Abstract
This paper explained the uncertainty of discharge due to the uncertainty of rainfall theoretically and mathematically. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation), because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be estimated based on the theory of stochastic processes, and it can be applied to the probabilistic risk of flood management.
