Critical Values for Şen’s Trend Analysis

Abstract

Trends in measured hydrologic data can greatly influence projected values; therefore, trends need to be identified and quantitatively modeled. First, it is necessary to verify whether or not a trend actually exists in the sample data. Tests of significance are most often used to verify whether or not a trend is statistically significant. Şen provided an easy-to-apply method of identifying the presence of trends in time series, but did not provide a quantitative method of verifying the statistical likelihood of an assumed trend in a measured time series [Şen, Z. 212. “Innovative trend analysis methodology.” J. Hydrol. Eng. 17 (9): 142–146]. A method of quantifying Şen’s approach is developed herein, with critical values of the test statistic developed to provide a means of making objective decisions. Critical values are presented for rejection probabilities from 1% to .1%. The power of the test, which is similar to that of other trend tests, is also approximated; analyses indicate powers from 1% to 3% for small samples.