Tropical cyclone genesis potential using a ventilated potential intensity

Genesis potential indices (GPIs) are widely used to understand the climatology of tropical cyclones (TCs). However, the sign of projected future changes depends on how they incorporate environmental moisture. Recent theory combines potential intensity and mid-tropospheric moisture into a single quantity called the ventilated potential intensity, which removes this ambiguity. This work proposes a new GPI ($GPI_v$) that is proportional to the product of the ventilated potential intensity and the absolute vorticity raised to a power. This power is estimated to be approximately 5 by fitting observed tropical cyclone best-track and ECMWF Reanalysis v5 (ERA5) data. Fitting the model with separate exponents yields nearly identical values, indicating that their product likely constitutes a single joint parameter. Likewise, results are nearly identical for a Poisson model as for the power law. $GPI_v$ performs comparably well to existing indices in reproducing the climatological distribution of tropical cyclone genesis and its covariability with El Ni\~no-Southern Oscillation, while only requiring a single fitting exponent. When applied to Coupled Model Intercomparison Project Phase 6 (CMIP6) projections, $GPI_v$ predicts that environments globally will become gradually more favorable for TC genesis with warming, consistent with prior work based on the normalized entropy deficit, though significant changes emerge only at higher latitudes under relatively strong warming. $GPI_v$ helps resolve the debate over the treatment of the moisture term and its implication for changes in TC genesis favorability with warming, and its clearer physical interpretation may offer a step forward towards a theory for genesis across climate states.