**Maikel Issermann and Fi-John Chang \*,†**

Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan; d04622003@ntu.edu.tw

**\*** Correspondence: changfj@ntu.edu.tw

† Current address: National Taiwan University, Department of Bioenvironmental Systems Engineering, No. 1, Section 4, Roosevelt Rd, Da'an District, Taipei City 10617, Taiwan.

Received: 28 November 2019; Accepted: 9 January 2020; Published: 14 January 2020

**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.

**Keywords:** flood-risk map; hydrodynamic modelling; Sequential Gaussian Simulation; urban stormwater
