Beyond Pointwise Error: A Multi-Metric Evaluation of Spatial Climate Downscaling

Abstract

Climate downscaling aims to reconstruct fine scale spatial fields from coarse resolution inputs. Evaluating the quality of these reconstructions is challenging: low pointwise error can come at the cost of fine scale variability, while realistic spatial variability can be achieved with inaccurate local structures. The evaluation metric can therefore change which method appears to perform best. This work presents a multi metric benchmark comparing five spatial downscaling methods on ERA5 temperature, wind, and precipitation fields. Five criteria assess complementary properties: pointwise error, structural similarity, distribution error, spectral error, and gradient error. The results reveal a systematic trade off between spatial fidelity and fine scale variability. Some methods perform best on pointwise and spatially aligned metrics, but lose high frequency content, while others preserve substantially more spectral variability at the cost of less accurately positioned local structures. Consequently, method rankings change across metrics and variables. These results show that there is no single best downscaling method. Multi metric evaluation is therefore essential for assessing which properties of a climate field are preserved.