Mathematics – Logic
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........6l&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF CALIFORNIA, LOS ANGELES, 1995.Source: Dissertation Abstracts International, Volume: 56-03, Sectio
Mathematics
Logic
Cumulus
Scientific paper
The observed macroscopic behavior of moist-convective processes is statistically analyzed to answer some of the key questions related to cumulus parameterization. The problem of cumulus parameterization is a closure problem in which we look for relationships between cumulus-convective processes and large-scale processes. Among various closures used in the current parameterization schemes, we focus on the following two basic ones: (I) constraint on the coupling of net warming and net moistening through a quasi -equilibrium assumption, and (II) constraint on the coupling of the "apparent heat source", Q_{ rm 1c}, and the "apparent moist sink", Q_2, through a cloud model. The main objectives of the analysis are to directly verify these closures against observations and to empirically find a proper way to formulate the closures. To achieve these objectives, a statistical method rotated principal component analysis (RPCA) performed on the combined two variables, is developed. The RPCA method is applied to (1) the vertical profiles of Q_{rm 1c}, and Q_2 diagnosed from observations as residuals in the budget equations, and (2) those of observed temperature and humidity. The goal of this analysis is to empirically classify cloud regimes, determine characteristic vertical distributions of cumulus heating and cumulus drying for each cloud regime, and seek a combination of thermodynamic state variables that is strongly constrained to be invariant in the quasi-equilibrium states. The results from the analysis indicate that each related principal component represents a physically realizable state. In terms of these components, we can identify several cloud regimes, such as squall clusters, scatter convection and non-squall clusters. Semi-prognostic tests of the Arakawa -Schubert cumulus parameterization are performed against data classified into the three cloud regimes: squall clusters, scattered convection, and non-squall clusters. These tests indicate that the quasi-equilibrium of the cloud work function seems basically valid. We further investigate the validity of the logical framework used in the Arakawa-Schubert parameterization. The RPCA of Q_{rm 1c} and Q_2 coupling (Type II coupling) using the GATE and Asian datasets shows that this coupling is valid in both regions. It is also shown that Q _{rm 1c} and Q_2 can be estimated separately from given gammaQ_{rm 1c} +Q_2 using RPCA obtained from a different dataset. Here the quantity gamma Q_{rm 1c}+Q _2 represents the time rate of change of -L(q - q*) due to cumulus convection. This series of analyses lead to development of a purely empirical cumulus parameterization scheme, which follows the logical framework of the Arakawa-Schubert cumulus parameterization but with no modeling assumptions on cloud processes. In this way the logical structure of the parameterization can be verified in a way isolated from errors due to deficiencies of the cloud model. The performance of the scheme is very encouraging. It suggests that cumulus convection in nature is basically parameterizable when the logical structure of the A-S parameterization is followed. The parameterization can also be used as a guide in developing more detailed physically-based parameterizations.
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