Abstract
A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bakr, A. A.; Gelhar, L. W.; Gutjahr, A. L.; MacMillan, J. R. 1978: Stochastic Analysis of Spatial Variability in Subsurface Flow, 1, Comparison of One and Three Dimensional Flows. Water Resources Research, 14(2):263–271
Becker, L.; Yeh, W. W-G. 1972: Identification of Parameters in Unsteady Open Channel Flows. Water Resources Research, 8(4):956–965
Bellman, R. A.; Kalaba, R. A. 1965: Quasilinearization and Nonlinear Boundary Value Problems. Elsevier, New York
Chiu, C-L.; Lin, H-C.; Mizumura, K. 1976: Simulation of Hydraulic Processes in Open Channels. Journal of the Hydraulics Division, ASCE, 102(HY2):185–206
Chu, W-S. 1985: Calibration of a Two-Dimensional Hydrodynamic Model. Coastal Engr., pp. 293–307
Chu, W-S. 1986: A Two-Dimensional Particle Tracking Estuarine Transport Model. Water Resources Bulletin, 22(2):183–189
Cushman, J.H. 1987: Development of Stochastic Parial Differential Equations for Subsurface Hydrology, Stochastic Hydrology and Hydraulics, 241–262 Chiu, C-L., and Isu, E. O, 1978: Kalman Filter in Open Channel Flow Estimation. Journal of the Hydraulics Division, ASCE, 104(HY8):1137–1152
Dagan, G. 1982: Analysis of Flow Through Heterogeneous Random Aquifers, 2, Unsteady Flow in Confined Formations. Water Resources Research, 18(5):1571–1585
Dagan, G. 1986: Statistical Theory of Groundwater Flow and Transport: Pore to Laboratory, Laboratory to Formation, and Formation to Regional Scale. Water Resources Research, 22(9):120–134
Davidson, B.; Vichnevetsky, R.; Wang, H. T. 1978: Numerical Techniques for Estimating Best-Distributed Manning's Roughness Coefficients for Open Estuarial River Systems. Water Resources REsearch. 14(5):777–789
Finnéy, B. A.; Bowles, D. S.; Windham, M. P. 1982: Random Differential Equations in River Water Quality Modeling. Water Resources Research, 18(1):122–134
French, R. H. 1985: Open Channel Hydraulics, McGraw-Hill, New York
Gelhar, L. W. 1986: Stochastic Subsurface Hydrology from Theory to Applications. Water Resources Research 22(5):135–145
Gutjahr, A. L.; Gelhar, L. W.; Bakr, A. A.; McMillan, J. R. Stochastic Analysis of Spatial Variability in Subsurface Flow, 2, Evaluation and Application. Water Resources Research, 14(5):953–959
Ippen, A. T. (ed.) 1966: Estuary and Coastline Hydrodynamics, New York: McGraw-Hill
Kaijser, T. 1971: A Stochastic Model Describing the Water Motion in a River. Nordic Hydrology, 2(4):243–265
Keller, J. B. 1964: Stochastic Equations and Wave Propagation in Random Media. Proceedings Symposium Applied Mathematics, American Mathematical Society, Providence, Rhode Island, pp. 145–170
Leendertse, J. J. 1970: A Water Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas. Vol. I, Principles of Computation. RM-6230-RC, Santa Monica: The Rand Corporation
Leendertse, J. J.; Gritton, E. C. 1971a: A Water Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas. Vol. II, Computation Procedures. R-708-NYC, New York: The New York City Rand Institute.
Leendertse, J. J.; Gritton, E. C. 1971b: A Water Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas. Vol. III, Jamaica Bay Simulation. R-709-NYC, New York: The New York City Rand Institute.
McKee, M.; Willis, R.; Hibler, L. 1986: A Monte Carlo Analysis of Uncertainty in Estuarine Hydraulics. Working Paper, Department of Environmental Engineering, Humboldt State University, Arcata, Calif.
Orlob, G. T. 1976: Mathematical Modeling of Estuarial Systems. In Proceedings of the International Symposium on Modelling Techniques in Water Resources Systems, ed. A. K. Biswas, Ottawa: Environment Canada, 78–124
Sagar, B. 1978: Analysis of Dynamic Aquifers with Stochastic Forcing Function. Water Resources Research, 14(2):207–216
Sagar, B. 1979: Solution of Linearized Boussinesq Equation with Stochastic Boundaries and Recharge. Water Resources Research, 15(3):618–624
Serrano, S. E.; Unny, T. E.; Lennox, W. C. 1985a: Analysis of Stochastic Groundwater Flow Problems. Part I. Deterministic Partial Differential Equations in Groundwater Flow: A Functional-Analytic Approach. J. of Hydrology, 82(1985):247–263
Serrano, S. E.; Unny, T. E.; Lennox, W. C. 1985b:, Analysis of Stochastic Groundwater Flow Problems. Part II. Stochastic Partial Differential Equations in Groundwater Flow: A Functional-Analytic Approach. J. of Hydrology, 82(1985):265–284
Serrano, S. E. 1988a: General Solutions to Random Advective-dispersive Equation in Porous Media. Part 1: Stochasticity in the Sources and in the Boundaries. Stochastic Hydrology and Hydraulics, 79–98
Serrano, S. E. 1988b: General Solutions to Random Advective-dispersive Equation in Porous Media. Part 2: Stochasticity in the Parameters. Stochastic Hydrology and Hydraulics, 79–98
Serrano, S. E.; Unny, T. E. 1987: Semigroup Solutions to STochastic Unsteady Groundwater Flow Subject to Random Parameters. Stochastic Hydrology and Hydraulics, 281–296
Smith, L., and Freeze, R. A. 1979: Stochastic Analysis of Steady Groundwater Flow in a Bounded Domain. 1. One-Dimensional Simulations. Water Resources Research. 15(3):521–528
Somlyody, L. 1983: Input Data Uncertainty and Parameter Sensitivity in a Lake Hydrodynamic Model. In Uncertainty and Forecasting of Water Quality, ed. Beck and Van Straten, New York: Springer-Verlag 129–155
Soong, T. T. 1973: Random Differential Equations in Science and Engineering. Academic Press, New York
Unny, T. E. 1989: Stochastic Partial Differential Equations in Groundwater Hydrology: Part 1-Theory. This journal (in press), to appear in vol 3(3)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Willis, R., Finney, B.A., McKee, M. et al. Stochastic analysis of estuarine hydraulics. Stochastic Hydrol Hydraul 3, 71–84 (1989). https://doi.org/10.1007/BF01544073
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01544073