A Model Fitting Analysis of Daily Rainfall Data

SUMMARY This paper discusses the fitting and use of models for daily rainfall observations. Nonstationary Markov chains are fitted to the occurrence of rain, and gamma distributions, with parameters which vary with-the time of year, are fitted to the rainfall amounts. Numerical methods are used to derive results from these models that are important in agricultural planning. Examples include the distributions of soil water content and lengths of dry spells. The process of fitting and using these models provides a straightforward and flexible analysis for rainfall records.

[1]  J. Kanellopoulos,et al.  Joint statistics analysis between rain depolarization and attenuation , 1981 .

[2]  N. Nicholls,et al.  Verification of an empirical long‐range weather forecasting technique , 1981 .

[3]  R. Crane,et al.  Worst-month statistics , 1978 .

[4]  D. P. Gaver,et al.  First-order autoregressive gamma sequences and point processes , 1980, Advances in Applied Probability.

[5]  Alan F. Karr,et al.  A point process model of summer season rainfall occurrences , 1983 .

[6]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[7]  D. Goldberg.  The detection of psychiatric illness by questionnaire : a technique for the identification and assessment of non-psychotic psychiatric illness , 1972 .

[8]  M. Glantz.  Nine fallacies of natural disaster: The case of the Sahel , 1977 .

[9]  G. J. G. Upton,et al.  An Introduction to Statistical Modelling , 1983 .

[10]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[11]  On the analysis of extreme rainfalls , 1983 .

[12]  M. Stone,et al.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[13]  A. C. Atkinson,et al.  Two graphical displays for outlying and influential observations in regression , 1981 .

[14]  David A. Woolhiser,et al.  Stochastic daily precipitation models: 2. A comparison of distributions of amounts , 1982 .

[15]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[16]  M. S. Bartlett,et al.  The spectral analysis of two-dimensional point processes , 1964 .

[17]  M. Rudemo.  Doubly stochastic Poisson processes and process control , 1972, Advances in Applied Probability.

[18]  D. Clayton,et al.  Generalised Linear Models in Epidemiological Research: Case-Control Studies. , 1984 .

[19]  J. Reffye.  Étude phénoménologique des précipitations pluvieuses. Modélisation mathématique des intensités de pluie en un point du sol , 1982 .

[20]  Roger E. Smith,et al.  Point processes of seasonal thunderstorm rainfall: 2. Rainfall depth probabilities , 1974 .

[21]  Rafael L. Bras,et al.  Intraseasonal water allocation in deficit irrigation , 1981 .

[22]  Peter A. W. Lewis,et al.  Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties , 1978 .

[23]  B. N. Harden,et al.  Measurements of rainfall for studies of millimetric radio attenuation , 1977 .

[24]  A Model for Rainfall Occurrence , 1964 .

[25]  G. G. S. Pegram,et al.  An autoregressive model for multilag Markov chains , 1980, Journal of Applied Probability.

[26]  A. Paraboni.  Characterization of rain profiles in a second-order approximation and application to attenuation beyond 10 GHz , 1982 .

[27]  J. Delleur,et al.  A cluster model for flood analysis , 1983 .

[28]  D. Vere-Jones.  Stochastic Models for Earthquake Occurrence , 1970 .