Article Type:
Research Article

Downscaling of Daily Rainfall Occurrence over Northeast Brazil Using a Hidden Markov Model

Andrew W. Robertson International Research Institute for Climate Prediction, The Earth Institute at Columbia University, Palisades, New York

Search for other papers by Andrew W. Robertson in
Current site
Google Scholar
PubMed Close
,
Sergey Kirshner School of Information and Computer Science, University of California, Irvine, Irvine, California

Search for other papers by Sergey Kirshner in
Current site
Google Scholar
PubMed Close
, and
Padhraic Smyth School of Information and Computer Science, University of California, Irvine, Irvine, California

Search for other papers by Padhraic Smyth in
Current site
Google Scholar
PubMed Close
Print Publication:
15 Nov 2004
DOI:
https://doi.org/10.1175/JCLI-3216.1
Page(s):
4407–4424
Restricted access

Abstract

A hidden Markov model (HMM) is used to describe daily rainfall occurrence at 10 gauge stations in the state of Ceará in northeast Brazil during the February–April wet season 1975–2002. The model assumes that rainfall occurrence is governed by a few discrete states, with Markovian daily transitions between them. Four “hidden” rainfall states are identified. One pair of the states represents wet-versus-dry conditions at all stations, while a second pair of states represents north–south gradients in rainfall occurrence. The estimated daily state-sequence is characterized by a systematic seasonal evolution, together with considerable variability on intraseasonal, interannual, and longer time scales. The first pair of states are shown to be associated with large-scale displacements of the tropical convergence zones, and with teleconnections typical of the El Niño–Southern Oscillation and the North Atlantic Oscillation.

A nonhomogeneous HMM (NHMM) is then used to downscale daily precipitation occurrence at the 10 stations, using general circulation model (GCM) simulations of seasonal-mean large-scale precipitation, obtained with historical sea surface temperatures prescribed globally. Interannual variability of the GCM's large-scale precipitation simulation is well correlated with seasonal- and spatial-averaged station rainfall-occurrence data. Simulations from the NHMM are found to be able to reproduce this relationship. The GCM-NHMM simulations are also able to capture quite well interannual changes in daily rainfall occurrence and 10-day dry spell frequencies at some individual stations. It is suggested that the NHMM provides a useful tool (a) to understand the statistics of daily rainfall occurrence at the station level in terms of large-scale atmospheric patterns, and (b) to produce station-scale daily rainfall sequence scenarios for input into crop models, etc.

Corresponding author address: Andrew W. Robertson, IRI–Monell 230, 61 Route 9W, Palisades, NY 10964. Email: awr@iri.columbia.edu

Abstract

A hidden Markov model (HMM) is used to describe daily rainfall occurrence at 10 gauge stations in the state of Ceará in northeast Brazil during the February–April wet season 1975–2002. The model assumes that rainfall occurrence is governed by a few discrete states, with Markovian daily transitions between them. Four “hidden” rainfall states are identified. One pair of the states represents wet-versus-dry conditions at all stations, while a second pair of states represents north–south gradients in rainfall occurrence. The estimated daily state-sequence is characterized by a systematic seasonal evolution, together with considerable variability on intraseasonal, interannual, and longer time scales. The first pair of states are shown to be associated with large-scale displacements of the tropical convergence zones, and with teleconnections typical of the El Niño–Southern Oscillation and the North Atlantic Oscillation.

A nonhomogeneous HMM (NHMM) is then used to downscale daily precipitation occurrence at the 10 stations, using general circulation model (GCM) simulations of seasonal-mean large-scale precipitation, obtained with historical sea surface temperatures prescribed globally. Interannual variability of the GCM's large-scale precipitation simulation is well correlated with seasonal- and spatial-averaged station rainfall-occurrence data. Simulations from the NHMM are found to be able to reproduce this relationship. The GCM-NHMM simulations are also able to capture quite well interannual changes in daily rainfall occurrence and 10-day dry spell frequencies at some individual stations. It is suggested that the NHMM provides a useful tool (a) to understand the statistics of daily rainfall occurrence at the station level in terms of large-scale atmospheric patterns, and (b) to produce station-scale daily rainfall sequence scenarios for input into crop models, etc.

Corresponding author address: Andrew W. Robertson, IRI–Monell 230, 61 Route 9W, Palisades, NY 10964. Email: awr@iri.columbia.edu

Save
Cover Journal of Climate
Journal of Climate

  • Bauer, F., 1951: Extended range weather forecasting. Compendium of Meteorology, T. F. Malone, Ed., American Meteorological Society, 814–833.

    • Search Google Scholar
    • Export Citation

  • Bellone, E., J. P. Hughes, and P. Guttorp, 2000: A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts. Climate Res, 15 , 1–12.

    • Search Google Scholar
    • Export Citation

  • Charles, S. P., B. C. Bates, and J. P. Hughes, 1999: A spatiotemporal model for downscaling precipitation occurrence and amounts. J. Geophys. Res, 104D , 31657–31669.

    • Search Google Scholar
    • Export Citation

  • Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci, 36 , 1205–1216.

  • Chiang, J. C. H., Y. Kushnir, and A. Giannini, 2002: Deconstructing Atlantic Intertropical Convergence Zone variability: Influence of the local cross-equatorial sea surface temperature gradient and remote forcing from the eastern equatorial Pacific. J. Geophys. Res.,107D, 4004, doi:10.1029/2000JD000307.

    • Search Google Scholar
    • Export Citation

  • Dempster, A. P., N. M. Laird, and D. B. Rubin, 1977: Maximum likelihood from incomplete data via EM algorithm. J. Roy. Stat. Soc, 39B , 1–38.

    • Search Google Scholar
    • Export Citation

  • Feldstein, S. B., 2000: The time scale, power spectra, and climate noise properties of teleconnection patterns. J. Climate, 13 , 4430–4440.

    • Search Google Scholar
    • Export Citation

  • Giannini, A., R. Saravanan, and P. Chang, 2004: The preconditioning role of Tropical Atlantic variability in the prediction of Nordeste rainfall during ENSO events. Climate Dyn, 22 , 839–855.

    • Search Google Scholar
    • Export Citation

  • Goddard, L., A. G. Barnston, and S. J. Mason, 2003: Evaluation of the IRI's “net assessment” seasonal climate forecasts: 1997– 2001. Bull. Amer. Meteor. Soc, 84 , 1761–1781.

    • Search Google Scholar
    • Export Citation

  • Gong, G., D. Entekhabi, and J. Cohen, 2003: Modeled Northern Hemisphere winter climate response to realistic Siberian snow anomalies. J. Climate, 16 , 3917–3931.

    • Search Google Scholar
    • Export Citation

  • Hastenrath, S., and L. Heller, 1977: Dynamics of climatic hazards in northeast Brazil. Quart. J. Roy. Meteor. Soc, 103 , 77–92.

  • Hughes, J. P., and P. Guttorp, 1994a: A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena. Water Resour. Res, 30 , 1535–1546.

    • Search Google Scholar
    • Export Citation

  • Hughes, J. P., and P. Guttorp, 1994b: Incorporating spatial dependence and atmospheric data in a model of precipitation. J. Appl. Meteor, 33 , 1503–1515.

    • Search Google Scholar
    • Export Citation

  • Hughes, J. P., P. Guttorp, and S. P. Charles, 1999: A non-homogeneous hidden Markov model for precipitation occurrence. J. Roy. Stat. Soc, 48C , 15–30.

    • Search Google Scholar
    • Export Citation

  • Hurrell, J. W., Y. Kushnir, G. Ottersen, and M. Visbeck, Eds.,. 2002: The North Atlantic Oscillation: Climatic Significance and Environmental Impact. Geophys. Monogr., No. 134, Amer. Geophys. Union, 279 pp.

    • Search Google Scholar
    • Export Citation

  • Jain, A. K., and R. C. Dubes, 1988: Algorithms for Clustering Data. Prentice Hall, 320 pp.

  • Juang, B. H., and L. R. Rabiner, 1985: Mixture autoregressive hidden Markov models for speech signals. IEEE Trans. Acoust. Speech Signal Process, 33 , 1404–1413.

    • Search Google Scholar
    • Export Citation

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc, 77 , 437–471.

  • Kass, R. E., and A. E. Raftery, 1995: Bayes factors. J. Amer. Stat. Assoc, 90 , 773–795.

  • Kirshner, S., A. W. Robertson, and P. J. Smyth, 2004: Conditional Chow-Liu tree structures for modeling discrete-valued vector time series. Tech. Rep. ICS-TR 04-04, Information and Computer Science, University of California, Irvine, CA, 26 pp.

    • Search Google Scholar
    • Export Citation

  • Liebmann, B., G. N. Kiladis, J. A. Marengo, T. Ambrizzi, and J. D. Glick, 1999: Submonthly convective variability over South America and the South Atlantic convergence zone. J. Climate, 12 , 1877–1891.

    • Search Google Scholar
    • Export Citation

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci, 20 , 130–141.

  • MacDonald, I. L., and W. Zucchini, 1997: Hidden Markov and Other Models for Discrete-valued Time Series. Meteor. Monogr., Statistics and Applied Probability, No. 70, Chapman & Hall, 236 pp.

    • Search Google Scholar
    • Export Citation

  • Moura, A. D., and J. Shukla, 1981: On the dynamics of droughts in northeast Brazil: Observations, theory and numerical experiments with a general circulation model. J. Atmos. Sci, 38 , 2653–2657.

    • Search Google Scholar
    • Export Citation

  • Nobre, P., and J. Shukla, 1996: Variations of sea surface temperature, wind stress, and rainfall over the tropical Atlantic and South America. J. Climate, 9 , 2464–2479.

    • Search Google Scholar
    • Export Citation

  • Rabiner, L. R., 1989: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE, 77 , 257–286.

  • Robertson, A. W., S. Kirshner, and P. J. Smyth, 2003: Hidden Markov models for modeling daily rainfall occurrence over Brazil. Tech. Rep. ICS-TR 03-27, Information and Computer Science, University of California, Irvine, CA, 38 pp.

    • Search Google Scholar
    • Export Citation

  • Roeckner, E., and Coauthors, 1996: The atmospheric general circulation model ECHAM4: Model description and simulation of present-day climate. Max-Planck-Institut fur Meteorologie Rep. 23, 90 pp.

    • Search Google Scholar
    • Export Citation

  • Smith, T. M., R. W. Reynolds, R. E. Livezey, and D. C. Stokes, 1996: Reconstruction of historical sea surface temperatures using empirical orthogonal functions. J. Climate, 9 , 1403–1420.

    • Search Google Scholar
    • Export Citation

  • Sun, L., D. F. Moncunill, H. Li, A. D. Moura, and F. A. D. S. Filho, 2005: Climate downscaling over Nordeste Brazil using NCEP RSM97. J. Climate, in press.

    • Search Google Scholar
    • Export Citation

  • Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15 , 1421–1428.

    • Search Google Scholar
    • Export Citation

  • Tippett, M. K., M. Barlow, and B. Lyon, 2003: Statistical correction of central southwest Asia winter precipitation simulations. Int. J. Climatol, 23 , 1421–1433.

    • Search Google Scholar
    • Export Citation

  • Titterington, D. M., 1990: Some recent research in the analysis of mixture distributions. Statistics, 21 , 619–641.

  • Wilby, R. L., 2001: Downscaling summer rainfall in the UK from North Atlantic Ocean temperatures. Hydrol. Earth Syst. Sci, 5 , 245–257.

    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., 1998: Multisite generalization of a daily stochastic precipitation generation model. J. Hydrol, 210 , 178–191.

  • Wilks, D. S., 2002: Realizations of daily weather in forecast seasonal climate. J. Hydrometeor, 3 , 195–207.

  • Wilks, D. S., and R. L. Wilby, 1999: The weather generation game: A review of stochastic weather models. Prog. Phys. Geogr, 23 , 329–357.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1043 230 39
PDF Downloads 822 184 28