The importance of topography-controlled sub-grid process heterogeneity and semi-quantitative prior constraints in distributed hydrological models

Abstract. Heterogeneity of landscape features like terrain, soil, and vegetation properties affects the partitioning of water and energy. However, it remains unclear to what extent an explicit representation of this heterogeneity at the sub-grid scale of distributed hydrological models can improve the hydrological consistency and the robustness of such models. In this study, hydrological process complexity arising from sub-grid topography heterogeneity was incorporated into the distributed mesoscale Hydrologic Model (mHM). Seven study catchments across Europe were used to test whether (1) the incorporation of additional sub-grid variability on the basis of landscape-derived response units improves model internal dynamics, (2) the application of semi-quantitative, expert-knowledge-based model constraints reduces model uncertainty, and whether (3) the combined use of sub-grid response units and model constraints improves the spatial transferability of the model.

Unconstrained and constrained versions of both the original mHM and mHMtopo, which allows for topography-based sub-grid heterogeneity, were calibrated for each catchment individually following a multi-objective calibration strategy. In addition, four of the study catchments were simultaneously calibrated and their feasible parameter sets were transferred to the remaining three receiver catchments. In a post-calibration evaluation procedure the probabilities of model and transferability improvement, when accounting for sub-grid variability and/or applying expert-knowledge-based model constraints, were assessed on the basis of a set of hydrological signatures. In terms of the Euclidian distance to the optimal model, used as an overall measure of model performance with respect to the individual signatures, the model improvement achieved by introducing sub-grid heterogeneity to mHM in mHMtopo was on average 13 %. The addition of semi-quantitative constraints to mHM and mHMtopo resulted in improvements of 13 and 19 %, respectively, compared to the base case of the unconstrained mHM. Most significant improvements in signature representations were, in particular, achieved for low flow statistics. The application of prior semi-quantitative constraints further improved the partitioning between runoff and evaporative fluxes. In addition, it was shown that suitable semi-quantitative prior constraints in combination with the transfer-function-based regularization approach of mHM can be beneficial for spatial model transferability as the Euclidian distances for the signatures improved on average by 2 %. The effect of semi-quantitative prior constraints combined with topography-guided sub-grid heterogeneity on transferability showed a more variable picture of improvements and deteriorations, but most improvements were observed for low flow statistics.