  Turbulent Rayleigh-B\'{e}nard convection is often modelled with a constant
surface temperature. However, the surface temperature of many geophysical
systems, such as lakes, is coupled to the atmospheric forcing. In this paper,
we account for this dynamic surface temperature through an additional parameter
$\beta$. Using an appropriately defined dynamical Rayleigh number $\RaD$, we
recover many of the results from the standard Rayleigh-B\'{e}nard model. We
hope that this work will simplify the application of Rayleigh-B\'{e}nard theory
in geophysical contexts, such as lakes.
