This paper investigates the robustness of rainfall–runoff models when their parameters are transferred in time. More specifically, we propose an approach to diagnose their ability to simulate water balance on periods with different hydroclimatic characteristics. The testing procedure consists in a series of parameter calibrations over 10 yr periods and the systematic analysis of mean flow volume errors on long records. This procedure was applied to three conceptual models of increasing structural complexity over 20 mountainous catchments in southern France. The results showed that robustness problems are common. Errors on 10 yr mean flow volume were significant for all calibration periods and model structures. Various graphical and numerical tools were used to investigate these errors and unexpectedly strong similarities were found in the temporal evolutions of these volume errors. We indeed showed that relative changes in simulated mean flow between 10 yr periods can remain similar, regardless of the calibration period or the conceptual model used. Surprisingly, using longer records for parameters optimisation or using a semi-distributed 19-parameter daily model instead of a simple 1-parameter annual formula did not provide significant improvements regarding these simulation errors on flow volumes. While the actual causes for these robustness problems can be manifold and are difficult to identify in each case, this work highlights that the transferability of water balance adjustments made during calibration can be poor, with potentially huge impacts in the case of studies in non-stationary conditions.

This paper investigates the actual extrapolation capacity of three hydrological models in differing climate conditions. We propose a general testing framework, in which we perform series of split‐sample tests, testing all possible combinations of calibration‐validation periods using a 10 year sliding window. This methodology, which we have called the generalized split‐sample test (GSST), provides insights into the model's transposability over time under various climatic conditions. The three conceptual rainfall‐runoff models yielded similar results over a set of 216 catchments in southeast Australia. First, we assessed the model's efficiency in validation using a criterion combining the root‐mean‐square error and bias. A relation was found between this efficiency and the changes in mean rainfall (P) but not with changes in mean potential evapotranspiration (PE) or air temperature (T). Second, we focused on average runoff volumes and found that simulation biases are greatly affected by changes in P. Calibration over a wetter (drier) climate than the validation climate leads to an overestimation (underestimation) of the mean simulated runoff. We observed different magnitudes of these models deficiencies depending on the catchment considered. Results indicate that the transfer of model parameters in time may introduce a significant level of errors in simulations, meaning increased uncertainty in the various practical applications of these models (flow simulation, forecasting, design, reservoir management, climate change impact assessments, etc.). Testing model robustness with respect to this issue should help better quantify these uncertainties.

Characterizing the impact of climate change on hydrology is not as simple as feeding a previously calibrated hydrological model with future climate scenarios. Nevertheless, hydrological modelling is often considered as a small contributor to the overall uncertainty in climate change impact studies. Running a model under conditions that can be significantly different from those used for calibration raises questions relative to the actual extrapolation capacity of the model. As hydrological models (as complex as they may be) are always a simplification of reality, they can never fully integrate all aspects of the rainfall–runoff relationship. Consequently, we prefer to consider them as patients that can certainly be in good health in average conditions, but may also be affected with pathologies when exposed to unusual conditions (namely conditions they have not been properly trained or structured for). Focusing on the robustness issues linked with non-stationary climatic conditions, this paper reviews some of the typical pathologies rainfall–runoff models can suffer from when asked to predict discharges under climate conditions different from the calibration ones.

Recent progress in collecting spatialized data with remote sensing techniques should allow the accounting for: (i) the spatial variability of rainfall and (ii) the basins' physical characteristics in rainfall-runoff models. To benefit from this spatial information, lumped approaches can quite easily be replaced by semi-distributed approaches. However, two questions need to be investigated. Does integrating additional information into a semi-distributed approach successfully improve the performance of flow simulations at the basin outlet? Which type of heterogeneity should first be taken into account to yield the most significant improvements? This paper presents a method to account for basin heterogeneity in lumped and semi-distributed models through the use of indices. Given the requirement for a large database to produce statistically significant results, chimera basins (virtual aggregation of two real basins) were used. We characterized 212 French basins using approximately 50 indices of pedology, geology, morphology and land use. Lumped and semi-distributed versions of a rainfall-runoff were compared on 3300 chimera basins. Results indicate that integrating useful spatial data in a lumped model can improve its performance without altering its parsimonious structure. Some indices correlated with rainfall confirm that the semi-distributed approach is more advantageous than the lumped approach for basins with high spatial variability of precipitation. The possible relations between physical characteristics and model parameters are investigated to help regionalization attempts and hence improve modelling abilities in ungauged basins.