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Development of a quasi-3D multi-scale modeling framework: Motivation, basic algorithm and preliminary results

Joon-Hee Jung & Akio Arakawa

1. Introduction
With the recent development of computer technology, it is becoming feasible to use a global cloud-resolving model (GCRM) for climate simulations (e.g., Sato et al. 2009). However, one cannot exclusively depend on such an expensive model for all kinds of climate studies, which require a number of long runs with different focuses in model dynamics/ physics and with different initial and/or external and internal conditions. Thus it is highly desirable to have a more flexible framework for climate simulation. A quasi-3D (Q3D) multi- scale modeling framework (MMF), which combines a GCM with a Q3D CRM, is proposed to be such a framework. The Q3D MMF can converge to a fully 3D GCRM as the GCM’s resolution is refined. Consequently, the horizontal resolution of the GCM can be freely chosen depending on the objective of application. As a step in developing the Q3D MMF, we have first constructed a Q3D CRM.

2. Algorithm of the Q3D CRM
The prediction algorithm developed for the Q3D CRM applies a 3D anelastic vector vorticity equation model of Jung and Arakawa (2008) to the Q3D network of grid points. Since the model uses an anelastic system of equations, sound waves are filtered out at their origin. The horizontal domain of the Q3D CRM consists of two perpendicular sets of channels intersecting at the center of a GCM grid cell, each of which contains a locally 3D grid-point array (Fig. 1). The perpendicular channels are coupled only through basic prognostic variables averaged over channel segments to avoid singularity at the intersection. The choice of the width of channel is flexible, but it is chosen to be narrow in practical applications for computing efficiency. Therefore, it is crucial to select a proper lateral boundary condition to realistically simulate the statistics of cloud and associated processes. After trying a variety of ways, it has been decided to choose the condition based on the assumption that the deviations from background fields are periodic across the channel. The background fields are obtained through interpolations from the GCM grid points.

3. Preliminary results
To evaluate the newly developed Q3D CRM in an efficient way, we have performed preliminary tests that basically follow the single-column modeling approach. The horizontal domain of the column is chosen to be roughly of the order of a typical grid size of coarse- resolution GCMs. Since the domain is too small to represent large-scale processes, we prescribe vertical profiles of horizontally uniform thermodynamic forcing to maintain the overall moist-convective activity. Applying the original 3D CRM to this setting, a benchmark simulation (BM) is performed first (see Fig. 2). The Q3D simulation is then performed and the statistics of the solution are closely compared with those of BM. Figure 3 shows the time series of surface precipitation rate and the normalized frequencies of surface precipitation defined as f ≡ Nevent / Ntotal , where Nevent denotes the number of precipitation events falling into a specific range of rate and Ntotal is the number of all events during the simulation period. Figure 4 shows the time- and domain-averaged profiles of vertical transports, obtained from BM and Q3D simulations.


4. Conclusions
Comparing the simulation results with those of the straightforward application of a 3D CRM, it is concluded that the Q3D CRM can reproduce most of the important statistics of the 3D solutions including the vertical distributions of cloud water and precipitants, vertical transports of potential temperature and water vapor, and the variances and covariances of dynamical variables.

Acknowledgements
This work has been supported by the National Science Foundation Science and Technology Center for Multi-Scale Modeling of Atmospheric Processes, managed by Colorado State University under cooperative agreement No. ATM-0425247.

References

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