Colorado State University General Circulation Model

Cumulus Ensemble Simulation

The model used is the UCLA CEM, developed by S. K. Krueger. It has been modified and improved at CSU in the last few years.

CEMs are designed to simulate the formation of an ensemble of clouds under a given large-scale condition as if the CEM was situated with a grid box of a large-scale numerical model. Thus, information on large-scale destabilizing and moistening rates is imposed on CEM grid points uniformly in the horizontal.

Some idealized simulations were performed at UCLA by assuming time-varying (periodic) large-scale advective forcing to examine the modulation of cumulus activities to prescribed large-scale forcing (Xu, Arakawa and Krueger 1992).

Simulated data were used to evaluate the Arakawa-Schubert (1974) cumulus parameterization and to examine the sensitivity of the parameterization to the grid resolution of large-scale models (Xu and Arakawa 1992). The assumption of cloud work function quasi-equilibrium was also examined. The main conclusion is that the CWF quasi-equilibrium assumption is more accurate for inputs averaged over smaller domain sizes that resolve some mesoscale processes.

In addition, some diagnostic cloudiness parameterizations used in large-scale numerical models (Xu and Krueger 1991) and closure assumptions used in existing cumulus parameterizations (Xu 1994) were also evaluated, especially their dependency on the horizontal resolutions of large-scale models.

At CSU, the CEM is used to study the mechanisms of cloud-radiation interactions. It is found that the direct radiation-convection interaction is responsible for the diurnal variation of oceanic precipitation. (Xu and Randall 1995)

Simulated data were analyzed to partition mass, heat, and moisture budgets of cumulus ensembles into convective and stratiform components. A method based primarily on the horizontal distribution of maximum cloud draft strength below the melting level in a CEM grid column was developed. The stratiform region includes both precipitating and nonprecipitating anvils. (Xu 1995)

Ongoing research includes: (i) simulation of cloud ensembles with observed large-scale data such as GATE, ASTEX, ARM, and TOGA-COARE; (ii) development of a semi-empirical cloudiness parameterization; (iii) low-frequency oscillations in a radiative-convective equilibrium environment; and (iv) applicability of Arakawa-Schubert cumulus parameterization to mesoscale models.

The UCLA cloud ensemble model was developed by S. K. Krueger in the early 1980s. It has been modified to include an interactive radiative transfer parameterization at CSU (Xu and Randall 1995a). It also includes a modified ice-phase microphysics parameterization (Krueger et al. 1995), a new turbulence length scale formulation and many other minor modifications in the past five years.

Time sequences of the hourly rate of entire domain-averaged surface precipiration (solid) for Q02, Q03 and Q04 (see Xu, Arakawa and Krueger 1992). As a reference, time sequence of the imposed large-scale advective effect is shown with an arbitrarily chosen amplitude by the dashed line. The amplitude of large-scale effect is identical in these three simulations. Q03 used a non-sheared basic wind profile, but Q02 used a sheared basic wind profile. Both of them used a horizontal domain size of 512 km. Q04 is identical to Q02 except for a larger domain, 1024 km. In all these simulations, radiative heating rates were prescribed.

Lag correlation coefficients for apparent heat source as a function of height for the 512-km (top panel), 256-km (second from top), 128-km (third from top), and 64-km subdomains (bottom panel) of simulation Q02 (Xu, Arakawa and Krueger 1992) from the control test (left column), i.e., with the standard Arakawa-Schubert cumulus parameterization, and the nonequilibrium test (right column), i.e., with the effect of the time change-rate of the cloud work function. See Xu and Arakawa (1992) for details. Hatched areas correspond to correlation coefficients greater than 0.5 with a contour interval of 0.05; contour interval is 0.1 outside the hatched areas. A positive lag time indicates that the parameterized cumulus convection precedes the simulated cumulus convection.

Time-height cross section of the ensemble mean of mass flux deviation in the cloudy regions for (a) I05, a simulation with interactive radiation, and (b) N05, a simulation with non-interactive radiation. The domain averaged radiative heating rates are identical in both simulations. The contour interval is 0.2 mb/h. See Xu and Randall (1995) for details.

Time-height cross section of the ensemble mean of (a) shortwave cloud radiative forcing (CRF), (b) longwave CRF, and (c) their sum for a simulation with interactive radiation. The contour interval is 0.5 K/day. Contour over 0.5 K/day are hatched. See Xu and Randall (1995) for details.

Time-height cross section of latent heat release in (a) convective region, and (b) stratiform region of simulated cumulus ensembles. The contour interval is 2 and 1 K/day in (a) and (b), respectively. Contours over 14 K/day and 4 K/day are hatched in (a) and (b), respectively. See Xu (1995) for details.