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Ecological variables are estimated from both field observations and laboratory studies. Estimates made from field observations (such as fish passage timing or mortality rates) are used with the corresponding environmental variables (Fig. 4). Estimates made from laboratory experiments are analyzed assuming the corresponding laboratory conditions and are used to infer the relevant ecological variables. For example, the estimation of mortality from gas bubble disease is made based upon laboratory experiments.
The calibration involves mixing results from laboratory experiments, isolated field studies on aspects of migration, and system-wide studies of survival and timing. The calibration proceeds in a hierarchy of steps where calibration of the first steps are required to calibrate the lower ones. The sequence which is reflected in the chapter organization is: River and Environmental Description, Flow Processes, Passage Processes, Dam Processes and finally Reservoir Mortality. The final two steps are in part connected depending on the data set and parameters being calibrated.
| Fig. 4 Calibration process involves using passage and environmental data to estimate the model ecological variables |
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Goodness-of-fit
In calibration, the variables are adjusted so an equation prediction best fits the observations according to statistical criteria within ecological constraints. A variety of goodness-of-fit measures are applied in the calibrations. The choice of method depends on the type and quantity of data and the dimensions of the data being fit. Where possible graphical examples are given along with statistical measures of the goodness-of-fit. The following approaches are used.
- Least Squares, 2 dimensional regressions (Numerical Recipes, Press et al. 1988) used for
- nitrogen mortality rates vs. time
- size vs. mortality rate
- spill efficiency equations
- Nonlinear regression using the Gauss-Newton algorithm to minimize sums of squares (SPLUS 1991) used for
- nitrogen mortality rate vs. nitrogen level
- prediction of migration rate parameters vs. flow and fish age
- Hyperbolic "amoeba routine" (Numerical Recipes, Press et al. 1988) used for
- nitrogen mortality rate vs. nitrogen level
- Fourier series analysis (SPLUS 1991) used for
- determining scenario mode flow modulators
- Maximum likelihood estimators (Zabel 1994) used for
- determining migration rate parameters
In some cases, with limited data statistical techniques do not converge on a unique solution in that an equation can fit the data equally well with different model parameters. In these cases the parameter set is fit by selecting one of the parameters, either arbitrarily or justified on its range inferred from ecological constraints.
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Columbia River Salmon Passage Model CRiSP.1.5 Theory, Calibration & Validation Manual
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