Abstract
BackgroundThis study tested a first-order perturbation method based on Karhunen-Loevè expansion (FP-KLE), to analyze flood inundation modeling under uncertainty. The floodplain roughness over a 2-dimensional domain was assumed to be a statistically heterogeneous field with log-normal distributions. Firstly, we attempted to use KLE to decompose the random field of log-transferred floodplain roughness N(x), which was based on the eigenvalues and eigenfunctions of the covariance function of N(x), and a set of orthogonal normal random variables. Secondly, the maximum flow depths were expanded by the first-order perturbation method by using the same set of random variables as used in the KLE decomposition. Then, a flood inundation model, named FLO-2D, was adopted to numerically solve the corresponding perturbation expansions.ResultsTo illustrate the methodology, a one-in-five-years flood event was chosen as the study case. The results indicated that the mean of the maximum flow-depth field obtained from the proposed method was fairly close to that from Monte Carlo Simulation (MCS), but the standard deviation was somewhat higher. However, the FP-KLE method was computationally more efficient than MCS.ConclusionsThe study verified the applicability of FP-KLE in handling uncertainties of flood modeling in a more efficient manner; further test with multiple inputs of random fields is desired.
Highlights
This study tested a first-order perturbation method based on Karhunen-Loevè expansion (FP-KLE), to analyze flood inundation modeling under uncertainty
The floodplain roughness is assumed as a random field with lognormal probability distribution function (PDF)
This study attempted to use a first-order perturbation called FP-KLE to investigate the impact of uncertainty associated with floodplain roughness coefficients on a 2D flooding modelling process
Summary
This study tested a first-order perturbation method based on Karhunen-Loevè expansion (FP-KLE), to analyze flood inundation modeling under uncertainty. Many studies were devoted to analyse uncertainty propagation from manning’s roughness coefficients during flood modelling, such as Generalized Likelihood Uncertainty Estimation (GLUE) and traditional Monte Carlo simulations (MCS) (Aronica et al, 1998; Aronica et al, 2002; Van Vuren et al, 2005; Reza Ghanbarpour et al, 2011; Jung and Merwade, 2012) Most of these studies tend to adopt homogenous values of roughness coefficient over the study domain, and this could lead to significant discrepancies between the observed data and simulation results
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