A Deterministic-Based Model to Apply Type-Based Statistics for Ungauged Catchments

In the previous Chap. 15, a methodology was proposed to directly regionalise the statistical model for consistent stochastic simulations of flood peaks, volumes and shapes of hydrographs under consideration of flood types. However, in practise often a different approach is required: the regionalisation of a deterministic model to generate flood series for which then flood frequency analyses can be performed. By using a deterministic model, it is possible to determine the complete flood hydrograph using long precipitation series, which are usually available more frequently than runoff series. However, the demands on deterministic models are high if they are to be applied to unobserved watersheds and the diversity of possible flood events. The parameters should have a physical meaning and the model should be applicable for different hydrological processes alike (e.g., flow from saturated areas, runoff processes driven by rainfall intensities, snow retention etc.). There is some contradiction in using a model with a small number of meaningful parameters and representing the complex processes of flood formation. A deterministic model is suitable for all situations in which the processes taking place are completely determined by known initial and boundary conditions. This is not the case for flood generation, where only the meteorological drivers are known. However, deterministic models can also incorporate stochastic aspects by incorporating randomness into certain parameters or inputs. Here, a simple deterministic model is proposed that takes into account the differences between flood types by considering different input distributions for the initial conditions, the main parameters and the meteorological drivers. More precisely, a model chain is proposed that can be used to obtain not only the peak for a given return period, but the flood-type specific flood volume corresponding to the flood peak. The generation of these pairs, which are identical in their statistical distribution to the observed ones, is obtained solely by combining the distribution of the precipitation sum, the runoff coefficient and a relation between flood peak and volume. This allows for a regionalisation of the stochastic event generator without considering additional catchment, precipitation or runoff attributes. Based on these generated samples, flood frequency analyses can be performed for the ungauged basins, confidence bands can be derived as well as a generation of synthetic design hydrographs.