Compound Risk Assessment of Low River Flows and High Urban Runoff: Frequency of critical drainage conditions in relation to pollutant inputs

Abstract. Urbanization and climate variability increasingly intensify hydrological extremes that impair water quality. A critical compound stress arises when pollutant-rich urban runoff coincides with limited river dilution capacity. To characterize this interaction, we analyze compound events in two directional modes: (i) low river flow paired with corresponding urban runoff, and (ii) high urban runoff paired with concurrent river flow. While these modes represent distinct pathways leading to loss of dilution capacity, the underlying variables exhibit weak and inconsistent dependence, limiting the applicability of conventional bivariate extreme value approaches. To address this limitation, we introduce the Urban-Runoff-to-River-Flow ratio as a direct indicator of dilution stress. A ratio-based extreme value framework is developed using both block maxima and peak-over-threshold approaches, with parameters estimated via maximum likelihood and L-moment methods. The analysis is based on more than two decades of discharge data from three catchments in Lower Saxony, Germany, representing contrasting hydrological regimes. Model performance and compound risk estimates are evaluated against two reference benchmarks: (i) a synthetic benchmark derived from marginal extremes under independence assumptions, and (ii) a conditional benchmark based on historically co-occurring events. Results show that conditional approaches systematically underestimate compound risk in weakly dependent systems, while synthetic estimates provide an upper bound by enforcing coincidence of extremes. In contrast, the ratio-based approach captures the interaction between pollutant loading and dilution capacity more consistently across sites. Overall, the proposed framework provides a robust and physically interpretable method for assessing compound dilution stress, particularly in systems where dependence between drivers is weak or unstable.