Testing for trends on a regional scale: Beyond local significance

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  • 1 Dept. of Physical Geography and Geoecology, Faculty of Science, Charles Unversity, Prague, Czechia
  • 2 Institute of Atmospheric Physics, Czech Academy of Sciences, Prague, Czechia
  • 3 Global Change Research Institute, Czech Academy of Sciences, Brno, Czechia
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Abstract

Studies detecting trends in climate elements typically concentrate on their local significance, ignoring the question on whether the significant local trends may or may not have occurred due to chance. The present paper fills this gap by examining several approaches to detecting statistical significance of trends defined on a grid, that is on a regional scale. To this end, we introduce a novel simple procedure of significance testing, which is based on counting signs of local trends (sign test), and compare it with five other approaches to testing collective significance of trends (counting, extended Mann-Kendall, Walker, 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 Walker, fdr, and regression tests by quite 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: Walker and fdr tests for high temporal autocorrelations; sign test under high spatial autocorrelations.

Corresponding author: email huth@ufa.cas.cz

Abstract

Studies detecting trends in climate elements typically concentrate on their local significance, ignoring the question on whether the significant local trends may or may not have occurred due to chance. The present paper fills this gap by examining several approaches to detecting statistical significance of trends defined on a grid, that is on a regional scale. To this end, we introduce a novel simple procedure of significance testing, which is based on counting signs of local trends (sign test), and compare it with five other approaches to testing collective significance of trends (counting, extended Mann-Kendall, Walker, 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 Walker, fdr, and regression tests by quite 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: Walker and fdr tests for high temporal autocorrelations; sign test under high spatial autocorrelations.

Corresponding author: email huth@ufa.cas.cz
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