To avoid confusion, I have adopted the following terminology in referring to the PIT tag data.
I chose 3 cohort sets to analyze in this section. The first two are fish that were captured, tagged, and released at the Snake River trap and recaptured at Lower Granite Dam, also on the Snake river (Figure 4.13). The reach length is 52 kilometers. One of the cohort sets consists of chinook salmon of unknown origin (hatchery versus wild), often referred to as "run-of-the-river" fish. Although the run type (spring or yearling versus fall or subyearling) of these fish is not determined, it is likely that the vast majority of these fish are spring chinooks based on the distribution of lengths (most fish longer than 110 millimeters) and the timing of migration (early spring). Also, I excluded groups released after May 15 because after this date average fish length and migration rate began declining, indicating a possible presence of fall chinook. I refer to these fish as "spring" chinook, but acknowledge that a small percentage of the fish may actually be fall chinook. This is consistent with other treatments of this group of fish (e.g., Fish Passage Center, 1991). Groups were released from early March through mid May. 101 cohorts were analyzed over the 5 year period 1989-1993. Beginning in 1992, hatchery stocks were distinguished at release time, and wild stocks were distinguished in 1992 and 1993. I lump these groups together, though, to be consistent with earlier years.
The third set of fish included in this analysis are wild, fall chinook captured, tagged, and released in the Hanford reach of the mid-Columbia River (see Figure 4.11). Releases occurred during the three years 1991-1993 in early to mid June. They were recaptured at McNary Dam, which is 121 kilometers downstream.
The basic travel time model (equation (4.7)) is applied to each cohort. Maximum likelihood estimates (equations (4.11) and (4.12) are calculated for r and 
, with 95 percent confidence intervals (based on equations (4.17) and (4.19)) constructed around these estimates. Also, X2 goodness-of-fit test for continuous data (as described in Chapter 3) is performed for each cohort. The computer code used to perform these algorithms is provided in appendix 3.
Table 4.4 - Table 4.6 (in the appendix of this chapter) contains parameter estimates, confidence intervals, and the results of the goodness-of-fit tests for each cohort. Since there is a large amount of information in these tables, I have condensed the results into summary statistics and plots.
It is clear from Table 4.4 - Table 4.6 that there is a great deal of variability in the parameter estimates within cohort sets. In particular, it appears that r increases through the season in some cases. I will analyze this variability in greater detail in the following chapters. In this chapter, I will present the means and standard errors of the cohorts for each of the cohort sets for qualitative comparisons (Table 4.3).
| Table 4.3 Summary statistics of the parameter estimates averaged on a yearly basis for each of the three cohort sets. | |||
|---|---|---|---|
| year | number of cohorts | mean value (standard error) | |
| r | | ||
| Snake River spring chinook | |||
| 1989 | 38 | 5.79 ( 1.41) | 8.44 ( 2.00) |
| 1990 | 13 | 6.71 ( 2.78) | 8.86 ( 3.64) |
| 1991 | 17 | 4.85 ( 1.82) | 6.38 ( 2.36) |
| 1992 | 6 | 4.50 ( 2.87) | 7.04 ( 4.50) |
| 1993 | 27 | 8.23 ( 2.37) | 7.81 ( 2.22) |
| Snake River steelhead | |||
| 1989 | 16 | 18.11 ( 6.68) | 15.57 ( 5.73) |
| 1990 | 27 | 12.97 ( 3.66) | 10.66 ( 3.01) |
| 1991 | 20 | 14.67 ( 4.84) | 11.02 ( 3.62) |
| 1992 | 18 | 10.86 ( 3.78) | 10.36 ( 3.62) |
| 1993 | 20 | 16.80 ( 5.50) | 13.66 ( 4.48) |
| mid Columbia fall chinook | |||
| 1991 | 2 | 3.33 ( 4.71) | 9.62 ( 13.65) |
| 1992 | 5 | 3.58 ( 2.53) | 6.93 ( 4.91) |
| 1993 | 6 | 3.79 ( 2.40) | 7.50 ( 4.76) |
From Table 4.3 it can be seen that the Snake River steelhead migrate at a substantially greater rate (approximately twice as fast) than the Snake River chinook, while the Snake River chinook migrate at a greater rate than the mid-Columbia fall chinook. The comparison between the Snake River steelhead and chinook is particularly relevant because they migrated in the same river reach during the same time period. The estimates of were slightly higher for the steelhead than the spring chinook and fall chinook, which were similar to each other.
Figure 4.14 is a plot of the goodness-of-fit test results for the Snake River chinook. While none of the years fall on the 45 degree line, some of the years have quite favorable results. The cohorts from 1989 perform the best overall, with cohorts from 1990, 1991, and 1993 also having the vast majority of p-values above 0.01. The cohorts from 1992 performed poorly relative to the others. 1992 was an extremely low flow year, and this may have affected the behavior of the fish.
The results of the goodness-of-fit tests for the Snake River steelhead (Figure 4.15) are not as favorable as with the chinook. In all years, at least 50 percent of the cohorts have p-values less than 0.01.The results from the mid Columbia fall chinook are also not favorable, with 8 out of 13 cohorts having p-values less than 0.001. This indicates that the model is not fully capturing the behavior of these two groups of fish.
Figure 4.16 contains plots of cumulative distribution functions from the fitted models for the Snake River chinook. The data are included in these plots. These example plots are from cohorts with a variety of p-values to demonstrate the range of model performance. It is clear from these plots that the model does well in describing the data. Even in the case where p = 0.001, there is not a wide departure between the model and the data. Figure 4.17 and Figure 4.18 contain similar plots for the steelhead and fall chinook. In these plots, cohorts with p-values below 0.001 were chosen to examine why the model failed. In the case of the steelhead, approximately 75 percent of the fish arrived during a very short period, with the remaining fish trickling in over a more extended period. The model could not capture this behavior. In the case of the fall chinook, it appears that most of the fish delayed migration (or migrated extremely slowly) for over 20 days and then started arriving at the dam. Again, the model could not capture this behavior.
