STATISTICAL METHODS AND OPTIMAL SAMPLING DESIGNS FOR DETECTION OF AQUATIC ECOLOGICAL CHANGE (TIME SERIES, JACKKNIFE)

Aquatic monitoring programs can have many objectives, including estimation of environmental parameters, detection of standards violations, and detection of changes associated with large scale projects, such as electric power or wastewater treatment plants. Four basic models for aquatic monitoring data collected for a program whose objective is the detection of ecological change are described in detail. The models are distinguished by the type of change hypothesized (step vs. ramp), and the assumption on the error distribution (independent vs. spatially correlated). The sampling cost is assumed to be the sum of a fixed initial cost plus components for replicates, number of stations visited, and number of sampling occasions. Three ways of optimizing a sampling program based upon one of the four models are discussed: maximizing power for a fixed cost, minimizing cost for a fixed power, or minimizing type I error probability for a fixed cost and power. All optimization problems are solved using a Lagrange Multiplier Formulation. The resulting system of constrained nonlinear equations is solved using a modified Newton-Raphson method. Sensitivity analyses show that the monitoring design is relatively robust with respect to the decision variables as long as the power associated with the optimal design is modest.

Analysis of some typical equatic monitoring data shows that while the errors are highly spatially correlated, temporal correlation is negligible. A Monte Carlo study shows that the type I error is inflated above the assumed (alpha)-level when errors are positively correlated in space or time.

Models incorporating spatially correlated errors are based upon standard multivariate theory. Models that allow for temporally correlated errors are not considered as bases for monitoring program optimization due to the intractable nature of the power function for small to moderate sample sizes. Some new methods for performing hypothesis tests for linear regression models with autocorrelated errors for small sample sizes are presented. The most successful method relies on a jackknifed estimate of standard deviation, and performs better (in terms of maintaining the assumed (alpha)-level) than the usual likelihood-based tests.

A general guide to designing aquatic monitoring programs based upon the results and methods of this dissertation is presented.