A Markov chain analysis of fish movements to determine entrainment zones

Abstract

Abstract Fish can become entrained at water withdrawal locations such as fish bypasses, hydroelectric turbines, and power plant cooling water intakes. Accordingly, the size of a fish entrainment zone (FEZ) is often of interest to fisheries managers and facility operators because of the need to protect fish from injury or mortality. This study developed a new technique to map the FEZ, defined here as the region immediately upstream of a portal where the probability of fish movement toward the portal is greater than 90%. To map the FEZ, we applied a Markov chain analysis to fish movement data collected with an active fish tracking sonar. This sonar device locked onto and followed fish targets, recording their positions through a set of volumetric cells comprising the sampled volume. The probability of a fish moving from one cell to another was calculated from fish position data. These probabilities were used to populate a Markov transition matrix. In 2000, we developed and applied the technique using data on salmon smolts migrating near the ice/trash sluiceway at The Dalles Dam on the Columbia River. The FEZ of the sluiceway entrance as determined with this procedure was approximately 5 m across and extended 6–8 m out from the face of the dam in the surface layer 2–3 m deep. In conclusion, using a Markov chain analysis of fish movement data, we were able to describe and quantify the FEZ of the sluiceway at The Dalles dam. This Markov chain analysis could be used in a comparative before/after study to look at changes in FEZ caused by engineered structures. The technique is generally applicable to bio-engineering efforts aimed at protecting fish populations affected by water withdrawals.