U.S. Geological Survey
Water-Resources Investigations Report 91-4040

By Terry L. Schertz, Richard B. Alexander, and Dane J. Ohe

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Computerized statistical and graphical procedures were developed for use in U.S. Geological Survey (USGS) investigations of trend in stream water-quality data. These procedures, identified as EStimate TREND (ESTREND), are described in this paper to assist USGS investigators involved in multiple-station studies of water-quality trends. Additional discussion focuses on certain statistical and operational decisions required in multiple-station analysis of trends. The statistical methods used in ESTREND overcome common statistical problems encountered by conventional statistical trend techniques in the analysis of water-quality data. The problems include data that are non-normal and seasonally varying and water-quality records with missing values, "less-than" (censored) values, and outliers, all of which adversely affect the performance of conventional statistical techniques. Parametric and nonparametric statistical trend tests are used in ESTREND. A nonparametric method, the Seasonal Kendall test, is used for data that have few less-than values or data that have been censored at only one reporting limit. A parametric test for trend involving a maximum likelihood estimation method is used for data that have been censored at multiple reporting limits. The Seasonal Kendall test for uncensored data allows for the removal of flow variability in water-quality data which improves the performance of the statistical trend tests. Menu-driven procedures in ESTREND allow the user to easily retrieve water-quality data, analyze data for trend, and view tabular and graphical results of analyses.






Purpose and Scope
Station and data characteristics

Geographic locations of stations

Sample collection

Period of record

Overview of statistical procedures for detection of trends in water quality data

Scope of the methods

Summary of the methods

Seasonal Kendall test for uncensored data

Seasonal Kendall test for censored data

Tobit test for censored data

Testing criteria

Statistical procedures for uncensored water-quality data

Seasonal Kendall test

Adjustment for seasonal effects in water-quality data

Selection of seasonal water-quality values

Selection of seasonal periods

Comparison of seasonal trends

Trend slope estimator

Interpretation of trend slopes

Trends in flow-adjusted concentration

Regression flow adjustment

LOWESS flow adjustment

Interpretation of flow-adjusted trends

Criteria for trend analysis of uncensored data

Estimates of moments and percentiles

Statistical procedures for censored water-quality data

Seasonal Kendall test

Criteria for trend analysis of censored data with the Seasonal Kendall test

Tobit test

Tobit trend slope estimate

Estimates of reporting limits in Tobit

Criteria for trend analysis of uncensored data with the Tobit test

Estimates of moments and percentiles

Data selection and management

ESTREND system

Overview of programs



Data files

Support files


Retrieval of water-quality data

Preparation of support files



Param info.file

Season info.file



Selection 1--make datafile

Selection 2--define seasons

Selection 3--run. seasonal comparisons

Selection 4--select best seasonal definition

Selection 5--select flow models or seasons

Selection 6--run trends

Selection 7--table results for a constituent

Selection 8--map results for a constituent

Selection 9--plot results

Selection 10--table results for all stations

Selection 11--table flow model information

Selection 12--table seasonal trend results


Appendix I: Subdirectory contents in ESTREND


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