  Convection occurs ubiquitously on and in rotating geophysical and
astrophysical bodies. Prior spherical shell studies have shown that the
convection dynamics in polar regions can differ significantly from the lower
latitude, equatorial dynamics. Yet most spherical shell convective scaling laws
use globally-averaged quantities that erase latitudinal differences in the
physics. Here we quantify those latitudinal differences by analyzing spherical
shell simulations in terms of their regionalized convective heat transfer
properties. This is done by measuring local Nusselt numbers in two specific,
latitudinally separate, portions of the shell, the polar and the equatorial
regions, $Nu_p$ and $Nu_e$, respectively. In rotating spherical shells,
convection first sets in outside the tangent cylinder such that equatorial heat
transfer dominates at small and moderate supercriticalities. We show that the
buoyancy forcing, parameterized by the Rayleigh number $Ra$, must exceed the
critical equatorial forcing by a factor of $\approx 20$ to trigger polar
convection within the tangent cylinder. Once triggered, $Nu_p$ increases with
$Ra$ much faster than does $Nu_e$. The equatorial and polar heat fluxes then
tend to become comparable at sufficiently high $Ra$. Comparisons between the
polar convection data and Cartesian numerical simulations reveal quantitative
agreement between the two geometries in terms of heat transfer and averaged
bulk temperature gradient. This agreement indicates that spherical shell
rotating convection dynamics are accessible both through spherical simulations
and via reduced investigatory pathways, be they theoretical, numerical or
experimental.
