| CRiSP1.6 Theory & Calibration Manual: III.3 - Predation Rate Parameter Calibration | |
III.3 - Predation Rate Parameter Calibration
The final sets of parameters to be calibrated are those for predation rate-including temperature response-and migration rate. Both of these sets are calibrated by using optimization routines to adjust parameters so as to best fit the model to relevant data.
Though travel time is not explicitly represented in the predation rate, it clearly factors into overall predation mortality in the model since slower migrants have more opportunity to become prey. In the same way, predation rate implicitly affects median travel time in the model since a higher predation rate has greater effect on the slower migrants. For this reason, the travel time and predation rate calibrations are run alternately until both calibrations have converged. We only have survival data for one stock from each species (spring chinook, fall chinook, steelhead); as a result, the predation rate parameters found by this process are then used for all stocks in that species.
The predation rate equation is based on the following parameters (from equations (61) and (63)):
,
and
= predator activity in the river zones
- CMAX,
and TINF = temperature response equation parameters
- P = predator density (by zone in each river segment)
- T = water temperature in the river segment.
Note that CMAX multiplies the three activity coefficients (depending on river zone) and thus can be thought of as scaling them. It was never intended that CMAX,
,
and
be calibrated simultaneously (as that would confound the optimization).
Survival Data
The survival data consists of National Marine Fisheries Service (NMFS) survival estimates and standard errors for both wild and hatchery released fish. The NMFS survival estimates for spring chinook, fall chinook, and steelhead were taken from the following studies.
- Spring chinook and steelhead
- Iwamoto et al. 1994
- Muir et al. 1995
- Muir et al. 1996
- Smith et al. 1998
- Hockersmith et al. 1999
- Smith et al. 2000
- Fall chinook
- Williams and Bjornn 1997
- Williams and Bjornn 1998
- Muir et al. 1999
Fall chinook survival estimates for 1998 were provided directly by Steve Smith of NMFS, Northwest Fisheries Science Center.
The spring chinook survival estimates consist of fish released above the Lower Granite Reservoir (RES) on multiple days in 1993-1995, and fish releases regrouped by week in the Lower Granite tailrace (LGR) for 1995-1998. A survival reach is defined as being from tailrace to tailrace. Estimates for survival are given from release (RLS) to Lower Granite tailrace (LGR), LGR to Little Goose tailrace (LGS), LGS to Lower Monumental tailrace (LMN), and LMN to McNary tailrace (MCN). Not all data exists for all years.
The fall chinook survival estimates consist of fish releases regrouped by week in Lower Granite tailrace (LGR) for 1995-1998 with estimates to LGS and LMN.
The steelhead survival estimates consist of fish releases regrouped by week in Lower Granite tailrace (LGR) for 1995-1998 with estimates to LGS, LMN and MCN, and fish releases regrouped by week in McNary tailrace for 1997-1998 with estimates to John Day tailrace (JDA) and Bonneville tailrace (BON).
Survival Calibration Process
For survival/predation parameter calibration, we produce a modeled survival Sm corresponding to each point So of the survival data. This relationship can be expressed as:
The model-estimated survivals depend both on parameters that are fixed
(e.g. flows, temperatures, predator densities as well as the migration rate parameters) and on the predation rate parameters
that are adjusted to calibrate the modeled survival to the survival data.
The calibration process utilizes a conjugate gradient method (an optimization technique) to minimize the sum-of-squares difference between the survival data and the model-predicted survival in each survival reach j for each cohort (or release) i in each year:
where the weights are given (as they are in Hockersmith et al. 1999) as
The survival data in the numerator of the weighting counteracts the tendency of lower survivals having lower variances. This weighting also diminishes the relative weight of the lower survivals (which are thought to be less accurate).
III.3.1 - Parameter Determination and Calibration
Predator Densities
The predator densities have been determined (by zone and reach) from CPUE indices as described in Section II.4.2 Predation Mortality. We will revisit this below in the Section III.3.2 because of difficulties encountered in the calibration process due, in part, to the high variability of the predator densities between reaches.
Predator Activity Coefficient Determination
Since the survival data is given by reach, from tailrace to tailrace, there is currently no data to differentiate predation occurring in the forebay from that occurring in the reach (pool) and tailrace (or from mortality due to total dissolved gas supersaturation or dam passage). If we were to calibrate the three activity coefficients
simultaneously, it is likely that the calibration tool would allocate all of the predation activity to the one segment of the model (e.g., forebay) that most closely mimics the survival data.
To avoid this problem, we set
and
in the ratio of consumption rates (per predator) of smolt by pikeminnow as found by Vigg et al. (1991). That is we set
and
for spring migrants (chinook and steelhead), and we set
and
for fall chinook (see Table 17 and Table 18). Calibration of the parameter CMAX then scales the activity coefficients.
The tailrace mortality is handled differently in the model (see Zone Specific Formulations of the Predation Model). In the calibration, we set
so that tailrace mortality would be 1% for spring migrants and 2% for fall migrants (set by PATH) if the temperature was at its mean (10.9°C for spring migrants, 17°C for fall migrants) and the tailrace predator density was at its mean (15000 preds/km2). The tailrace predations will, of course, vary since the actual temperatures and densities vary.
Temperature Response
Vigg and Burley (1991) provide laboratory results showing the activity response of predators (pikeminnow) to temperature. We thought it is important to try to see this temperature response in the survival data, so we did not wish to use their parameter values.
The survival data for spring chinook and steelhead, for example, corresponds only to temperatures in the 7-14°C range (mostly 8-12°C), and so the data cannot be used to predict the upper asymptote of the sigmoidal response. It turned out that many sigmoidal curves would produce a nearly-optimal fit. To counter this problem, we chose that the 95% level of consumption should correspond to a temperature of 15°C (22°C for fall). This is reasonable given the temperature range of the survival data.
The results from these fixed 95% level runs were used to provide good initial values for our final calibration runs (without the fixed point).
III.3.2 - Predator Density - Temperature Response Interaction
The most challenging problem of the spring chinook calibration effort related to the interaction between the predator density data and the temperature response equation and parameters in the spring chinook calibration. Three factors combined to cause the difficulty:
- lower than expected (by the model) survival data from Lower Monumental tailrace through McNary tailrace,
- lower predator densities in Ice Harbor and McNary reaches than in surrounding reaches, and
- slightly higher water temperatures in Ice Harbor and McNary reaches than between Lower Granite Reservoir and Lower Monumental Dam.
We observed that the calibration tool was trying to jack up the temperature response, using slightly higher downstream temperatures (i.e., higher activity) to make up for lower densities but higher predation in Ice Harbor and McNary reaches. To do this, the calibration tool was producing an extremely steep temperature response function-one with a predation rate as much as 50 times higher at 15°C than at 10°C for a given predator density. For comparison, Vigg and Burley's (1991) laboratory study found the predation rate to be approximately a 5.5 times higher at 15°C than at 10°C.
As a result, the late-season modeled survival rates were very low compared to the NMFS survival estimates. Also, the model was decimating the smolt downstream in the Columbia where both temperatures and densities were high.
Density Data Revised
In reaction to this problem of overly steep temperature response, we decided to level out the predator densities-either by averaging the densities for all reaches, all forebays and all tailraces, or by finding an average for each separately in the Snake (Lower Granite Reservoir to confluence), Mid-Columbia (confluence to Bonneville) and Estuary (below Bonneville) regions.
- The five predator density options we studied were:
- River-wide density averages (from 1990 data) for reach, forebay and tailrace.
- Separate density averages (from 1990 data) in the Snake, Mid-Columbia and below Bonneville.
- River-wide averages; adjusted (after 1990) for the pikeminnow removal program.
- Separate averages in the Snake, Mid-Columbia and below Bonneville; adjusted (after 1990) for the pikeminnow removal program.
- Original densities; adjusted (after 1990) for the pikeminnow removal program.
When the averaged density options (first four) were used, the calibrated sum-of-squares was in the range of 145 to 151. Also, the temperature response curves were of similar steepness to those found by Vigg and Burley (1991) (with
). It would be meaningless to compare our temperature response curve to Vigg and Burley's directly, since our
is scaled by the activity coefficient as well as by the relative predator density in each reach, forebay and tailrace.
When the full original density data (fifth option) was used, the minimum sum-of-squares was 174 and the temperature response curve was unreasonably steep (
much too large).
We opted for the 4th option as most reasonable: separate averages in the Snake, Mid-Columbia and below Bonneville; adjusted (after 1990) for the pikeminnow removal program. The predator densities in the data files (for spring chinook and steelhead) reflect this simplification. At this time, the predator densities for the fall chinook migration have not been averaged in this way.
III.3.3 - Results for Snake River Stocks
Tables 53, 54 and 55 compare CRiSP.1 modeled yearly average survivals to NMFS yearly average survivals in the research reach (for which NMFS estimates are given) and for the extended reach (research reach extended to Bonneville).
Figures 56, 57 and 58 show modeled verses observed (NMFS estimated) weekly survivals for spring and fall chinook and steelhead over all years for which data exists.
For fall chinook in particular (Fig. 58), the model has difficulty explaining variations in the data. Notice first that for the late season releases (after julian day 230, August 18) the NMFS estimates tend to be particularly low. An explanation for this might include fish residualizing. Also, the 1997 survivals tended to be low. This may be partially explained by the fact that 1997 was an extremely high flow year.
In fitting the predation parameters for the fall chinook, we found no temperature response. Since CRiSP.1 ultimately models changes in migration and predation due to changes in flow and temperature, the model has a particularly difficult time mimicking variations in the fall chinook survival estimates.
Fig. 56 Spring chinook, modeled vs. observed (NMFS estimated) survivals. The LGR - MCN survivals for 1995 were singled out to highlight the poor behavior of the late season portion of that data.
Fig. 57 Steelhead, modeled vs. observed (NMFS estimated) survival.
Fig. 58 Fall chinook, modeled vs. observed (NMFS estimated) survivals. The late season releases have been singled out as have the 1997 releases.
III.3.4 - Results for Upper Columbia River Stocks
As with the Snake River fall chinook, the model had a difficult time explaining variations in survival estimates (data) for the Upper Columbia yearling fall chinook. Figure 59, presenting modeled versus observed (NMFS estimated) survivals on a reach by reach basis, illustrates this. Figure 60, showing modeled versus observed survival from release to the John Day Dam tailrace, puts this fitting in a somewhat better light and indicates that the problems are at least partially caused by the irregularity of the survival estimates. Figures 61 and especially 62 show that the survival/predation calibration effort for the Upper Columbia steelhead was more successful.
Table 56 compares CRiSP.1 modeled yearly average survivals to estimated yearly average survivals in the research reach and for the extended reach (research reach extended to Bonneville). The survival estimates for the calibration of fall chinook are from Tables 10-16 in Eppard et al. (1999). The survival estimates for the calibration of steelhead are from Tables 4-2 and 4-7 in Stevenson et al. (2000). The yearly averages reported in Table 56 are weighted averages for all releases calculated from those data sources.
For steelhead, the calibration decisively indicated no temperature response. But, with only a single year of data (1999), this is not a meaningful result. It should be noted that the calibration appeared to produce a temperature response, but it was an apparition. The first clue is that TINF was near zero (to be meaningful it should be between about 7 and 18). Second, the SS was equal to that of a calibration where the temperature response was turned off (that is, with
= 0). Third, by plotting the temperature response curve, one can see that all of the variation in response took place below 5°C--below the range of temperatures to be encountered.
Note that for the Upper Columbia fall chinook stocks, the species level information in the .dat file is
Chinook_1based on their yearling status and on their April to May downstream migration dates.Calibration strategy for fall chinook
For the Upper Columbia fall chinook, the response surface was nearly flat within the range of physically reasonable temperature response parameters. Unfortunately, parameters outside this range produced the best fit as measured by the sum of squares (SS) difference between modeled and observed survivals.
The strategy for calibrating the predation/survival parameters was then to fix the temperature response steepness parameter
It should also be noted that the zone-specific predation activity coefficients for each Upper Columbia species were taken from the Snake River species calibration. The two reasons for this were: only a single year of survival estimates was available for each species (so fitting of additional parameters would be of dubious value); and there is only space in the .dat files for one set of these parameters per species.
Predator Density
One possible factor in the calibration difficulties is the predator density values for the Upper Columbia. These were calculated at a different time from the Snake/Lower Columbia densities and may not be as reliable. Also, since the densities are relative, not absolute, it is possible that the Upper Columbia densities are not scaled properly as compared to the Lower Columbia densities.
Because of the high variability of densities between reaches (and the questionable reliability), the densities were averaged for each zone in the Upper Columbia.
Recently received CPUE data for all river zones on the Columbia and Snake Rivers will certainly improve our density values in future calibrations and may remedy these problems as well as other density related problems recounted in Section III.3.2.
Caveat
It should be pointed out again that for both Upper Columbia chinook and steelhead, there exists only one year of survival estimates. This is certainly not enough data to obtain a very meaningful calibration.
Fig. 59 Upper Columbia yearling fall chinook, modeled vs. observed (NMFS estimated) survivals. 1998 releases (RLS) are from Rock Island, Rocky Reach and Wells tailraces as well as Rocky Reach forebay. The dotted line is the one-to-one line, the solid line is the linear best fit to the modeled vs. observed plot.
Fig. 60 Upper Columbia yearling fall chinook, modeled vs. observed (NMFS estimated) survivals from release to John Day Dam. 1998 releases are from Rocky Reach forebay, Rocky Reach, Rock Island, and Wells Dam tailraces.
Fig. 61 Upper Columbia steelhead, modeled vs. observed (NMFS estimated) survivals. 1999 releases (RLS) are from Rock Island and Rocky Reach Dam tailraces.
Fig. 62 Upper Columbia steelhead, modeled vs. observed (NMFS estimated) survivals from release to John Day Dam. 1999 releases are from Rocky Reach and Rock Island Dam tailraces.
| CRiSP1.6 Theory & Calibration Manual: III.3 - Predation Rate Parameter Calibration | |
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