A new efficiency metric for the spatial evaluation and inter-comparison of climate and geoscientific model output

Abstract. Developing and evaluating spatial efficiency metrics is essential for assessing how well climate or other models of the Earth's system reproduce the observed patterns of variables like precipitation, temperature, atmospheric pollutants, and other environmental data presented in a gridded format. In this study, we propose a new metric, the Modified Spatial Efficiency (MSPAEF), designed to overcome limitations identified in existing metrics, such as the Spatial Efficiency (SPAEF), the Wasserstein Spatial Efficiency (WSPAEF), or the Spatial Pattern Efficiency metric (Esp). The performance of MSPAEF is systematically compared to these metrics across a range of synthetic data scenarios characterized by varying spatial correlation coefficients, biases, and standard deviation ratios. Results demonstrate that MSPAEF consistently provides robust and intuitive performance, accurately capturing spatial patterns under diverse conditions. Additionally, two realistic but synthetic case studies are presented to further evaluate the practical applicability of the metrics. In both examples, MSPAEF delivers results that align with intuitive expectations, while the other metrics exhibit limitations in identifying specific features in at least one case. Finally, as a real-world application, we rank global Coupled Model Intercomparison Project phase 6 (CMIP6) model data according to their skill in representing precipitation and temperature using the four different metrics. This application highlights that the MSPAEF rankings are most similar with Esp with a normalized absolute ranking difference of 2.8 for precipitation, and 3.8 for temperature. These findings highlight the added value of the MSPAEF metric in evaluating spatial distributions and its potential to be used in climate or other environmental model evaluation or inter-comparison exercises.