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

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.

Trend Assessment for Groundwater Pollutants: A Brief Review and Some Remarks

“…Various statistical methods are available for identifying and locating steps in a time series [46][47][48]. Piecewise LR is used to detect significant changes in a trend (breakpoints), which means there are two different linear relationships in the data with a sudden, sharp change in direction.…”

Water Quality Monitoring and Network Design

“…The use of most of these techniques is shown by data analyses, often including regression techniques and standard error criteria in estimation of parameters that relate to the information conveyed by data (HipeI, 1988;Hirsch, 1988;Lettenmaier, 1988;Tirsch and Male, 1984;. For example, Gupta (1982) uses the Modified Langbein Method, which is essentially based on regression techniques, to maximize information gain via optimum data lengths determined for primary and secondary gaging stations.…”

“…Yet sufficient amount of research effort has not been devoted particularly to this aspect of the design problem. Among the few available, one may refer to Hirsch (1988) who compares long-term continuous sampling versus rotational sampling where data are collected in bursts of sm all periods. Hirsch claims that more research is needed in this area because his results, although very interesting, could not be generalized for practical network design before the approach is tested on other sets of data.…”

Some effects of sampling design on water quality estimation in streams / Quelques effets de la stratégie d’échantillonnage sur l’estimation de la qualité de l’eau des rivières

“…However, this is not realizable for variables such as alkalinity at the Hore. This difficulty suggests setting a threshold on what is thought to be a scientifically significant trend, and then sampling with sufficient frequency to detect such a trend over a specified time period (Hirsch, 1988).…”