Uncertainty Analysis of Spatiotemporal Models with Point Estimate Methods (PEMs)—The Case of the ANUGA Hydrodynamic Model

Practitioners often neglect the uncertainty inherent to models and their inputs. Point Estimate Methods (PEMs) offer an alternative to the common, but computationally demanding, method for assessing model uncertainty, Monte Carlo (MC) simulation. PEMs rerun the model with representative values of the probability distribution of the uncertain variable. The results can estimate the statistical moments of the output distribution. Hong’s method is the specific PEM implemented here for a case study that simulates water runoff using the ANUGA model for an area in Glasgow, UK. Elevation is the source of uncertainty. Three realizations of the Sequential Gaussian Simulation, which produces the random error fields that can be used as inputs for any spatial model, are scaled according to representative values of the distribution and their weights. The output from a MC simulation is used for validation. A comparison of the first two statistical moments indicates that Hong’s method tends to underestimate the first moment and overestimate the second moment. Model efficiency performance measures validate the usefulness of Hong’s method for the approximation of the first two moments, despite the method suffering from outliers. Estimation was less accurate for higher moments but the moment estimates were sufficient to use the Grams-Charlier Expansion to fit a distribution to them. Regarding probabilistic flood-inundation maps, Hong’s method shows very similar probabilities in the same areas as the MC simulation. However, the former requires just three 11-minute simulation runs, rather than the 500 required for the MC simulation. Hong’s method therefore appears attractive for approximating the uncertainty of spatiotemporal models.

[1]  R. Suchomel,et al.  Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c–φ soil , 2010 .

[2]  P. Bates,et al.  The impact of uncertainty in satellite data on the assessment of flood inundation models , 2012 .

[3]  Christian Onof,et al.  Quantifying the impact of small scale unmeasured rainfall variability on urban runoff through multifractal downscaling: A case study , 2012 .

[4]  P. Bates.  Integrating remote sensing data with flood inundation models: how far have we got? , 2012 .

[5]  M. Harr.  Probabilistic estimates for multivariate analyses , 1989 .

[6]  P. Deschamps,et al.  Declining water budget in a deep regional aquifer assessed by geostatistical simulations of stable isotopes: Case study of the Saharan “Continental Intercalaire” , 2015 .

[7]  Y. Tung.  Mellin Transform Applied to Uncertainty Analysis in Hydrology/Hydraulics , 1990 .

[8]  S. G. Roberts,et al.  Validation of ANUGA hydraulic model using exact solutions to shallow water wave problems , 2013 .

[9]  P. Forsyth,et al.  Efficient uncertainty quantification in fully-integrated surface and subsurface hydrologic simulations , 2018 .

[10]  Yeou-Koung Tung,et al.  Monte Carlo Simulation for Correlated Variables with Marginal Distributions , 1994 .

[11]  Adam Hapij,et al.  Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification , 2015, Reliab. Eng. Syst. Saf..

[12]  Paul D. Bates,et al.  Improving the stability of a simple formulation of the shallow water equations for 2‐D flood modeling , 2012 .

[13]  Gabriele Freni,et al.  Validation of hydrological models: conceptual basis, methodological approaches and a proposal for a code of practice , 2010 .

[14]  Samuela Franceschini,et al.  Point estimate methods based on Taylor Series Expansion – The perturbance moments method – A more coherent derivation of the second order statistical moment , 2012 .

[15]  Paul D. Bates,et al.  How much physical complexity is needed to model flood inundation? , 2012 .

[16]  F. Klijn,et al.  Explaining differences in flood management approaches in Europe and in the USA – a comparative analysis , 2017 .

[17]  Guohe Huang,et al.  A PCM-based stochastic hydrological model for uncertainty quantification in watershed systems , 2015, Stochastic Environmental Research and Risk Assessment.

[18]  Soroosh Sorooshian,et al.  Evolution of ensemble data assimilation for uncertainty quantification using the particle filter‐Markov chain Monte Carlo method , 2012 .

[19]  Chang Che-hao,et al.  Evaluation of probability point estimate methods , 1995 .

[20]  Hans Petter Langtangen,et al.  Chaospy: An open source tool for designing methods of uncertainty quantification , 2015, J. Comput. Sci..

[21]  Kuo‐Chin Hsu,et al.  Dynamic interactions of groundwater flow and soil deformation in randomly heterogeneous porous media , 2013 .

[22]  T. J. Dodwell,et al.  A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow , 2013, SIAM/ASA J. Uncertain. Quantification.

[23]  Quan J. Wang,et al.  A review of advances in flash flood forecasting , 2011 .

[24]  Paul D. Bates,et al.  Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches , 2010 .

[25]  Michael F. Goodchild,et al.  Accounting for Spatial Uncertainty in Optimization with Spatial Decision Support Systems , 2003, Trans. GIS.

[26]  J. Tejchman,et al.  Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity , 2008 .

[27]  D. McLaughlin,et al.  Stochastic analysis of nonstationary subsurface solute transport: 2. Conditional moments , 1989 .

[28]  Emilio Rosenblueth,et al.  Two-point estimates in probabilities , 1981 .

[29]  Dennis McLaughlin,et al.  A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis , 1991 .

[30]  Jinglai Li,et al.  A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification , 2016, J. Comput. Phys..

[31]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[32]  Anthony J. Jakeman,et al.  Flood inundation modelling: A review of methods, recent advances and uncertainty analysis , 2017, Environ. Model. Softw..

[33]  Joseph H. A. Guillaume,et al.  Characterising performance of environmental models , 2013, Environ. Model. Softw..

[34]  H. Hong.  An efficient point estimate method for probabilistic analysis , 1998 .

[35]  E. Rosenblueth.  Point estimates for probability moments. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Galina Merkuryeva,et al.  Advanced river flood monitoring, modelling and forecasting , 2015, J. Comput. Sci..