Constructing an Uncertainty Budget for a Two-Dimensional Hydraulic Model

In this study, combined uncertainty of a two-dimensional hydraulic model expanded at a 95% confidence level is estimated and uncertainty budget for model outputs is attempted to be constructed. Many sources of uncertainty in inputs as well as applied procedure have a significant impact on the accuracy of two-dimensional hydraulic modeling, including: the uncertainties in the model inputs due to variations in the Manning’s Coefficient (M’sC) assigned, the bridge modeling methods, the equation sets (Diffusion Wave and Full Momentum Equations) employed and the geometric datasets for the same river system in the Black Sea Region of Turkey. Estimating an appropriate M’sC for a river system with 2D flow area is a daunting task. It is widely accepted by the scientific community that the uncertainty of the M’sC for a river system is best estimated at around 20 to 25 percent. Therefore, any attempt to quantify uncertainty for the assigned M’sC must be based on a sample large enough to obtain statistically significant results. To achieve this task, the Monte Carlo Simulation (MCS) is utilized to estimate the contribution of probable variations of the M’sC in ‘the combined uncertainty expanded at a 95% confidence level in two-dimensional hydraulic modeling’. MCS procedure—based on input variations simulated by random numbers large enough to reliably estimate an input—is considered an appropriate way of providing the corresponding variations in the model’s output, which also provides its own probability distribution. To achieve an accurate representation of probability outcomes, the model is re-run by assigning 100 different values of M’sC within 25 percent of its average value with Full Momentum Equation, the bridge modeling (Momentum and Energy) and geometrical dataset chosen. Then, uncertainty due to variation in geometric data is assessed by selecting different sections derived randomly from the same Digital Elevation Model. A similar process is followed to estimate variants in outputs due to variation in geometric datasets. Finally, the model is run utilizing Diffusion Equation and ‘Energy Only’ option for the bridge modeling with the chosen M’sC and geometric dataset to estimate variations in water levels at the sections chosen along the river. The methodology articulated in ‘Guide to the Expression of Uncertainty in Measurement’ is employed by utilizing HECRAS 5.05 Version.