Applying ANN emulators in uncertainty assessment of flood inundation modelling: a comparison of two surrogate schemes

Abstract A generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis.

[1]  Ilias Bilionis,et al.  Multi-output local Gaussian process regression: Applications to uncertainty quantification , 2012, J. Comput. Phys..

[2]  Holger R. Maier,et al.  Neural networks for the prediction and forecasting of water resource variables: a review of modelling issues and applications , 2000, Environ. Model. Softw..

[3]  Christine A. Shoemaker,et al.  Comparison of function approximation, heuristic, and derivative‐based methods for automatic calibration of computationally expensive groundwater bioremediation models , 2005 .

[4]  Giuseppe T. Aronica,et al.  Estimation of flood inundation probabilities using global hazard indexes based on hydrodynamic variables , 2012 .

[5]  Robert B. Gramacy,et al.  Ja n 20 08 Bayesian Treed Gaussian Process Models with an Application to Computer Modeling , 2009 .

[6]  Paul D. Bates,et al.  Distributed Sensitivity Analysis of Flood Inundation Model Calibration , 2005 .

[7]  Andrea Castelletti,et al.  Emulation techniques for the reduction and sensitivity analysis of complex environmental models , 2012, Environ. Model. Softw..

[8]  Micha Werner,et al.  Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling , 2003 .

[9]  E. Bruce Pitman,et al.  Computational Statistics and Data Analysis Mechanism-based Emulation of Dynamic Simulation Models: Concept and Application in Hydrology , 2022 .

[10]  P. D. Batesa,et al.  A simple raster-based model for flood inundation simulation , 2000 .

[11]  M. Giles.  Improved Multilevel Monte Carlo Convergence using the Milstein Scheme , 2008 .

[12]  Keith Beven,et al.  Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model , 1998 .

[13]  V. Merwade,et al.  Uncertainty Quantification in Flood Inundation Mapping Using Generalized Likelihood Uncertainty Estimate and Sensitivity Analysis , 2012 .

[14]  P. Bates,et al.  Calibration of uncertain flood inundation models using remotely sensed water levels. , 2009 .

[15]  M. Werner,et al.  Impact of grid size in GIS based flood extent mapping using a 1D flow model , 2001 .

[16]  Jun Xia,et al.  Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model , 2012 .

[17]  Sai Hung Cheung,et al.  Bayesian uncertainty analysis with applications to turbulence modeling , 2011, Reliab. Eng. Syst. Saf..

[18]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

[19]  Søren Liedtke Thorndahl,et al.  Event based uncertainty assessment in urban drainage modelling applying the GLUE methodology , 2008 .

[20]  Keith Beven,et al.  Fuzzy set approach to calibrating distributed flood inundation models using remote sensing observations , 2006 .

[21]  Jan Feyen,et al.  Constraining soil hydraulic parameter and output uncertainty of the distributed hydrological MIKE SHE model using the GLUE framework , 2002 .

[22]  Mitchell J. Small,et al.  State Water Pollution Control Policy Insights from a Reduced-Form Model , 2004 .

[23]  Keith Beven,et al.  Bayesian updating of flood inundation likelihoods conditioned on flood extent data , 2004 .

[24]  Henrik Madsen,et al.  Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov chain Monte Carlo sampling , 2006 .

[25]  Mitchell J. Small,et al.  Evaluating response surface designs for uncertainty analysis and prescriptive applications of a large-scale water quality model , 2006 .

[26]  Dimitri Solomatine,et al.  A novel approach to parameter uncertainty analysis of hydrological models using neural networks , 2009 .

[27]  Robin K. S. Hankin,et al.  Bayesian calibration of a flood inundation model using spatial data , 2011 .

[28]  Keith Beven,et al.  Influence of uncertain boundary conditions and model structure on flood inundation predictions. , 2006 .

[29]  D Butler,et al.  Use of surrogate modelling for multiobjective optimisation of urban wastewater systems. , 2009, Water science and technology : a journal of the International Association on Water Pollution Research.

[30]  Holger R. Maier,et al.  Water Distribution System Optimization Using Metamodels , 2005 .

[31]  P. Bates,et al.  A probabilistic methodology to estimate future coastal flood risk due to sea level rise , 2008 .

[32]  Ronald L. Iman,et al.  Risk methodology for geologic disposal of radioactive waste: small sample sensitivity analysis techniques for computer models, with an application to risk assessment , 1980 .

[33]  Jesús Abaurrea,et al.  Forecasting local daily precipitation patterns in a climate change scenario , 2005 .

[34]  Bryan A. Tolson,et al.  Review of surrogate modeling in water resources , 2012 .

[35]  Qi Zhang,et al.  Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model , 2010 .

[36]  Paul D. Bates,et al.  Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE , 2002 .

[37]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[38]  Sai Hung Cheung,et al.  Stochastic sampling using moving least squares response surface approximations , 2012 .

[39]  Oskar von Stryk,et al.  A mixed-integer simulation-based optimization approach with surrogate functions in water resources management , 2008 .

[40]  Florian Pappenberger,et al.  Estimating uncertainty associated with water stages from a single SAR image , 2008 .

[41]  K. Beven,et al.  Uncertainty in the calibration of effective roughness parameters in HEC-RAS using inundation and downstream level observations , 2005 .

[42]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[43]  K. Bevenb,et al.  Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data , 1998 .