A modified form of the relaxed weak temperature gradient (WTG) approximation is described and implemented in a cloud resolving model. In this scheme, the vertical heating profile is spectrally decomposed into normal modes. The relaxation time scale of each mode is set proportional to the corresponding vertical wave number of the mode, as would be expected if gravity waves were responsible for the relaxation. Buoyancy adjustment exhibits greater realism than in conventional relaxed WTG, with nonlocal adjustment occurring as in the weak pressure gradient model of Romps. Furthermore, no boundary layer taper is needed when using the improved scheme. Experiments from the literature are revisited; mass flux profiles are smoother and multiple equilibrium experiments are more robust.

We investigate the response of convection to idealized perturbations in the thermodynamic environment in simulations which parameterize the large-scale circulations using the weak temperature gradient (WTG) approximation. The perturbations include a combination of modifying the environmental moisture and atmospheric stability via imposing anomalies in reference moisture and temperature profiles. We find that changes in atmospheric stability strongly influence the character of convection by drastically modifying the vertical motion profile, whereas changes to atmospheric moisture modulate the intensity of precipitation produced by the convection, but do not qualitatively change the shape of the vertical motion profile. An important question is how does horizontal moisture advection into the domain affect convection? We test several different parameterizations of this process; these include lateral entrainment by circulations induced by enforcing WTG, a moisture relaxation which parameterizes the advection of moisture by large-scale nondivergent circulations, and control simulations in which both of these mechanisms are turned off so horizontal advection is assumed negligible compared to vertical advection. Interestingly, the most significant differences resulting from the choice of horizontal moisture advection scheme appear in environmental conditions which suppress-rather than support-the development of deep tropical convection. In this case, lateral entrainment related to WTG circulations is the only parameterization which results in extreme drying of the troposphere in environments which suppress convection. Consequently, this is the only parameterization which permits multiple equilibria-dry or precipitating steady states-in convection.

As part of an international intercomparison project, a set of single-column models (SCMs) and cloud-resolving models (CRMs) are run under the weak-temperature gradient (WTG) method and the damped gravity wave (DGW) method. For each model, the implementation of the WTG or DGW method involves a simulated column which is coupled to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. The simulated column has the same surface conditions as the reference state and is initialized with profiles from the reference state. We performed systematic comparison of the behavior of different models under a consistent implementation of the WTG method and the DGW method and systematic comparison of the WTG and DGW methods in models with different physics and numerics. CRMs and SCMs produce a variety of behaviors under both WTG and DGW methods. Some of the models reproduce the reference state while others sustain a large-scale circulation which results in either substantially lower or higher precipitation compared to the value of the reference state. CRMs show a fairly linear relationship between precipitation and circulation strength. SCMs display a wider range of behaviors than CRMs. Some SCMs under the WTG method produce zero precipitation. Within an individual SCM, a DGW simulation and a corresponding WTG simulation can produce different signed circulation. When initialized with a dry troposphere, DGW simulations always result in a precipitating equilibrium state. The greatest sensitivities to the initial moisture conditions occur for multiple stable equilibria in some WTG simulations, corresponding to either a dry equilibrium state when initialized as dry or a precipitating equilibrium state when initialized as moist. Multiple equilibria are seen in more WTG simulations for higher SST. In some models, the existence of multiple equilibria is sensitive to some parameters in the WTG calculations.

Using a cloud system resolving model with the large scale parameterized by the weak temperature gradient approximation, we investigated the influence of interactive versus noninteractive radiation on the characteristics of convection and convective organization. The characteristics of convecting environments are insensitive to whether radiation is interactive compared to when it is not. This is not the case for nonconvecting environments; interactive radiative cooling profiles show strong cooling at the top of the boundary layer which induces a boundary layer circulation that ultimately exports moist entropy (or analogously moist static energy) from dry domains. This upgradient transport is associated with a negative gross moist stability, and it is analogous to boundary layer circulations in radiative convective equilibrium simulations of convective self-aggregation. This only occurs when radiation cools interactively. Whether radiation is static or interactive also affects the existence of multiple equilibria-steady states which either support precipitating convection or which remain completely dry depending on the initial moisture profile. Interactive radiation drastically increases the range of parameters which permit multiple equilibria compared to static radiation; this is consistent with the observation that self-aggregation in radiative-convective equilibrium simulations is more readily attained with interactive radiation. However, the existence of multiple equilibria in absence of interactive radiation suggests that other mechanisms may result in organization.

As part of an international intercomparison project, the weak temperature gradient (WTG) and damped gravity wave (DGW) methods are used to parameterize large-scale dynamics in a set of cloudresolving models (CRMs) and single column models (SCMs). The WTG or DGW method is implemented using a configuration that couples a model to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. We investigated the sensitivity of each model to changes in SST, given a fixed reference state. We performed a systematic comparison of the WTG and DGW methods in different models, and a systematic comparison of the behavior of those models using the WTG method and the DGW method. The sensitivity to the SST depends on both the large-scale parameterization method and the choice of the cloud model. In general, SCMs display a wider range of behaviors than CRMs. All CRMs using either the WTG or DGW method show an increase of precipitation with SST, while SCMs show sensitivities which are not always monotonic. CRMs using either the WTG or DGW method show a similar relationship between mean precipitation rate and column-relative humidity, while SCMs exhibit a much wider range of behaviors. DGW simulations produce large-scale velocity profiles which are smoother and less topheavy compared to those produced by the WTG simulations. These large-scale parameterization methods provide a useful tool to identify the impact of parameterization differences on model behavior in the presence of two-way feedback between convection and the large-scale circulation.