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A Monte Carlo study of rainfall forecasting with a stochastic model

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Abstract

A procedure for short-term rainfall forecasting in real-time is developed and a study of the role of sampling on forecast ability is conducted. Ground level rainfall fields are forecasted using a stochastic space-time rainfall model in state-space form. Updating of the rainfall field in real-time is accomplished using a distributed parameter Kalman filter to optimally combine measurement information and forecast model estimates. The influence of sampling density on forecast accuracy is evaluated using a series of a simulated rainfall events generated with the same stochastic rainfall model. Sampling was conducted at five different network spatial densities. The results quantify the influence of sampling network density on real-time rainfall field forecasting. Statistical analyses of the rainfall field residuals illustrate improvement in one hour lead time forecasts at higher measurement densities.

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References

  • Austin, G. L.; Bellon, A. 1982: Very-short-range forecasting of precipitation by the objective extrapolation of radar and satellite data. In: Browning, K. A. (ed.) Nowcasting. Academic, New York, New York

    Google Scholar 

  • Bras, R. L.; Rodriguez-Iturbe, I. 1985: Random functions and hydrology. Addison-Wesley. Reading, Massachuusetts

    Google Scholar 

  • Browning, K. A.; Collier, C. G. 1989: Nowcasting of precipitation systems. Reviews of Geophysics 27 (3), 345–370

    Google Scholar 

  • Chandrasekar, V; Krajewski, W. F.; Lakshmi, V. 1990: A Monte-Carlo study of radar-rainfall sampling for hydrologic applications. Preprint: Eighth Conference on Hydrometeorology. American Meteorological Society. October

  • Eagleson, P. S.; Fennessey, N. M.; Qinliang, W.; Rodriguez-Iturbe, I. 1987: Application of spatial Poisson models to air mass thunderstorm rainfall. Journal of Geophysical Research 92 (D8), 9661–9678

    Google Scholar 

  • Frank, R.; Krajewski, W. F.; Rodriguez-Iturbe, I. 1990: Visualization of space-time rainfall modeling. Video Poster Presented at First Conference of Applications of Computer Visualization and Imaging in Research. Image Analysis Facility, Eckstein Medical Research Building, University of Iowa. March 2

  • Gelb, A. (ed.) 1974: Applied optimal estimation. MIT Press, Cambridge, MA

    Google Scholar 

  • Georgakakos, K. P.; Bras, R. L. 1984a: A hydrologically useful station precipitation model, 1. Formulation. Water Resources Research 20 (11), 1585–1596

    Google Scholar 

  • Georgakakos, K. P.; Bras, R. L. 1984b: A hydrologically useful station precipitation model, 2. Case studies. Water Resources Research 20 (11), 1597–1610

    Google Scholar 

  • Georgakakos, K. P.; Hudlow, M. D. 1984: Quantitative precipitation forecast techniques for use in hydrologic forecasting. Bulletin American Meteorological Society 65 (11), 1186–1200

    Google Scholar 

  • Georgakakos, K. P.; Kavvas, M. L. 1987: Precipitation analysis, modeling, and prediction in hydrology. Reviews of Geophysics 25 (2), 163–178

    Google Scholar 

  • Gupta, V. K.; Waymire, E. C. 1979: A stochastic kinematic study of subsynoptic space-time rainfall. Water Resources Research 15 (3), 637–644

    Google Scholar 

  • Gupta, V. K.; Waymire, E. C. 1987: On Taylor's hypothesis and dissipation in rainfall. Journal of Geophysical Research 92 (D8), 9657–9660

    Google Scholar 

  • Houze, R. A. Jr. 1981: Structures of atmospheric precipitation systems: A global survey. Radio Science 16 (5), 671–689

    Google Scholar 

  • Islam, S.; Bras, R. L.; Rodriguez-Iturbe, I. 1988: Multidimensional modeling of cumulative rainfall: Parameter estimation and model adequacy through a continum of scales. Water Resources Research 24 (7), 985–992

    Google Scholar 

  • Jacobs, B. L.; Rodriguez-Iturbe, I.; Eagleson, P. S. 1988: Evaluation of a homogeneous point process description of Arizona thunderstorm rainfall. Water Resources Research 24 (7), 1174–1186

    Google Scholar 

  • Jazwinski, A. H. 1970: Stochastic processes and filtering theory. Academic, San Diego, California

    Google Scholar 

  • Johnson, E. R.; Bras, R. L. 1979: Real-time estimation of velocity and covariance structure of rainfall events using telemetered raingege data - A comparison of methods. Journal of Hydrology 44, 97–123

    Google Scholar 

  • Johnson, E. R.; Bras, R. L. 1980: Multivatiate short-term rainfall prediction. Water Resources Research 16 (1), 173–185

    Google Scholar 

  • Kavvas, M. L.; Delleur, J. 1981: A stochastic cluster model of daily rainfall occurrences. Water Resources Research 17 (4), 1151–1160

    Google Scholar 

  • Kavvas, M. L.; Herd, K. R. 1985: A radar-based stochastic model of short-time-increment rainfall. Water Resources Research 21 (9), 1437–1455

    Google Scholar 

  • Krajewski, W. F. 1990: Rainfall simulation models-RMODC3. Iowa Institute of Hydraulic Research, Department of Civil and Environmental Engineering, University of Iowa, Iowa City, Iowa

    Google Scholar 

  • Krajewski, W. F.; Smith, J. A. 1989: Sampling properties of parameter estimators for a storm field rainfall model. Water Resources Research 25 (9), 2067–2075

    Google Scholar 

  • Lee, T. H.; Georgakakos, K. P. 1990: A two-dimensional stochastic-dynamical quantitative precipitation forecasting model. Journal of Geophysical Research 95 (D3), 2113–2126

    Google Scholar 

  • Maybeck, P. S. 1979: Stochastic models, estimation, and control. Academic Press, New York, New York

    Google Scholar 

  • McLaughlin, D.; Islam, S.; Entekhabi, D.; French, M.; Bras, R. 1990: A distributed filtering approach to real-time rainfall forecasting. Preprint: Eighth Conference on Hydrometeorology. American Meteorological Society. October

  • Orlanski, I. 1975: A rational subdivision of scales for atmospheric processes. Bulletin American Meteorological Society 56 (5), 527–530

    Google Scholar 

  • Pielke, R. A. 1982: The role of mesoscale numerical models in very-short-range forecasting. In: Browning, K. A. (ed.) Nowcasting. Academic Press, New York, New York

    Google Scholar 

  • Ramirez, J. A.; Bras, R. L. 1985: Conditional distributions of Neyman-Scott models for storm arrivals and their use in irrigation scheduling. Water Resources Research 21 (3), 317–330

    Google Scholar 

  • Rodriguez-Iturbe, I.; Cox, D. R.; Eagleson, P. S. 1986: Spatial modeling of total storm rainfall. Proceedings of the Royal Society of London, Series A 403, 27–50

    Google Scholar 

  • Rodriguez-Iturbe, I.; Eagleson, P. S. 1987: Mathematical models of rainstorm events in space and time. Water Resources Research 23 (1), 181–190

    Google Scholar 

  • Sivapalan, M.; Wood, E. 1987: A multidimensional model of nonstationary space-time rainfall at the catchment scale. Water Resources Research 23 (7), 1289–1299

    Google Scholar 

  • Smith, J. A.; Karr, A. F. 1985: Parameter estimation for a model of space-time rainfall. Water Resources Research 21 (8), 1251–1257

    Google Scholar 

  • Smith, J. A.; Krajewski, W. F. 1987: Statistical modeling of space-time rainfall using radar and raingage observations. Water Resources Research 23 (10), 1893–1900

    Google Scholar 

  • Tarboton, D.; Bras, R. L.; Puente, C. E. 1988: Hydrological sampling: A characterization in terms of rainfall and basin properties. Report Number 319, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

  • Valdes, J. B.; Nakamoto, S.; Shen, S. P.; North, G. R. 1990: Estimation of multidimensional precipitation paremeters by areal estimates of oceanic rainfall. Journal of Geophysical Research 95 (D3), 2101–2111

    Google Scholar 

  • Waymire, E.; Gupta, V. K.; Rodriguez-Iturbe, I. 1984: A spectral theory of rainfall intensity at the Meso-β scale. Water Resources Research 20 (10), 1453–1465

    Google Scholar 

  • Wood, E. F.; Sivapalan, M.; Beven, K. 1990: Simularity and scale in catchment storm response. Reviews of Geophysics 28 (1), 1–18

    Google Scholar 

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Authors and Affiliations

  1. Iowa Institute of Hydraulic Research, University of Iowa, 52242, Iowa City, IA

    M. N. French & W. F. Krajewski

  2. Massachusetts Institute of Technology, 02139, Cambridge, MA

    R. L. Bras

Authors
  1. M. N. French
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  2. R. L. Bras
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  3. W. F. Krajewski
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French, M.N., Bras, R.L. & Krajewski, W.F. A Monte Carlo study of rainfall forecasting with a stochastic model. Stochastic Hydrol Hydraul 6, 27–45 (1992). https://doi.org/10.1007/BF01581673

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  • DOI: https://doi.org/10.1007/BF01581673

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