Modeling Monsoon‐Affected Rainfall of Pakistan by Point Processes
Publication: Journal of Water Resources Planning and Management
Volume 118, Issue 6
Abstract
Statistical analysis showed that monsoon reduced the variabilities of rainfall occurrences in Rechna Doab, an important agricultural region of Pakistan; but besides rainfall depths, it had little effect on other rainfall properties. Among the point‐process models explored, two continuous‐time models (Neyman‐Scott clustering or white noise [NSWN] and Rectangular Pulses models, [RPM]) and a discrete‐time model (Markov renewal [MRM]), NSWN is non‐Markovian, RPM is Markovian, and MRM is semi‐Markovian. Based on the variance ratio, variance at an arbitrary time scale to variance at daily time scale, none of the models calibrated (three out of six cases reported) was consistently better than others. However, after recalibrating them with data from six stations mixed together, only MRM predicted variance ratios that are consistent with their empirical counterparts. This is probably because MRM could account for the time discreteness of the rainfall sample process and accommodate data of high variabilities. Applying continuous point‐process models to time scales higher than daily and different from those used in calibration is discouraged, particularly the latter.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmad, Z. (1990). Applications of point processes to model the rainfall of Pakistan, Asian Inst. of Tech., Bangkok, Thailand.
2.
Baker, R. J., and Nelder, J. A. (1978). The GLIM system, Oxford: NAG, United Kingdom.
3.
Enterkhabi, D., Iturbe, I. R., and Eagleson, P. S. (1989). “Probability representation of temporal rainfall process by a modified Neyman‐Scott rectangular pulse model: Model parameter estimation and validation.” Water Resour. Res., 25(2), 295–302.
4.
Foufoula‐Georgiou, E. (1985). “Discrete point process model for daily rainfall.” Water Resour. Series Tech. Report No. 93, Univ. of Washington, Seattle, Wash.
5.
Foufoula‐Georgiou, E., and Lettenmaier, D. P. (1986). “Continuous‐time versus discrete‐point process models for rainfall occurrence series.” Water Resour. Res., 22(4), 531–542.
6.
Foufoula‐Georgiou, E., and Guttorp, P. (1986). “Compatibility of continuous rainfall occurrence models with discrete rainfall observations.” Water Resour. Res., 22(8), 1316–1322.
7.
Foufoula‐Georgiou, E., and Lettenmaier, D. P. (1987). “A Markov renewal model for rainfall occurrences.” Water Resour. Res., 23(5), 875–884.
8.
Islam, S., Bras, R. L., and Rodriguez‐Iturbe, I. (1989). Comment on “On parameter estimation of temporal rainfall models.” Water Resour. Res., 25(4), 764.
9.
Johnson, B. L. C. (1969). South Asia, selective studies of essential geography of India, Pakistan and Ceylon. Heinemann Educational Books Ltd., London, England, (1981).
10.
Kavvas, M. L., and Delleur, J. W. (1981). “A stochastic cluster model for daily rainfall sequences.” Water Resour. Res., 17(4), 1160.
11.
Nelder, J. A., and Mead, R. (1965). “A simplex method for function minimization.” Comput. J., 1, 308–313.
12.
Obeysekera, J. T. B., Tabios, G. Q. III, and Salas, J. D. (1987). “On parameter estimation of temporal rainfall models.” Water Resour. Res., 23(10), 1837–1850.
13.
Raza, M. H. (1971). Where the mountains meet. Elite Publisher Ltd., Karachi, Pakistan.
14.
Rodriguez‐Iturbe, I. (1986). “Scale of fluctuation of rainfall models.” Water Resour. Res., 22(9), 15S–37S.
15.
Rodriguez‐Iturbe, I., Gupta, V. K., and Waymire, E. (1984). “Scale consideration in the modeling of temporal rainfall.” Water Resour. Res., 20(11), 1611–1619.
16.
Stern, R. D., and Coe, R. (1984). “A model fitting analysis of daily rainfall data.” J. Royal Statistical Society A., 147, 1–34.
17.
Smith, J. A. (1987). “Statistical modeling of daily rainfall occurrences.” Water Resour. Res., 23(5), 885–893.
18.
Smith, J. A., and Karr, A. F. (1983). “A point process model of summer season rainfall occurrences.” Water Resour. Res., 95–103.
19.
Smith, R. E., and Schreiber, H. A. (1973). “Point process of seasonal thunderstorm rainfall, 1, Distribution of rainfall events.” Water Resour. Res., 9(4), 871–884.
20.
Todorovic, P., and Yevjevich, V. (1969). “Stochastic process of precipitation.” Hydrology Papers No. 35, Colorado State Univ., Fort Collins, Colo.
21.
Valdes, J. B., Iturbe, I. R., and Gupta, V. K. (1985). “Approximation of temporal rainfall from multidimensional model.” Water Resour. Res., 21(8), 1259–1270.
22.
Waymire, E., and Gupta, V. K. (1981). “The mathematical structure of rainfall representations, 3, Some applications of the point process theory to rainfall processes.” Water Resour. Res., 17(5), 1287–1294.
23.
Waymire, E., and Gupta, V. K., and Iturbe, I. R. (1984). “A spectral theory of rainfall intensity at the meso β‐scale.” Water Resour. Res., 20(10), 1453–1465.
24.
Woolhiser, D. A., and Roldan, J. (1982). “Stochastic daily precipitation models, 2, A comparison of distributions of amounts.” Water Resour. Res., 18(5), 1461–1468.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 118 • Issue 6 • November 1992
Pages: 671 - 688
Copyright
Copyright © 1992 ASCE.
History
Published online: Nov 1, 1992
Published in print: Nov 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.