Regional frequency analysis (RFA) is commonly used to improve design-rainfall estimates by combining information from multiple rain gauges within a generally homogeneous region of influence (ROI), where stations are expected to exhibit broadly similar extreme-rainfall characteristics. In particular, partial duration series approaches are attractive in RFA because they make use of all threshold exceedances rather than just annual maxima. While applying RFA to rainfall datasets using the station-year method, I became increasingly interested in a seemingly simple question: when we pool extreme rainfall observations from many stations, are we really counting independent events? For instance, if a large storm moves across a monitoring network, the same storm may generate exceedances at several stations that are subsequently treated as separate events. This violates the independence assumption that underpins most frequency-analysis methods and raised an important question for us: could these repeated storm observations systematically bias rainfall-frequency estimates?  

Rather than using complex dependence models, we sought a practical solution that could be implemented using commonly available rain-gauge data. The idea was simple: if two exceedances occur at nearby stations and the timing between them is consistent with the travel time of a moving storm, they may not represent independent events. To formalize this concept, we developed a dual-criterion framework based on storm motion and station proximity. Candidate dependent exceedances were connected in a graph, where each exceedance was represented as a node and edges indicated likely dependence. Using network-analysis methods, connected exceedances formed clusters that were interpreted as resulting from the same storm system. We then retained only the largest exceedance within each cluster when constructing the regional partial duration series (rPDS).  

An important design goal of this work was simplicity and transferability. Modern weather-radar datasets contain detailed information that can often be used to identify storm footprints directly. However, many regions around the world either lack high-resolution radar observations or do not maintain long-term radar archives suitable for frequency analysis. We therefore sought a method that relies primarily on information commonly available from rain-gauge networks. By using only storm motion, station proximity, and exceedance timing, the proposed framework can be implemented in a wide range of practical settings without requiring specialized datasets or computationally intensive analyses. 

One particularly rewarding aspect of the study was testing this simplified framework against a weather-radar dataset. By visually examining radar-derived storm footprints, we were able to verify whether exceedances flagged as dependent truly originated from the same storm. Despite its simplicity, the framework achieved surprisingly high agreement with radar observations, yielding more than 90% accuracy in three manually validated cases involving more than 3,000 dependent exceedance clusters. The validation process was far more involved than a simple statistical comparison. For each selected ROI defined for applying RFA, we examined radar animations together with station locations and rainfall time series to determine whether exceedances assigned to the same cluster actually originated from a common moving storm system. This manual examination included situations involving storm merging, storm splitting, nearby convective cells, and more diffuse stratiform rainfall structures.  

Beyond identifying dependent exceedances, we also wanted to quantify their influence on rainfall-frequency estimates, namely the depth-duration-frequency (DDF) values. For this purpose, we developed a dependence metric, denoted r(x), which measures how spatial dependence alters the exceedance distribution at different rainfall magnitudes (x). The metric revealed an important result: spatial dependence does not affect all parts of the distribution equally. Naturally, moderate storms and exceedances are far more frequent than rare storms and exceedances. Because of this, rPDSs overrepresent moderate exceedances relative to rare extremes. Based on this simple intuition and the existing literature, we theoretically validated our method and derived relationships for r(x). Specifically, r(x) ≥ 1 for x ∈ Qbody ​, whereas r(x) ≤ 1 for x ∈ Qtail​.  Here, Qbody and Qtail denote the low-to-moderate rainfall depths (body of the distribution) and extremely large exceedances (tail of the distribution), respectively. Our results confirm this behavior, validating that our method enhances the spatial independence of regional partial duration series. The implication of these results is that dependence systematically changes the shape of the fitted distribution rather than merely shifting it upward or downward. Across the analyzed short durations (10, 15, 20, 30, 45, 60, 90, and 120 minutes), this effect translated into average overestimations of approximately 14% for 1-year average recurrence interval (ARI) events and underestimations of about 5% for 100-year ARI events. These biases can lead to unnecessarily conservative designs for low-risk infrastructure while simultaneously underestimating design rainfall for infrastructure intended to withstand rare, high-impact events. By improving the spatial independence of regional partial duration series, the proposed framework provides more reliable rainfall frequency estimates for hydrologic design, flood-risk assessment, and infrastructure resilience planning.

As is often the case in research, the study continued to evolve during peer review. The thoughtful comments of the editor and reviewers helped strengthen both the theoretical and experimental aspects of this work and improve the final manuscript.  Looking back, several important improvements to both the mathematical development and the practical evaluation emerged directly from this process. We are grateful to Paula Meier for helping us with the schematic illustrating the concepts of storm motion and spatial dependence. We are also grateful to Koshika Timsina for her assistance with the manual validation.

 What I find most encouraging about this work is that a relatively simple framework can materially improve rainfall-frequency estimates without requiring additional observations or highly complex modeling. More broadly, it highlights how seemingly minor assumptions in widely used methods can have important consequences for engineering design and risk assessment. As observational networks become denser and datasets continue to grow, accounting for spatial dependence will become increasingly important. We hope that this approach provides both researchers and practitioners with a practical pathway toward more reliable design-rainfall estimates and improved flood-risk assessments.