Simulation Models of Sequences of Dry and Wet Days
Publication: Journal of Irrigation and Drainage Engineering
Volume 115, Issue 3
Abstract
A new statistical model has been developed for the simulation of sequences of dry and wet days. The model is based on the discrete autoregressivemoving average (DARMA) family of stochastic processes, which includes the Markov chain as a particular case. The model building is based on a three‐step procedure consisting of identification, estimation, and model selection. The model identification and parameter estimation are based on the best fit of the autocorrelation function, while the selection of the optimum model is based on the best reproduction of the probability distribution function of the lengths of the runs of dry days and wet days. The model has thus the property of reproducing the persistence of dry spells and wet spells which are important in the evaluation and forecast of droughts and floods. Excellent results were obtained with rainfall data from Indiana, which indicate that the models are useful for scheduling irrigation of crops in the Central United States and possibly elsewhere.
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References
1.
Box, G. E. P., and Jenkins, G. P. (1976). Time series analysis, forecasting and control. Holden‐Day.
2.
Chang, T. J., Kavvas, M. L., and Delleur, J. W. (1982). “Daily precipitation and streamflow modeling by discrete autoregressive moving average processes.” Rept. 146, Water Resour. Res. Ctr., Purdue Univ., West Lafayette, Ind.
3.
Chang, T. J., Kavvas, M. L., and Delleur, J. W. (1984a). “Modeling sequences of wet and dry days by binary discrete autoregressive moving average processes.” J. of Climate and Appl. Meterology, 23 (Sept.), 1367–1378.
4.
Chang, T. J., Kavvas, M. L., and Delleur, J. W. (1984b). “Daily precipitation by discrete autoregressive moving average processes.” Water Resour. Res., 20(5), 565–580.
5.
Chang, T. J., Delleur, J. W., and Kavvas, M. L. (1987). “Application of discrete autoregressive moving average models for estimation of daily runoff.” J. of Hydr., 91, 119–135.
6.
Cordova, J. R., and Bras, R. L. (1981). “Physically based probabilistic models of infiltration, soil moisture and actual evapotranspiration.” Water Resour. Res., 17(1), 93–106.
7.
Jacobs, P. A., and Lewis, P. A. W. (1977). “A mixed autoregressive‐moving average exponential sequence and point process.” Adv. Appl. Prob. 9, 87–104.
8.
Jacobs, P. A., and Lewis, P. A. W. (1978a). “Discrete tima series generated by mixtures I: Correlational and run properties.” J. Roy. Stat. Soc., B40, 94, 105.
9.
Jacobs, P. A., and Lewis, P. A. W. (1978b). “Discrete time series generated by mixtures II: Asymptotic properties.” J. Roy. Stat. Soc., B40, 222–228.
10.
Jacobs, P. A., and Lewis, P. A. W. (1978c). “Discrete time series generated by mixtures III: Autoregressive process DAR(b). “Rept., Naval Postgraduate School, Monterey, Calif.
11.
Jacobs, P. A., and Lewis, P. A. W. (1982). “Stationary discrete autoregressive moving average time series generated by mixtures.” Rept., Naval Postgraduate School, Monterey, Calif.
12.
Kavvas, M. L., and Delleur, J. W. (1975). “The stochastic and chronologic structure of rainfall sequences: Application to Indiana.” Tech. Rept. 57, Water Resour. Res. Ctr., Purdue Univ., West Lafayette, Ind.
13.
Kavvas, M. L., and Delleur, J. W. (1981). “A stochastic cluster model of daily rainfall sequences.” Water Resour. Res., 17(4), 1151–1160.
14.
Marquardt, D. W. (1963). “An algorithm for least squares estimation of nonlinear parameters.” SIAM J., 2, 431–441.
15.
Ramirez, J. A., and Bras, R. L. (1985). “Conditional distribution of Neyman‐Scott models for storm arrivals and their use in irrigation scheduling.” Water Resour. Res., 21(3), 317–330.
16.
Salas, J., et al. (1980). “Applied modeling of hydrologic time series.” Water Resour. Publications.
17.
Stewart, J., et al. (1977). “Optimization of crop production through control of water and salinity levels in the soil.” Utah Water Res. Lab., Utah State Univ., Sept.
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Copyright © 1989 ASCE.
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Published online: Jun 1, 1989
Published in print: Jun 1989
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