Critical assessment of metrics and methods used to quantify temporal loading of rainfall events

Abstract. The distribution of rainfall over a storm's duration, known as the event temporal loading, can significantly influence hydrological and geomorphological responses, including run-off generation, urban flood risk, and soil erosion. A wide range of approaches have been developed to analyse rainfall event temporal loading, but these differ in how they characterise rainfall behaviour and in the aspects of storm structure they emphasise. Early research further suggests that climate change may alter rainfall temporal loading in complex and regionally dependent ways, underlining the importance of clear and consistent approaches to its quantification. In this study, we identify 52 metrics that have been applied to describe event temporal loading, and categorise them as classification metrics, summary statistics, or intermittency metrics. We calculate these metrics for 233,128 rainfall events recorded at Danish rain gauges, and demonstrate that, while some metrics are robust to changes in rainfall event temporal resolution and pre-processing, others are highly sensitive. Data-driven cluster analysis further reveals how various metrics relate to one another, highlighting groups of metrics that may be used interchangeably, and others that describe fundamentally different properties. Based on this, we conceptualise five aspects of temporal loading (mass timing, peak timing, magnitude concentration, temporal concentration, and intermittency) and recommend metrics to quantify each. Overall, the study provides a foundation for more deliberate and informed metric selection, helping to align research questions with appropriate representations of rainfall temporal loading, and offering a clearer basis for cross-study comparison.