GiST: A Stochastic Model for Generating Spatially and Temporally Correlated Daily Rainfall Data

Guillermo A. Baigorria Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida

Search for other papers by Guillermo A. Baigorria in
Current site
Google Scholar
PubMed
Close
and
James W. Jones Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida

Search for other papers by James W. Jones in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Weather generators are tools that create synthetic daily weather data over long periods of time. These tools have also been used for downscaling monthly to seasonal climate forecasts, from global and regional circulation models to daily values for use as inputs for crop and other environmental models. One main limitation of most weather generators is that they do not take into account the spatial structure of weather. Spatial correlation of daily rainfall is important when one aggregates, for example, simulated crop yields or hydrology in a watershed or region. A method was developed to generate realizations of daily rainfall for multiple sites in an area while preserving the spatial and temporal correlations among sites. A two-step method generates rainfall events at multiple sites followed by rainfall amounts at sites where generated rainfall events occur. The generation of rainfall events was based on a new orthogonal Markov chain for discrete distributions. For generating rainfall amounts, a vector of random numbers (from a uniform distribution), of order equal to the number of locations with rainfall events that were generated to occur in a day, was matrix-multiplied by the corresponding factorized correlation matrix to create spatially correlated random numbers. Elements from the resulting vector were transformed to a gamma distribution using cumulative probability functions for each location and rescaled to rainfall amounts. One study area was located in north-central Florida, where correlated rainfall data were generated for seven weather stations to evaluate its performance versus a widely used single-site weather generator. A second area was in North Carolina, where rainfall was generated for 25 weather stations to evaluate the effects of a larger number of stations in other regions. One thousand yearlong replications of daily rainfall data were generated for each area. Monthly spatial correlations of generated daily rainfall events and amounts among all pairs of weather stations closely matched their observed counterparts. For daily rainfall amounts the correlation coefficients between the observed pairwise correlation coefficients and the ones estimated from synthetic data among weather stations were 0.977 for Florida and 0.964 for North Carolina. The performance of the geospatial–temporal (GiST) weather generator was also analyzed by comparing the distributions of lengths of dry and wet spells, joint probabilities, Markov transitional probabilities, distance decay of correlation functions, and regionwide days without rainfall at any station. Multiannual mean and standard deviation of the number of rainy days per month and mean monthly rainfall were also calculated. All comparisons between observed and generated rainfall events and amounts using the GiST weather generator were highly correlated. The root-mean-square errors of pairwise correlation values ranged from 0.05 to 0.11 for rainfall events and from 0.03 to 0.06 for amounts.

Corresponding author address: Guillermo A. Baigorria, Agricultural and Biological Engineering Department, University of Florida, 261 Frazier Rogers Hall, Gainesville, FL 32611-0570. Email: gbaigorr@ifas.ufl.edu

Abstract

Weather generators are tools that create synthetic daily weather data over long periods of time. These tools have also been used for downscaling monthly to seasonal climate forecasts, from global and regional circulation models to daily values for use as inputs for crop and other environmental models. One main limitation of most weather generators is that they do not take into account the spatial structure of weather. Spatial correlation of daily rainfall is important when one aggregates, for example, simulated crop yields or hydrology in a watershed or region. A method was developed to generate realizations of daily rainfall for multiple sites in an area while preserving the spatial and temporal correlations among sites. A two-step method generates rainfall events at multiple sites followed by rainfall amounts at sites where generated rainfall events occur. The generation of rainfall events was based on a new orthogonal Markov chain for discrete distributions. For generating rainfall amounts, a vector of random numbers (from a uniform distribution), of order equal to the number of locations with rainfall events that were generated to occur in a day, was matrix-multiplied by the corresponding factorized correlation matrix to create spatially correlated random numbers. Elements from the resulting vector were transformed to a gamma distribution using cumulative probability functions for each location and rescaled to rainfall amounts. One study area was located in north-central Florida, where correlated rainfall data were generated for seven weather stations to evaluate its performance versus a widely used single-site weather generator. A second area was in North Carolina, where rainfall was generated for 25 weather stations to evaluate the effects of a larger number of stations in other regions. One thousand yearlong replications of daily rainfall data were generated for each area. Monthly spatial correlations of generated daily rainfall events and amounts among all pairs of weather stations closely matched their observed counterparts. For daily rainfall amounts the correlation coefficients between the observed pairwise correlation coefficients and the ones estimated from synthetic data among weather stations were 0.977 for Florida and 0.964 for North Carolina. The performance of the geospatial–temporal (GiST) weather generator was also analyzed by comparing the distributions of lengths of dry and wet spells, joint probabilities, Markov transitional probabilities, distance decay of correlation functions, and regionwide days without rainfall at any station. Multiannual mean and standard deviation of the number of rainy days per month and mean monthly rainfall were also calculated. All comparisons between observed and generated rainfall events and amounts using the GiST weather generator were highly correlated. The root-mean-square errors of pairwise correlation values ranged from 0.05 to 0.11 for rainfall events and from 0.03 to 0.06 for amounts.

Corresponding author address: Guillermo A. Baigorria, Agricultural and Biological Engineering Department, University of Florida, 261 Frazier Rogers Hall, Gainesville, FL 32611-0570. Email: gbaigorr@ifas.ufl.edu

Save
  • Apipattanavis, S., G. Podestá, B. Rajagopalan, and R. Katz, 2007: A semiparametric multivariate and multisite weather generator. Water Resour. Res., 43 , 119.

    • Search Google Scholar
    • Export Citation
  • Baigorria, G. A., 2007: Assessing the use of seasonal-climate forecasts to support farmers in the Andean highlands. Climate Prediction and Agriculture: Advances and Challenges, M. V. K. Sivakumar and J. W. Hansen, Eds., Springer, 99–110.

    • Search Google Scholar
    • Export Citation
  • Baigorria, G. A., and C. C. Romero, 2007: Assessment of erosion hotspot in a watershed: Integrating the WEPP model and GIS in a case study in the Peruvian Andes. Environ. Modell. Software, 22 , 11751183.

    • Search Google Scholar
    • Export Citation
  • Baigorria, G. A., J. W. Jones, and J. J. O’Brien, 2007a: Understanding rainfall spatial variability in the southeast USA at different timescales. Int. J. Climatol., 27 , 749760.

    • Search Google Scholar
    • Export Citation
  • Baigorria, G. A., J. W. Jones, D. W. Shin, A. Mishra, and J. J. O’Brien, 2007b: Assessing uncertainties in crop model simulations using daily bias-corrected regional circulation model outputs. Climate Res., 34 , 211222.

    • Search Google Scholar
    • Export Citation
  • Beersma, J. J., and T. A. Buishand, 2003: Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation. Climate Res., 25 , 121133.

    • Search Google Scholar
    • Export Citation
  • Benoît, C., 1924: Note sur une méthode de résolution des équations normales provenant de l’application de la méthode des moindres carrés à un système d’équations linéaires en nombre inférieur à la résolution d’un système défini d’équations linéaires (Procédé du Commandant A.-L. Cholesky). Bull. Geod., 2 , 6777.

    • Search Google Scholar
    • Export Citation
  • Brezinski, C., 2006: The life and work of André Cholesky. Numer. Algorithms, 41 , 197202.

  • Brissette, F. P., M. Khalili, and R. Leconte, 2007: Efficient stochastic generation of multi-site synthetic precipitation data. J. Hydrol., 345 , 121133.

    • Search Google Scholar
    • Export Citation
  • Burton, A., C. G. Kilsby, H. J. Fowler, P. S. P. Cowpertwait, and P. E. O’Connell, 2008: RainSim: A spatial–temporal stochastic rainfall modelling system. Environ. Modell. Software, 23 , 13561369.

    • Search Google Scholar
    • Export Citation
  • Cannon, A., 2008: Probabilistic multisite precipitation downscaling by an expanded Bernoulli–Gamma density network. J. Hydrometeor., 9 , 12841300.

    • Search Google Scholar
    • Export Citation
  • Fowler, H. J., C. G. Kilsby, P. E. O’Connell, and A. Burton, 2005: A weather-type conditioned multi-site stochastic rainfall model for the generation of scenarios of climatic variability and change. J. Hydrol., 308 , 5066.

    • Search Google Scholar
    • Export Citation
  • Greenwood, J. A., and D. Durand, 1960: Aids for fitting the gamma distribution by maximum likelihood. Technometrics, 2 , 5565.

  • Grondona, M. O., G. P. Podestá, M. Bidegain, M. Marino, and H. Hordij, 2000: A stochastic precipitation generator conditioned on ENSO phase: A case study in southeastern South America. J. Climate, 13 , 29732986.

    • Search Google Scholar
    • Export Citation
  • Hansen, J. W., and A. V. M. Ines, 2005: Stochastic disaggregation of monthly rainfall data for crop simulation studies. Agric. For. Meteor., 131 , 233246.

    • Search Google Scholar
    • Export Citation
  • Hilbert, D., 1904: Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 4991.

    • Search Google Scholar
    • Export Citation
  • Hotelling, H., 1933: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol., 24 , 417441.

  • Iman, R. L., and W. J. Conover, 1982: A distribution-free approach to inducing rank correlation among input variables. Commun. Stat. Simul. Comput., 11 , 311334.

    • Search Google Scholar
    • Export Citation
  • Keener, V. W., K. T. Ingram, B. Jacobson, and J. W. Jones, 2007: Effects of El Niño/Southern Oscillation on simulated phosphorus loadings in south Florida. Trans. ASABE, 50 , 20812089.

    • Search Google Scholar
    • Export Citation
  • Khalili, M., R. Leconte, and F. Brissette, 2007: Stochastic multisite generation of daily precipitation data using spatial autocorrelation. J. Hydrometeor., 8 , 396412.

    • Search Google Scholar
    • Export Citation
  • Leander, R., and T. A. Buishand, 2009: A daily weather generator based on a two-stage resampling algorithm. J. Hydrol., 374 , 185195.

  • Markov, A. A., 1906: Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga. Izv. Fiz.-Mat. Obsch. Kazan. Univ. Ser. 2, 15 , 135156.

    • Search Google Scholar
    • Export Citation
  • Mehrotra, R., R. Srikanthan, and A. Sharma, 2006: A comparison of three stochastic multi-site precipitation occurrence generators. J. Hydrol., 331 , 280292.

    • Search Google Scholar
    • Export Citation
  • Nicks, A. D., L. J. Lane, and G. A. Gander, 1995: Weather generator. USDA-Water Erosion Prediction Project (WEPP): WEPP users summary. USDA-ARS NSERL Rep. 10, 2.1–2.22. [Available online at http://www.ars.usda.gov/SP2UserFiles/ad_hoc/36021500WEPP/chap2.pdf].

    • Search Google Scholar
    • Export Citation
  • Palutikof, J. P., C. M. Goodess, S. J. Watkins, and T. Holt, 2002: Generating rainfall and temperature scenarios at multiple sites: Examples from the Mediterranean. J. Climate, 15 , 35293548.

    • Search Google Scholar
    • Export Citation
  • Podestá, G. Coauthors 2002: Use of ENSO-related climate information in agricultural decision making in Argentina: A pilot experience. Agric. Syst., 74 , 371392.

    • Search Google Scholar
    • Export Citation
  • Qian, B., J. Corte-Real, and H. Xu, 2002: Multisite stochastic weather models for impact studies. Int. J. Climatol., 22 , 13771397.

  • Racsko, P., L. Szeidl, and M. A. Semenov, 1991: A serial approach to local stochastic weather models. Ecol. Modell., 57 , 2741.

  • Rebonato, R., and P. Jäckel, 2000: The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. J. Risk, 2 , 1726.

    • Search Google Scholar
    • Export Citation
  • Richardson, C. W., and D. A. Wright, 1984: WGEN: A model for generating daily weather variables. USDA ARS Bull. ARS-8, 86 pp.

  • Rodriguez-Iturbe, I., B. Febres de Power, and J. B. Valdes, 1987: Rectangular pulse point process models for rainfall: Analysis of empirical data. J. Geophys. Res., 92 , 96459656.

    • Search Google Scholar
    • Export Citation
  • Romero, C. C., G. A. Baigorria, and L. Stroosnijder, 2007: Changes of erosive rainfall for El Niño and La Niña years in the northern Andean highlands of Peru. Climatic Change, 85 , 343356.

    • Search Google Scholar
    • Export Citation
  • Romero, C. C., M. D. Dukes, G. A. Baigorria, and R. Cohen, 2009: Comparing theoretical irrigation requirement and actual irrigation for citrus in Florida. Agric. Water Manage., 96 , 473483.

    • Search Google Scholar
    • Export Citation
  • Scheuer, E. M., and D. S. Stoller, 1962: On the generation of normal random vectors. Technometrics, 4 , 278281.

  • Semenov, M. A., R. J. Brooks, E. M. Barrow, and C. W. Richardson, 1998: Comparison of the WGEN and LARS-WG stochastic weather generators for diverse climates. Climate Res., 10 , 95107.

    • Search Google Scholar
    • Export Citation
  • Serfling, R. J., 1968: The Wilcoxon two-sample statistic on strongly mixing processes. Ann. Math. Stat., 39 , 12021209.

  • Shin, D-W., G. A. Baigorria, Y-K. Lim, S. Cocke, T. E. LaRow, J. J. O’Brien, and J. J. Jones, 2010: Assessing maize and peanut yield simulations with various seasonal climate data in the southeastern United States. J. Appl. Meteor. Climatol., 49 , 592603.

    • Search Google Scholar
    • Export Citation
  • Srikanthan, R., and G. G. S. Pegram, 2009: A nested multisite daily rainfall stochastic generation model. J. Hydrol., 371 , 142153.

  • Taussky, O., and J. Todd, 2006: Cholesky, Toeplitz and the triangular factorization of symmetric matrices. Numer. Algorithms, 41 , 197202.

    • Search Google Scholar
    • Export Citation
  • Toeplitz, O., 1907: Die Jacobische Transformation der quadratischen Formen von unendlich vielen Veränderlichen. Nachr. Akad. Wiss. Goettingen, Math.-Phys. Kl., 2 , 101110.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., O. J. Tomlinson, and C. W. Dawson, 2003: Multi-site simulation of precipitation by conditional resampling. Climate Res., 23 , 183194.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 1998: Multisite generalization of a daily stochastic precipitation generation model. J. Hydrol., 210 , 178191.

  • Zhang, X. C., and J. D. Garbrecht, 2003: Evaluation of CLIGEN precipitation parameters and their implication on WEPP runoff and erosion prediction. Trans. ASAE, 46 , 311320.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 853 337 44
PDF Downloads 432 116 2