| CRiSP1.6 Theory & Calibration Manual: III.4 - Calibration of Fish Travel Time Algorithms | |
III.4 - Calibration of Fish Travel Time Algorithms
After the combined survival/travel time calibrations are performed for each species (or a particular stock), the travel time parameters for the remaining stocks in each species are calibrated. The predation rate parameters found in the combined runs for each species are used in these additional stock runs.
The migration rate equation (eq (48)) has the following coefficients:
- r(t) = migration rate (miles/day)
- t = julian date
0,
- Vf = average river velocity during the average migration period
1,
- TSEASN = inflection point of flow dependent term (julian day)
- TRLS = release date (julian day).
Other models containing a subset of these parameters are also used when appropriate (see eq (50) and eq (51)).
Travel Time Calibration Process
The procedure is to first organize fish into cohorts, which is comprised of fish released on the same day or on several consecutive days (see Construction of Cohorts for details). Based on these cohorts, the weighted sum of squares difference between modeled and observed median travel times is minimized with respect to the migration rate parameters:
where the weights are given (as they are in Hockersmith et al. 1999) as:
for each j, where
, n is the total number of cohorts, and k is the total number of observation sites. This equation is fit using a conjugate gradient routine or a Levenberg-Marquardt routine (Press et al. 1992), with derivatives calculated numerically using a finite difference method (Gill, Murray, and Wright 1981).
The estimated migration rate parameters are provided, along with plots that compare the model-predicted average travel times to observed average travel times in Section III.4.1.
Estimating Velocity Variance (Vvar)
Velocity variance (Vvar) determines the rate of spreading of the cohort of fish and requires more detailed information to estimate than the migration rate parameters, which just require average travel time information. Estimating Vvar requires the distribution of travel times for a cohort; thus the unit of information for calibration is the daily counts. Since there is a great deal of variability in the variances associated with the daily counts, generalized least squares (Draper and Smith 1981) is used to estimate Vvar. Zabel (1994) provides the details of this procedure.
Smolt Start/Stop Date
The smolt dates determine when fish initiate migration. Before smolt start date, no migration occurs. After smolt start date and before smolt stop date, a proportion of the release initiate migration on a daily basis. After smolt stop date, all fish in the release have initiated migration. Note that these dates are only relevant if fish are released before they are ready to migrate. If the fish are active migrants, then smolt start and stop dates should be set to dates previous to release dates.
In order to estimate these dates, we require data of fish released before they are ready to migrate. Based on the arrival distribution at the first observation point and the travel time to reach that point, smolt start and stop dates can be estimated.
Migration Rate Variance
Variability in plots of observed versus modeled average travel times result from variations among particular releases. To account for this, a multiplicative variance is introduced by eq (52) where:
V(i) is drawn from the broken-stick distribution. The default values for spring and fall chinook and steelhead are mean = 1, low = 0.7, and high = 1.3.
Travel Time Data
Several criteria are used to select appropriate data sets. First, because migration rate is related to date in season and date of release, it is essential that the calibration data sets have fish released over long periods of time so these effects can be measured. Also, it is desirable to have fish released from the same site over multiple years so that a variety of river conditions are encountered. Sufficient numbers of fish must be observed at downstream observation sites, and fish must be observed at multiple sites. Finally, data sets are selected to represent as many stocks of fish and sections of the river as possible.
Construction of Cohorts
Before the calibration can be run, cohorts are constructed from available PIT-tag data. We set a target number of observations at downstream observation sites, minimum sample size at each site, and a maximum number of consecutive days that could be combined when forming a cohort. The goals of this process are to create relatively uniform sample sizes, restrict the range of release dates to capture seasonal variation, and maintain a minimum sample size to permit calculation of the rate of spreading of the population. Two methods were used to construct cohorts, depending on whether fish were tagged during the period of active migration or at upstream rearing grounds. In each case, all releases on the same julian day were combined in the same cohort.
For actively migrating fish, cohorts were formed based on dates of release. Releases were combined into a cohort until the target sample size was obtained for all included observation sites. If the target sample size was not reached when the maximum span of consecutive release days was reached and the minimum sample size was not achieved, then the cohort was rejected. In this case, the first julian day of releases in the cohort was dropped and the subsequent julian day of releases was added. This process was repeated until the cohort met the criteria and all release groups were examined.
In some cases, fish were collected in their rearing grounds and tagged prior to active migration. The travel time to the first observation site includes both pre-migration and migration periods. In our study of migration rates, this pre-migration period confounds the analysis. To restrict the analysis to actively migrating fish, we ignored migration prior to the first observation of an individual fish. To do this, we first identified individual fish that were observed at Lower Granite Dam and at least one subsequent site. This yields a measure of travel time between two points in the system for actively migrating fish. Each fish was assigned the "release date" of its observation at Lower Granite Dam and all the fish from a single day were considered a single release. Cohorts were constructed from these releases as above.
III.4.1 - Results for Snake River Stocks
Figures 63, 64 and 65 show modeled versus observed (PIT-tag data) travel times for spring and fall chinook and steelhead.
Fig. 63 Spring chinook, modeled vs. observed travel times
Fig. 64 Steelhead, modeled vs. observed travel times
Fig. 65 Fall chinook, modeled vs. observed travel times
III.4.2 - Results for Upper Columbia Stocks
Figures 66 and 67 show modeled versus observed (PIT-tag data) travel times for Upper Columbia yearling fall chinook and Upper Columbia steelhead. The Upper Columbia yearling fall chinook calibration was troublesome. As mentioned in Section III.3.4, it was extremely sensitive to the choice of predation parameters. The result (see Fig. 66) was less satisfying than any of the other travel time calibrations. Factors in this could include the lack of data (only two years of light data) and the fact that much of the data consisted of travel times in the range of 25 to 40 days (Wells Dam releases being monitored at McNary, John Day and Bonneville as well as Rocky Reach). For most other species, the bulk of the data was between 5 and 20 days.
These long travel times are characteristic of fall chinook, which typically spend time, after release, milling about before heading downstream. Until we get a better handle on modeling that difficult aspect of their migration, the model will continue to have difficulty with calibration to the travel time data for fall chinook. Some of those difficulties are discussed in Section III.3.4.
Fig. 66 Upper Columbia yearling fall chinook, modeled vs. observed travel times for 1997-1998 releases from Wells Dam tailrace.
Fig. 67 Upper Columbia steelhead, modeled vs. observed travel times for 1989-1999 releases from Rock Island Dam tailrace
| CRiSP1.6 Theory & Calibration Manual: III.4 - Calibration of Fish Travel Time Algorithms | |
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