Simulations of Walker circulation with sparse space and time superparameterization

Interactions between large-scale flow and convection are a crucial aspect of the tropical atmosphere. However, the wide discrepancy in spatial and temporal scales makes it practically impossible to resolve numerically all the relevant processes. Traditionally, this issue is addressed in large-scale models through the use of convective parameterizations that account for the effects of convective motions on the mean atmospheric temperature and humidity profiles. Over the last decade, an alternative approach, the Superparameterization (SP - Grabowski and Smolarkiewicz 1999; Grabowski 2004), has emerged in which a high-resolution cloud-resolving model is embedded within a global model to actively simulate the interactions between the global scale and the convective scale.

Over the years, different algorithms have been proposed to best implement the SP framework. In this paper, we  evaluate the ability of the Sparse Space and Time-Super Parameterization (SSTSP) to accurately reproduce the interactions between convection and the large-scale flow. In the SSTSP framework, the embedded cloud-resolving  model is only used to simulate convection on a domain whose area is small in comparison to the resolution of the large-scale model, and for a time-period that is short when compared to the time-step in the global model. The SSTSP  greatly reduces the  computational cost but requires extrapolating the dynamics of the small scales over a larger domain and longer time scales. Xing et al. (2009) have already shown that the SSTSP can accurately capture the  propagation of a squall line. Here, we investigate the accuracy of the SSTSP algorithm at reproducing the interactions between convection and large-scale flow in the context of an idealized Walker cell.

The SSTSP algorithm has been implemented within the  EULAG model (Smolarkiewicz and Margolin 1997; Prusa et al. 2008). The model is used to simulate a Walker circulation over a 40 000 km domain. The circulation is forced by energy fluxes from a prescribed sea surface temperature (SST)  distribution, with fixed radiative cooling, which drives a planetary scale circulation. Simulations using EULAG in a cloud-resolving model configuration provide benchmarks for various SST distributions. The CRM simulations are then compared with the SSTSP model for various value of the spatial and temporal accelerations. The ability of the SSTSP algorithm to reproduce the distribution of precipitation and cloudiness, as well as their spatio-temporal variability, is evaluated.

References:

Grabowski, W. W., and P. K. Smolarkiewicz, 1999: CRCP: A cloud resolving convection parameterization for modeling the tropical convecting atmosphere. Physica D, 133, 171-178.

Grabowski, W. W., 2004: An improved framework for superparameterization. J. Atmos. Sci., 61, 1940-1952.

Prusa, J. M., P. K. Smolarkiewicz, and A. A. Wyszogrodzki, 2008: EULAG, a computational model for multiscale flows. Comput. Fluids, 37, 1193-1207.

Smolarkiewicz, P. K., and L. G. Margolin, 1997: On forward-in-time differencing for fluids: An Eulerian/semi-Lagrangian nonhydrostatic model for stratified flows. Atmos.-Ocean, 35, 127-152.

Xing, Y., A. J. Majda, and W. W. Grabowski, 2009: New efficient sparse space-time algorithms for superparameterization on mesoscales. Mon. Wea. Rev., 137, 4307-4324.