Stochastic response surface methods for supporting flood modelling under uncertainty
Date of Issue2016
School of Civil and Environmental Engineering
Institute of catastrophe risk management
Flood inundation modelling is a fundamental tool for supporting flood risk assessment and management. However, it is a complex process, involving cascade consideration of meteorological, hydrological, and hydraulic processes. In order to successfully track the flood-related processes, different kinds of models, including stochastic rainfall, rainfall-runoff and hydraulic models are widely employed. However, a variety of uncertainties, originated from model structures, parameters, and inputs, tend to make the simulation results diverge from the real flood situations. Traditional stochastic uncertainty-analysis methods are suffering from time-consuming iterations of model runs based on parameter distributions. It is thus desired that uncertainties associated with flood modelling be more efficiently quantified, without much compromise of model accuracy. This thesis is devoted to developing a series of stochastic response surface methods (SRSMs) and coupled approaches to address forward and inverse uncertainty-assessment problems in flood inundation modelling. Flood forward problem is an important and fundamental issue in flood risk assessment and management. This study firstly investigated the application of a spectral method, namely, Karhunen-Loevè expansion (KLE) to approximate one-dimensional and two-dimensional coupled (1D/2D) heterogeneous random field of roughness. Based on KLE, first-order perturbation (FP-KLE) method was proposed to explore the impact of uncertainty associated with floodplain roughness on a 2D flooding modelling process. The predicted results demonstrated that FP-KLE was computationally efficient with less numerical executions and comparable accuracy compared with conventional Monte Carlo simulation (MCS) and the decomposition of heterogeneous random field of uncertain parameters by KLE was verified. Secondly, another KLE-based approach was proposed to further tackle heterogeneous random field by introducing probabilistic collocation method (PCM). Within the framework of this combined forward uncertainty quantification approach, namely PCM/KLE, the output fields of the maximum flow depths were approximated by the 2nd-order PCM. The study results indicated that the assumption of a 1D/2D random field of the uncertain parameter (i.e. roughness) could efficiently alleviate the burden of random dimensionality within the analysis framework, and the introduced method could significantly reduce repetitive numerical simulations of the physical model as required in the traditional MCS. Thirdly, a KLE-based approach for flood forward uncertainty quantification, namely pseudospectral collocation approach (i.e. gPC/KLE) was proposed. The method combined the generalized polynomial chaos (gPC) with KLE. To predict the two-dimensional flood flow fields, the anisotropic random input field (logarithmic roughness) was approximated by the normalized KLE and the output field of flood flow depth was represented by the gPC expansion, whose coefficients were obtained with a nodal set construction via Smolyak sparse grid quadrature. This study demonstrated that the gPC/KLE approach could predict the statistics of flood flow depth with less computational requirement than MCS; it also outperformed the PCM/KLE approach in terms of fitting accuracy. This study made the first attempt to apply gPC/KLE to flood inundation field and evaluated the effects of key parameters on model performances. Flood inverse problems are another type of uncertainty assessment of flood modeling and risk assessment. The inverse issue arises when there is observed flood data but limited information of model uncertain parameters. To address such a problem, the generalized likelihood uncertainty estimation (GLUE) inferences are introduced. First of all, an uncertainty analysis of the 2D numerical model called FLO-2D embedded with GLUE inference was presented to estimate uncertainty in flood forecasting. An informal global likelihood function (i.e. F performance) was chosen to evaluate the closeness between the simulated and observed flood inundation extents. The study results indicated that the uncertainty in channel roughness, floodplain hydraulic conductivity, and floodplain roughness would affect the model predictions. The results under designed future scenarios further demonstrated the spatial variability of the uncertainty propagation. Overall, the study highlights that different types of information (e.g., statistics of input parameters, boundary conditions, etc.) could be obtained from mappings of model uncertainty over limited observed inundation data. Finally, the generalized polynomial chaos (gPC) approach and Differential Evolution Adaptive Metropolis (DREAM) sampling scheme were introduced to enhance the sampling efficiency of the conventional GLUE method. By coupling gPC with DREAM (gPC-DREAM), samples from high-probability region could be generated directly without additional numerical executions if a suitable gPC surrogate model of likelihood function was constructed in advance. Three uncertain parameters were tackled, including floodplain roughness, channel roughness, and floodplain hydraulic conductivity. To address this inverse problem, two GLUE inferences with the 5th and the 10th gPC-DREAM sampling systems were established, which only required 751 numerical executions, respectively. Solutions under three predefined subjective levels (i.e. 50%, 60% and 65%) were provided by these two inferences. The predicted results indicated that the proposed inferences could reproduce the posterior distributions of the parameters; however, this uncertainty assessment did not require numerical executions during the process of generating samples; this normally were necessary for GLUE inference combined with DREAM to provide the exact posterior solutions with 10,000 numerical executions. This research has made a valuable attempt to apply a series of collocation-based PC approaches to tackle flood inundation problems and the potential of these methods has been demonstrated. The research also presents recommendations for future development and improvement of these uncertainty approaches, which can be applicable for many other hydrological/hydraulics areas that require repetitive runs of numerical models during uncertainty assessment and even more complicated scenarios.
DRNTU::Engineering::Civil engineering::Water resources