Abstract
An inverse model is proposed to calculate unit hydrographs as well as the impulse response of fluxes from rainfall‐runoff or rainfall‐flux data, the purpose of which is hydrograph separation. Contrary to what hydrologists have been doing for years, hydrograph separation is carried out by using transfer functions in their entirety, which enables accurate separation of fluxes. All the components that participate in the global hydrologic balance are calculated in order to fit historical and computed flow and fluxes. The effective rainfall and the effective input fluxes are calculated from inversion. Unit hydrograph as well as impulse response of fluxes are decomposed into a quick and a slow component, and, consequently, the effective rainfall is decomposed into two parts, one contributing to the quick flow (or flux) and the other contributing to the slow flow generation. A regularization method is proposed to inverse the problem, whatever the degree of stability of the numerical systems since the regularization parameters are optimized. This regularization method borrows most of its principles from the L curve theory. The inverse method is applied to understand the mechanisms affecting nitrate transport in the Coët‐Dan catchment, Brittany (France), where high levels of nitrate pollution result from intensive agriculture. The hydrograph response to dissolved species is decomposed into quick and slow components, the former being separated into two subcomponents related to shallow and deep groundwater, respectively. Variable pollution levels and efficient denitrification of deep groundwater through pyrite oxidation lead to variable chemical composition in the groundwater column. By using nitrate and sulfate fluxes, the slow component of the unit hydrograph response can be separated into nitrate‐contaminated and denitrified groundwater responses to rainfall, which enables an accurate assessment of the denitrification capacity of the catchment.
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