DETECTABILITY OF STEP TRENDS IN THE RATE OF ATMOSPHERIC DEPOSITION OF SULFATE¹

Abstract

A method is presented to assist policy makers in determining the combination of number of sampling stations and number of years of sampling necessary to state with a given probability that a step reduction in atmospheric deposition rates of a given magnitude has occurred at a pre-specified time. This pre-specified time would typically be the time at which a sulfate emission control program took effect, and the given magnitude of reduction is some percentage change in deposition rate one might expect to occur as a result of the emission control. In order to determine this probability of detection, a stochastic model of sulfate deposition rates is developed, based on New York State bulk collection network data. The model considers the effect of variation in precipitation, seasonal variations, serial correlation, and site-to-site (cross) correlation. A nonparametric statistical test which is well suited to detection of step changes in such multi-site data sets is developed. It is related to the Mann-Whitney Rank-Sum test. The test is used in Monte Car10 simulations along with the stochastic model to derive statistical power functions. These power functions describe the probability of detecting (&0.05) a step trend in deposition rate as a function of the size of the step-trend, record length before and after the step-trend, and the number of stations sampled. The results show that, for an area the size of New York State, very little power is gained by increasing the number of stations beyond about eight. The results allow policy makers to determine the tradeoff between the cost of monitoring and time required to detect a step-trend of a given magnitude with a given probability.

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.…”

Detecting acid precipitation impacts on lake water quality

“…We present this example, however, to suggest that our choices of P0 = 0.0, 0.20, and 0.40 in Figures 2 and 3 have some relevance to a real-world situation. In the example, no attempt was made to relate interlake correlations to distance between lakes, although this would be a logical next step in the analysis of a particular region for which adequate data were available (Hirsch and Gilroy, 1985).…”

TIME SERIES ANALYSIS IN PERSPECTIVE1

“…In the section on Data Analysis, references are given for a range of data filling procedures. A procedure in this set of papers which can be used with unevenly spaced data is the nonparametric statistical test of Hirsch and Gilroy (1985) for detecting step changes in multisite data sets.…”

“…The statistical effects of natural or man-made interventions upon the mean levels of a series can often conveniently be modeled using an intervention model which is, in essence, a special kind of TFN model @pel and McLeod, 1986). Various approaches for modeling nonstationarity in the form of trends are presented by authors such as McLeod, et al (1983), and Hirsch and Gilroy (1985).…”