Relationships among water storage variables Article

Yevjevich, V, Obeysekera, JTB. (1987). Relationships among water storage variables . JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT, 113(3), 353-367. 10.1061/(ASCE)0733-9496(1987)113:3(353)

cited authors

  • Yevjevich, V; Obeysekera, JTB

authors

abstract

  • Among a large number of random variables related to water storage for given sample size n, the most studied are the range Rn, deficit Dn, and negative run-sum Vn. 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 (Rn = Dn) in 50% of generated samples, while in the other 50% the range is greater that the deficit (Rn>Dn). Probabilities of Dn = Vn range from zero to more than 0.60; they decrease as n and skewness Q increase, but increase as the lag-1 autocorrelation coefficient increases. The case of Rn = Dn = Vn 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 Dn/Rn increase with n, converging to an asymptotic value of 0.7854 in case of 5,000 samples; (2) for Rn > Dn samples, the ratios Dn/Rn are much smaller than for the entire set of 5,000 samples with Rn ≥ Dn; (3) ratios Vn/Dn and Vn/Rn are much smaller than Dn/Rn. The pairwise lag-0 correlation coefficients of Rn, Dn, and V„ for 5,000 sample estimates show that corr (Rn,Dn) changes around 0.45 as n increases in the case Cs = 0; this correlation is small (0 – 0.25), but increase with n for Cs = 3. For Rn > Dn samples, corr (Rn, Dn) becomes negative, oscillating around –0.07. corr (Dn, Vn) shows a decrease with an increase of n for Cs = 3, but increases with an increase of autocorrelation, corr (Rn, Vn) decreases with an increase of n, changes slightly with autocorrelation and with skewness. © ASCE.

publication date

  • January 1, 1987

published in

start page

  • 353

end page

  • 367

volume

  • 113

issue

  • 3