[1] 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.

No abstract

Abstract. This paper investigates the robustness of rainfallrunoff 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.

Abstract. We present a new method to derive the empirical (i.e., data-based) elasticity of streamflow to precipitation and potential evaporation. This method, which uses long-term hydrometeorological records, is tested on a set of 519 French catchments. We compare a total of five different ways to compute elasticity: the reference method first proposed by Sankarasubramanian et al. (2001) and four alternatives differing in the type of regression model chosen (OLS or GLS, univariate or bivariate). We show that the bivariate GLS and OLS regressions provide the most robust solution, because they account for the co-variation of precipitation and potential evaporation anomalies. We also compare empirical elasticity estimates with theoretical estimates derived analytically from the Turc–Mezentsev formula. Empirical elasticity offers a powerful means to test the extrapolation capacity of those hydrological models that are to be used to predict the impact of climatic changes.

Results indicate that in the two study basins, no single model performed best in all cases. In addition, no distributed model was able to consistently outperform the lumped model benchmark. However, one or more distributed models were able to outperform the lumped model benchmark in many of the analyses. Several calibrated distributed models achieved higher correlation and lower bias than the calibrated lumped benchmark in the calibration, validation, and combined periods. Evaluating a number of specific precipitation-runoff events, one calibrated distributed model was able to perform at a level equal to or better than the calibrated lumped model benchmark in terms of event-averaged peak and runoff volume error. However, three distributed models were able to provide improved peak timing compared to the lumped benchmark. Taken together, calibrated distributed models provided specific improvements over the lumped benchmark in 24% of the model-basin pairs for peak flow, 12% of the model-basin pairs for event runoff volume, and 41% of the model-basin pairs for peak timing. Model calibration improved the performance statistics of nearly all models (lumped and distributed). Analysis of several precipitation/runoff events indicates that distributed models may more accurately model the dynamics of the rain/snow line (and resulting hydrologic conditions) compared to the lumped benchmark model. Analysis of SWE simulations shows that better results were achieved at higher elevation observation sites. Although the performance of distributed models was mixed compared to the lumped benchmark, all calibrated models performed well compared to results in the DMIP 2 Oklahoma basins in terms of run period correlation and %Bias, and event-averaged peak and runoff error. This finding is noteworthy considering that these Sierra Nevada basins have complications such as orographicallyenhanced precipitation, snow accumulation and melt, rain on snow events, and highly variable topography. Looking at these findings and those from the previous DMIP experiments, it is clear that at this point in their evolution, distributed models have the potential to provide valuable information on specific flood events that could complement lumped model simulations.