Which grid points are statistically significant? Revisiting false discovery rate correction in geospatial data

Scientific publications in the geosciences routinely assess statistical significance in spatially distributed environmental and geophysical data. When statistical significance is indicated, it is most often assessed independently at each grid point, while formal adjustment for multiple testing is rarely applied. However, applying multiple testing corrections, such as the global false discovery rate (FDR) approach is not always straightforward, as environmental and geophysical data are often spatially correlated.

In our work, we highlight how neglecting multiple testing correction can substantially inflate the number of false positives. We further show that commonly used FDR implementations can yield counterintuitive and potentially misleading results when applied to strongly spatially correlated data.

To illustrate the latter point, we provide an example based on near-surface air temperature composites following sudden stratospheric warmings. We first show that when anomalies are spatially coherent, restricting the spatial domain can increase the FDR-adjusted significance threshold. As a result, the same underlying field may display a larger share of statistically significant grid points solely due to domain selection. We analyze the origin of this behavior from a rank-based perspective and discuss its implications for spatial inference and uncertainty quantification in environmental sciences.

Based on these insights, we propose practical recommendations for robust and transparent significance assessment, such as spatially aggregated or spatially aware alternatives. Our results highlight both the need to account for multiple-testing and potential issues with a naïve application and interpretation of FDR correction. While illustrated using atmospheric data, the findings are directly relevant to hydrology and other environmental sciences where statistical significance is assessed across spatial fields.