Testing for Trends on a Regional Scale: Beyond Local Significance

Studies detecting trends in climate elements typically concentrate on their local significance, ignoring the question of whether the significant local trends may or may not have occurred as a result of chance. This paper fills this gap by examining several approaches to detecting statistical significance of trends defined on a grid (i.e., on a regional scale). To this end, we introduce a novel simple procedure of significance testing that is based on counting signs of local trends (sign test), and we compare it with five other approaches to testing collective significance of trends: counting, extended Mann-Kendall, Walker, false detection rate (FDR), and regression tests. Synthetic data are used to construct null distributions of trend statistics, to determine critical values of the tests, and to assess the performance of tests in terms of type-II error. For lower values of spatial and temporal autocorrelations, the sign test and extended Mann-Kendall test perform slightly better than the counting test; these three tests outperform the Walker, FDR, and regression tests by a wide margin. For high autocorrelations, which is a more realistic case, all tests become similar in their performance, with the exception of the regression test, which performs somewhat worse. Some tests cannot be used under specific conditions because of their construction: the Walker and FDR tests for high temporal autocorrelations, and the sign test under high spatial autocorrelations.