An Idealized 1½-Layer Isentropic Model with Convection and Precipitation for Satellite Data Assimilation Research. Part I: Model Dynamics

Abstract

An isentropic 1½-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, 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 1½-layer model from an isentropic 2-layer model without convection and precipitation is shown in a companion paper (Part II).

Experiments with the modified Rotating Shallow Water model (modRSW, v.1.0): assessing the relevance for convective-scale data assimilation research

“…In this regard, by combining the strong nonlinearity due to the onset of convection and precipitation and the hydrodynamic (advective) nonlinearity of the shallow water equations, the modRSW model captures some fundamental dynamical processes of convective-scale weather systems and provides an interesting and useful testbed for data assimilation research at convective scales (Kent, 2016;Kent et al, 2017). This has also been recognised in studies that, for example, implement the model directly (Kriegmair et al, 2022), develop a variation of the model for satellite DA research (Bokhove et al, 2022;Cantarello et al, 2022), and propose its use in other idealised DA studies (Fowler, 2019).…”

“…The modRSW model is an improved (hyperbolic and rotating) version of the simpler cumulus convection model developed by Würsch and Craig (2014) -hereafter W&C -which has already been used extensively in many DA studies (Ruckstuhl and Janjić, 2018;Zeng et al, 2018Zeng et al, , 2019. A revised, isentropic and multi-layer version of the modRSW model (is-modRSW) has also been developed (Cantarello et al, 2022;Bokhove et al, 2022) and used in Cantarello (2021) to investigate idealised satellite DA.…”