[an error occurred while processing this directive]

Modeling the Moist-convective Atmosphere with a Quasi 3-D Multi-scale Modeling Framework

Joon-Hee Jung & Akio Arakawa

1. Introduction
Quasi 3-D multi-scale modeling framework (Q3-D MMF) is a new way of modeling the moist-convective atmosphere, which has a coupled GCM/CRM grid structure following the "Super-parameterization" approach. However, unlike the prototype MMF, the Q3-D MMF adopts cloud-resolving grids extended beyond a GCM grid cell so that the coupled GCM/CRM can converge to a 3-D global CRM as the resolution of GCM approaches that of CRM. Consequently, the Q3-D MMF can be applicable to any resolution of GCM down to that of CRM without changing the formulation of model physics.

2. Q3-D MMF grid system
The Q3-D MMF grid system consists of a GCM grid and two perpendicular sets of cloud-resolving grid channels intersecting at the center of a GCM grid cell (Fig. 1). These channels are coupled only through the GCM, intersecting only virtually with no singularity at their formal intersections. For computing efficiency, the CRM channel width is chosen to be just a typical cloud size, i.e., a few grid points.

3. Coupling between the GCM and CRM components
The GCM influences the CRM in two ways: one through the lateral boundary condition variables are separated into "background" and "deviation". The background is obtained from the GCM through interpolation while the deviation is assumed to be cyclic across the channel. Through the normal gradient of background given by the GCM, the CRM is able to recognize the large-scale three dimensionality. However, the use of cyclic condition on the deviation limits the full representation of the cloud-scale 3-D effects. In order to maintain the compatibility of the GCM and CRM solutions, the deviation is relaxed to zero with a resolution-dependent time scale. When the horizontal resolution of GCM is low, the time scale is chosen to be sufficiently longer than the lifetime of cloud evolution to avoid excessive damping of cloud processes. When the GCM resolution is equal to the CRM resolution, on the other hand, GCM and CRM are supposed to produce identical solutions. The relaxation time scale for high GCM resolutions is then chosen to be sufficiently shorter than the lifetime of cloud evolution. In this way, Q1 and Q2 simulated by the Q3-D MMF converge to the true source and sink as the GCM resolution is refined. The CRM effect on GCM in the Q3-D MMF consists of the mean diabatic effects and the mean eddy effects of advective and dynamical processes simulated by the CRM. The "eddy" component of the solution is identified as the deviation of the CRM solution from the corresponding background field. The implementation of only eddy effects for these processes is to avoid double-counting or spurious stabilization of the GCM solutions.

4. Experimental setting and results
To test the Q3-D MMF developed, an idealized case simulating the transition of wave to vortices over the tropical ocean through the dynamics-convection interaction is chosen. For this case, a benchmark simulation (BM) is performed with the fully 3-D CRM developed by Jung and Arakawa (2008), which is the base model for the development of the Q3-D MMF. The BM is used to provide initial conditions for the Q3-D MMF simulations and also used as a reference. The horizontal and vertical domain sizes are 3072 km x 3072 km and 30 km, respectively. The horizontal grid sizes of CRM and GCM are 3 km and 96 km, respectively. There are 34 layers in the vertical, using a stretched grid with the size ranging from about 0.1 km near the surface to about 2 km near the model top. The GCM and CRM share the same vertical grids.

The top panels of Fig. 2 show the time sequence of the vertical component of vorticity at z = 1.5 km taken from BM. In the time sequence, it is seen that this period is characterized by development and subsequent persistence of two intense vortices. The middle panels show the corresponding time sequence taken from the Q3-D simulation. As in BM, two intense vortices are developed and maintained in the Q3-D simulation although there are some differences in the location and intensity of the vortices toward the end of the period. The bottom panels show the results from a "GCM-only" run in which GCM operates the dynamics and large-scale condensation with no feedback from the Q3-D CRM. In this simulation, the two vortices do not intensify and tend to merge into one vortex. These results confirm that the dynamics-convection interaction is crucial for the development and persistence of the vortices and the Q3-D simulation is reasonably successful in representing that interaction.

Figure 3 shows the time series of the precipitation rate, evaporation rate and sensible heat flux at the surface taken from the BM and Q3-D simulations averaged over their respective horizontal domains. After the initial adjustment period of a day or so, the surface precipitation rate becomes very close to that of BM. The surface evaporation rate is, however, under-predicted for the early-to-middle part of the period. The surface sensible heat flux of Q3-D simulation is, on the other hand, quite well simulated.

To evaluate the effects of vertical eddy transports, we diagnostically calculate those effects in the BM and Q3-D simulations following the way used in the predictions. Figures 4 and 5 show the potential temperature and moisture changes, respectively, due to the convergence of the vertical eddy transports over one GCM time step (= 5 min.). The dominant feature of the eddy transport effects on potential temperature shown in Fig. 4 (a) is the persistent negative and positive effects in the lower and upper atmosphere, respectively. In addition, there is a thin layer of the positive effect immediately below the freezing level (~5 km), presumably responding to the cooling due to the melting of snow or graupel. In the Q3-D simulation shown in Fig. 4 (b), these features are generally well captured. On the moisture, the eddy transport effects from BM shown in Fig. 5 (a) are mostly positive except for the thin layer next to the surface representing the sub-cloud layer. In the Q3-D simulation shown in Fig. 5 (b), qualitatively the same features can be seen. The intensity of the eddy effect, however, is considerably weaker than BM. This causes the under-prediction of the surface evaporation rate shown in Fig. 3 (b) although the rate increases toward the end of the period as the GCM-scale vertical transport becomes more dominant (not shown).
More details including the discussion on the remaining problem and comparisons with a 2-D framework will be presented in a forth-coming paper by Jung and Arakawa.

Acknowledgements References

[an error occurred while processing this directive]