Effect of Likelihood Function Selection on Estimating Uncertainty of HEC-HMS Flood Simulation Model Using Markov Chain Monte Carlo Algorithm

In the present study, DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis) is used to investigate uncertainty of parameters in the HEC-HMS flood modeling in Tamar watershed (1530 km2) in Golestan province. In order to assess the uncertainty of 24 parameters used in HMS three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of five different likelihood functions (L1–L5) was assessed by means of DREAM(ZS) approach. Three likelihood functions, L1, L2 and L3, are considered as informal whereas remaining (L4 and L5) is represented as formal categories. Likelihood function L1 is Nash–Sutcliffe (NS) efficiency and L2 is based on minimum mean square error. L3 uses estimation of model error variance and L4 focuses on the relationship between the traditional least squares fitting and the Bayesian inference. In likelihood function L5 the serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results sensitivities of the parameters depend strongly on the likelihood function and vary for different likelihood functions. Most of the parameters were better defined by likelihood functions L4 and L5 and showed high sensitivities to model performance. Calculating P-factor values (percentage of measured data bracketed by 95% prediction uncertainty) showed that 75–100% of observed data were ranged in 95% total prediction uncertainty. Considering all the statistical indicators and criteria of uncertainty assessment, including P-factor and R-factor (relative width of the 95% prediction uncertainty), root-mean-square error (RMSE), Kling-Gupta Efficiency (KGE), and Nash–Sutcliffe (NS) the results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L4 and L5.