CRCP: a Cloud Resolving Convection Parameterization for modeling the tropical convecting atmosphere

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Abstract

A new computational approach, CRCP, is proposed in which both the large-scale (LS) tropical dynamics and cloud-scale (CS) dynamics are captured explicitly. The leading idea is to represent subgrid scales of the LS model by imbedding a 2D CS model in each column of the 3D LS model – the approach tailored for distributed memory architectures. The overall philosophy underlying CRCP is the reinvestment of efforts from large-eddy simulation to elaborate yet ‘embarrassingly parallel’ turbulence models. Similar as in the traditional ‘convection parameterization’, the LS model provides ‘ambient forcings’ for the CS model imbedded inside each LS column, and the CS model feeds back a ‘convective response’ for every column of the LS model. Furthermore, availability of the cloud-scale data allows for explicit coupling of moist convection with radiative and surface processes. Following our experience with cloud-resolving modeling of the tropical convection, the CS model is oriented along the E–W direction inside each LS model column. A simple strategy for the coupling the LS and CS models derives from physical understanding of interactions between LS flow and moist tropical convection. Theoretical considerations are illustrated with an example of application to observational data from the Phase III of the Global Atmospheric Research Programme Atlantic Tropical Experiment (GATE).

Introduction

Tropics cover a significant part of the Earth surface and play an important role in the Earth climate system. Yet dynamics of the tropical atmosphere is poorly understood when compared to the dynamics of the middle latitudes. This is because in the tropics – unlike in the middle latitudes where rotational effects dominate – the large-scale (LS) dynamics depends critically on the diabatic processes through which the atmosphere exchanges energy with the underlying surface and space aloft. Among various diabatic energy transfer mechanisms, moist convection plays an essential role. Most of the energy available to drive tropical circulations originates as the latent heat associated with the evaporation from the ocean surface. This latent heat is released within updraft cores of convective clouds. In turn, convective processes affect exchange of heat, water and momentum between the atmosphere and the ocean and have a strong impact on solar and terrestrial radiative fluxes. Modeling all these processes using state-of-the art computers is still impractical. It requires horizontal grid spacing of ∼1 km, to represent adequately convective cloud dynamics over horizontal areas of O(108) km2. Thus, it is not surprising that representing tropical moist convection in LS and climate models is one of the most fundamental and outstanding problems in atmospheric CFD.

The paradigm described above is typical in many areas of CFD. For instance, engineering reactive flows involve many decades of spatial scales separating the LS flow from the dissipation scales (the Kolmogorov and Batchelor microscales). Since these dissipative processes are essential for the volume-averaged rates of chemical reactions, an adequate representation of the microscale processes and associated chemical reactions is vital. One possible approach, the linear eddy model [1], a simple 1D analog of the turbulent stirring and molecular diffusion, appears particularly effective when applied inside every gridbox of the resolved LS flow to represent subgrid-scale turbulent mixing and chemical reactions [2]. The approach we advocate in this paper bears some conceptual similarity to the idea of the linear eddy model.

CRCP stems from our earlier numerical studies of moist tropical convection driven by observed LS conditions over a period of O(10) days (for a discussion, see [3], [4], [5]). There, the authors have demonstrated that a 2D computational framework oriented along the E–W direction results in tropical cloud systems whose integral effects (including effects on surface and radiative processes) reproduce both the observations and 3D model results. Thus, using a 2D cloud-scale (CS) model inside each column of the 3D LS model should be capable to directly represent the interaction between moist convection and the LS flow, convection organization, and the effects of convection on surface and radiative processes. Most important, CRCP amounts to 2–3 orders of magnitude reduction of the computational effort required for a hypothetical cloud-resolving model of the 3D LS tropical dynamics.

The convection parameterization problem has a long history in the atmospheric literature (cf. [6] for reviews). CRCP is an alternate parameterization scheme, and it is subject to similar criticisms as those applied to traditional parameterization techniques. For example, in order to justify our scheme, scale separation between the LS and CS dynamics must be assumed. Furthermore, the interaction between the LS and CS dynamics must be representable in terms of the LS control of the convection and convective feedback onto the LS dynamics (cf. [7]). As these assumptions are controversial [8], CRCP cannot be the ultimate tool to study interactions between LS dynamics and convection in the tropics. On the other hand, CRCP does represent a significant advancement when compared to existing convection parameterization schemes. Traditional schemes represent cloud dynamics and thermodynamics in a simplistic way by neglecting convection organization and convection interaction with radiative and surface processes (cf. [7], [9]).

An important aspect of CRCP is its ideal suitability for high-performance computing on distributed memory architectures. Because cloud resolving models communicate with each other only through the LS flow, CS computations inside each column of the LS model proceed independently from each other. It means that the timing of the entire system should scale linearly with the number of processors, and the only deviation from the perfect scaling will be that associated with the overhead due to the LS model. In fact, our earlier experience with massively parallel computations (cf. [10] and the references therein) played an important role in designing CRCP. The overall philosophy underlying CRCP is the reinvestment of efforts from large-eddy simulation to elaborate yet ‘embarrassingly parallel’ turbulence models.

The next section discusses the physical rationale behind CRCP and outlines the model equations. Section 3 reviews the results of simulations of a 3D tropical convection, where CRCP is compared with a direct approach with fully resolved cloud and mesoscale dynamics.

Section snippets

Rationale

The strategy underlying CRCP is to consider two distinct flow models coupled with each other in a particular way. The first model is a 3D LS flow model, considered within a framework of either equatorial β-plane dynamics or global dynamics. The LS model uses horizontal grid length of ∼100 km to adequately represent LS dynamics associated with, e.g., equatorially trapped tropical disturbances. The second model is a 2D CS model formulated on the xz plane aligned along the E–W direction

Application to the GATE data

CRCP has been successfully compared with 2D cloud-resolving simulations [13] of the LS circulation driven by a gradient of the underlying sea surface temperature. The primary purpose of such an exercise was to verify the ‘reflexivity’ of the two-model relation, i.e., to assure that CRCP and the LS/CS model coupling do work for 2D flows. Here, we apply CRCP to the GATE

Concluding remarks

We propose a modeling approach in which both the LS dynamics and the CS dynamics are allowed to interact explicitly. Such an interaction plays a fundamental role in the tropical dynamics, yet it cannot be resolved with the present computational technology. The approach advocated here, CRCP, resolves LS dynamics in three spatial dimensions using averaged thermodynamic fields, predicted by a 2D cloud-resolving model imbedded inside each column of the LS model. The 2D cloud-resolving model can be

Acknowledgements

Numerical experiments were performed on NCAR’s Cray YMP and HP Exemplar computers. Assistance of Dr. Richard Loft (NCAR’s Scientific Computing Division) with parallel implementation of the CRCP approach is gratefully acknowledged. Personal review of the manuscript by Dr. Xiaoqing Wu is acknowledged as well, as is the editorial assistance of Martine Bunting. This work was supported in part by the NCAR ‘Clouds in Climate Program’ (CCP) and the Department of Energy ‘Computer Hardware, Advanced

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