Editorial Type:
Article
Article Type:
Research Article

Empirical Probability Models to Predict Precipitation Levels over Puerto Rico Stations

Nazario D. Ramirez-Beltran Department of Industrial Engineering, University of Puerto Rico, Mayagüez, Puerto Rico

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William K. M. Lau Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland

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Amos Winter Department of Marine Sciences, University of Puerto Rico, Mayagüez, Puerto Rico

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Joan M. Castro Department of Electrical and Computer Engineering, University of Puerto Rico, Mayagüez, Puerto Rico

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Nazario Ramirez Escalante Department of Civil Engineering, University of Puerto Rico, Mayagüez, Puerto Rico

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Print Publication:
01 Mar 2007
DOI:
https://doi.org/10.1175/MWR3290.1
Page(s):
877–890
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Abstract

A new algorithm is proposed to predict the level of rainfall (above normal, normal, and below normal) in Puerto Rico that relies on probability and empirical models. The algorithm includes a theoretical probability model in which parameters are expressed as regression equations containing observed meteorological variables. Six rainfall stations were used in this study to implement and assess the reliability of the models. The stations, located throughout Puerto Rico, have monthly records that extend back 101 yr. The maximum likelihood method is used to estimate the parameters of the empirical probability models. A variable selection (VS) algorithm identifies the minimum number of variables that maximize the correlation between predictors and a predictand. The VS algorithm is used to identify the initial point and the maximum likelihood is optimized by using the sequential quadratic programming algorithm. Ten years of cross validation were applied to the results from six stations. The proposed method outperforms both climatology and damped persistence models. Results suggest that the methodology implemented here can be used as a potential tool to predict the level of rainfall at any station located on a tropical island, assuming that at least 50 yr of monthly rainfall observations are available. Model analyses show that meteorological indices can be used to predict rainfall stages.

Corresponding author address: Dr. Nazario D. Ramirez-Beltran, Department of Industrial Engineering, University of Puerto Rico, Mayagüez, 00680 Puerto Rico. Email: nazario@ece.uprm.edu

Abstract

A new algorithm is proposed to predict the level of rainfall (above normal, normal, and below normal) in Puerto Rico that relies on probability and empirical models. The algorithm includes a theoretical probability model in which parameters are expressed as regression equations containing observed meteorological variables. Six rainfall stations were used in this study to implement and assess the reliability of the models. The stations, located throughout Puerto Rico, have monthly records that extend back 101 yr. The maximum likelihood method is used to estimate the parameters of the empirical probability models. A variable selection (VS) algorithm identifies the minimum number of variables that maximize the correlation between predictors and a predictand. The VS algorithm is used to identify the initial point and the maximum likelihood is optimized by using the sequential quadratic programming algorithm. Ten years of cross validation were applied to the results from six stations. The proposed method outperforms both climatology and damped persistence models. Results suggest that the methodology implemented here can be used as a potential tool to predict the level of rainfall at any station located on a tropical island, assuming that at least 50 yr of monthly rainfall observations are available. Model analyses show that meteorological indices can be used to predict rainfall stages.

Corresponding author address: Dr. Nazario D. Ramirez-Beltran, Department of Industrial Engineering, University of Puerto Rico, Mayagüez, 00680 Puerto Rico. Email: nazario@ece.uprm.edu

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  • Bazaraa, M. S. , H. D. Sherali , and C. M. Shetty , 1993: Nonlinear Programming: Theory and Algorithms. 2d ed. John Wiley and Sons, 638 pp.

    • Search Google Scholar
    • Export Citation

  • Bickel, P. J. , and K. A. Doksum , 1977: Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day, 492 pp.

  • Box, G. E. P. , and G. M. Jenkins , 1976: Times Series Analysis: Forecasting and Control. Holden-Day, 575 pp.

  • Brockwell, P. J. , and R. A. Davis , 2002: Introduction to Time Series and Forecasting. 2d ed. Springer-Verlag, 434 pp.

  • Carter, M. M. , 1999: A quantitative precipitation forecast experiment for Puerto Rico. Ph.D. dissertation, The Florida State University, 123 pp.

  • Carter, M. M. , and J. B. Elsner , 1997: A statistical method for forecasting rainfall over Puerto Rico. Wea. Forecasting, 12 , 515–525.

    • Search Google Scholar
    • Export Citation

  • Chiu, L. S. , and B. Kedem , 1990: Estimating the exceedance probability of rain rate by logistic-regression. J. Geophys. Res., 95 , D3. 2217–2227.

    • Search Google Scholar
    • Export Citation

  • Comarazamy, D. E. , 2001: Atmospheric modeling of the Caribbean region: Precipitation and wind analysis in Puerto Rico for April 1998. M.S. thesis, Department of Mechanical Engineering, University of Puerto Rico, Mayagüez, Puerto Rico, 112 pp.

  • Gahrs, G. E. , S. Applequist , R. L. Pfeffer , and X-F. Niu , 2003: Improved results for probabilistic quantitative precipitation forecasting. Wea. Forecasting, 18 , 879–890.

    • Search Google Scholar
    • Export Citation

  • Gray, W. M. , P. J. Klotzbach , and W. Thorson , cited. 2005: Extended range forecast of Atlantic seasonal hurricane activity and U.S. landfall strike probability for 2005. [Available online at http://hurricane.atmos.colostate.edu/Forecasts/2005.].

  • Hurrell, J. W. , 1995: Decadal trends in the North Atlantic Oscillation: Regional temperatures and precipitation. Science, 269 , 676–679.

    • Search Google Scholar
    • Export Citation

  • Janowiak, J. E. , 1988: An investigation of interannual rainfall variability in Africa. J. Climate, 1 , 240–255.

  • Malmgren, B. A. , A. Winter , and D. Chen , 1998: El Niño–Southern Oscillation and North Atlantic Oscillation control of climate in Puerto Rico. J. Climate, 11 , 2713–2717.

    • Search Google Scholar
    • Export Citation

  • MathWorks , 2000: Optimization toolbox for use with Matlab: User’s guide. MathWorks, Inc., 331 pp.

  • Montgomery, D. C. , E. A. Peck , and G. G. Vining , 2001: Introduction to Linear Regression Analysis. 3d ed. John Wiley and Sons, 641 pp.

    • Search Google Scholar
    • Export Citation

  • Mood, A. M. , F. A. Graybill , and D. C. Boes , 1974: Introduction to the Theory of Statistics. 3d ed. McGraw-Hill, 564 pp.

  • Murphy, A. H. , 1992: Climatology, persistence, and their linear combination as standards of reference in skill scores. Wea. Forecasting, 7 , 692–698.

    • Search Google Scholar
    • Export Citation

  • Pandit, S. M. , and S. M. Wu , 1983: Time Series and System Analysis, with Applications. John Wiley and Sons, 586 pp.

  • Reklaitis, G. V. , A. Ravindran , and K. M. Ragsdell , 1983: Engineering Optimization: Methods and Applications. John Wiley and Sons, 684 pp.

    • Search Google Scholar
    • Export Citation

  • Sohn, K. T. , J. H. Lee , S. H. Lee , and Ch S. Ryu , 2005: Statistical prediction of heavy rain in South Korea. Adv. Atmos. Sci., 22 , 703–710.

    • Search Google Scholar
    • Export Citation

  • Taylor, M. A. , D. B. Enfield , and A. A. Chen , 2002: Influence of the tropical Atlantic versus the tropical Pacific on Caribbean rainfall. J. Geophys. Res., 107 .3127, doi:10.1029/2001JC001097.

    • Search Google Scholar
    • Export Citation

  • Thompson, D. W. J. , and J. M. Wallace , 1998: The Artic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett., 25 , 1297–1300.

    • Search Google Scholar
    • Export Citation

  • Trenberth, K. E. , 1984: Signal versus noise in the Southern Oscillation. Mon. Wea. Rev., 112 , 326–332.

  • Ward, M. N. , and C. K. Folland , 1991: Prediction of seasonal rainfall in the northeast of Brazil using eigenvectors of sea surface temperature. Int. J. Climatol., 11 , 711–743.

    • Search Google Scholar
    • Export Citation

  • Wei, W. W. S. , 1990: Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley, 478 pp.

  • Wilks, D. S. , 1995: Statistical Methods in the Atmospheric Sciences: An Introduction. Academic Press, 467 pp.

  • Wilson, F. W. , 2004: Probabilistic forecasts of cloud impacts at San Francisco International Airport. Proc. 20th Int. Conf. on Interactive Information and Processing Systems (IIPS) for Meteorology, Oceanography, and Hydrology, Seattle, WA, Amer. Meteor. Soc., CD-ROM, 18.1.

  • Winston, W. L. , 2004: Operations Research: Applications and Algorithms. 4th ed. Brooks/Cole, 1418 pp.

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