Calibration of the Stream Salmonid Simulator (S3) model to estimate annual survival, movement, and food consumption by juvenile Chinook salmon (Oncorhynchus tshawytscha) in the restoration reach of the Trinity River, California, 2006–18

The Trinity River is managed in two sections: (1) from the upper 64-kilometer “restoration reach” downstream from Lewiston Dam to the confluence with the North Fork Trinity River, and (2) the 120-kilometer lower Trinity River downstream from the restoration reach. The Stream Salmonid Simulator (S3) has been previously applied to these reaches and the Klamath River. To estimate fish growth, past S3 calibration efforts in the Trinity and Klamath Rivers used maximum likelihood methods that considered only the abundance of juvenile Chinook salmon (Oncorhynchus tshawytscha) passing a fish trap to estimate survival and movement parameters, but not fish consumption. Previous calibrations did not estimate the average proportion of maximum consumption (C_y) when estimating survival (S_y) and movement (M_0y) parameters across years (y) of data, but because no other information was available in the literature a fixed value of C_y=0.66 was assumed. Therefore, the goal of this report is to present an alternative approach that calibrates the S3 model to multivariate data (that is, abundance and size), enabling the estimation of the average proportion of maximum consumption, in conjunction with survival and movement parameters for a particular migration year. We fit the S3 model to individual years of weekly trap abundance estimates and mean fish sizes (fork length) at the Pear Tree Gulch (hereafter referred to as Pear Tree) fish trap representing the restoration reach. We used the Earth Mover’s Distance (EMD) as the objective value to be minimized in parameter optimization. This approach estimated survival, movement, and consumption parameters for each migration year. Because we had information on the abundance of natural and hatchery produced juvenile salmon at the fish traps, we estimated survival and movement for natural and hatchery fish.

S3 is a deterministic life-stage-structured population model that tracks daily growth, movement, and survival of juvenile Chinook Salmon. A key theme of the model is that river discharge affects habitat availability and capacity, which in turn drives density-dependent population dynamics. To explicitly link population dynamics to habitat quality and quantity, the river environment is constructed as a one-dimensional series of linked habitat units, each of which has an associated daily timeseries of discharge, water temperature, and useable habitat area or carrying capacity. In turn, the physical characteristics of each habitat unit and the number of fish occupying each unit drive survival and growth within each habitat unit and movement of fish among habitat units.

The physical template of the restoration reach of the Trinity River was classified into 356 meso-habitat units comprised of runs, riffles, and pools. For each habitat unit, we developed a timeseries of daily discharge, water temperature, amount of available spawning habitat, and fry and parr carrying capacity. Capacity time series were constructed using state-of-the-art models of spatially explicit hydrodynamics and quantitative fish habitat relationships developed for the Trinity River. These variables were then used to drive population dynamics such as egg maturation and survival, and in turn, juvenile movement, growth, and survival.

We estimated movement, survival, and consumption parameters by calibrating the model to 12 years of weekly juvenile abundance estimates and fish sizes at the Pear Tree fish trap near the downstream end of the restoration reach. We estimated parameters for 12 years that included a wide range of female spawner abundances (1,414–11,494) and water year types (critically dry–extremely wet). We contrast the estimated parameters to the corresponding number of female spawners and the total annual volume of water discharged for the Trinity River (Trinity River Restoration Program; https://www.trrp.net/restoration/flows/summary/).

The calibration consisted of replicating historical conditions as closely as possible (for example, discharge; temperature; spawner abundance, spawning location and timing, and hatchery releases), and then running the model to predict weekly abundance passing the trap location from each brood year of adults and subsequent migration year of their juvenile progeny. Because density-dependent movement was favored in past evaluations, we estimated S3 parameters based on density-independent survival and density-dependent movement. Likewise, each year’s estimated survival parameter for natural (S_Ny) and hatchery (S_Hy) fish may be interpreted as the mean daily survival probability from emergence or hatchery release to the Pear Tree fish trap. Under density dependence, the estimated movement parameter for natural (M_0Ny) and hatchery (M_0Hy) fish represents the intercept of the Beverton-Holt model; the probability of remaining in a habitat at near-zero abundance.

We estimated C_y by using EMD and incorporating abundance and fish size into model calibration. Average daily proportions of maximum consumption, , across the years were generally high (=0.640; standard deviation (SD) SD=0.176), suggesting that fish were feeding at about two-thirds of expected maximum consumption rates. This average proportion of maximum consumption,is very similar to what has been assumed (=0.66) in previous Trinity and Klamath River S3 calibration and simulation efforts. In 2017, we estimated the lowest C_y, suggesting lower average consumption for juvenile salmon in high-discharge water years. When this high discharge year was excluded, there was no apparent trend in C_y with annual water volume. Estimates of survival showed little trend over the range in spawner abundances, but a trend towards higher natural and hatchery fish survival with higher annual volumes of water was apparent. Over the 12 years, the average survival of hatchery fish was =0.888 (SD=0.079) and the average survival natural fish was=0.969 (SD=0.01).

With respect to fish movement, we estimated higher M_0Ny and M_0Hy with higher annual volumes of water in the Trinity River. Higher M_N0y or M_H0y suggest greater probability of remaining in a habitat at low fish densities, with potential for density-dependent processes in movement to occur. The highest M_{0Ny =} 0.676 was estimated during brood year 2012, and the overall average for natural fish was =0.276 (SD=0.188) and for hatchery fish was=0.467 (SD=0.235). Under the Beverton-Holt model, as M_0Ny or M_0Hy approach zero, there is less capacity for change in fish movement as fish density increases.

The S3 model was initialized with only the spatiotemporal distribution of spawners, so it performed well at capturing the essential outmigration features that are ultimately governed by rates of growth, movement, and mortality. We used a new optimization method that could accommodate multivariate data on abundance and fish size collected at the Pear Tree fish trap, enabling the calibration of S3 to estimate five parameters for 12 separate years of data. Incorporating weekly fish size data for each year in our parameter optimization process made the estimation of C_y possible and represents a step forward in the fitting of the S3 model to fish trap data for the purposes of parameter calibration and the estimation of growth parameters with respect to annual conditions. We identified lack of fit and adding important effects into the S3 model may improve the S3 estimation and simulation of water scenarios.

The Trinity River Restoration Program (TRRP) Science Advisory Board recommended that the TRRP focus on developing core elements of a decision support system (DSS; Buffington and others, 2014). Toward that end, the habitat and S3 models described in this report are both core elements of the DSS. The structure of S3 makes it a particularly useful fish production model for the DSS because population dynamics are sensitive to (1) water temperature, (2) daily discharge management, and (3) habitat quality and quantity. Each of these variables are key management parameters under consideration in the TRRP. As such, the S3 model may provide valuable insights into the potentially variable effects of different management decisions on the Trinity River.