Development and application of a prognostic cumulus parameterization

June 1995.Also issued as author's dissertation (Ph.D.) -- Colorado State University, 1995.Includes bibliographical references.The Arakawa-Schubert cumulus parameterization assumes a quasi-equilibrium between the cumulus convection and the "large-scale forcing." It is, however, not very clear that it is always possible to distinctly separate the "non-convective processes" from the convective processes. We therefore propose a prognostic approach for implementing the Arakawa-Schubert parameterization. We relax the assumption of cloud work function quasi-equilibrium by explicitly using a cumulus kinetic energy (CKE) equation. This approach bypasses the ambiguity in separating the large-scale forcing from the cumulus convection, and may be the first step toward improving the interactions between parameterized physics in large-scale numerical models. The CKE approach also simplifies the calculation and hence allows more sophisticated physics of convection, such as downdrafts, to be taken into account. Simple experiments with constant radiative cooling in a one dimensional (1-D) model showed that the steady-state solution depends on the value of a., a parameter that relates CKE to cloud base mass flux. Experiments also showed that LSP (large-scale precipitation) is a part of the "forcing" for the cumulus convection, and that how we parameterize the LSP has direct effects on the results. In the meantime, the LSP is also a response to convective detrainment. Therefore, we cannot really clearly separate forcing and response, as Arakawa and Schubert (1974) did. The prognostic CKE approach was tested in the 1-D model to simulate observations from the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment. We can successfully simulate the time evolution of the precipitation rate and the vertical distribution of the apparent heat source and moisture sink. The atmosphere is saturated too often in the simulation, however. This can be attributed to the over-simplified largescale saturation parameterization (LSP) which re-evaporates the precipitation falling from upper levels. LSP does not become active until the whole grid box is saturated. Two different values of ex were tested in the GATE simulation. Results indicate that one value of ex produces a better time evolution, while the other generates a more realistic vertical structure of the heating rate. This may be due to the fact that we have used only one ex for all cloud types. According to the relation derived from the definitions of CKE and cloud-base mass flux, ex should be a function of cloud depth. We tested the prognostic CKE approach against the cloud work function quasi-equilibrium with the Colorado State University general circulation model. It was found that the model produces much higher anvil incidence which dramatically reduces the absorbed solar radiation in the tropics. A "fractional coverage" has been introduced in the simple anvil parameterization. Using the fractional anvils with the CKE approach, we found improvements in the January global precipitation distribution, especially over land. Cumulus convection also occurs much more often. As a part of the development of the prognostic CKE cumulus parameterization, the fractional entrainment rate, A, is used as the cloud spectral parameter, replacing the detrainment- level height as chosen by Lord (1978). Lord (1978)'s approach had been questioned by other authors (e.g. Kao and Ogura, 1987) and was proven incompatible with the CKE approach. With this approach, A is an independent variable and the value of ex should depend on llA and the vertical resolution of the model. The independent variable A appears to be a physically more reasonable identifier for cloud types.Sponsored by the National Science Foundation ATM-9121629 and ATM-9214981; and the U.S. Department of Energy DE-FG03-94ER91629