Scale Dependence of Stochastic-Deterministic Flood Statistics

Scale dependencies are a core element of hydrological sciences. The inclusion of deterministic aspects in flood statistics requires a cross-scale approach that takes into account the differences in flood generation and, in particular, the importance of local and regional processes as well as the interdependencies of flood waves at different spatial scales. The interaction of meteorological drivers with the spatially and temporally variable catchment conditions, e.g. antecedent soil moisture, snow cover or confluences, determines a variety of flood events that are scale-dependent. For example, heavy rainfall floods usually lead to extremely large flood peaks if the catchment is small and has a critical size relative to the spatial extent of the rain cell. The situation is different for synoptic rainfall, where large basins are affected and the total rainfall and the superposition of floods from tributaries can lead to extreme events. Thus, the consideration of flood generation becomes more complex when large river basins are considered instead of small catchments. In addition to the meteorological and catchment-specific factors, the interaction between the individual sub-catchments must also be taken into account. In particular, the superposition of flood waves from tributaries can critically alter the flood hydrograph. How such differences can be determined statistically-deterministically and how the individual factors can be taken into account in a statistical model for estimating design floods is presented here. Univariate mixture models for local floods as well as multivariate statistical models for regional floods help to better understand floods and their development. Their relevance on different spatial scales is discussed here. The result forms the basis for improved flood modelling that extends the classical peak-based flood frequency analysis by essential spatial aspects.