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

Maikel Issermann,Fi-John Chang

doi:10.3390/w12010229

Abstract

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.

Highlights

Flood inundation, in its many forms, is one the most devastating types of natural disaster for civilization [1]
ANUGA is mainly written in the Python programming language, which allows for flexible usage [39]
We focus on the first and second statistical moments because of their more important relationship with real-world applications, and consider the third and fourth moments because they permit the fitting of a probability distribution to the output variable

Summary

Introduction

In its many forms, is one the most devastating types of natural disaster for civilization [1]. Floods are involved in the majority of fatalities associated with natural disasters [2]. Cause severe economic damage by disrupting and destroying processes within the society and economy. The socio-economic impact of flood inundations has given rise to studies on the subject receiving widespread interest. Flood-risk assessments are in particular focus and are legally required in some parts of the world, for example in the European Directive on the Assessment and Management of Flood Risks [3]. Maps are one of the best ways to present the spatial distribution of uncertainty and risk. Flood-risk maps are event-based and show the probability of the occurrence and consequences of a flood [1]

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