Interpretation of simple and cloud-resolving simulations of moist convection-radiation interaction with a mock-Walker circulation

An idealized two-dimensional mock-Walker circulation in the tropical atmosphere forced by prescribed horizontal gradients in sea-surface temperature (SST) is discussed. This model problem includes feedbacks between cumulus convection and tropical large-scale circulations that have proved challenging for global climate models to predict accurately. Three-dimensional cloud-resolving model (CRM) simulations that explicitly simulate turbulent circulations within individual cloud systems across 4,096 and 1,024 km-wide Walker circulations are compared with a simple theoretical model, the Simplified Quasiequilibrium Tropical Circulation Model (SQTCM). This theoretical model combines the weak-temperature-gradient approximation with a unimodal truncation of tropospheric vertical structure coupled to highly simplified formulations of moist precipitating cumulus convection and its cloud-radiative feedbacks. The rainfall, cloud and humidity distribution, circulation strength, energy fluxes and scaling properties are compared between the models. The CRM-simulated horizontal distribution of rainfall and energy fluxes are adequately predicted by the SQTCM. However, the humidity distribution (drier subsidence regions and high-humidity boundary layers in the CRM), vertical structure and domain-size scaling of the circulation differ significantly between the models. For the SQTCM, the concept of gross moist stability - related to advection of moist static energy (MSE) out of tropospheric columns by the mean divergent circulation - is used to explain the width and intensity of the rainy region. Column MSE budgets averaged across the ascent branch of the simulated Walker circulation provide similar insight into the cloud-resolving simulations after consideration of the more complex horizontal and vertical circulation structure and the role of transient eddies. A nondimensional ascent-region moist stability ratio alpha, analogous to the SQTCM gross moist stability, is developed. One term of alpha is related to the vertical profiles of ascent-region mean vertical motion and ascent-region edge MSE; a second term is proportional to eddy export from the ascent region. Smaller alpha induces a narrower, rainier ascent region. The sensitivity of the SQTCM and CRM to a uniform 2 K increase in SST is compared, and the rainy upward branch of the circulation narrows in both models. MSE budget arguments are used to explain this behavior. In the simple model, the gross moist stability is a decreasing function of tropospheric temperature. Hence gross moist stability reduces and the ascent region narrows as the SST increases. In the CRM, increased atmospheric radiative cooling due to the warmer and moister troposphere destabilizes the MSE profile and decreases alpha, inducing a narrower ascent region. In the CRM, and to a lesser extent in the SQTCM, intensified shortwave cloud forcing in the warmer climate causes a negative radiative feedback on the SST change.