• Biggerstaff, M. I., Seo E. K. , Hrstove-Veleva S. M. , and Kim K. Y. , 2006: Impact of cloud model microphysics on passive microwave retrievals of cloud properties. Part I: Model comparison using EOF analyses. J. Appl. Meteor. Climatol., 45 , 930954.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Castro, C. L., 2005: Investigation of the summer climate of North America: A regional atmospheric modeling study. Ph.D. dissertation, Colorado State University, Fort Collins, CO, 223 pp.

  • Castro, C. L., Cheng W. Y. Y. , Beltrán A. B. , Pielke R. A. Sr., and Cotton W. R. , 2002: The incorporation of the Kain–Fritsch cumulus parameterization scheme in RAMS with a terrain-adjusted trigger function. Fifth RAMS Users and Related Applications Workshop, Santorini, Greece, ATMET, Inc.

    • Search Google Scholar
    • Export Citation
  • Castro, C. L., Pielke R. A. Sr., and Adegoke J. , 2007a: Investigation of the summer climate of the contiguous U.S. and Mexico using the Regional Atmospheric Modeling System (RAMS). Part I: Model climatology (1950–2002). J. Climate, 20 , 38443865.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Castro, C. L., Pielke R. A. Sr., Adegoke J. , Schubert S. D. , and Pegion P. J. , 2007b: Investigation of the summer climate of the contiguous U.S. and Mexico using the Regional Atmospheric Modeling System (RAMS). Part II: Model climate variability. J. Climate, 20 , 38663887.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, C., and Cotton W. R. , 1987: The physics of the marine stratocumulus-capped mixed layer. J. Atmos. Sci., 44 , 29512977.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chevallier, F., Chéruy F. , Scott N. A. , and Chédin A. , 1998: A neural network approach for a fast and accurate computation of a longwave radiative budget. J. Appl. Meteor., 37 , 13851397.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davis, R. E., 1976: Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean. J. Phys. Oceanogr., 6 , 249266.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dong, X., Xi B. , and Minnis P. , 2006: A climatology of midlatitude continental clouds from the ARM SCP central facility. Part II: Cloud fraction and surface radiative forcing. J. Climate, 19 , 17651783.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fu, Q., and Liou K. N. , 1992: On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres. J. Atmos. Sci., 49 , 21392156.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gabriel, P. M., Stephens G. L. , and Wittmeyer I. L. , 2000: Adjoint perturbation and selection rule methods for solar broadband two-stream fluxes in multi-layer media. J. Quant. Spectrosc. Radiat. Transfer, 65 , 693728.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gabriel, P. M., Partain P. T. , and Stephens G. L. , 2001: Transfer. Part II: Selection rules. J. Atmos. Sci., 58 , 34113423.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harrington, J. Y., 1997: The effects of radiative and microphysical processes on simulated warm and transition season Arctic stratus. Dept. Of Atmospheric Science Bluebook 637, Colorado State University, Fort Collins, CO, 289 pp.

  • Harrington, J. Y., Meyers M. P. , Cotton W. R. , and Kreidenweis S. M. , 1999: Cloud resolving simulations of Arctic stratus. Part II: Transition season clouds. Atmos. Res., 55 , 4575.

    • Search Google Scholar
    • Export Citation
  • Josey, S. A., Pascal R. W. , Taylor P. K. , and Yelland M. J. , 2003: A new formula for determining the atmospheric longwave flux at the ocean surface at mid-high latitudes. J. Geophys. Res., 108 .3108, doi:10.1029/2002JC001418.

    • Search Google Scholar
    • Export Citation
  • Kain, J. S., and Fritsch J. M. , 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–170.

    • Search Google Scholar
    • Export Citation
  • Kaiser, H. F., 1958: The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23 , 187200.

  • Kravtsov, S., Robertson A. W. , and Ghil M. , 2006: Multiple regimes and low-frequency oscillations in the Northern Hemisphere’s zonal-mean flow. J. Atmos. Sci., 63 , 840860.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, W. T., Tang W. , and Niiler P. P. , 1991: Humidity profiles over the ocean. J. Climate, 4 , 10231034.

  • Lorenz, E. N., 1956: Empirical orthogonal function and statistical weather prediction. Statistical Forecasting Project Science Rep. 1, Dept. of Meteorology, Massachusetts Institute of Technology, 49 pp. [NTIS AD 110268.].

  • Lorenz, E. N., 1977: An experiment in nonlinear statistical weather forecasting. Mon. Wea. Rev., 105 , 590602.

  • Majewski, D., and Coauthors, 2002: The operational global icosahedral–hexagonal gridpoint model GME: Description and high-resolution tests. Mon. Wea. Rev., 130 , 319338.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mesinger, F., and Coauthors, 2006: North American Regional Reanalysis. Bull. Amer. Meteor. Soc., 87 , 343360.

  • Natraj, V., Jiang X. , Shia R. , Huang X. , Margolis J. S. , and Yung Y. L. , 2005: Application of principal component analysis to high spectral resolution radiative transfer: A case study of the O2 A band. J. Quant. Spectrosc. Radiat. Transfer, 95 , 539556.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • North, G. R., Bell T. L. , Cahalan R. F. , and Moeng F. J. , 1982: Sampling errors in the estimation of empirical orthogonal functions. Mon. Wea. Rev., 110 , 699706.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oppenheim, A. V., Schafer R. W. , and Buck J. R. , 1999: Discrete-Time Signal Processing. 2nd ed. Prentice-Hall, 870 pp.

  • Pielke R. A. Sr., , and Coauthors, 2006: A new paradigm for parameterizations in numerical weather prediction and other atmospheric models. Natl. Wea. Dig., 30 , (12). 9399.

    • Search Google Scholar
    • Export Citation
  • Quadrelli, R., Bretherton C. S. , and Wallace J. M. , 2005: On sampling errors in empirical orthogonal functions. J. Climate, 18 , 37043710.

  • Schubert, S. D., Suarez M. J. , Pegion P. J. , and Kistler M. A. , 2002: Predictability of zonal means during boreal summer. J. Climate, 15 , 420434.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Part I: The basic experiment. Mon. Wea. Rev., 91 , 99164.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and Wallace J. M. , 2000: Annular modes in the extratropical circulation. Part I: Month-to month variability. J. Climate, 13 , 10001016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • von Storch, H., and Hannoschöck G. , 1985: Statistical aspects of estimated principal vectors (EOFs) based on small sample sizes. J. Climate Appl. Meteor., 24 , 716724.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Walko, R. L., and Coauthors, 2000: Coupled atmosphere–biophysics–hydrology models for environmental modeling. J. Appl. Meteor., 39 , 931944.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2006: Statistical Methods for the Atmospheric Sciences. 2nd ed. Academic Press, 648 pp.

  • Zhang, H., Nakajima T. , Shi G. , Suzuki T. , and Imasu R. , 2003: An optimal approach to overlapping bands with correlated k distribution method and its application to radiative calculations. J. Geophys. Res., 108 .4641, doi:10.1029/2002JD003358.

    • Search Google Scholar
    • Export Citation
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From Model-Based Parameterizations to Lookup Tables: An EOF Approach

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
  • | 2 Cooperative Institute for Research in Environmental Sciences, Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado
  • | 3 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

The goal of this study is to transform the Harrington radiation parameterization into a transfer scheme or lookup table, which provides essentially the same output (heating rate profile and short- and longwave fluxes at the surface) at a fraction of the computational cost. The methodology put forth here does not introduce a new parameterization simply derived from the Harrington scheme but, rather, shows that given a generic parameterization it is possible to build an algorithm, largely not based on the physics, that mimics the outcome of the parent parameterization. The core concept is to compute the empirical orthogonal functions (EOFs) of all of the input variables of the parent scheme, run the scheme on the EOFs, and express the output of a generic input sounding exploiting the input–output pairs associated with the EOFs. The weights are based on the difference between the input and EOFs water vapor mixing ratios. A detailed overview of the algorithm and the development of a few transfer schemes are also presented. Results show very good agreement (r > 0.91) between the different transfer schemes and the Harrington radiation parameterization with a very significant reduction in computational cost (at least 95%).

Corresponding author address: Giovanni Leoncini, Meteorology Dept., University of Reading, P.O. Box 243, Reading, RG6 6BB, United Kingdom. Email: g.leoncini@reading.ac.uk

Abstract

The goal of this study is to transform the Harrington radiation parameterization into a transfer scheme or lookup table, which provides essentially the same output (heating rate profile and short- and longwave fluxes at the surface) at a fraction of the computational cost. The methodology put forth here does not introduce a new parameterization simply derived from the Harrington scheme but, rather, shows that given a generic parameterization it is possible to build an algorithm, largely not based on the physics, that mimics the outcome of the parent parameterization. The core concept is to compute the empirical orthogonal functions (EOFs) of all of the input variables of the parent scheme, run the scheme on the EOFs, and express the output of a generic input sounding exploiting the input–output pairs associated with the EOFs. The weights are based on the difference between the input and EOFs water vapor mixing ratios. A detailed overview of the algorithm and the development of a few transfer schemes are also presented. Results show very good agreement (r > 0.91) between the different transfer schemes and the Harrington radiation parameterization with a very significant reduction in computational cost (at least 95%).

Corresponding author address: Giovanni Leoncini, Meteorology Dept., University of Reading, P.O. Box 243, Reading, RG6 6BB, United Kingdom. Email: g.leoncini@reading.ac.uk

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