22The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE

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[1] We show that Mean Squared Error (MSE) and Nash-Sutcliffe Efficiency (NSE) type metrics typically vary on bounded ranges under optimization and that negative values of NSE imply severe mass balance errors in the data. Further, by constraining simulated mean and variability to match those of the observations (diagnostic approach), the sensitivity of both metrics is improved, and NSE becomes linearly related to the cross-correlation coefficient. Our results have important implications for analysis of the information content of data and hence about inferences regarding achievable parameter precision.Citation: Gupta, H. V., and H. Kling (2011), On typical range, sensitivity, and normalization of Mean Squared Error and NashSutcliffe Efficiency type metrics, Water Resour. Res., 47, W10601,

This study is a contribution to a model intercomparison experiment initiated during a workshop at the 2013 IAHS conference in Göteborg, Sweden. We present discharge simulations with the conceptual precipitation-runoff model COSERO in 11 basins located under different climates in Europe, Africa and Australia. All of the basins exhibit some form of non-stationary conditions, due, for example, to warming, droughts or land-cover change. The evaluation of the daily discharge simulations focuses on the overall model performance and its decomposition into three components measuring temporal dynamics, mean flow volume and distribution of flows. Calibration performance is similarly high as in previous COSERO applications. However, when looking at evaluation periods independent of the calibration, the model performance drops considerably, mainly due to severely biased discharge simulations in semi-arid basins with strong non-stationarity in rainfall. Simulations are more robust in European basins with humid climates. This highlights the fact that hydrological models frequently fail when simulations are required outside of calibration conditions in basins with non-stationary conditions. As a consequence, calibration periods should be sufficiently long to include both wet and dry periods, which should yield more robust predictions.

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Abstract:In mountainous regions of mid latitudes, the accumulation and melting of snow plays an important role for the seasonal water balance. These processes not only exhibit a strong seasonality, but also a high spatial variability, which has to be accounted for when establishing distributed water balances in alpine environments. A methodology was developed for seasonal, spatially distributed modelling of accumulation and melting of snow and was embedded in a water balance model that uses only monthly values of precipitation and air temperature as meteorological input data. Hence, this methodology can also be applied in regions with limited data availability. The model uses a conceptual approach with a spatial resolution of a 1 km ð 1 km raster. Snow accumulation is computed from temperature and precipitation data. Snowmelt is computed with a temperature-index approach. A direct application of these simple concepts using monthly inputs would not yield satisfying results. Therefore, precipitation is disaggregated into rainfall and snowfall by using a transition range considering temporal variations of temperature within a month and the mean deviation of temperature on days with and without precipitation. For modelling snowmelt, two different approaches were tested to incorporate variable temperatures within a month. The model was applied for the whole of Austria (84 000 km 2 ) and simulated runoff was compared with observed runoff at 135 gauges for a 30 year period. The model performs best in high and medium mountainous catchments. Lower model performances are achieved in lowland catchments, where the contribution of snowmelt to river runoff decreases. It can be concluded that modelling accumulation and melting of snow in mountainous areas with monthly data yields good results if a temporal disaggregation of precipitation and temperature is applied.

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