Technical Note: Streamflow Seasonality using Directional Statistics

Abstract. Hydrological fluxes typically vary across seasons, with several existing metrics available to characterize their seasonality. These metrics are beneficial when many catchments across diverse climates and landscapes are studied concurrently. Here, we present directional statistics to characterize streamflow seasonality, capturing the timing of streamflow (center of mass) and the strength of its seasonal cycle (concentration). We show that directional statistics is mathematically more robust than several widely used metrics to quantify streamflow seasonality. We extend the application of directional statistics to analyse seasonality in other hydrological fluxes, including precipitation, evapotranspiration, and snowmelt, and we introduce a trend analysis framework for both the timing and strength of seasonal cycles. Using an Alpine catchment (Dischma, Switzerland) as a testbed for this methodology, we identify a shift in the streamflow center of mass to earlier in the year and a weakening of the seasonal cycle. Additionally, we apply directional statistics to streamflow data from 11,118 European catchments, highlighting its utility for large-scale hydrological analyses. The introduced metrics, leveraging directional statistics, can improve our understanding of streamflow seasonality and associated changes, and can also be used to study the seasonality of other environmental fluxes, within and beyond hydrology.