Relationships Among Water Storage Variables
Publication: Journal of Water Resources Planning and Management
Volume 113, Issue 3
Abstract
Among a large number of random variables related to water storage for given sample size n, the most studied are the range deficit and negative run‐sum A simulation of 5,000 samples for various n was performed for three assumed population processes: normal independent, normal dependent, and gamma independent. It was found by simulation, and verified by an analytical derivation, that the range and deficit are equal in 50% of generated samples, while in the other 50% the range is greater that the deficit Probabilities of range from zero to more than 0.60; they decrease as n and skewness increase, but increase as the lag‐1 autocorrelation coefficient increases. The case of has similar patterns. The ratios of sample means for these three storage‐related variables, either for 5,000 samples or only the samples for which the values of these variables are not equal, exhibit these general patterns: (1) Ratios increase with n converging to an asymptotic value of 0.7854 in case of 5,000 samples; (2) for samples, the ratios are much smaller than for the entire set of 5,000 samples with (3) ratios and are much smaller than The pairwise lag‐0 correlation coefficients of and for 5,000 sample estimates show that corr changes around 0.45 as n increases in the case this correlation is small but increase with n for For samples, corr becomes negative, oscillating around corr shows a decrease with an increase of n for but increases with an increase of autocorrelation, corr decreases with an increase of n, changes slightly with autocorrelation and with skewness.
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References
1.
Feller, W. (1951). “The asymptotic distribution of the range of sums of independent random variables.” Ann. Math. Statis., 22, 427–432.
2.
Gomide, F. L. S. (1979). “The asymptotic distribution of the maximum deficit of partial sums of independent random variables.” Water Resour. Res., 15(2), 495–497.
3.
Pegram, G. G. S., et al. (1980). “Stochastic properties of water storage.” Colorado State Univ. Hydrology Papers Series, No. 100, Aug.
4.
Thomas, H. A., Jr., and Burden, R. P. (1963). “Operations research in water quality management.” Harvard Univ., Cambridge, Mass.
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Copyright © 1987 ASCE.
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Published online: Jul 1, 1987
Published in print: Jul 1987
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