Abstract
The paper discusses aspects of solutions to nonlinear stochastic differential equations applicable to catchment modelling within the context of conceptual reservoirs of the Nash type. The particular stochastic differential equation studied herein is derived from the mass balance equation stated for a single reservoir by representing the input term, as well as the environmental (external) parameters within it, as white stationary stochastic processes. Also noted are certain properties of the solution, numerical evaluation techniques, and the environmentally induced instability problem of concern in this context.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akcasu, A. A., and M. Karasulu (1976), “Non-linear response of point-reactors to stochastic inputs”. Annals of Nuclear Energy 3, 11–18.
Ariaratnam, S. T., and P. W. U. Graefe (1965), “Linear systems with stochastic coefficients”. International Journal of Control 2, 205–215.
Arnold, L. (1974), Stochastic Differential Equations: Theory and Applications. New York: Wiley and Sons.
Bodo, B. (1985), “Linear stochastic conceptual catchment response models”. Ph.D. Thesis submitted to the University of Waterloo, Waterloo, Ontario, Canada.
Bodo, B., and T. E. Unny (1985), “On the outputs of stochasticized Nash-Dooge reservoir cascade.” Paper presented at this symposium.
Chow, V. T. (1964), “Runoff”. In Handbook of Applied Hydrology, ed. V. T. Chow, 14-1–14-54. New York: McGraw-Hill.
Gihman, I. I., and A. V. Skorohod (1972), Stochastic Differential Equations. New York: Springer-Verlag.
Horsthemke, W., and R. Lefever (1984), Noise-induced Transitions. New York: Springer-Verlag.
Jazwinski, A. H. (1970), Stochastic Processes and Filtering Theory. New York: Academic Press.
Nash, J. E. (1957), “The form of the instantaneous unit hydrograph”. International Association of Scientific Hydrology Monograph Publication 45, Volume 3, pp. 114–121.
Stratonovich, R. L. (1967), Topics in the Theory of Random Noise, Vol. 2, translated from Russian by R. A. Solverman. New York: Gordon Breach.
Unny, T. E. (1984), “Numerical integration of stochastic differential equations in catchment modeling.” Water Resources Research 20, 360–368.
Unny, T. E., and Karmeshu (1984), “Stochastic nature of outputs from conceptual reservoir model cascades.” Journal of Hydrology 68, 161–180.
Wong, W., and M. Zakai (1965), “On the relation between ordinary and stochastic differential equations.” International Journal of Engineering Science 3, 213–222.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Unny, T.E. (1987). Solutions to Nonlinear Stochastic Differential Equations in Catchment Modelling. In: MacNeill, I.B., Umphrey, G.J., McLeod, A.I. (eds) Advances in the Statistical Sciences: Stochastic Hydrology. The University of Western Ontario Series in Philosophy of Science, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4792-4_6
Download citation
DOI: https://doi.org/10.1007/978-94-009-4792-4_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8625-7
Online ISBN: 978-94-009-4792-4
eBook Packages: Springer Book Archive