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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.

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Abstract:The temporal-spatial resolution of input data-induced uncertainty in a watershed-based water quality model, Hydrologic Simulation Program-FORTRAN (HSPF), is investigated in this study. The temporal resolution-induced uncertainty is described using the coefficient of variation (CV). The CV is found to decrease with decreasing temporal resolution and follow a log-normal relation with time interval for temperature data while it exhibits a power-law relation for rainfall data. The temporal-scale uncertainties in the temperature and rainfall data follow a general extreme value distribution and a Weibull distribution, respectively. The Nash-Sutcliffe coefficient (NSC) is employed to represent the spatial resolution induced uncertainty. The spatial resolution uncertainty in the dissolved oxygen and nitrate-nitrogen concentrations simulated using HSPF is observed to follow a general extreme value distribution and a log-normal distribution, respectively. The probability density functions (PDF) provide new insights into the effect of temporal-scale and spatial resolution of input data on uncertainties involved in watershed modelling and total maximum daily load calculations. This study exhibits non-symmetric distributions of uncertainty in water quality modelling, which simplify weather and water quality monitoring and reducing the cost involved in flow and water quality monitoring.