On the implementation of Prabhu's exact solution of the stochastic reservoir equation

Advances in Water Resources

Volumn 32, Issue 4, 2009, Pages 594-606

  Hamed, K H ^a  

^a CAIRO UNIVERSITY   (Egypt)

Author keywords

Equilibrium storage; Exact solution; Gamma inflow; Prabhu; Reservoir storage; Stochastic reservoir

Indexed keywords

MATLAB; NUMERICAL ANALYSIS; NUMERICAL METHODS; RANDOM PROCESSES;

EQUILIBRIUM STORAGE; EXACT SOLUTION; GAMMA INFLOW; PRABHU; RESERVOIR STORAGE; STOCHASTIC RESERVOIR;

PROBABILITY DISTRIBUTIONS;

INFLOW; NUMERICAL MODEL; PROBABILITY; RESERVOIR; SKEWNESS; STOCHASTICITY; WATER STORAGE;

EID: 62349089280     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2009.01.007     Document Type: Article

References (41)

1. Barnes F.B. Storage required for a city water supply. J Inst Eng Aust 26 198 (1957) 203
2. Bayazit M., and Bulu A. Generalized probability distribution of reservoir capacity. J Hydrol 126 (1991) 195-205
3. Buchberger SG. A diffusion theory for stochastic storage analysis. PhD dissertation, Graduate School, University of Texas at Austin; 1988.
4. Chapra S.C., and Canale R.P. Numerical methods for engineers. 5th ed. (2006), McGraw-Hill
5. Fletcher S.G., and Ponnambalam K. Estimation of reservoir yield and storage distribution using moments analysis. J Hydrol 182 1 (1996) 259-275
6. Gani J. Some problems in the theory of provisioning and of dams. Biometrica 42 (1955) 179-200
7. Gomide FLS. Range and deficit analysis using Markov chains. Hydrol Pap. 79, Colorada State University, Fort Collins, CL; 1975.
8. Gould B.W. Statistical methods for estimating the design capacity of dams. J Inst Eng Aust 33 12 (1961) 405-416
9. Hazen A. Storage to be provided in impounding reservoirs for municipal water supply. Trans ASCE 77 (1914) 1539-1640
10. Hogg R.V., and Tanis E.A. Probability and statistical inference (1988), MacMillan Publishing Company, NY
11. Hurst H.E. Long term capacity of storage reservoirs. Trans ASCE 116 (1951) 770-799
12. Klemeš V. Discrete representation of storage for stochastic reservoir optimization. Water Resour Res 13 (1977) 149-158
13. Klemeš V. Applied stochastic theory of storage in evolution. In: Chow VT, editor. Advances in hydroscience, vol. 12; 1981. p. 79-141.
14. Koutsoyiannis D. Reliability concepts in reservoir design. In: Lehr J.H., and Keeley J. (Eds). Water encyclopedia, surface and agricultural water vol. 4 (2005), Wiley, New York 259-265
15. Kritskiy S.N., and Menkel M.F. Long-term streamflow regulation. Gidrotekh Stroit 2 (1935) 3-10 [in Russian]
16. Kritskiy S.N., and Menkel M.F. Generalized methods for runoff control computations based on mathematical statistics. Gidrotekh Stroit 2 (1940) 3-10 [in Russian]
17. Langbein W.B. Queuing theory and water storage. J Hydraul Division ASCE 84 HY5 (1958) 1-24
18. Lloyd E.H. The theory of storage with serially correlated inputs. J Hydrol 1 (1963) 99-128
19. Lloyd E.H. The stochastic reservoir: exact and approximate evaluations of the storage distribution. Invited review. J Hydrol 151 (1993) 65-107
20. Lochart P., and Phatarfod R.M. On the problem of discretization in dam theory. Water Resour Res 15 (1979) 1593-1597
21. McMahon T.A., Pegram G.G.S., Vogel R.M., and Peel M. Review of Gould-Dincer reservoir storage-yield-reliability estimates. Adv Water Resour 30 (2007) 1873-1882
22. McMahon T.A., Pegram G.G.S., Vogel R.M., and Peel M. Revisiting reservoir storage-yield-reliability relationships using a global streamflow database. Adv Water Resour 30 (2007) 1858-1872
23. McMahon T.A., Vogel R.M., Peel M., and Pegram G.G.S. Global streamflows - Part 1: Characteristics of annual streamflows. J Hydrol 347 (2007) 243-259
24. Moran P.A.P. A probability theory of dams and storage systems. Aust J Appl Sci 5 (1954) 116-124
25. Moran P.A.P. A probability theory of dams and storage systems: modifications of the release rules. Aust J Appl Sci 6 (1955) 117-130
26. Moran P.A.P. The theory of storage (1959), Methuen, London
27. Pegram G.G.S. On reservoir reliability. J Hydrol 47 (1980) 269-296
28. Phien H.N. Reservoir storage capacity with gamma inflows. J Hydrol 146 (1993) 383-389
29. Phatarfod R.M. The effect of serial correlation on reservoir size. Water Resour Res 22 6 (1986) 927-934
30. Phatarfod R.M. Riverflow and reservoir storage models. Math Comput Model 12 (1989) 1057-1077
31. Phatarfod R.M., and Srikanthan R. Seasonality of flows and its effect on reservoir size. In: Hipel K.W. (Ed). Stochastic and statistical methods in hydrology and environmental engineering. Time series analysis in hydrology and environmental engineering vol. 3 (1994), Springer 395-407
32. Prabhu N.U. On the integral equation of the finite dam. Quart J Math 9 35 (1958) 183-188
33. Pretto P.B., Chiew F.H.S., McMahon T.A., Vogel R.M., and Stedinger J.R. The (mis)behavior of behavior analysis storage estimates. Water Resour Res 33 4 (1997) 703-709
34. Richardson L.F. The deferred approach to the limit. Phil Trans Roy Soc Lond Ser A 226 (1927) 299-349
35. Rippl W. Capacity of storage reservoirs for water supply. Minutes Proc Inst Civil Eng 71 (1883) 270-278
36. Savarenskiy A.D. A method for streamflow control computations. Gidrotekh Stroit 2 (1940) 24-28 [in Russian]
37. Sudler C.E. Storage required for the regulation of stream flow. Trans ASCE 91 (1927) 622-660
38. Vogel R.M., and Bolognese R.A. Storage-reliability-yield relations for over-year water supply systems. Water Resour Res 31 3 (1995) 645-654
39. Vogel R.M., and McMahon T.A. Approximate reliability and resilience indices of over-year reservoirs fed by AR(1) gamma and normal flows. Hydrol Sci J 41 1 (1996) 75-95
40. Vogel R.M., and Stedinger J.R. Generalized storage-reliability-yield relationships. J Hydrol 89 (1987) 303-327
41. Vogel R.M., and Wilson I. The probability distribution of annual maximum, minimum, and average streamflow in the United States. J Hydrol Eng ASCE 1 2 (1996) 69-76