  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.
