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Migration rate is calculated on a reach and time step basis. (See Fish Migration section.) At each time step that fish are released at the top of a reach, a unique migration rate is determined for that reach. Migration rate is defined by eq (52). The equation has the following coefficients:
- r(t) = migration rate (miles/day)
- t = Julian date
's = regression coefficients - Vf = average river velocity during the average migration period
= slope parameter - TSEASN = inflection point of flow dependent term (in Julian date)
- TRLS = release date (in Julian date).
The minimum flow independent migration rate (min) is equal to 0 + 1/2, and the maximum flow independent migration rate is equal to 0 + 1. The parameters that must be estimated are min, max, flow, , and Tseasn. Note that if min = max, there is no increase in the flow independent component with time. Also, flow dependency can be eliminated by setting flow = 0.
These parameters are estimated using a calibration program that is, in effect, a stripped-down version of CRiSP that only encompasses the travel time component. The migration rate parameters and river flow information are provided to the program, and it returns average travel times to several points along the river. These model-predicted average travel times are then compared to observed average travel times. Migration rate parameters are selected that give the best model fit to the 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.
The procedure is to first organize fish into cohorts, which comprise fish released on the same day or on several consecutive days. Based on these cohorts, the following equation is minimized with respect to the migration rate parameters:
(56)
where n is the total number of cohorts, and k is the total number of observation sites. This equation is fit using a Levenberg-Marquardt routine (Press, et al., 1992), with derivatives calculated numerically using a finite difference method (Seber and Wild, 1989; Gill, Murray, and Wright, 1981).
In the following sections, the estimated migration rate parameters are provided, along with plots that compare the model-predicted average travel times to observed average travel times.
Estimating Vvar
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) provide 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.
Travel time data sets
As of the writing of this manual, these are the data sets that have been analyzed for travel time calibration. The number of stocks analyzed is being expanded, and in the next release of the manual, several more stocks will be included.
Snake River spring chinook
These are PIT tagged fish released at the Snake Trap (top of Lower Granite Pool) and observed at Lower Granite, Little Goose, and McNary Dams. The release period is from early April to early May, with separate releases occurring daily. Although these fish are classified as run-of-the-river fish, it is likely that the vast majority of these fish are spring chinook based on the distribution of lengths (most fish longer than 110 millimeters) and the timing of migration (early spring). This is consistent with other treatments of these fish (e.g., Fish Passage Center, 1991). Release cohorts were formed by lumping together releases from up to three consecutive days to achieve sample sizes of at least 80 individuals observed at Lower Granite Dam. Data from the years 1989-1994 were analyzed; 52 cohorts were analyzed over this period.
The migration rate equation was fit to all three of the observation points simultaneously. Plots of the results are contained in Fig. 30, and the parameter estimates are in Table 11. Because these fish are active migrants, smolt start and stop dates are set to day 90, which is the earliest day that fish are observed at Snake Trap.
Mid-Columbia fall chinook
Two groups of mid-Columbia summer/fall chinook were analyzed: Priest Rapids hatchery fish (brand) and run-of-the-river fish collected and released at Rock Island Dam (PIT tag).
The brand release hatchery fish were released at Priest Rapids and observed at McNary and John Day Dams. Five groups were released each year on separate days, and these release groups were the units of the analysis. Data was analyzed from 1988, 1989, 1991, 1992, 1993 (1990 has censored data). The release groups from all the years were analyzed together to estimate migration rate parameters. Also, smolt dates were estimated from these data.
The run-of-the-river PIT tag fish were collected, tagged, and released at Rock Island Dam. The fish analyzed were identified as summer/fall chinook by Chapman, et al. (1994) for the 1992 and 1993 fish. We used the same criteria to identify the 1994 summer fall chinook. Release groups over 7 consecutive days were lumped together to form cohorts of adequate sample size. This resulted in 3 cohorts for 1992, 8 cohorts in 1993, and 6 cohorts in 1994. These fish are active migrants, so smolt start and stop dates could not be estimated.
There is no evidence that these fish increase their migration rate as they spend more time in the river, so min = max. The parameter estimates are contained in Table 11, and plots of the results for both groups are contained in Fig. 31.
Snake River fall chinook
Wild fall chinook were collected (by beach seining) in the Snake River above the confluence of the Clearwater River in the years 1991-1994. The fish were PIT tagged and then detected as they passed Lower Granite and Little Goose Dams. Fish were also detected at McNary Dam but sample sizes there were very low (approximately 5-10 fish per year). Many of the fish sampled were in the premigratory phase (well below 85 mm in length) making travel time calibration more difficult.
To calibrate Snake River fall chinook travel time our approach was to use the travel time parameters obtained for the Rock Island fall chinook (Table 11) and vary smolt start/stop dates on a yearly basis. For consistency, the duration between smolt start and stop dates was kept constant over the four years. The modeled average arrival dates at Lower Granite and Little Goose Dams were fit to the observed average arrival dates to these dams. The results are contained in Fig. 32 and Table 12. In the future, we will relate variability in smolt start/stop date for fall chinook to river temperature.
Dworshak Hatchery steelhead
Five years of PIT tag data were analyzed to estimate travel time parameters for Dworshak Hatchery steelhead. The fish were released at the hatchery and observed at Lower Granite, Little Goose and McNary Dams. The travel time parameters were estimated by comparing observed average travel times to the 3 collection sites to model predicted values. The results are contained in Table 11 and Fig. 33. These data were also used to estimate FGE (see Steelhead FGE section II.9.2).
Snake River wild Steelhead
Wild Snake River steelhead were PIT tagged at the Snake River trap and observed at Lower Granite, Little Goose, and McNary dams. These fish were released over the seven year period 1989-1995. Results are given in Table 11.
Variance in migration rate
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 (54) where
- r = determined
- V(i) = variance factor that varies between releases only.
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
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Columbia River Salmon Passage Model CRiSP.1.5 Theory, Calibration & Validation Manual
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