Bayesian Inference for the Urban Drainage Models Uncertainty Quantification Based on Heteroscedastic Residual Assumption

Model calibration and uncertainty analysis are critical steps for urban drainage models prior to their use. Bayesian inference has been widely utilized for calibrating model parameters due to its ability to quantify both the uncertainty of model parameters and model predictions. Existing methods generally assume that the residuals are homoscedastic and follow a normal distribution with a constant variance. However, given the inherent uncertainties in inputs, model structure, parameters, and observations, the variance of residuals varies inconsistently across model prediction steps. To address this issue, a Bayesian inference method based on the assumption of heteroscedastic residuals is developed for model calibration and uncertainty quantification. The results demonstrate that the heteroscedasticity residual-based method generates more reasonable prediction uncertainty intervals and provides more reliable prediction distributions compared to the existing homoscedasticity residual-based method.