| AFFILIATIONS | - Charles University, Faculty of Science, Praha, Czechia
- Institute of Atmospheric Physics, Praha, Czechia
- Global Change Research Institute, Brno, Czechia
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| ABSTRACT | Detection of trends in climate elements and assessment of whether they are statistically significant are among the most important tasks in current climatology. The vast majority of studies only assesses the significance of trends at individual stations or grid points, that is, on a local level, providing no information on whether the occurrence of significant local trends is significant as a whole, that is, on a regional scale.
To fill this gap and provide a guidance on how to evaluate the regional-scale significance of trends, we compare five methods of assessing the collective (global, field) significance of local trends: (i) counts of trends of one sign regardless of their local (in)significance; (ii) counts of locally significant trends; (iii) multi-site Kendall test extended to compensate for spatial autocorrelation; (iv) Walker test, based on the smallest p-value (highest significance) of all local tests; (v) false detection rate, which can be considered a generalization of Walker test. The evaluation is based on synthetic data, consisting of 10,000 realizations of time series on a regular rectangular grid with a given spatial and temporal autocorrelation and magnitude of trend, assuming first-order autoregressive process both in time and space. The data are generated by software tool SPAGETTA (SPAtial GEneraTor for Trend Analysis). Time series with no trend are used to create null distributions of test statistics and determine the critical values of the tests. Type II errors, that is, the probability of accepting the null hypothesis of no trend when it is false, are assessed using time series with non-zero trends. We set the type II error of 5% as the limit of detectability of trends, and calculate the magnitude of a trend that can be detected with such an error for a wide range of spatial and temporal autocorrelations, grid sizes, and lengths of the series. The performance of tests is better (that is, trends of smaller magnitude are detected with type II error of 5%) for longer time series, larger grids, and lower autocorrelations. The multi-site Kendall and sign-counting trends perform best; the gap in the performance between them and the Walker and fdr tests gets narrower with increasing autocorrelations. The sign-counting test is, however, not applicable to cases with very high spatial autocorrelations because of its discrete nature.
The tests are applied to the detection of annual and seasonal temperature trends over the Meditarranean and adjacent parts of Europe, Africa, and North Atlantic, for various reanalyses and gridded datasets. The different performance of the tests is explained by different aspects of trends that they look at and by a different sensitivity to breaking their assumptions. |