Variational derivation of a moist thermal rotating shallow water model

We introduce a new energy-conserving, moist shallow water model with thermal stratification and rotation. The model is derived from a variational principle, using a Lagrangian expressed in terms of enthalpy. In this model, the latent heat from phase transitions modifies the buoyancy dynamics, which in turn feeds back to alter the vertically integrated hydrodynamic motion. Finally, we generalise this moisture parameterisation to non-hydrostatic Green-Naghdi equations.