Performance Evaluation of four Statistical Tests for Trend and Non-stationarity and Assessment of Observed and Projected Annual Maximum Precipitation Series in Major United States Cities

In this study, the performance of four statistical tests was evaluated to assess the following time-series types: stationary in variance and trend in mean (S_T), stationary in variance and no trend in mean (S_NT), nonstationary in variance and trend in mean (NS_T), and nonstationary in variance and no trend in mean (NS_NT). The four statistical tests included two stationarity tests, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Philips and Perron (PP) tests, and two trend tests, the Mann-Kendall (M-K) and regression tests. In each case, the sample size, standard deviation for noise, and several parameters were randomly generated to produce 1000 samples. The four tests were then conducted to determine if the data were stationary or non-stationary with trend or without trend. The results showed that there are several important patterns depending on the conditions of Monte Carlo experiments to investigate the performances of the four statistical tests with the four time-series types. These tests were also conducted to evaluate the time-series types of the observed and projected annual daily maximum precipitation series in eight cities of the United States. Results showed that cases of S_NT, which is the general assumption for the classical statistical frequency analysis, became less represented, while the two trend cases (NS_T and S_T) became more represented as time went on from HIST (1950–1999) to a representative concentration pathway (RCP) 4.5 or RCP 8.5 (2000–2099). NS_T cases in RCP 8.5 occurred more frequently than those in RCP 4.5. These results suggest that because of climate change, the assessment of time-series types should be considered when examining annual maximum precipitation and designing water-related infrastructure.