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Hydrologic Advances in Space-Time Precipitation Modeling and Forecasting

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Recent Advances in the Modeling of Hydrologic Systems

Part of the book series: NATO ASI Series ((ASIC,volume 345))

Abstract

The spatial and temporal rainfall characteristics influence the runoff hydrograph of a catchment, while accurate forecasting of precipitation is crucial to the prediction of floods and flash floods. This study presents a review of recent hydrologic advances in space-time rainfall modeling and forecasting. The strengths and weaknesses of the available models are discussed and directions for further research and improvements are given.

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References

  • American Geophysical Union Hydrology Section, Committee on Precipitation: 1984, ‘A New Interdisciplinary Focus on Precipitation Research,’ EOS Transactions 65(23), 377, 380.

    Article  Google Scholar 

  • Amorocho, J., and J. Slack: 1970, ‘Simulation of Cyclonic Storm Fields for Hydrologic Modelling,’ Amer. Geophys. Union Meeting, Wash., DC.

    Google Scholar 

  • Amorocho, J., and D. Morgan: 1974, ‘Convective Storm Field Simulation for Distributed Catchment Models,’ Proc. Warsaw Symposium on Mathematical Models in Hydrology, 1971, IAHS, 598–607.

    Google Scholar 

  • Amorocho, J.: 1981, ‘Stochastic Modeling of Precipitation in Space and Time,’ in V. P. Singh (ed.), Statistical Analysis of Rainfall and Runoff, Water Resour. Publ., Fort Collins, CO.

    Google Scholar 

  • Amorocho, J., and B. Wu: 1977, ‘Mathematical Models for the Simulation of Cyclonic Storm Sequences and Precipitation Fields,’ J. of Hydrology 32, 329–345.

    Article  Google Scholar 

  • Austin, P. M., and R. A. Houze, Jr.: 1972, ‘Analysis of the Structure of Precipitation Patterns in New England,’ J. Appl. Meteorology 11,926–935.

    Article  Google Scholar 

  • Bell, R. S.: 1978, ‘The Forecasting of Orographically Enhanced Rainfall Accumulations Using 10-Level Model Data,’ Meteorological Magazine 107, 113–124.

    Google Scholar 

  • Bras, R. L., and I. Rodriguez-Iturbe: 1976, ‘Rainfall Generation: A Nonstationary Time-Varying Multidimensional Model,’ Water Resour. Res. 12(1), 450–456.

    Article  Google Scholar 

  • Buishand, T. A.: 1978, ‘Some Remarks on the Use of Daily Rainfall Models,’ J. Hydrology 36, 295–308.

    Article  Google Scholar 

  • Carey, D. I., and C. T. Haan: 1978, ‘Markov Process for Simulating Daily Point Rainfall,’ J. Irrig. & Drainage Div., ASCE 104(IRI), 111–125.

    Google Scholar 

  • Caskey, J. E.: 1963, ‘A Markov Chain Model for the Probability of Precipitation Occurrence in Intervals of Various Lengths,’ Mon. Weather Rev.91(6),298–301.

    Article  Google Scholar 

  • Chang, T. J., M. L. Kavvas, and J. W. Delleur: 1984, ‘Daily Precipitation Modeling by Discrete Autoregressive Moving Average Processes,’ Water Resour. Res. 20(5), 565–580.

    Article  Google Scholar 

  • Chin, E. H.: 1977, ‘Modeling Daily Precipitation Occurrence Process with Markov Chain,’ Water Resour. Res. 13(6), 949–956.

    Article  Google Scholar 

  • Cho, H-R.: 1985, ‘Stochastic Dynamics of Precipitation: An Example,’ Water Resour. Res. 21(8), 1225–1232.

    Article  Google Scholar 

  • Cho, H-R., and D. S. T. Chan: 1987, ‘Mesoscale Atmospheric Dynamics and Modeling of Rainfall Fields,’ J. of Geophys. Res. 98(D8),9687–9692.

    Article  Google Scholar 

  • Court, A.: 1979, ‘Precipitation Research, 1975–1978,’ Rev of Geophys. and Space Phys. 17(6), 1165–1175.

    Article  Google Scholar 

  • Cox, D. R., and V. Isham: 1980, Point Processes, Chapman and Hall, London.

    Google Scholar 

  • Cox, D. R., and P. A. W. Lewis: 1978, The Statistical Analysis of Series of Events, Methuen, London.

    Google Scholar 

  • Drufuca, G.: 1977, ‘Radar-derived Statistics on the Structure of Precipitation Patterns,’ J. Appl. Meteor. 16(10),1920–1035.

    Article  Google Scholar 

  • Eagleson, P. S.: 1978, ‘Climate, Soil and Vegetation, 2, The Distribution of Annual Precipitation Derived from Observed Storm Sequences,’ Water Resour. Res. 14(5), 713–721.

    Article  Google Scholar 

  • Eagleson, P. S.: 1984, ‘The Distribution of Catchment Coverage by Stationary Rainstorms,’ Water Resour. Res. 20(5), 581–590.

    Article  Google Scholar 

  • Eagleson, P. S., and O. Wang: 1985, ‘Moments of Catchment Storm Area,’ Water Resour. Res. 21(8), 1185–1194.

    Article  Google Scholar 

  • Eagleson, P. S., N. M. Fennessey, W. Qinliang, and I. Rodriguez-Iturbe: 1987, ‘Application of Spatial Poisson Models to Air Mass Thunderstorm Rainfall,’ J. of Geophys. Res. 92(D8), 9661–9678.

    Article  Google Scholar 

  • Elliott, R. D., and R. W. Shaffer: 1962, ‘The Development of Quantitative Relationships Between Orographic Precipitation and Air-Mass Parameters for Use in Forecasting and Cloud Seeding Evaluation,’ J. of Appl. Meteorology 1,218–228.

    Article  Google Scholar 

  • Feyerherm, A. M., and L. D. Bark: 1967, ‘Goodness of Fit of a Markov Chain Model for Sequences of Wet and Dry Days,’ J. Appl. Meteorol. 6, 770–773.

    Article  Google Scholar 

  • Foufoula-Georgiou, E., and D. P. Lettenmaier: 1986, ‘Continuous-time Versus Discrete-time Point Process Models for Rainfall Occurrence Series,’ Water Resour. Res. 22(4), 531–542.

    Article  Google Scholar 

  • Foufoula-Georgiou, E., and R Guttorp: 1986, ‘Compatibility of Continuous Rainfall Occurrence Models with Discrete Rainfall Observations,’ Water Resour. Res. 22(8), 1316–1322.

    Article  Google Scholar 

  • Foufoula-Georgiou, E., and D. P. Lettenmaier: 1987, ‘A Markov Renewal Model for Rainfall Occurrences,’ Water Resour. Res. 23(5), 875–884.

    Article  Google Scholar 

  • Foufoula-Georgiou, E., and P. Guttorp: 1987, ‘Assessment of a Class of Neyman-Scott Models for Temporal Rainfall,’ J. of Geophys. Res. 92(D8), 9679–9682.

    Article  Google Scholar 

  • Gabriel, K. R., and J. Neumann: 1957, ‘On a Distribution of Weather Cycles by Lengths,’ Quart. J. R. Meteor. Soc. 83, 375–380.

    Article  Google Scholar 

  • Gabriel, K. R., and J. Neumann: 1962, ‘A Markov Chain Model for Daily Rainfall Occurrences at Tel Aviv,’ Quart. J. R. Meteor. Soc. 88,90–95.

    Article  Google Scholar 

  • Galloy, E., A. Le Breton, and S. Martin: 1981, ‘A Model for Weather Cycles Based on Daily Rainfall Occurrences,’ in M. Cosnard et al. (eds.), Rhythms in Biology and Other Fields of Application, Springer Lecture Notes in Biomathematics, Vol. 49, pp. 303–318.

    Google Scholar 

  • Georgakakos, K. R: 1984, ‘State Estimation of a Scalar Dynamic Precipitation Model from Time-Aggregate Observations,’ Proceedings of the 16th IEEE Southeastern Symposium on System Theory, March 25–27, Mississippi, pp. 111–115.

    Google Scholar 

  • Georgakakos, K. R, and R. L. Bras: 1984a, ‘A Hydrologically Useful Station Precipitation Model, 1, Formulation,’ Water Resour. Res. 20(11), 1585–1596.

    Article  Google Scholar 

  • Georgakakos, K. P., and R. L. Bras: 1984b, ‘A Hydrologically Useful Station Precipitation Model, 2, Case Studies,’ Water Resour. Res. 20(11), 1597–1610.

    Article  Google Scholar 

  • Georgakakos, K. R, and L. Brazil: 1987, ‘Real-Time Flood and Flash-Flood Forecasting Using Hydrometeorological Models and Modern Estimation Theory Techniques,’ in L. Bergal, and J. Dolz (eds.), Flood Warning Systems, Imprime Cooperativa de Publicaciones del Colegio de Ingenieros de Caminos, Canales y Puertos, Almagro, 42–28010 Madrid, pp. 184–227.

    Google Scholar 

  • Georgakakos, K. R, and M. D. Hudlow: 1984, ‘Quantitative Precipitation Forecast Techniques for Use in Hydrologic Forecasting,’ Bull. Amer. Meteor. Society 65(11), 1186–1200.

    Article  Google Scholar 

  • Georgakakos, K. R, and M. L. Kavvas: 1987, ‘Precipitation Analysis, Modeling, and Prediction in Hydrology,’ Reviews of Geophysics 25(2), 163–178.

    Article  Google Scholar 

  • Georgakakos, K. R, and T. H. Lee: 1987, ‘Estimation of Mean Areal Precipitation Fields Using Operationally Available Hydrometeorological Data and a Two-Dimensional Precipitation Model,’ Iowa Inst. of Hydraulic Research, The University of Iowa, IIHR Report No. 315, 80 pp.

    Google Scholar 

  • Georgakakos, K. R: 1986, ‘State Estimation of a Scalar Dynamic Precipitation Model from Time-Aggregate Observations,’ Water Resour. Res. 22(5), 744–748.

    Article  Google Scholar 

  • Georgakakos, K. P.: 1987, ‘Real Time Flash Flood Prediction,’ J Geophys. Res. 92(D8), 9615–9629.

    Article  Google Scholar 

  • Grace, R. A., and P. S. Eagleson: 1966, ‘The Synthesis of Short-Time-Increment Rainfall Sequences,’ Hydrodynam. Lab. Rep. 91, Dept. of Civil Engr., Mass. Inst. of Techn., Cambridge, MA.

    Google Scholar 

  • Green, J. R.: 1964, ‘A Model for Rainfall Occurrence,’ J R. Statist. Soc., B, 26, 345–353.

    Google Scholar 

  • Green, J. R.: 1965, ‘Two Probability Models for Sequences of Wet or Dry Days,’ Monthly Weather Review 93, 155–156.

    Article  Google Scholar 

  • Gupta, V. K., and L. Duckstein: 1975, ‘A Stochastic Analysis of Extreme Droughts,’ Water Resour. Res. 12(2), 221–228.

    Article  Google Scholar 

  • Gupta, V. K., and E. Waymire: 1979, ‘A Stochastic Kinematic Study of Subsynoptic Space-Time Rainfall,’ Water Resour. Res. 15(3), 637–644.

    Article  Google Scholar 

  • Gupta, V. K., and E. Waymire: 1987, ‘On Taylor’s Hypothesis and Dissipation in Rainfall,’ J. of Geophys. Res. 92(D8), 9657–9660.

    Article  Google Scholar 

  • Guttorp, P.: 1986, ‘On Binary Time Series Obtained from Continuous Time Point Processes Describing Rainfall,’ Water Resour. Res. 22(6), 897–904.

    Article  Google Scholar 

  • Haan, T. N., D. M. Allen, and J. O. Street: 1976, ‘A Markov Chain Model of Daily Rainfall,’ Water Resour. Res. 12(3), 443–449.

    Article  Google Scholar 

  • Hamlin, M. J.: 1983, ‘The Significance of Rainfall in the Study of Hydrological Processes at Basin Scale,’ J of Hydrology 65, 73–94.

    Article  Google Scholar 

  • Hobbs, P. V.: 1978, ‘Organization and Structure of Clouds and Precipitation on the Mesoscale in Cyclonic Storms,’ Rev. Geophys. and Space Phys. 16(4), 741–755.

    Article  Google Scholar 

  • Hobbs, R V., and J. D. Locatelli: 1978, ‘Rainbands, Precipitation Cores and Generating Cells in a Cyclonic Storm,’ J. Atmos. Sci. 35, 230–241.

    Google Scholar 

  • Hoel, P. G.: 1954, ‘A Test for Markov Chains,’ Biometrika 41, 430–433.

    Google Scholar 

  • Hopkins, J. W., and R Robillard: 1964, ‘Some Statistics from the Canadian Prairie Provinces,’ J. Appl. Meteorology 3, 600–602.

    Article  Google Scholar 

  • Houze, R. A., Jr.: 1981, ‘Structure of Atmospheric Precipitation Systems: A Global Survey,’ Radio Science 16(5), 671–689.

    Article  Google Scholar 

  • Ison, N. T., A. M. Feyerherm, and L. D. Bark: 1971, ‘Wet Period Precipitation and the Gamma Distribution,’ J. Appl. Meteorology 10(4), 658–665.

    Article  Google Scholar 

  • Jacobs, R A., and R A. W. Lewis: 1978a, ‘A Discrete Time Series Generated by Mixtures I: Correlational and Run Properties,’ J R. Statist. Soc.,B, 40(1), 94–105.

    Google Scholar 

  • Jacobs, R A., and R A. W. Lewis: 1978b, ‘A Discrete Time Series Generated by Mixtures II: Asymptotic Properties,’ J R. Statist. Soc., B, 40(2), 222–228.

    Google Scholar 

  • Katz, R. W: 1977, ‘An Application of Chain-Dependent Processes to Meteorology,’ J. Appl. Prob. 14, 598–603.

    Article  Google Scholar 

  • Kavvas, M. L., and J. W. Delleur: 1981, ‘A Stochastic Cluster Model for Daily Rainfall Sequences,’ Water Resour. Res. 17(4), 1151–1160.

    Article  Google Scholar 

  • Kavvas, M. L., and K. R. Herd: 1985, ‘A Radar-based Stochastic Model for Short-Time-Increment Rainfall,’ Water Resour. Res. 21(9), 1437–1455.

    Article  Google Scholar 

  • Kavvas, M. L., R S. Puri, and M. N. Saquib: 1987a, ‘On a Stochastic Description of the Time-Space Behavior of Extratropical Cyclonic Precipitation Fields,’ J. of Stochastic Hydrology and Hydraulics.

    Google Scholar 

  • Kavvas, M. L., P. S. Puri, and M. N. Saquib: 1987b, ‘Feasibility Studies on a Stochastic Geometric Model for Precipitation Fields,’ J. of Stochastic Hydrology and Hydraulics.

    Google Scholar 

  • Keenan, D. M.: 1980, ‘Time Series Analysis of Binary Data,’ Ph.D. Thesis, The Univ. of Chicago, IL.

    Google Scholar 

  • Khanal, N. N., and R. L. Hamrick: 1974, ‘A Stochastic Model for Daily Rainfall Data Synthesis,’ Proceedings of the Symposium of Statistical Hydrology, Meson, AZ, U.S. Dept. of Agric., Publ. No. 1275, 197–210.

    Google Scholar 

  • Konrad, T. G.: 1978, ‘Statistical Models of Summer Rainstorms Derived from Fine Scale Radar Observations,’ J. of Appl. Meteorology 17, 171–188.

    Article  Google Scholar 

  • Krajewski, W. E: 1987, ‘Radar Rainfall Data Quality Control by the Influence Function Method,’ Water Resour. Res. 5, 837–844.

    Article  Google Scholar 

  • Krajewski, W. E, and K. P. Georgakakos: 1985, ‘Synthesis of Radar Rainfall Data,’ Water Resour Res. 21, 764–768.

    Article  Google Scholar 

  • Lovejoy, S., and B. B. Mandelbrot: 1985, ‘Fractal Properties of Rain, and a Fractal Model,’ Tellus 37A, 209–232.

    Article  Google Scholar 

  • Lovejoy, S., and D. Schertzer: 1985, ‘Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain,’ Water &sour. Res. 21(8), 1233–1250.

    Article  Google Scholar 

  • Mielke, P. W, Jr.: 1973, ‘Another Family of Distributions for Describing and Analyzing Precipitation Data,’ J Appl. Meteorol. 10(2), 275–280.

    Article  Google Scholar 

  • Mielke, P. W., Jr., and E. S. Johnson: 1974, ‘Some Generalized Beta Distributions of the Second Kind Having Desirable Application Features in Hydrology and Meteorology,’ Water Resour. Res. 10(2), 223–236.

    Article  Google Scholar 

  • Milly, P. C. D., and P. S. Eagleson: 1982, ‘Infiltration and Evaporation at Inhomogeneous Land Surfaces,’ Tech. Rep. 278, Ralph M. Parsons Lab., Dept. of Civil Engr., Mass. Inst. of Tech., Cambridge.

    Google Scholar 

  • Milly, P. C. D., and P. S. Eagleson: 1988, ‘Effect of Storm Scale on Surface Runoff Volume,’ Water Resour. Res. 24(4), 620–624.

    Article  Google Scholar 

  • Nicks, A. D.: 1982, ‘Space-Time Quantification of Rainfall Inputs for Hydrological Transport Models,’ J of Hydrology 59, 249–260.

    Article  Google Scholar 

  • Obeysekera, J. T. B., and R. D. Salas: 1983, ‘GAR Modeling of Streamflow Series,’ Presented at the AGU Fall Meeting, San Francisco, AGU Abstract: EOS 63(45), 935.

    Google Scholar 

  • Obeysekera, J. T. B., G. O. Tabios III, and J. D. Salas: 1987, ‘On Parameter Estimation of Temporal Rainfall Models,’ Water Resour. Res. 23(10), 1837–1850.

    Article  Google Scholar 

  • Petterssen, S.: 1969, Introduction to Meteorology, 3rd Ed., McGraw-Hill, New York.

    Google Scholar 

  • Raudkivi, A. J., and N. Lawgun: 1972, ‘Generation of Serially Correlated Non-normally Distributed Rainfall Durations,’ Water Resour. Res. 8(2), 398–409.

    Article  Google Scholar 

  • Rhea, J. O.: 1978, ‘Orographic Precipitation Model for Hydrometeorological Use,’Atmospheric Science Paper No. 287, Dept. of Atmospheric Sci., Colorado State Univ., Fort Collins, CO, 198 pp.

    Google Scholar 

  • Restrepo-Posada, J. P., and R S. Eagleson: 1982, ‘Identification of Independent Rainstorms,’ J. of Hydrology 55, 303–319.

    Article  Google Scholar 

  • Richardson, C. W: 1981, ‘Stochastic Models of Daily Precipitation, Temperature, and Solar Radiation,’ Water Resour. Res. 17(1), 182–190.

    Article  Google Scholar 

  • Rodriguez-Iturbe, I., V. K. Gupta, and E. Waymire: 1984, ‘Scale Considerations in the Modeling of Temporal Rainfall,’ Water Resour. Res. 20(11), 1611–1619.

    Article  Google Scholar 

  • Rodriguez-Iturbe, I., D. R. Cox, and R S. Eagleson: 1986, ‘Spatial Modeling of Total Storm Rainfall,’ Proc. R. Soc. Lond., A, 403, 27–50.

    Article  Google Scholar 

  • Rodriguez-Iturbe, I., D. R. Cox, and V. Isham: 1987a, ‘Some Models for Rainfall Based on Stochastic Point Processes,’ Proc. R. Soc. Lond.,A, 410, 269–288.

    Article  Google Scholar 

  • Rodriguez-Iturbe, I., B. Febres de Power, and J. B. Valdes: 1987b, ‘Rectangular Pulses Point Process Models for Rainfall: Analysis of Empirical Data,’ Jour. of Geophys. Res. 92(D8), 9645–9656.

    Article  Google Scholar 

  • Rodriguez-Iturbe, I., D. R. Cox, and V. Isham: 1987c, ‘A Point Process Model for Rainfall: Further Developments,’ Proc. Royal Soc. London, A.

    Google Scholar 

  • Rodriguez-Iturbe, I., B. E de Power, M. B. Sharifi, and K. P. Georgakakos: 1989, ‘Chaos in Rainfall,’ Water Resour. Res. 25(7), 1667–1675.

    Article  Google Scholar 

  • Roldan, J., and D. A. Woolhiser: 1982, ‘Stochastic Daily Precipitation Models, 2, A Comparison of Distributions of Amounts,’ Water Resour. Res. 18(5), 1461–1468.

    Article  Google Scholar 

  • Schertzer, D., and S. Lovejoy: 1987, ‘Physical Modeling and Analysis of Rain and Clouds by Anisotropic Scaling Multiplicative Processes,’ J. of Geophys. Res. 92(D8), 9693–9714.

    Article  Google Scholar 

  • Sharifi, M. B., K. P. Georgakakos, and I. Rodriguez-Iturbe: In Press, ‘Evidence of Deterministic Chaos in the Pulse of Storm Rainfall,’ Journal of Atmospheric Sciences.

    Google Scholar 

  • Sivapalan, M., and E. F. Wood: 1987, ‘A Multidimensional Model of Non-stationary Space-Time Rainfall at the Catchment Scale,’ Water Resour. Res. 23(7), 1289–1299.

    Article  Google Scholar 

  • Skees, P. M., and L. R. Shenton: 1974, ‘Comments on the Statistical Distribution of Rainfall Per Period Under Various Transformations,’ Proceedings of the Symposium on Statistical Hydrology, Tucson, AZ, U.S. Dept. of Agr., Misc. Publ. No. 1275, 172–196.

    Google Scholar 

  • Small, M. J., and D. J. Morgan: 1986, ‘The Relationship Between a Continuous-Time Renewal Model and a Discrete Markov Chain Model of Precipitation Occurrence,’ Water Resour. Res. 22(10), 1422–1430.

    Article  Google Scholar 

  • Smith, E. R., and H. A. Schreiber: 1973, ‘Point Processes of Seasonal Thunderstorm Rainfall, Part 1, Distribution of Rainfall Events,’ Water Resour. Res. 9(4),871–884.

    Article  Google Scholar 

  • Smith, J. A.: 1987, ‘Statistical Modeling of Daily Rainfall Occurrences,’ Water Resour. Res. 23(5), 855–893.

    Article  Google Scholar 

  • Smith, J. A., and A. E Karr: 1983, ‘A Point Process Model of Summer Season Rainfall Occurrence,’ Water Resour. Res. 19(1),95–103.

    Article  Google Scholar 

  • Smith, J. A., and A. E Karr: 1985a, ‘Statistical Inference for Point Process Models of Rainfall,’ Water Resour. Res. 21(1), 73–80.

    Article  Google Scholar 

  • Smith, J. A., and A. F. Karr: 1985b, ‘Parameter Estimation for a Model of Space-Time Rainfall,’ Water Resour. Res. 21(8), 1251–1257.

    Article  Google Scholar 

  • Smith, J. A., and W. E Krajewski: 1987, ‘Statistical Modeling of Space-Time Rainfall Using Radar and Rain Gage Observations,’ Water Resour. Res. 10, 1893–1900.

    Article  Google Scholar 

  • Stern, R. D., and R. Coe: 1984, ‘A Model Fitting Analysis of Rainfall Data (With Discussion),’ J. Roy. Stat. Soc. Ser. A. 147, 1–34.

    Article  Google Scholar 

  • Tabios, G. O., J. T. B. Obeysekera, and H. W. Shen: 1987, ‘The Influence of Storm Movement on Streamflow Hydrograph Through Space-Time Rainfall Generation and Hydraulic Routing,’ preprint.

    Google Scholar 

  • Taylor, G. I.: 1938, ‘The Spectrum of Turbulence,’ Proc. R. Soc. London, A, 164, 476–490.

    Article  Google Scholar 

  • Thom, H. G.: 1958, ‘A Note on the Gamma Distribution,’ Monthly Weather Review 86(4), 117–122.

    Article  Google Scholar 

  • Todorovic, P., and D. A. Woolhiser: 1971, ‘Stochastic Model of Daily Rainfall,’ Proc. of the USDA-IASPS Symposium on Statist. Hydrology,Tucson, AZ.

    Google Scholar 

  • Todorovic, P., and V. Yevjevich: 1969, ‘Stochastic Processes of Precipitation,’ Colorado State Univ., Hydro. Paper 35, 1–61.

    Google Scholar 

  • Tong, H.: 1975, ‘Determination of the Order of a Markov Chain by Akaike’s Information Criterion,’ J. Appl. Prob. 12, 488–497.

    Article  Google Scholar 

  • Valdes, J. B., I. Rodriguez-Iturbe, and V. K. Gupta: 1985, ‘Approximations of Temporal Rainfall from a Multidimensional Model,’ Water Resour. Res. 21(8), 1259–1270.

    Article  Google Scholar 

  • Waymire, E.: 1985, ‘Scaling Limits and Self-Similarity in Precipitation Fields,’ Water Resour Res. 21(8),1271–1281.

    Article  Google Scholar 

  • Waymire, E., and V. K. Gupta: 1981a, ‘The Mathematical Structure of Rainfall Representations, 1, A Review of Stochastic Rainfall Models,’ Water Resour. Res. 17(5),1261–1272.

    Article  Google Scholar 

  • Waymire, E., and V. K. Gupta: 1981b, ‘The Mathematical Structure of Rainfall Representations, 2, A Review of the Theory of Point Processes,’ Water Resour. Res. 17(5),1273–1285.

    Article  Google Scholar 

  • Waymire E., and V. K. Gupta: 1981c, ‘The Mathematical Structure of Rainfall Representations, 3, Some Applications of the Point Process Theory to Rainfall Processes,’ Water Resour. Res. 17(5) 1287–1294.

    Article  Google Scholar 

  • Waymire, E., V K. Gupta, and I. Rodriguez-Iturbe: 1984, ‘A Spectral Theory of Rainfall Intensity at the Meso-p Scale,’ Water Resour. Res. 20(10), 1453–1465.

    Article  Google Scholar 

  • Weiss, L. L.: 1964, ‘Sequences of Wet and Dry Days Described by a Markov Chain Model,’ Monthly Weather Review 92, 169–176.

    Article  Google Scholar 

  • Wilson, C. B., J. B. Valdes, and I. Rodriguez-Iturbe: 1979, ‘On the Influence of the Spatial Distribution of Rainfall on Storm Runoff,’ Water Resour. Res. 15(2),321–328.

    Article  Google Scholar 

  • Wiser, E. H.: 1965, ‘Modified Markov Probability Models of Sequences of Precipitation Events,’ Monthly Weather Review 93, 511–516.

    Article  Google Scholar 

  • Woolhiser, D. A., and G. G. S. Pegram: 1979, ‘Maximum Likelihood Estimation of Fourier Coefficients to Describe Seasonal Variations of Parameters in Stochastic Daily Precipitation Models,’ J. Appl. Meteorol. 8(1), 34–42.

    Article  Google Scholar 

  • Zawadzki, I.: 1973, ‘Statistical Properties of Precipitation Patterns,’ J. Appl. Meteor. 12, 459–472.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Civil and Mineral Engineering St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minnesota, 55414, USA

    Efi Foufoula-Georgiou

  2. Department of Civil and Environmental Engineering Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa, 52242, USA

    Konstantine P. Georgakakos

Authors
  1. Efi Foufoula-Georgiou
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  2. Konstantine P. Georgakakos
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Editors and Affiliations

  1. Utah Water Research Laboratory, Utah State University, Logan, Utah, USA

    David S. Bowles

  2. Department of Civil Engineering, University of Newcastle upon Tyne, Claremont Road, Newcastle upon Tyne, NE1 7RU, UK

    P. Enda O’Connell

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Foufoula-Georgiou, E., Georgakakos, K.P. (1991). Hydrologic Advances in Space-Time Precipitation Modeling and Forecasting. In: Bowles, D.S., O’Connell, P.E. (eds) Recent Advances in the Modeling of Hydrologic Systems. NATO ASI Series, vol 345. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3480-4_3

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