Luca Cantarello , Onno Bokhove, Steven Tobias

An isentropic 1.5-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira's methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified for k = R/cp = 1, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or ``truth'' in conducting future (satellite) data-assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1.5-layer model from a 2-layer isetropic model without convection and precipitation is shown in a companion paper (Part II).