Order Matters: The Benefits of Ordinal Fragility Curves for Damage and Loss Estimation.

Probabilistic loss assessments from natural hazards require the quantification of structural vulnerability. Building damage data can be used to estimate fragility curves to obtain realistic descriptions of the relationship between a hazard intensity measure and the probability of exceeding certain damage grades. Fragility curves based on the lognormal cumulative distribution function are popular because of their empirical performance as well as theoretical properties. When we are interested in estimating exceedance probabilities for multiple damage grades, these are usually derived per damage grade via separate probit regressions. However, they can also be obtained simultaneously through an ordinal model which treats the damage grades as ordered and related instead of nominal and distinct. When we use nominal models, a collapse fragility curve is constructed by treating data of "near-collapse" and "no damage" the same: as data of noncollapse. This leads to a loss of information. Using synthetic data as well as real-life data from the 2015 Nepal earthquake, we provide one of the first formal demonstrations of multiple advantages of the ordinal model over the nominal approach. We show that modeling the ordering of damage grades explicitly through an ordinal model leads to higher sensitivity to the data, parsimony and a lower risk of overfitting, noncrossing fragility curves, and lower associated uncertainty.

Flow-tub model: A modified bathtub flood model with hydraulic connectivity and path-based attenuation.

Global climate change and sea level rise are increasing the risks of flooding for coastal communities. Probabilistic coastal flood risk analysis at regional or global scales requires flood models with relatively low data requirements and low computational costs. Bathtub inundation models, which compute flood depth as the difference between water level and ground elevation, are well-suited for large-scale flood risk analysis. However, these models may overestimate floods because they do not capture some of the relevant underlying hydrodynamic processes that govern flood propagation on land. We present Flow-Tub, a modified bathtub inundation model that integrates two hydrodynamic processes to improve the accuracy of the bathtub inundation model while retaining computational efficiency: hydraulic connectivity and path-based attenuation.1.Hydraulic connectivity ensures that inundation is restricted to areas connected to the water source.2.Path-based attenuation ensures that the modeled flood water depths are reduced along the flow paths to represent the effects of surface friction and the temporary nature of storm surges. We validate the Flow-tub model against a hydrodynamic model. We also compare results of the bathtub model and the Flow-Tub model, highlighting the improved accuracy in the estimation of flood depths in the latter.