An Extended Version of the Richardson Model for Simulating Daily Weather Variables

Marc B. Parlange Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, Maryland

Search for other papers by Marc B. Parlange in
Current site
Google Scholar
PubMed
Close
and
Richard W. Katz Environmental and Societal Impacts Group, National Center for Atmospheric Research,* Boulder, Colorado

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

Abstract

The Richardson model is a popular technique for stochastic simulation of daily weather variables, including precipitation amount, maximum and minimum temperature, and solar radiation. This model is extended to include two additional variables, daily mean wind speed and dewpoint, because these variables (or related quantities such as relative humidity) are required as inputs for certain ecological/vegetation response and agricultural management models. To allow for the positively skewed distribution of wind speed, a power transformation is applied. Solar radiation also is transformed to make the shape of its modeled distribution more realistic. A model identification criterion is used as an aid in determining whether the distributions of these two variables depend on precipitation occurrence. The approach can be viewed as an integration of what is known about the statistical properties of individual weather variables into a single multivariate model.

As an application, this extended model is fitted to weather data in the Pacific Northwest. To aid in understanding how such a stochastic weather generator works, considerable attention is devoted to its statistical properties. In particular, marginal and conditional distributions of wind speed and solar radiation are examined, with the model being capable of representing relationships between variables in which the variance is not constant, as well as certain forms of nonlinearity.

Corresponding author address: Dr. Richard W. Katz, Environmental and Societal Impacts Group, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000.

rwk@ucar.edu

Abstract

The Richardson model is a popular technique for stochastic simulation of daily weather variables, including precipitation amount, maximum and minimum temperature, and solar radiation. This model is extended to include two additional variables, daily mean wind speed and dewpoint, because these variables (or related quantities such as relative humidity) are required as inputs for certain ecological/vegetation response and agricultural management models. To allow for the positively skewed distribution of wind speed, a power transformation is applied. Solar radiation also is transformed to make the shape of its modeled distribution more realistic. A model identification criterion is used as an aid in determining whether the distributions of these two variables depend on precipitation occurrence. The approach can be viewed as an integration of what is known about the statistical properties of individual weather variables into a single multivariate model.

As an application, this extended model is fitted to weather data in the Pacific Northwest. To aid in understanding how such a stochastic weather generator works, considerable attention is devoted to its statistical properties. In particular, marginal and conditional distributions of wind speed and solar radiation are examined, with the model being capable of representing relationships between variables in which the variance is not constant, as well as certain forms of nonlinearity.

Corresponding author address: Dr. Richard W. Katz, Environmental and Societal Impacts Group, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000.

rwk@ucar.edu

Save
  • Brockwell, P. J., and R. A. Davis, 1991: Time Series: Theory and Methods., 2d ed. Springer-Verlag, 577 pp.

  • Brown, B. G., R. W. Katz, and A. H. Murphy, 1984: Time series models to simulate and forecast wind speed and wind power. J. Climate Appl. Meteor.,23, 1184–1195.

  • Bruhn, J. A., W. E. Fry, and G. W. Fick, 1980: Simulation of daily weather data using theoretical probability distributions. J. Appl. Meteor.,19, 1029–1036.

  • Brutsaert, W., 1982: Evaporation into the Atmosphere. Reidel, 299 pp.

  • Carlin, J., and J. Haslett, 1982: The probability distribution of wind power from a dispersed array of wind turbine generators. J. Appl. Meteor.,21, 303–313.

  • Easterling, W. E., N. J. Rosenberg, M. S. McKenney, C. A. Jones, P. T. Dyke, and J. R. Williams, 1992: Preparing the erosion productivity impact calculator (EPIC) model to simulate crop response to climate change and the direct effects of CO2. Agric. For. Meteor.,59, 17–34.

  • Graybill, F. A., 1969: Introduction to Matrices with Applications in Statistics. Wadsworth, 372 pp.

  • Hansen, J. E., and D. M. Driscoll, 1977: A mathematical model for the generation of hourly temperatures. J. Appl. Meteor.,16, 935–948.

  • Hanson, C. L., and G. L. Johnson, 1998: GEM (Generation of weather Elements for Multiple applications): Its application in areas of complex terrain. Hydrology, Water Resources and Ecology in Headwaters, K. Kovar, U. Tappeiner, N. E. Peters, and R. G. Craig, Eds., International Association of Hydrological Sciences (IAHS) Press, 27–32.

  • Haslett, J., and A. E. Raftery, 1989: Space–time modeling with long-memory dependence: Assessing Ireland’s wind power resource (with discussion). Appl. Stat.,38, 1–50.

  • Hayhoe, H. N., 1998: Relationship between weather variables in observed and WXGEN generated data series. Agric. For. Meteor.,90, 203–214.

  • Hutchinson, M. F., 1995: Stochastic space–time weather models from ground-based data. Agric. For. Meteor.,73, 237–264.

  • Johnson, G. L., C. L. Hanson, S. P. Hardegree, and E. B. Ballard, 1996: Stochastic weather simulation: Overview and analysis of two commonly used models. J. Appl. Meteor.,35, 1878–1896.

  • Jolliffe, I. T., and P. B. Hope, 1996: Bounded bivariate distributions with nearly normal marginals. Amer. Stat.,50, 17–20.

  • Katz, R. W., 1977: Precipitation as a chain-dependent process. J. Appl. Meteor.,16, 671–676.

  • v 1996: Use of conditional stochastic models to generate climate change scenarios. Climatic Change,32, 237–255.

  • Katz, R. W., 1999: Moments of power transformed time series. Environmetrics,10, 301–307.

  • Katz, R. W., and J. Garrido, 1994: Sensitivity analysis of extreme precipitation events. Int. J. Climatol.,14, 985–999.

  • Katz, R. W., and M. B. Parlange, 1995: Generalizations of chain-dependent processes: Application to hourly precipitation. Water Resour. Res.,31, 1331–1341.

  • Katz, R. W., and M. B. Parlange, 1998: Overdispersion phenomenon in stochastic modeling of precipitation. J. Climate,11, 591–601.

  • Katz, R. W., and X. Zheng, 1999: Mixture model for overdispersion of precipitation. J. Climate,12, 2528–2537.

  • Kimball, J. S., S. W. Running, and R. Nemani, 1997: An improved method of estimating surface humidity from daily minimum temperature. Agric. For. Meteor.,85, 87–98.

  • Mearns, L. O., C. Rosenzweig, and R. Goldberg, 1997: Mean and variance change in climate scenarios: Methods, agricultural applications, and measures of uncertainty. Climatic Change,35, 367–396.

  • National Renewable Energy Laboratory, 1992: User’s Manual: 1961–1990 National Solar Radiation Data Base, Version 1.0. NSRDB-Vol. 1. 243 pp. [Available from NREL Document Distribution Service, 1617 Cole Blvd., Golden, CO 80401-3393.].

  • Neilson, R. P., 1995: A model for predicting continental-scale vegetation distribution and water balance. Eco. Appl.,5, 362–385.

  • Nicks, A. D., C. W. Richardson, and J. R. Williams, 1990: Evaluation of the EPIC model weather generator. Erosion/Productivity Impact Calculator, 1. Model Documentation, A. N. Sharpley and J. R. Williams, Eds., USDA-ARS Tech. Bull. 1768, 235 pp. [Available from U.S. Government Printing Office, Washington, DC 20402.].

  • Rajagopalan, B., U. Lall, D. G. Tarboton, and D. S. Bowles, 1997: Multivariate nonparametric resampling scheme for generation of daily weather variables. Stochastic Hydrol. Hydraulics,11, 65–93.

  • Richardson, C. W., 1981: Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour. Res.,17, 182–190.

  • Richardson, C. W., 1982: Dependence structure of daily temperature and solar radiation. Trans. Amer. Soc. Agric. Eng.,25, 735–739.

  • Richardson, C. W., and D. A. Wright, 1984: WGEN: A model for generating daily weather variables. USDA Publication ARS-8, 83 pp. [Available from National Technical Information Center, 5285 Port Royal Rd., Springfield, VA 22161.].

  • 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, 95–107.

  • Todorovic, P., and D. A. Woolhiser, 1975: A stochastic model of n-day precipitation. J. Appl. Meteor.,14, 17–24.

  • Wallis, T. W. R., and J. F. Griffiths, 1995: An assessment of the weather generator (WXGEN) used in the erosion/productivity impact calculator (EPIC). Agric. For. Meteor.,73, 115–133.

  • Wilks, D. S., 1992: Adapting stochastic weather generation algorithms for climate change studies. Climatic Change,22, 67–84.

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

  • Wilks, D. S., 1999: Simultaneous stochastic simulation of daily precipitation, temperature, and solar radiation at multiple sites in complex terrain. Agric. For. Meteor.,96, 85–101.

  • Young, K. C., 1994: A multivariate chain model for simulating climatic parameters from daily data. J. Appl. Meteor.,33, 661–671.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 430 148 7
PDF Downloads 342 122 4