# 2.7. Uncertainty Quantification¶

Multiple sources of uncertainty are considered in this testbed, including: the uncertainty in asset representation, hazard characterization, and damage and loss assessment. For these uncertainty sources, different strategies were implemented in the workflow to quantify their influence. The following sections will introduce the details about each component.

## 2.7.1. In Asset Representation¶

As discussed in Asset Representation, the HAZUS Hurricane Technical Manual differentiates buildings based on asset attributes for the subjected hazard type (wind or storm surge). These attributes are the building properties or structural features that would influence the resulting damage and loss of the asset under the given hazard. Among these key attributes, some are determined by developed rulesets with more basic building information. These rules are based on the statistics in the available data. Taking the shutters of assets that were built before 2000, the Human Subjects Data indicates that roughly 45% of house owners were likely to apply shutters on some or all of their windows before a hurricane makes landfall. Accordingly, in the asset representation (ruleset), a pre-2000 house has a 45% probability to be assigned to have shutters, and a 55% probability to be assigned with no shutter. Note that the resulting HAZUS building type is deterministic for each individual sample while the uncertainty induced by different possible attribute options are evaluated via multiple random realizations. Table 3.7.1.1 summarizes the three building attributes whose values

are randomly generated in this testbed.

Table 2.7.1.1 Random sampling in the rulesets.

Building Attribute

Basic Attributes

Example sampling law

Second Water Resistance (SWR)

YearBuilt, RoofShape

IF YearBuiltNJDEP > 2000, RoofShape = Gable or Hip, SWR = yes (60%) and no (40%)

Roof Deck Attachment (RDA)

YearBuilt

IF YearBuilt <= 2000, RDA = A (50%) and B (50%)

Shutters

YearBuilt, Wind Bore Debris (WBD)

IF YearBuilt <= 2000, WBD = yes, shutters = yes (45%) and no (55%)

## 2.7.2. In Hazard Characterization¶

Given a specific category of hurricane, there are two different sources of uncertainty for site peak wind speed and storm surge values: (1) the uncertainty induced by possible different storm tracks, storm radii, storm translational speeds, central pressures, or heading angles (which is usually termed as epistemic uncertainty); and (2) the inherent variation in observing the random events at the site (which is usually termed as aleatory uncertainty). Both these two uncertainty sources can be taken into account for in the introduced workflow.

For the epistemic uncertainty, multiple scenarios can be simulated using the synthetic simulation methods as introduced in Synthetic Storm Scenario. For instance, the linear analytical simulation for the boundary layer winds ([Snaiki17a], [Snaiki17b]) can be performed with randomly sampled storm properties (e.g., central pressure) to generate multiple realizations of peak wind speed that are possible at the given site. These multiple realizations are then randomly sampled and used as the EDP in simulating the damage and loss assessment (more details in the next section).

For the aleatory uncertainty, this workflow adapts a nearest-neighbors method to propagate uncertainty through the workflow, as illustrated in Fig. 1.6.1.1. The peak wind speed and storm surge values are simulated

a prescribed grid (wind fields) or pre-selected save points (storm surge) (blue round dots), and for each selected asset location (red square dot), the workflow randomly selects 5 samples of the intensity measure (wind speed and storm surge) from the 4 nearest neighbors (yellow circles). Note that this random sampling is performed along with the multiple realizations from the epistemic uncertainty quantification, so the two uncertainty sources are considered simultaneously.

Fig. 2.7.2.1 Nearest-neighbors method for sampling site hazard uncertainty.

## 2.7.3. In Damage and Loss Assessment¶

The testbed implemented pelicun (Probabilistic Estimation of Losses, Injuries, and Community resilience Under Natural disasters) to quantify damage (damage states) and loss (in the form of decision variables, e.g., loss ratio). Uncertainty from the hazard characterization step is first considered by the random sampling module in pelicun to numerically sample the (joint) distribution of intensity measures (which are treated as engineering parameter demands, EDPs in the HAZUS method). Specifically, 1000 samples of combined wind speed and storm surge pairs are generated for each asset in this testbed. Second, the corresponding damage and loss models are populated for each asset from HAZUS based on the Asset Representation. As described in Damage and Loss Estimation, the damage models are continuous functions (normal or lognormal distribution functions) fit to the synthetic data by maximizing the likelihood of the observations assuming a Binomial distribution of outcomes at each intensity level in the HAZUS database. Hence, at a given intensity level (a certain wind speed or storm surge), the damage state and corresponding loss ratio of an asset follow probabilistic distributions, considering all uncertainty in the key properties that can influence the building performance.