• Alexander, G. D., G. S. Young, and D. V. Ledvina, 1993: Principal component analysis of vertical profiles of Q1 and Q2 in the Tropics. Mon. Wea. Rev.,121, 535–548.

  • Arakawa, A., 1993: Closure assumptions in the cumulus parameterization problem. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 1–15.

  • ——, and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci.,31, 674–701.

  • ——, and J.-M. Chen, 1987: Closure assumptions in the cumulus parameterization problem. Short- and Medium-Numerical Prediction, T. Matsuno, Ed., Meteorological Society of Japan, 107–131.

  • Cattell, R. B., 1966: The scree test for the number of factors. Mult. Behav. Res.,1, 245–276.

  • Chen, J.-M., 1989: Observational study of the macroscopic behavior of moist-convective processes. Ph.D. dissertation, University of California, Los Angeles, 264 pp. [Available from UCLA, Los Angeles, CA 90095.].

  • Cheng, M.-D., and M. Yanai, 1989: Effects of downdrafts and mesoscale convective organization on the heat and moisture budgets of tropical cloud clusters. Part III: Effects of mesoscale convective organization. J. Atmos. Sci.,46, 1566–1588.

  • Cooley, W. W., and P. R. Lohnes, 1971: Multivariate Data Analysis. Wiley, 364 pp.

  • Cox, S. K., and K. T. Griffith, 1979: Estimates of radiative divergence during Phase III of the GARP Atlantic Tropical Experiment. Part I: Methodology. J. Atmos. Sci.,36, 576–585.

  • DeMott, C. A., and S. A. Rutledge, 1998: The vertical structure of TOGA COARE convection. Part I: Radar echo distributions. J. Atmos. Sci.,55, 2730–2747.

  • Esbensen, S. K., E. I. Tollerud, and J.-H. Chu, 1982: Cloud-cluster-scale circulations and the vorticity budget of synoptic-scale waves over the eastern Atlantic intertropical convergence zone. Mon. Wea. Rev.,110, 1677–1692.

  • Frank, W. M., H. Wang, and J. L. McBride, 1996: Rawinsonde budget analyses during the TOGA COARE IOP. J. Atmos. Sci.,53, 1761–1780.

  • Gibson, J. K., P. Kållberg, S. Uppala, A. Hernandez, A. Nomura, and E. Serrano, 1997: ERA description. ECMWF Re-Analysis Final Report Series, Vol. 1, 71 pp.

  • Harman, H. H., 1976: Modern Factor Analysis. The University of Chicago Press, 487 pp.

  • Harris, C. W., and H. F. Kaiser, 1964: Oblique factor analytic solutions by orthogonal transformations. Psychometrika,29, 347.

  • He, H., J. W. McGinnis, Z. Song, and M. Yanai, 1987: Onset of the Asian summer monsoon in 1979 and the effects of the Tibetan Plateau. Mon. Wea. Rev.,115, 1966–1995.

  • Hendrickson, A. E., and P. O. White, 1964: Promax: A quick method for rotation to oblique simple structure. Br. J. Stat. Psychol.,17, 65–70.

  • Hurley, J. R., and R. B. Cattell, 1962: The Procrustes program: Producing direct rotation to test a hypothesized factor structure. Behav. Sci.,7, 258.

  • Johnson, R. H., T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski, and W. H. Schubert, 1999: Trimodal characteristics of tropical convection. J. Climate,12, 2397–2418.

  • Jolliffe, I. T., 1986: Principal Component Analysis. Springer-Verlag, 271 pp.

  • ——, 1987: Rotation of principal components: Some comments. J. Climatol.,2, 313–329.

  • Kaiser, H. F., 1958: The Varimax criterion for analytic rotation in factor analysis. Psychometrika,23, 187.

  • Kuo, H.-L., 1965: On formation and intensification of tropical cyclones through latent heat release by cumulus convection. J. Atmos. Sci.,22, 40–63.

  • ——, 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci.,31, 1232–1240.

  • LeMone, M. A., E. J. Zipser, and S. B. Trier, 1998: The role of environmental shear and thermodynamic conditions in determining the structure and evolution of mesoscale convective systems during TOGA COARE. J. Atmos. Sci.,55, 3493–3518.

  • Lin, C., 1999: Some bulk properties of cumulus ensembles simulated by a cloud-resolving model. Part II: Entrainment profiles. J. Atmos. Sci.,56, 3736–3748.

  • ——, and A. Arakawa, 1997: The macroscopic entrainment processes of simulated cumulus ensemble. Part II: Testing the entraining-plume model. J. Atmos. Sci.,54, 1044–1053.

  • Liou, K.-N., 1992: Radiation and Cloud Processes in the Atmosphere:Theory, Observation and Modeling. Oxford Monogr. on Geology and Geophysics, No. 20, Oxford, 487 pp.

  • Liu, Y.-Z., 1995: The representation of the macroscopic behavior of observed moist-convective processes. Ph.D. dissertation, University of California, Los Angeles, 227 pp. [Available from UCLA, Los Angeles, CA 90095.].

  • Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. Sci. Rep. 1, Statistical Forecasting Project, Department of Meteorology, Massachusetts Institute of Technology, 48 pp. [Available from MIT, Cambridge, MA 02139.].

  • Manabe, S., J. Smagorinsky, and R. F. Strickler, 1965: Simulated climatology of a general circulation model with a hydrological cycle. Mon. Wea. Rev.,93, 769–798.

  • McBride, J. L., B. W. Gunn, G. J. Holland, T. D. Keenan, N. E. Davidson, and W. M. Frank, 1989: Time series of total heating and moistening over the Gulf of Carpentaria radiosonde array during AMEX. Mon. Wea. Rev.,117, 2701–2713.

  • Misra, V., 1997: A statistically based cumulus parameterization scheme that makes use of heating and moistening rates derived from observations. Ph.D. dissertation, The Florida State University, 184 pp. [Available from The Florida State University, Tallahassee, FL 23206.].

  • Mulaik, S. A., 1972: The Foundations of Factor Analysis. McGraw-Hill, 453 pp.

  • Newman, M., and P. Sardeshmukh, 1995: A caveat concerning singular value decomposition. J. Climate,8, 352–360.

  • Nitta, T., 1977: Response of cumulus updraft and downdraft to GATE A/B-scale motion systems. J. Atmos. Sci.,34, 1163–1186.

  • Ooyama, K., 1987: Scale-controlled objective analysis. Mon. Wea. Rev.,115, 2476–2506.

  • Preisendorfer, R. W., 1988: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 425 pp.

  • ——, and T. P. Barnett, 1977: Significance tests for empirical orthogonal functions. Preprints, Fifth Conf. on Probability and Statistics in Atmospheric Sciences, Las Vegas, NV, Amer. Meteor. Soc., 169–172.

  • Richman, M. B., 1986: Rotation of principal components. J. Climatol.,6, 293–335.

  • ——, and P. J. Lamb, 1985: Climatic pattern analysis of three- and seven-day summer rainfall in the central United States: Some methodological considerations and a regionalization. J. Climate Appl. Meteor.,24, 1325–1343.

  • Sui, C.-H., and M. Yanai, 1986: Cumulus ensemble effects on the large-scale vorticity and momentum fields of GATE. Part I: Observational evidence. J. Atmos. Sci.,43, 1618–1642.

  • Thurstone, L. L., 1947: Multiple Factor Analysis. The University of Chicago Press, 535 pp.

  • Tung, W.-W., C. Lin, B. Chen, M. Yanai, and A. Arakawa, 1999: Basic modes of cumulus heating and drying observed during TOGA-COARE IOP. Geophys. Res. Lett.,26, 3117–3120.

  • Vargas, W. M., and R. H. Compagnucci, 1983: Methodological aspects of principal component analysis in meteorological fields. Preprints, Second Int. Meeting on Statistical Climatology, Lisbon, Portugal, National Institute of Meteorology and Geophysics, 5.3.1.

  • Yanai, M., S. Esbensen, and J. Chu, 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci.,30, 611–627.

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Empirical Determination of the Basic Modes of Cumulus Heating and Drying Profiles

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  • 1 Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, California
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Abstract

The constraint on the coupled vertical profiles of cumulus heating and drying, which can be used as a partial closure in cumulus parameterization, is examined using observational data from convectively active regions in the summertime. The data used in this study include those derived from Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment Phase III, Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment over the intensive flux array region, and four subsets of the European Centre for Medium-Range Weather Forecasts Re-Analysis data that cover areas ranging from tropical to midlatitude continents. The profiles of Q1 and Q2 calculated from those data are analyzed using a statistical method. The proposed method is a revised version of the rotated principal component analysis based on the Promax rotation (RPCAPromax), which is believed suitable for identifying basic structures embedded within a given dataset. It is designed in such a way that the distortion of identified structures due to the use of a linear model is minimized. The revised RPCAPromax, together with some selected statistical tools, are evaluated using synthetic datasets before they are applied to observations.

The analysis of the observational data shows that, for all the convectively active regions examined, most of the variance of observed Q1 and Q2 can be explained by retaining only two modes. Moreover, while these two modes have different amplitudes in time and space, the shapes of the Q1 and Q2 profiles associated with each mode are similar from one region to another. In this sense, they are analogous to the cloud types in the spectral cumulus ensemble model of the Arakawa–Schubert cumulus parameterization, in which the spectral distribution of cloud-base mass flux varies with large-scale conditions while the vertical profile of normalized mass flux is fixed for each cloud type. It is suggested that, as far as deep convection is concerned, the cloud model in cumulus parameterization probably can be constructed based on the empirically determined Q1 and Q2 profiles.

Corresponding author address: Dr. Akio Arakawa, Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, CA 90095.

Email: aar@atmos.ucla.edu

Abstract

The constraint on the coupled vertical profiles of cumulus heating and drying, which can be used as a partial closure in cumulus parameterization, is examined using observational data from convectively active regions in the summertime. The data used in this study include those derived from Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment Phase III, Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment over the intensive flux array region, and four subsets of the European Centre for Medium-Range Weather Forecasts Re-Analysis data that cover areas ranging from tropical to midlatitude continents. The profiles of Q1 and Q2 calculated from those data are analyzed using a statistical method. The proposed method is a revised version of the rotated principal component analysis based on the Promax rotation (RPCAPromax), which is believed suitable for identifying basic structures embedded within a given dataset. It is designed in such a way that the distortion of identified structures due to the use of a linear model is minimized. The revised RPCAPromax, together with some selected statistical tools, are evaluated using synthetic datasets before they are applied to observations.

The analysis of the observational data shows that, for all the convectively active regions examined, most of the variance of observed Q1 and Q2 can be explained by retaining only two modes. Moreover, while these two modes have different amplitudes in time and space, the shapes of the Q1 and Q2 profiles associated with each mode are similar from one region to another. In this sense, they are analogous to the cloud types in the spectral cumulus ensemble model of the Arakawa–Schubert cumulus parameterization, in which the spectral distribution of cloud-base mass flux varies with large-scale conditions while the vertical profile of normalized mass flux is fixed for each cloud type. It is suggested that, as far as deep convection is concerned, the cloud model in cumulus parameterization probably can be constructed based on the empirically determined Q1 and Q2 profiles.

Corresponding author address: Dr. Akio Arakawa, Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, CA 90095.

Email: aar@atmos.ucla.edu

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