II.2 - Calibration Overview

Some equations are mechanistic and are derived from some underlying theory. In these equations the parameters have ecological or physical meanings. The equation relating water flow to velocity, for example, is based on principles of hydrology. A second type of equation is empirical and has no underlying ecological or physical meaning. These are used because they fit the data and are amenable to statistical fitting techniques. The parameters of these types of equations (submodels) seldom have ecological interpretations. For example, in the nitrogen supersaturation submodel four alternative equations are available to relate nitrogen supersaturation to spill. The first two alternatives are empirical. A third type of equation uses a mixture of empirical and mechanistic based equations. The predator mortality equation is such an equation.

The calibration of these equation types points up their advantages and drawbacks. The advantage of the empirical equations is their simplicity which makes it relatively easy to fit them to data. Their drawback is they can only be fit with data specific to the given situation. Mechanistic equations are advantageous in that their parameters have ecological meanings. In these cases the possible ranges or values of the parameters often can be determined from data sets from other unrelated studies and systems. The disadvantage of mechanistic equations is that fitting them to data is often more difficult and often involves nonlinear fitting algorithms.

The model has a significant number of parameters that must be estimated through a calibration and validation process. Because of this complexity, a variety of data from both field and laboratory studies are used in the calibration. The end result is that through the calibration process diverse theories and data sets are synthesized into a consistent picture of the process of fish migration and survival through the river system. The calibration involves determining the set of parameters that yield the observed passage observations for a given set of river conditions. The relationship between environmental conditions, passage observations and ecological variables is illustrated in Fig. 5.

Environmental variables describe the observable state of the environment in which fish live. These variables are monitored in the system and include weather-related factors such as temperature, and system operating factors such as flow, spill and fish transportation. These variables are accessed in the model with the Headwater, Reach and Dam buttons.These variables have been determined from historical records dating back to 1970 for all variables and back to 1937 for a subset of variables. Future values of these variables are assessed from runs of hydromodels and management-derived scenarios of river operations.

Fish passage observations involve a variety of data, extending back several decades, on the passage timing and survival of fish through various segments of the river and hydrosystem. This ranges from relatively small-scale information on the passage of individual groups of fish at individual dams to system-wide estimates of passage and survival of species over specific years plus a number of observations at levels of detail between the smallest and largest scales. Observations include brand release studies conducted from 1970's and 80's and PIT tag studies conducted beginning in the late 80's. These data sets yield two levels of information. The direct observations provide passage numbers and timing at individual dams as well as returns of adults to dams and collection points. These raw numbers can be further reduced to estimates of migration rates and fish survival between points in the river and in some cases collection efficiencies at dams. The model can use both raw information and statistically analyzed data. The model runs on data expressed as initial release numbers and numbers of fish passing any point or bypass route in the river system. Release information is accessed through the Release button. Passage information is accessed through the Passage Histogram button of the model. This provides detailed information of passage at any level from passage of a specific dam route to passage through the entire system.

Ecological variables are developed from first principles of how the environmental variables interact with fish behavioral and physiological factors to determine fish passage. These variables, for the most part, characterize the rates of fish passage and survival, which through equations, generate predicted passage for a set of environmental variables. Model calibration requires estimating these variables. Model validation requires assessing how close our assessments are to actual values. In the model these variables are contained under Behavior, Dam and Reservoir buttons.

Our understanding of the ecological interactions of fish is incomplete and several levels of complexity of interactions can be envisioned. The CRiSP.1 model contains a number of different theoretical constructs that can be selected at run time. Any calibration of the model is only specific to a particular choice of theoretical constructs. The selection of which construct to use depends on the available information, the effect of the feature on the calibration, and its ecological soundness.