The SPAtial EFficiency metric (SPAEF): multiple-component evaluation of spatial patterns for optimization of hydrological models

The process of model evaluation is not only an integral part of model development and calibration but also of paramount importance when communicating modelling results to the scientific community and stakeholders. The modelling community has a large and well-tested toolbox of metrics to evaluate temporal model performance. In contrast, spatial performance evaluation does not correspond to the grand availability of spatial observations readily available and to the sophisticate model codes simulating the spatial variability of complex hydrological processes. This study makes a contribution towards advancing spatial-pattern-oriented model calibration by rigorously testing a multiple-component performance metric. The promoted SPAtial EFficiency (SPAEF) metric reflects three equally weighted components: correlation, coefficient of variation and histogram overlap. This multiple-component approach is found to be advantageous in order to achieve the complex task of comparing spatial patterns. SPAEF, its three components individually and two alternative spatial performance metrics, i.e. connectivity analysis and fractions skill score, are applied in a spatial-pattern-oriented model calibration of a catchment model in Denmark. Results suggest the importance of multiple-component metrics because stand-alone metrics tend to fail to provide holistic pattern information. The three SPAEF components are found to be independent, which allows them to complement each other in a meaningful way. In order to optimally exploit spatial observations made available by remote sensing platforms, this study suggests applying bias insensitive metrics which further allow for a comparison of variables which are related but may differ in unit. This study applies SPAEF in the hydrological context using the mesoscale Hydrologic Model (mHM; version 5.8), but we see great potential across disciplines related to spatially distributed earth system modelling.