A Multivariable Approach to the Regional Calibration of the Galvez Davison Index across Mexico Climate Regimes
The Gálvez Davison Index (GDI) is a thermodynamic diagnostic designed to summarize convective favorability in the tropical regions, yet its transferability across complex terrain and heterogeneous hydroclimates remains uncertain. Here we assess the climatological behavior and precipitation relevance of the GDI over Mexico using ERA5 hourly fields and CHIRPS daily precipitation for 1981 to 2024. We characterize the seasonal cycle and spatial contrasts of GDI and evaluate its association with rainfall using grid point and regional Pearson and Spearman correlations between daily maximum GDI and daily precipitation. To introduce an independent convective proxy, we also quantify the relationship between hourly GDI and ERA5 outgoing longwave radiation (OLR). Event level discrimination skill is assessed with receiver operating characteristic (ROC) curves and area under the curve (AUC) across regions and months. While GDI precipitation correlations are moderate and region dependent, GDI OLR coupling is consistently stronger, partly because OLR approaches a lower bound once deep convection develops, supporting its use as an intermediate proxy between thermodynamic favorability and rainfall. However, GDI values are systematically lower over elevated terrain because of the pressure level formulation of the index, which should be considered when interpreting the GDI over mountainous regions. ROC results indicate skill above random chance in nearly all region month combinations, with AUC frequently exceeding 0.75 during the core convective season. Building on these diagnostics, we propose a regionally calibrated GDI convective regime scale for May to October, adapted from the original GDI framework but recalibrated for Mexico using event conditioned distributions defined from OLR and precipitation and quantified with bootstrap uncertainty.