Which spatial discretization for distributed hydrological models? Proposition of a methodology and illustration for medium to large-scale catchments

Abstract. Distributed hydrological models are valuable tools to derive distributed estimation of water balance components or to study the impact of land-use or climate change on water resources and water quality. In these models, the choice of an appropriate spatial discretization is a crucial issue. It is obviously linked to the available data, their spatial resolution and the dominant hydrological processes. For a given catchment and a given data set, the "optimal" spatial discretization should be adapted to the modelling objectives, as the latter determine the dominant hydrological processes considered in the modelling. For small catchments, landscape heterogeneity can be represented explicitly, whereas for large catchments such fine representation is not feasible and simplification is needed. The question is thus: is it possible to design a flexible methodology to represent landscape heterogeneity efficiently, according to the problem to be solved? This methodology should allow a controlled and objective trade-off between available data, the scale of the dominant water cycle components and the modelling objectives.

In this paper, we propose a general methodology for such catchment discretization. It is based on the use of nested discretizations. The first level of discretization is composed of the sub-catchments, organised by the river network topology. The sub-catchment variability can be described using a second level of discretizations, which is called hydro-landscape units. This level of discretization is only performed if it is consistent with the modelling objectives, the active hydrological processes and data availability. The hydro-landscapes take into account different geophysical factors such as topography, land-use, pedology, but also suitable hydrological discontinuities such as ditches, hedges, dams, etc. For numerical reasons these hydro-landscapes can be further subdivided into smaller elements that will constitute the modelling units (third level of discretization).

The first part of the paper presents a review about catchment discretization in hydrological models from which we derived the principles of our general methodology. The second part of the paper focuses on the derivation of hydro-landscape units for medium to large scale catchments. For this sub-catchment discretization, we propose the use of principles borrowed from landscape classification. These principles are independent of the catchment size. They allow retaining suitable features required in the catchment description in order to fulfil a specific modelling objective. The method leads to unstructured and homogeneous areas within the sub-catchments, which can be used to derive modelling meshes. It avoids map smoothing by suppressing the smallest units, the role of which can be very important in hydrology, and provides a confidence map (the distance map) for the classification. The confidence map can be used for further uncertainty analysis of modelling results. The final discretization remains consistent with the resolution of input data and that of the source maps. The last part of the paper illustrates the method using available data for the upper Saône catchment in France. The interest of the method for an efficient representation of landscape heterogeneity is illustrated by a comparison with more traditional mapping approaches. Examples of possible models, which can be built on this spatial discretization, are finally given as perspectives for the work.