Results

Table 2 . Parameter estimates, standard errors, sum of squares, and R2 for the four migration rate models for all cohorts in the years 1989 - 1996. The model 4 parameter estimates for the cohorts with the 1996 data omitted are also provided. The units for MIN and MAX are km/day. FLOW and are non-dimensional. TSEASN has units of Julian date, and 2 has units km2/day. For model 4, the listed in this table corresponds to 2 in equation eq (11). For models 1-3, MIN in this table corresponds to 0.
model	parameter estimates (standard error)					2	resid. ss	R2
	MIN	MAX	FLOW		TSEASN
1	10.52 (0.798)	-	-	-	-	323.30 (9.00)	9634.487	-
2	0.686 (0.149)	-	0.893 (0.038)	-	-	185.02 (4.74)	4603.405	0.522
3	2.75 (0.126)	-	0.666 (0.085)	0.118 (0.017)	115.57 (2.72)	140.95 (3.19)	2104.099	0.782
4	2.27 (0.196)	13.72 (2.25)	0.517 (0.031)	0.093 (0.0093)	119.03 (2.61)	159.01 (3.36)	1233.628	0.872
41	2.45 (0.383)	12.60 (2.14)	0.541 (0.150)	0.105 (0.034)	119.72 (4.69)	152.08 (3.32)	1136.256	-

The linear flow component (model 2) explains 52.2 percent of the variability in the first model. This model yields a flow-independent migration rate of 0.686 km per day, and the fish utilize 89.3 percent of the river velocity. The plot in Figure 3 shows that although this model offers an improvement over the first, quite a bit of spread and bias is evident.

Figure 3 . Observed average travel times versus modeled average travel time for each of the four migration rate models. The travel times are from Snake Trap to each of the observation sites - Lower Granite, Little Goose, and McNary Dams. Each point represents a cohort at a single observation site; therefore, each cohort is represented three times in each plot.

Introducing a flow/season interaction (model 3) substantially improves model performance; The R² increases to 0.782. With this model, the fish use less river flow before the seasonal inflection point (day 116 or April 26 in non-leap years) and substantially more later in the season. It is clear from Figure 3 that this model underestimates shorter travel times and overestimates longer travel times.

The experience factor added to the non-flow term (model 4) corrects the bias of model 3, with the R² increasing to 0.872. The flow-independent maximum migration rate (_MAX) is over 11 km per day faster than the minimum rate (_MIN). Model 4 yields essentially unbiased predictions over the entire range of observed travel times, and the standard errors are relatively small compared to the parameter values indicating that this model is stable.

Another interesting feature is that as model performance improves, the estimated value for ² decreases. Recall that ² describes the rate of spreading of the cohort as it moves downstream. Some of the variability ascribed to population spreading in the less complex models is really due to lack of fit of the migration rate model. As the ability to predict migration rate improves, so does the precision of predicting the individual cohort's behavior.

The results of the 1996 passage predictions are contained in Figure 4. Model 4 successfully predicts the arrival distributions at the first two sites, Lower Granite and Little Goose. At McNary Dam, the early fish migrate faster than expected, but after 80 per cent passage, the model is very consistent with the data.

Figure 4 . Comparisons of predicted and observed cumulative passage versus date at the three observation sites for the 1996 migration year. The solid line represents the data, and the dotted line represents the model prediction. The prediction is based on parameters derived from 1989-1995 data. One set of parameters is used to generate predictions to all three sites. Day 100 is April 10 in non-leap years.