Introduction

For some stocks of juvenile salmon, travel times through the Snake and Columbia Rivers have doubled since the development of dams (Raymond 1979), and thus mitigation efforts have focused on improving fish migration speed under the assumption that faster migration results in higher survival. One strategy to improve migration speed is to increase water velocity by either: (1) increasing flow from the storage reservoirs in the upper Columbia and Snake Rivers, or (2) lowering the reservoir levels (drawdown) behind the dams on the mainstem Columbia and Snake Rivers (NMFS 1995). The first approach increases water velocity by increasing river flow while maintaining reservoir volumes. The second approach increases velocity by decreasing the cross-sectional area of the river. Both actions have ecological and economic consequences. Draining the up-river storage reservoirs for the spring migration adversely affects resident fish in the storage reservoirs and uses water that could otherwise be used for power generation, irrigation, or augmenting flow for summer migrants. Drawdown has a number of unknown ecological impacts on the riverine habitat and complicates the dam passage of both juvenile and adult salmon. Thus, which ever method is used to improve fish migration rate it is essential that the action be used in the most effective manner possible.

The focus of this paper is to present a mathematical model for fish migration behavior that captures many of the basic factors controlling juvenile salmonid migration rate. The paper builds on earlier work (Zabel and Anderson 1996) that details an equation to determine the distribution of travel times for a cohort of fish migrating through a single river reach. In this earlier paper the downstream movement of a group of fish is characterized in terms of two parameters: an average migration rate and a rate of population spreading. In this paper we extend the model to multiple reaches and identify environment and fish specific factors that determine the migration rate for juvenile spring chinook. In addition, we develop statistical methods to extract parameters from data on the arrival times of cohort of fish through a series of dams.

Factors affecting migration timing of juvenile salmon have been the focus of several studies. In particular, flow has been demonstrated to be an important factor in determining travel times of yearling and subyearling chinook and steelhead through the Columbia and Snake Rivers (Berggren and Filardo 1993; Smith et al. 1993). From a mechanistic standpoint, the magnitude of the flow effect is determined by the fish's position in the river and the proportion of the day spent migrating. In the Hanford reach of the mid-Columbia, Dauble et al. (1989) found that subyearling chinook preferred shallow near-shore locations in slower river velocities, and yearling chinook smolts preferred deeper mid-channel locations where river velocities are greater. Bax (1982) determined that juvenile salmonids in the Hood Canal in Washington migrate close to the shore early in the season and further offshore later in the season. Mains and Smith (1964) demonstrated that the majority of subyearling chinook migration occurs at night in the Columbia and Snake Rivers. Yearling chinook have less of a tendency for strictly nocturnal migration (Bell 1958; Healy 1991). It is also clear that migration behavior varies during the season. Several researchers have demonstrated the importance of photoperiod (Hoar 1976; Giorgi et al. 1990; Muir et al. 1994) to migration rate and timing; accelerated photoperiod resulted in faster migration rates. Also, Johnson and Groot (1963) determined that migrating sockeye increased migration speed later in the season. They attributed this to an increased "migration drive."

This paper formulates migration models based on these studies and others in an effort to relate juvenile salmon travel times to measurable factors. We apply the models to a multi-reach system in which fish are observed at several points along the migration route. This allows determination of the change in migration rate as the fish migrate down the river. Model predicted travel times are compared to observed travel times at several points along the river. Using a nested sequence of nonlinear models, we relate migration rate to river flow, date in the season, and length of time in the river and determine the importance of these factors as formulated in the models.

The simplest model has a constant migration rate throughout the season. In most cases this is too simplistic, but the model serves as a comparison to other models. The second model assumes migration rate is linearly related to river velocity. The third model introduces a season/flow interaction that assumes the effect of river velocity increases as the season progresses. The fourth model adds a non-flow related experience effect. As the fish spend more time in the river, they migrate faster.

The migration model is applied to yearling chinook (Oncorhynchus tshawytscha) originating in the Snake River and is tributaries. The fish were captured at the Lewiston trap on the Snake River, fitted with PIT (passive integrated transponder) tags (Prentice et al. 1990), and released daily during the seven year period 1989-1996. PIT tags are small electronic tags that allow for individual fish to be identified as they pass each detection site. The fish were observed at Lower Granite and Little Goose Dams on the Snake River and McNary Dam on the Columbia River.

To demonstrate the utility of the model as a predictive tool, we compare our predictions of 1996 arrival distributions to the observations. The predictions are based on release distributions at Snake Trap, flow information, and model parameters obtained from the 1989-1995 data.