Analysis of uncertainty propagation through model parameters and structure

Estimation of uncertainty propagation in watershed models is challenging but useful to total maximum daily load (TMDL) calculations. This paper presents an effective approach, involving the combined application of Rosenblueth method and sensitivity analysis, to the determination of uncertainty propagation through the parameters and structure of the HSPF (Hydrologic Simulation Program-FORTRAN) model. The sensitivity analysis indicates that the temperature is a major forcing function in the DO-BOD balance and controls the overall dissolved oxygen concentration. The mean and standard deviation from the descriptive statistics of dissolved oxygen data obtained using the HSPF model are compared to those estimated using Rosenblueth's method. The difference is defined as the error propagated from water temperature through dissolved oxygen. The error propagation, while considering the second order sensitivity coefficient in Rosenblueth's method, is observed to have a mean of 0.281 mg/l and a standard deviation of 0.099 mg/l. A relative low error propagation value is attributed to low skewness of dependent and independent variables. The results provide new insights into the uncertainty propagation in the HSPF model commonly used for TMDL development.