Introduction

This paper focuses on the travel time of outmigrating juvenile salmonids. The length of time juveniles migrate downstream has several implications for salmon populations. During outmigration juvenile salmon undergo a series of physiological and behavioral changes called smoltification, preparing them for saltwater (Hoar 1976). Since arrival to the estuary is coordinated with smoltification (Folmar and Dickhoff 1980), outmigration timing is important to ensure that smolts reach saltwater when they are physiologically ready. From a management standpoint, the ability to predict fish arrival time distributions at dams aids in directing hydrosystem operations to enhance fish survival. The results presented here are currently being used in the Columbia River Salmon Passage (CRiSP) model (Anderson, et al. 1996), a system model that describes smolt passage and survival.

Our approach to the travel time problem is to develop a probabilistic model of the process. The model is based on an advection-diffusion equation, which describes the spatial and temporal distribution of a migrating population. Travel time through a river reach is expressed by first-passage time to the end of the reach. Diffusion-based models have been applied to many dispersing populations (see (Okubo 1980) for a review). The advection term adds directed movement, allowing the population to move downstream. We expand upon previous applications of advection-diffusion equations to fish migration (Saila and Flowers 1969; DeAngelis and Yeh 1984; Hiramatsu and Ishida 1989; Crittenden 1994) by including a first-passage component and a detailed statistical analysis.

The model is evaluated using data on the migration of yearling chinook salmon Oncorhynchus tshawytscha through the Lower Granite Reservoir of the Snake River, the primary tributary of the Columbia River. Active migrants were collected in the river, marked with a PIT (passive interrogative transponder) tag, and released at the head of the reservoir. PIT tags give the exact time of crossing at downstream interrogation sites (Prentice, et al. 1990), so a travel time distribution can be determined for a cohort of fish released at a single time. For each cohort, model parameters are estimated using maximum likelihood, and goodness-of-fit is assessed using Pearson's X² test.