The climate modelling community has trialled a large number of metrics for evaluating the temporal performance of general circulation models (GCMs), while very little attention has been given to the assessment of their spatial performance, which is equally important. This study evaluated the performance of 36 Coupled Model Intercomparison Project 5 (CMIP5) GCMs in relation to their skills in simulating mean annual, monsoon, winter, pre-monsoon, and post-monsoon precipitation and maximum and minimum temperature over Pakistan using state-of-the-art spatial metrics, SPAtial EFficiency, fractions skill score, Goodman–Kruskal's lambda, Cramer's V, Mapcurves, and Kling–Gupta efficiency, for the period 1961–2005. The multi-model ensemble (MME) precipitation and maximum and minimum temperature data were generated through the intelligent merging of simulated precipitation and maximum and minimum temperature of selected GCMs employing random forest (RF) regression and simple mean (SM) techniques. The results indicated some differences in the ranks of GCMs for different spatial metrics. The overall ranks indicated NorESM1-M, MIROC5, BCC-CSM1-1, and ACCESS1-3 as the best GCMs in simulating the spatial patterns of mean annual, monsoon, winter, pre-monsoon, and post-monsoon precipitation and maximum and minimum temperature over Pakistan. MME precipitation and maximum and minimum temperature generated based on the best-performing GCMs showed more similarities with observed precipitation and maximum and minimum temperature compared to precipitation and maximum and minimum temperature simulated by individual GCMs. The MMEs developed using RF displayed better performance than the MMEs based on SM. Multiple spatial metrics have been used for the first time for selecting GCMs based on their capability to mimic the spatial patterns of annual and seasonal precipitation and maximum and minimum temperature. The approach proposed in the present study can be extended to any number of GCMs and climate variables and applicable to any region for the suitable selection of an ensemble of GCMs to reduce uncertainties in climate projections.

Satellite-based earth observations offer great opportunities to improve spatial model predictions by means of spatial-pattern-oriented model evaluations. In this study, observed spatial patterns of actual evapotranspiration (AET) are utilised for spatial model calibration tailored to target the pattern performance of the model. The proposed calibration framework combines temporally aggregated observed spatial patterns with a new spatial performance metric and a flexible spatial parameterisation scheme. The mesoscale hydrologic model (mHM) is used to simulate streamflow and AET and has been selected due to its soil parameter distribution approach based on pedo-transfer functions and the build in multi-scale parameter regionalisation. In addition two new spatial parameter distribution options have been incorporated in the model in order to increase the flexibility of root fraction coefficient and potential evapotranspiration correction parameterisations, based on soil type and vegetation density. These parameterisations are utilised as they are most relevant for simulated AET patterns from the hydrologic model. Due to the fundamental challenges encountered when evaluating spatial pattern performance using standard metrics, we developed a simple but highly discriminative spatial metric, i.e. one comprised of three easily interpretable components measuring co-location, variation and distribution of the spatial data. The study shows that with flexible spatial model parameterisation used in combination with the appropriate objective functions, the simulated spatial patterns of actual evapotranspiration become substantially more similar to the satellite-based estimates. Overall 26 parameters are identified for calibration through a sequential screening approach based on a combination of streamflow and spatial pattern metrics. The robustness of the calibrations is tested using an ensemble of nine calibrations based on different seed numbers using the shuffled complex evolution optimiser. The calibration results reveal a limited trade-off between streamflow dynamics and spatial patterns illustrating the benefit of combining separate observation types and objective functions. At the same time, the simulated spatial patterns of AET significantly improved when an objective function based on observed AET patterns and a novel spatial performance metric compared to traditional streamflow-only calibration were included. Since the overall water balance is usually a crucial goal in hydrologic modelling, spatial-pattern-oriented optimisation should always be accompanied by traditional discharge measurements. In such a multi-objective framework, the current study promotes the use of a novel bias-insensitive spatial pattern metric, which exploits the key information contained in the observed patterns while allowing the water balance to be informed by discharge observations.

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.