An Empirical Approach for Estimating the Precision of Hydroacoustic Fish Counts by Systematic Hourly Sampling

Abstract

Systematic hourly sampling is a logistically favorable method for hydroacoustic estimation of fish passage through constricted passageways or finite sections of a river monitored by fixed-location sonar systems. Similar to simple random and hourly stratified random sampling, systematic hourly sampling produces unbiased estimates of fish passage. Variances of estimates produced by systematic hourly sampling are determined by the sampling fraction, f, variance of the underlying process, S², and correlations among all hourly strata of the process. This intrahour correlation dependency makes it difficult to accurately evaluate the precision of the estimate when the complete temporal pattern of the process is unavailable. Fish passage is rarely counted continuously, so the uncertainty of estimated mean by systematically subsampled fish counts is traditionally estimated using variance estimators. Variance estimates by these estimators are likely biased and subject to potentially large errors. We present an alternative approach for estimating the precision of systematic hourly sampling using an empirical relation between precision and sampling fraction established from continuous fish counts acquired by imaging sonar for a wide range of migration scenarios of Pacific salmon Oncorhynchus spp. in the lower Fraser River. The empirical relation indicates that a CV (100·SD/mean) of 5.5% can be achieved by the systematic hourly counting of fish passage at a counting effort of 10 min/h, while increasing the counting effort to 20 min/h only leads to a marginally improved CV of 4.1%. The data-based analysis also shows that the precision of systematic sampling can be gained more efficiently and consistently by increasing the sampling rate than by lengthening the sampling time.

Received June 6, 2013; accepted January 21, 2014

ACKNOWLEDGMENTS

We thank the crew of the Pacific Salmon Commission's (PSC) hydroacoustic program for acquiring the sonar data for this study. Andrew P. Gray, Jacqueline L. Nelitz, Michael J. Bartel Sawatzky, and Joe D. Enns provided the full-count data. Suzanne L. Maxwell of Alaska Department of Fish and Game generously provided us with useful references on fish-counting methods in Alaska's major salmon production rivers. The PSC librarian Teri L. Tarita offered excellent assistance in the literature search and helped improve the English of the manuscript. This work was partially funded by the PSC Southern Boundary Restoration and Enhancement Fund.