A simple method for enhancing the spatial independence of regional partial duration series in extreme, short-duration rainfall frequency analyses

Abstract

Regional frequency analyses (RFA) using partial duration series (PDSs) generally produce more reliable rainfall depth-duration-frequency (DDF) estimates than those based on annual maxima. A common implementation of this approach, the station-year method, pools threshold exceedances across multiple sites within a region to construct a regional PDS (rPDS). However, there may be instances in which a specific rainstorm evolving over the region produces multiple exceedances (at different rain gauges) that happen to be selected in the rPDS; the resulting spatial dependence violates the independence assumption fundamental to frequency analysis. Furthermore, the nature and consequences of this spatial dependence on DDFs across the range of average recurrence intervals (ARIs) remain poorly understood. We address this gap with two contributions. First, we propose a dual-criterion filtering algorithm based on a highly simplified description of the motion of a rainstorm, to ensure that most events included in a rPDS are spatially independent. Second, we develop a mathematical framework to characterize how spatial dependence biases DDF values. Manual verification using radar-derived spatiotemporal footprints of storms show that the algorithm identifies and removes spatially dependent exceedances with above 90% accuracy. Theoretical analyses further establish its statistical consistency and engineering relevance. Results from 137 German stations reveal that the conventional station-year method systematically overestimates DDF values at low ARIs and underestimates them at high ARIs. This bias stems entirely from the inclusion of spatially dependent exceedances in the rPDS. Using the proposed filtering algorithm increases the accuracy of DDF estimates by enhancing the independence of the exceedances used for frequency analysis.