SPAtial EFficiency (SPAEF) metric is one of the most thoroughly metrics in hydrologic community. In this study, our aim is to improve SPAEF by replacing the histogram match component with other statistical indices, i.e. kurtosis and earth mover’s distance, or by adding a fourth or fifth component such as kurtosis and skewness. The existing spatial metrics i.e. SPAtial Efficiency (SPAEF), Structural Similarity (SSIM) and Spatial Pattern Efficiency Metric (SPEM) were compared with newly proposed metrics to assess their converging performance. The mesoscale Hydrologic Model (mHM) of the Moselle River is used to simulate streamflow (Q) and actual evapotranspiration (AET). The two-source energy balance (TSEB) AET during the growing season is used as monthly reference maps to calculate the spatial performance of the model. The Moderate Resolution Imaging Spectroradiometer (MODIS) based Leaf area index (LAI) is utilized by the mHM via pedo-transfer functions and multi-scale parameter regionalization approach to scale the potential ET. In addition to the real monthly AET maps, we also tested these metrics using a synthetic true AET map simulated with a known parameter set for a randomly selected day. The results demonstrate that the newly developed four-component metric i.e. SPAtial Hybrid 4 (SPAH4) slightly outperform conventional three-component metric i.e. SPAEF (3% better). However, SPAH4 significantly outperforms the other existing metrics i.e. 40% better than SSIM and 50% better than SPEM. We believe that other fields such as remote sensing, change detection, function space optimization and image processing can also benefit from SPAH4.

Optimization of spatially consistent parameter fields is believed to increase the robustness of parameter estimation and its transferability to ungauged basins. The current paper extends previous multi-objective and transferability studies by exploring the value of both multi-basin and spatial pattern calibration of distributed hydrologic models as compared to single-basin and single-objective model calibrations, with respect to tradeoffs, performance and transferability. The mesoscale Hydrological Model (mHM) is used across six large central European basins. Model simulations are evaluated against daily streamflow observations at the basin outlets and remotely sensed evapotranspiration patterns obtained with a two-source energy balance approach. Several model validation experiments are performed through combinations of single- (discharge) and multi-objective (discharge and spatial evapotranspiration patterns) calibrations with holdout experiments saving alternating basins for model evaluation. The study shows that there are very minimal tradeoffs between spatial and temporal performance objectives and that a joint calibration of multiple basins using multiple objective functions provides the most robust estimations of parameter fields that perform better when transferred to ungauged basins. The study indicates that particularly the multi-basin calibration approach is key for robust parametrizations, and that the addition of an objective function tailored for matching spatial patterns of ET fields alters the spatial parameter fields while significantly improving the spatial pattern performance without any tradeoffs with discharge performance. In light of model equifinality, the minimal tradeoff between spatial and temporal performance shows that adding spatial pattern evaluation to the traditional temporal evaluation of hydrological models can assist in identifying optimal parameter sets.

In general, calibration of a hydrologic model is essential to better simulate the basin processes and behaviour by fitting the model simulated fluxes to observed fluxes. A major challenge in the calibration process is to choose the appropriate length of the observed data series and spatio-temporal resolution of the model schematization. We present a multi-case calibration approach for determining three pillars of an optimum hydrological model configuration: calibration data length, spin-up period and spatial resolution of the hydrological model. The approach is evaluated for the Moselle River basin using calibration and validation results from the spatially distributed meso-scale Hydrological Model (mHM) for 105 different cases representing the combinations of three calibration data lengths, seven spin-up periods and five spatial model resolutions. A metaheuristic global optimization method, i.e. Dynamically Dimensioned Search (DDS) algorithm, and a well-known hydrological performance metric, i.e. Nash Sutcliffe Efficiency (NSE), are utilized for each of the 105 calibration cases. The results show that a 10-year calibration data length, 2-year spin-up period and a 4 km model resolution are appropriate for the Moselle basin to reduce the computational burden. Analyzing the combined effects further allowed us to understand the interactions of these three usually overlooked pillars in hydrological modeling.