrics, the highest correlation to SI C was for the percent of the time that the salinity at a station was less than 6 psu (r = 0.837). The highest correlation for a metric not based on salinity was for Secchi depth from the observed FMWT data (r = - 0.697). We also selected the water velocity metric with the highest correlation to SI C for further analysis. Of the 14 metrics based on water velocity, the metric that characterized the maximum depthaveraged current speed at each station was the most highly correlated with SI C (r = - 0.533). Seabed elevation, water depth, and distance to shoreline were all less correlated to SI C than the salinity, Secchi depth, and maximum depth-averaged current speed ( Table 2). The correlations with the catch-based station index, SI C , suggested that the 'poor' stations (colored red) were generally characterized by higher salinity, faster current speeds, and higher Secchi depth ( Figure 5). Conversely, 'good' stations (colored green) had lower salinity, slower current speed, and lower Secchi depth.

Prediction of the Station Index Using Complexity Metrics
The percent of time the depth-averaged salinity at a station was less than 6 psu, the maximum depthaveraged current speed at a station, and the Secchi depth at each station had the highest correlation with SI C , while still representing fundamentally different characteristics of each station, namely the salinity, hydrodynamics, and turbidity. We calculated the percent of time the depth-averaged salinity was less than 6 psu, and the maximum depthaveraged current speed metrics using the 2011 model predictions; we calculated the Secchi depth metric using the FMWT data. There was some correlation between the metrics themselves. The correlation coefficient between the percent of time the depthaveraged salinity at a station was less than 6 psu and the Secchi depth was - 0.44. The correlation coefficient between the percent of time the depthaveraged salinity at a station was less than 6 psu and the maximum depth-averaged current speed was - 0.34. The correlation coefficient between the Secchi depth and maximum depth-averaged current speed was 0.60.
In Equation 2, we used the percent of time the salinity at a station was less than 6 psu as the salinity variable (to predict S) and the maximum depth-averaged current speed at a station as the water velocity variable (to predict V). We used moving-average best-fit lines to relate the salinity ( Figure 6A) and velocity ( Figure 6B) metrics to SI C . We used the Secchi depth metric as the turbidity threshold variable (T) in Equation 2, and determined the Secchi depth threshold for negatively affecting the predictions of the SI C to be 0.5 m ( Figure 6C). When Secchi depth was included as a continuous variable in Equation 2 in the same manner as salinity and velocity, the range of values of SI H was not well predicted in either eastern Suisun Bay or the confluence region, whereas applying turbidity as a threshold variable in Equation 2 resulted in better predictions of SI H in these regions. We did not use direct turbidity measurements to predict SI C because of the very short history of measurement in the FMWT and because the correlation between turbidity and SI C was lower than the correlation between Secchi depth and SI C .
As expected, salinity was highly predictive of SI C , but including velocity and Secchi depth metrics further improved the predictions of SI C compared with using only salinity. Predicting SI H using only the salinity metric produced a slope to the best-fit line near one (0.98), indicating that the general west-to-east trend in the historical catch-based station index (SI C ) was captured using only salinity ( Figure 7A, Table 3). However, there was considerable scatter about the best-fit line. We then combined the salinity and the Secchi depth to predict SI H to determine how the addition of the Secchi depth modified the predictions ( Figure 7B). The addition of the Secchi depth threshold metric greatly improved the prediction of SI H at Stations 802 and 804 in the lower San Joaquin River, and also reduced the predicted SI H for the stations around Carquinez Strait, where SI C is generally less than about 0.1 ( Figure 7B). Finally, we used the salinity, Secchi depth, and velocity metrics to predict SI H ( Figure 7C, Table 3). The addition of the velocity metric further reduced the scatter about

Figure 6
Moving-average best-fit lines relating the complexity metrics to the catch-based station index, SI C , for (A) the predicted percent of time during the fall the depth-averaged salinity was less than 6 psu; (B) the predicted maximum depth-averaged current speed; and (C) the Secchi depth from the FMWT data. Each square represents the SI C and complexity metric for a single station. Stations are color coded based on Figure 4B. Shading in (C) highlights Secchi depths greater than the 0.5 m threshold.

Figure 7
The catch-based station index from the FMWT Delta Smelt catch data, SI C , and predicted using Equation 2 (SI H ) for each station in the vicinity of Suisun Bay: (A) is SI H based solely on the percent of time the depth-averaged salinity was less than 6 psu; (B) also includes the Secchi depth threshold at each station; and (C) is SI H based on the percent of time the depth-averaged salinity was less than 6 psu, the maximum depth-averaged current speed, and the Secchi depth threshold at each station. The black lines show a one-to-one line and the blue lines are the least-squares best-fit lines. Stations identified in the text are labeled. the best-fit line, and improved the prediction of SI H at many stations that are located in or near the main channels in Suisun Bay, for example stations 508, 509, 515, 517, 602, and 603 ( Figure 7C). The salinity metric was weighted about twice as strongly in Equation 2 as the velocity metric (C 1 = 0.67 and C 2 = 0.33).
Using Equation 2 and the coefficients developed above (Table 3), we predicted the value of SI H at every model grid cell in Suisun Bay. A 2-D map of SI H at each grid cell based solely on salinity (equivalent to Figure 7A) showed the west-to-east influence of decreasing salinity on SI H ( Figure 8A). A similar map of SI H at each grid cell based solely on the maximum depth-averaged current speed showed the negative influence of higher maximum depth-averaged current speed on SI H in the channels ( Figure 8B). Including both the salinity metric and the Secchi depth metric (equivalent to Figure 7B) reduced SI H in Carquinez Strait and in the San Joaquin portion of the confluence region of the Sacramento and San Joaquin rivers ( Figure 8C). Combining all three complexity metrics (equivalent to Figure 7C) produced a map of the spatial distribution of SI H with increasing index from west to east; lower SI H in the main channels and in the San Joaquin River from the influence of velocity and turbidity, respectively, and higher values of SI H in Grizzly Bay than were predicted solely using salinity ( Figure 8D).

Influence of the Location of Individual Tows on SI H
The approach used to correlate the catch-based station index (SI C ) to the hydrodynamic-based 16 VOLUME 14, ISSUE 1, ARTICLE 3 station index (SI H ) inherently assumed that the tows occurred exactly at the established geographic station location (Table 1). However, the information available on the exact start and end positions of the tows during 2010 and 2011 indicates that the tows did not always take place within the 550-m diameter circle assumed at each station (Figure 9). It is not known whether the FMWT tow locations in 2010 and 2011 are representative of the FMWT tow locations over the entire historical record between 1967 and 2012.
For the 45 stations used in this analysis, the difference between the value of SI H at the established geographic station location and at the midpoint of the eight tows during 2010 and 2011 was within the range of ± 0.2 SI H , with about 80% of the differences between - 0.05 and 0.05 SI H and about 95% of the differences between - 0.1 and 0.1 SI H . This suggests that, on average, it is not likely that the difference in locations meaningfully affected the prediction of SI H . However, at some FMWT stations the difference between the established geographic station location and the location of individual tows did noticeably influence the prediction of SI H in a meaningful way. For example, the prediction of SI H for Station 417 would be slightly lower if the location used to predict the station index was moved from the established geographic station location to the mid-point of the 2010 and 2011 tows (Figure 9, black), largely because 2010 and 2011 tows typically occurred closer to the main channel, where velocities tended to be higher than at the established geographic station location in a shallower location adjacent to the channel. A lower predicted value for SI H at Station 417 would result in a prediction closer to the value of SI C at this station ( Figure 7C). This suggests that some of the differences between SI C and SI H -and thus some of the scatter on Figure 7C

Validation of Approach Using Bay Study Data
When the value of SI C was calculated using the historical Bay Study catch data and Equation 1, the value of SI C at each Bay Study station in the vicinity of Suisun Bay ( Figure 4C, triangles) was similar to that predicted using the FMWT survey catch data at nearby FMWT stations ( Figure 4C, circles). This suggests that as long as the data set is of sufficient duration and scope, this method of determining SI C is robust.
We compared the SI C calculated from the Bay Study Delta Smelt catch data to the value of SI H calculated at each Bay Study station using the same three complexity metrics and the same three coefficients for Equation 2 as we used in the FMWT analysis. The value of SI H predicted at the 10 Bay Study stations was similar to the value of SI C derived from the Bay Study catch data ( Figure 10). The correlation between SI H and SI C using the Bay Study data (r = 0.94) was the same as the correlation between SI H and SI C using the FMWT data ( Figure 7C, r = 0.94) and the slope of the best-fit line was also nearly 1.0. The validation of SI H using an entirely different data set than was used to develop Equation 2 indicates that the method of predicting a station index from complexity metrics is likely broadly applicable throughout Suisun Bay.

Analysis of Interannual Variability
The model predictions and the FMWT data at each station showed that although salinity and turbidity metrics varied greatly from year to year, water velocity metrics were largely unchanged. The surface salinity in 2011 was lower than in 2010, and the percent of time the depth-averaged salinity was less than 6 psu was higher in 2011 (Figures 11A and 11B). In contrast to the salinity metrics, the metrics based on velocity were nearly identical for 2010 and 2011 ( Figures 11C through 11F).
Using 2-D maps to visualize the three complexity metrics included in Equation 2 highlights the different spatial patterns between 2010 and 2011. The percent of the time the salinity was less than 6 psu ( Figures 12A and 12B) and the average observed Secchi depth from the four FMWT surveys in each year ( Figures 12C and 12D) varied significantly between 2010 and 2011, although the maximum depth-averaged current speeds were nearly the same (Figures 12E and 12F). Figure 12 shows that the drier year (2010) had higher salinities and Secchi depths than the wetter year (2011). The interannual variability in salinity and Secchi depth resulted in markedly different spatial distributions of SI H in Suisun Bay between 2010 and 2011 ( Figure 13).

Prediction of the Station Index Using Complexity Metrics
The current literature on Delta Smelt in the San Francisco Estuary does not contain a quantified tabular metric for the ranking of sampling stations based on their historical catch of Delta Smelt. A simple metric was put forth based on both the number of fish caught and the percent of tows with a catch (presence vs. absence) that can be used to quantify the relative ranking of a station for Delta Smelt catch (Table 1). The same general ranking of stations developed using the entire FMWT catch data set could be reproduced even when the data set was evaluated by decade. This indicates that the relative station ranking is not highly sensitive to the decline in Delta Smelt abundance through time.
The consistency of the general ranking of stations based on SI C indicates that the stations that have 18 VOLUME 14, ISSUE 1, ARTICLE 3 historically been good for Delta Smelt catch have remained good throughout the period of declining Delta Smelt abundance.
To relate the quantified SI C values to current understandings of Delta Smelt based on environmental conditions, we predicted the ranking of stations (SI H ) using salinity, velocity, and turbidity metrics. We inferred the estuarine salinity gradient to be the cause of the general west-to-east increase in SI C ( Figure 4C) because the salinity metric was weighted twice as strongly as the velocity metric in the SI H predictions (Equation 2, Table 3). This is consistent with the consensus that Delta Smelt prefer regions of salinity less than 6 psu (Sommer and Mejia 2013). Our analysis indicated that in Carquinez Strait and the lower San Joaquin River the Secchi depth has historically been higher than the 0.5-m threshold used to calculate SI H , indicating lower turbidity and poorer conditions for Delta Smelt than would be predicted based only on salinity. This is consistent with other findings that show Delta Smelt broadly prefer higher turbidity Sommer and Mejia 2013) and that the lower San Joaquin River is generally less turbid and has a lower Delta Smelt catch than the Sacramento River during nearly co-occurring sampling (Bennett and Burau 2015).
Adding the velocity metric improved the prediction of SI H at many of the stations that were not wellpredicted based solely on the salinity and Secchi depth (Figure 7). This indicates that current speeds were also a useful metric for predicting the historical ranking of a station for Delta Smelt catch. The negative correlation between maximum depthaveraged current speed and SI C indicated that  Delta Smelt have historically been less likely to be caught in places that experience high current speeds. However, it is possible that the maximum depth-averaged current speed was not necessarily the mechanistic driver behind the spatial variation in SI C . Since high maximum depth-averaged current speeds typically occur in channels, selection against these areas may indicate fish movement between the channels and shoals (e.g., Aasen 1999;Bennett and Burau 2015), the vertical movement of Delta Smelt in the water column (e.g., Feyrer et al. 2013), or potential differences in sampling gear efficiency that lead to variations in Delta Smelt catch.
Since the general hypothesis is that shallow areas in Suisun Bay are more favorable for Delta Smelt catch than deeper areas (e.g., Moyle et al. 1992;Aasen 1999;Bennett 2005), we also calculated SI H using Equation 2, but substituting the seabed elevation (a metric for average water depth, see Table 2) for the maximum depth-averaged velocity to evaluate whether increased Delta Smelt catch is simply directed toward shallow regions of Suisun Bay rather than lower velocity areas. However, predictions of SI H using the seabed elevation were less accurate than the predictions that used the velocity metric. This indicates that although the seabed elevation is correlated to the maximum depth-averaged current speed (r = - 0.771), lower current speed regions are better predictors of Delta Smelt catch than shallow areas. The less accurate prediction of SI C using the seabed elevation instead of the maximum depthaveraged current speed is also consistent with seabed elevation (r = 0.343) and water depth (r = - 0.248) being less correlated to SI C than maximum depthaveraged current speed (r = - 0.533), as shown in Table 2. In addition, the covariance between the seabed elevation and each of the salinity, Secchi depth, and maximum depth-averaged current speed metrics is higher than the covariance between any of the three selected metrics, indicating that the seabed elevation may be a less suitable metric than the velocity for combining with the salinity and Secchi depth metrics. Since the velocity metric was a better predictor of the historical Delta Smelt catch than water depth, this analysis suggests that lower-velocity areas may be a more important habitat characteristic than shallow water depth for Delta Smelt.

Analysis of Interannual Variability
We investigated the values of SI H in 2-D throughout Suisun Bay to relate areas historically predicted to be favorable for Delta Smelt catch to environmental conditions which occurred during a drier year in 2010 and a wetter year in 2011. Two key regions for Delta Smelt are Grizzly Bay and Honker Bay, where shallow and flat shoals promote wind-driven resuspension of sediment that increases turbidity (Ruhl et al. 2001). During the fall of the drier year, salinity in Grizzly Bay was above 6 psu ( Figure 12A), even though the Secchi depth was less than the 0.5-m value used here as a threshold indicative of historically good conditions for catching Delta Smelt ( Figure 12C). The opposite was true for Honker Bay, which had low salinity in 2010 but high Secchi depth (low turbidity). In 2010, favorable salinity and turbidity conditions did not overlap in the regions with low maximum velocity such as Grizzly Bay, Honker Bay, or the  12B, and 12C). In contrast, the wetter year 2011 showed a large portion of Suisun Bay characterized by low salinity ( Figure 12B) and low Secchi depth (high turbidity, Figure 12D). The maximum velocity at any given point had much lower interannual variability than salinity and turbidity ( Figures 12E  and 12F). This results because the main driver behind water velocities in Suisun Bay is tidal forcing (Cheng and Gartner 1984), which when considered over a 4-month period, resulted in velocity metrics that were nearly identical from year to year. Because the velocity metrics are largely invariable on an interannual time scale, potentially favorable regions for Delta Smelt catch can be narrowed to consider the interannual variability in the salinity and turbidity outside of the high-velocity regions. Although the difference in outflow from the Delta between fall 2010 and fall 2011 was large, the differences in outflow in the winter and spring can be much greater than in the fall and some velocity metrics may show more interannual variability and sensitivity to Delta outflow in other seasons (e.g., Monismith et al. 2002).
Comparing the predicted value of SI H averaged over the fall periods of 2010 and 2011 provides insight into how the variability between wetter and drier years compares to the analysis that focuses on average historical conditions ( Figure 13).  Figure 13) to the map developed based on average conditions ( Figure 8D) provides insight into how interannual variability in environmental conditions affects predictions of the favorability of a region for Delta Smelt catch.  (2010) and wetter (2011) years highlight that the area of high SI H (taken here as greater than 0.5) is much greater when the low salinity and high turbidity overlap outside of high-velocity regions ( Figure 13). The overlap of low-salinity and high-turbidity regions is especially important because as Figures 12C and 12D and Ruhl et al. (2001) suggest, the majority of the turbidity in the region around Suisun Bay during low outflow periods-for example, from September through December-is generated through wave resuspension in the shallow areas of Grizzly Bay and Honker Bay.
Presumably, if the region of lower salinity retreats eastward, the lower-salinity and higher-turbidity regions may no longer overlap (as was the case in fall 2010), resulting in poorer conditions for Delta Smelt catch than would be predicted based only on the salinity. The FMWT data indicate that 2010 was a poor year for catching Delta Smelt, and 2011 had much higher Delta Smelt catches than 2010, which is consistent with the maps of SI H (Figure 13) for these 2 years.

Combing Long-term Data Sets and Numerical Model Predictions
A major benefit of a validated numerical model is the ability to sample the model predictions on spatial and temporal scales that would not be possible in a field setting. In this study we used the predicted maximum depth-averaged current speed over a 4-month period to develop the velocity metric. It would not be possible to directly measure this variable at every location within Suisun Bay over a 4-month period. Another benefit of numerical models is that the sub-sampling of model predictions can be done iteratively. If midway through the analysis it is determined that more information is needed, the model predictions could be further sampled to obtain the new information, or the model simulation could be repeated to obtain additional information. This is not possible in a field sampling study that has already been completed. Combining long-term data sets with numerical model predictions could be the 22 VOLUME 14, ISSUE 1, ARTICLE 3 focus of further work aiming to better understand historical data collection efforts using metrics that either could not be measured, were too expensive or difficult to observe, or were not thought to be important when the data were being collected. For example, 3-D model predictions could be subsampled at the exact times and locations of tows to better understand the hydrodynamic conditions relating to each specific tow, potentially providing insight into fish catch on a tow-by-tow basis.
The analysis described in this paper could also be performed on other fishes that may have different environmental preferences than Delta Smelt or to different Delta Smelt life stages, to quantitatively assess how environmental factors may have influenced the historical fish catch and to visualize in 2-D the locations predicted to be favorable for catches. The methods presented here can also be transferred to other estuaries with similar long-term fisheries data sets and numerical models. For example, the Virginia Institute of Marine Science trawl survey has tracked trends in seasonal distribution and abundance of finfish and invertebrates in Chesapeake Bay since 1955 (VIMS 2015). Using the approach developed for this study, numerical model predictions from Chesapeake Bay (e.g., Lanerolle et al. 2011;Scully 2013;Feng et al. 2015) could be combined with the trawl survey data to identify the variables most correlated to fish catch for individual species in the Chesapeake Bay.

CONCLUSIONS
A quantitative analysis contributed to a better understanding of the relative historical Delta Smelt catch in the FMWT and Bay Study data sets. The three complexity metrics defined as the percent of the time salinity was less than 6 psu, the maximum depth-averaged current speed, and the Secchi depth at each FMWT station in the vicinity of Suisun Bay were found to be most predictive of historical Delta Smelt catch. The relative ranking of stations for Delta Smelt catch in Suisun Bay across 4 decades could be predicted using these three quantitative metrics of environmental complexity derived from observed data and 3-D model predictions. The high correlation between SI C and SI H strongly suggests that the overlap of low salinity and low Secchi depth (high turbidity) in areas with low maximum depth-averaged current speed has historically led to conditions favorable for Delta Smelt catch in Suisun Bay by the FMWT. These results were validated through an independent analysis conducted using the Bay Study Delta Smelt catch data.
Although the salinity and Secchi depth metrics varied significantly between 2010 and 2011, the fall seasonally-averaged velocity metrics were quite similar at any location in Suisun Bay between these 2 years, indicating that interannual variability in the salinity and the Secchi depth metrics are large compared to the interannual variability in the velocity metrics. In 2011, low salinity and low Secchi depth (high turbidity) overlapped in areas with low maximum depth-averaged current speed, but in 2010 the low salinity and low Secchi depth did not overlap in any of the low-velocity regions spanning Grizzly Bay, Honker Bay, or the shallow middle region of Suisun Bay. This co-occurrence of favorable environmental conditions in 2011 but not in 2010 corresponded with the FMWT' reporting much higher Delta Smelt catches in Suisun Bay in 2011 than in 2010.
The predictions of the hydrodynamics from the 3-D numerical model were integral in further understanding spatial variability in the fish catch on scales smaller than the estuary-wide salinity gradient. These results demonstrate that numerical model hindcasts can be combined with long-term data sets to explore environmental conditions at different spatial and temporal scales in order to improve the understanding of observed biological data. Although the current study focused only on the relationship between hydrodynamic complexity and Delta Smelt in the San Francisco Estuary, the method applied here could be extended to other species and areas of interest in this estuary, or to other estuaries. Baxter et al. (2015) recommend "collaboration among physical and biological modelers, experimental and other scientists, managers, and stakeholders to develop and model management scenarios and strategies that move beyond the current focus on relatively crude distinctions among 'water year types' toward a more integrative ecosystem and landscape-based management approach." This work demonstrates that this type of collaborative approach http://dx.doi.org/10.15447/sfews.2016v14iss1art3 can inform future management decisions about the environmental conditions that favor fish catch, and demonstrates the importance of using multiple parameters acting over hourly to inter-annual timescales to identify the important characteristics of adult Delta Smelt habitat. Substantial effort has been invested in planning for restoration of ecological processes and resources in Suisun Bay and the Delta (BDCP 2014; Resources Agency 2014), and the threatened Delta Smelt has been a particular focus of these efforts. This analysis of the characteristics of habitats that have more consistently yielded Delta Smelt catches in the FMWT, which have been confirmed using the Bay Study, reinforces previous findings that the conditions most likely to support Delta Smelt include low salinity and high turbidity and suggests that the appropriate salinity and turbidity ranges must overlap in areas of relatively low velocity.