Proposal and Application of a New Theoretical Framework of Uncertainty Estimation in Rainfall Runoff Process Based on the Theory of Stochastic Process

The aim of this study is to clarify the effect of the uncertainty of inputs in respect of output by rainfall-runoff process. In Japan, we have performed runoff analysis using deterministic model such as storage function model in the past. However, natural phenomena have various uncertainties. For example, rainfall-runoff analysis includes uncertainties of parameters or structure of model, and observed value of rainfall and water level. In this study, we attend the uncertainty of rainfall which is input data of runoff analysis and introduce the theory of stochastic process to runoff analysis due to quantify the uncertainties stochastically. We indicate the theoretical framework to evaluate the uncertainties using the relationship among stochastic differential equation (SDE) and Fokker-Planck equation (FPE), because the lumped rainfall-runoff model is described by ordinary differential equation.As a result, we introduce the theory of stochastic process to runoff analysis. And we make a suggestion of a new theoretical framework of uncertainty estimation regarding reliability analysis with the distribution of water level as external force and the failure probability of levee as resistance.