STATISTICAL METHODS AND SAMPLING DESIGN FOR ESTIMATING STEP TRENDS IN SURFACE‐WATER QUALITY1

Abstract

ABSTRACT: This paper addresses two components of the problem of estimating the magnitude of step trends in surface water quality. The first is finding a robust estimator appropriate to the data characteristics expected in water‐quality time series. The Hodges‐Lehmann class of estimators is found to be robust in comparison to other nonparametric and moment‐based estimators. A seasonal Hodges‐Lehmann estimator is developed and shown to have desirable properties. Second, the effectiveness of various sampling strategies are examined using Monte Carlo simulation coupled with application of this estimator. The simulation is based on a large set of total phosphorus data from the Potomac River. To assure that the simulated records have realistic properties, the data are modeled in a multiplicative fashion incorporating flow, hysteresis, seasonal, and noise components. The results demonstrate the importance of balancing the length of the two sampling periods and balancing the number of data values between the two periods. The inefficiency of sampling at frequencies much in excess of 12 samples per year is demonstrated. Rotational sampling designs are discussed, and efficient designs, at least for this river and constituent, are shown to involve more than one year of active sampling at frequencies of about 12 per year.