The Mahalanobis Distance as a Multivariate Performance Metric for Selecting Physics Parameterizations in Meteorological Simulations

Selecting physics parameterizations for meteorological simulations is typically guided by univariate metrics, which are computed separately for each variable and station and frequently yield contradictory rankings and force subjective decisions. Although the Mahalanobis distance (MD) has previously been used for multivariate analysis, to the best of our knowledge, it has not previously been used as a decision criterion for selecting physics parameterizations in meteorological simulations. This study proposes the MD as a single multivariate performance metric that is dimensionless, invariant to measurement scales, and corrects for inter-variable correlations. The framework was demonstrated using 40 meteorological simulations combining microphysics, radiation, surface-layer, planetary boundary layer, and cumulus schemes, evaluated against hourly observations of temperature, relative humidity, and wind at surface stations in the Biobío region, south-central Chile. The traditional univariate metrics nominated different optimal configurations depending on the variable and station. In contrast, the MD identified a single configuration attaining the minimum distance at three of the four stations and the minimum cross-station mean, and revealed that performance was governed primarily by the surface-layer/PBL pairing rather than by microphysics or radiation choices. The MD thus provides an objective, reproducible, and easily interpretable criterion for parameterization selection, directly applicable to meteorological inputs for air quality modeling.