Many Structures with Uncertainty

Overview

The aggregated stage-damage function generated by HEC-FDA with many structures with uncertainty will result in a range of stages each associated with an empirical uncertainty distribution of dollar damages. The stage-damage function takes the same form as in One Structure with Uncertainty.

When stage-damage is computed with uncertainty, the uncertainty is defined in the occupancy type data. Structures in the same impact area of the same damage category will have asset damage estimates aggregated to the same stage-damage function for each asset category. Structures of different damage categories or from different impact areas will have their damage estimates aggregated to separate stage-damage functions for each asset category.

The occupancy type data contains defined distributions for uncertainty around asset percent damage and structure attributes: 

1. Structure Percent Damage
2. Content Percent Damage
3. Other Percent Damage
4. Structure Value
5. Content Value
6. Other Value
7. First Floor Elevation

In this section, uncertainty around structure percent damage, contents percent damage, and other percent damage, as well as structure value, content-to-structure value ratio (CSVR), other-to-structure value ratio (OSVR), and first floor elevation will be used as an example. 

Example Data

Structure

Some example structures and attributes are in Table 1 below. Structure 1 and Structure 2 have the same damage category, so their asset damages will be aggregated to the same stage-damage function. Structure 3 has a different damage category, so it'll aggregated damages to a separate stage-damage function despite being in the same impact area with Structure 1 and Structure 2.

Water Surface Profiles

The water surface elevations at the location of the structures and the impact area's index point in this example for eight AEP events are in Table 3 below.

Occupancy Type Data

Depth-damage functions define the relationship between the depth of flooding on a structure and the uncertainty around percent damage to the structure, contents, and other, as well as the structure value, content-to-structure value ratio, and other-to-structure value ratio. Depth-damage functions are defined in the Occupancy Type data, which contains other information about the structure. The depth-percent damage relationships with uncertainty for the structure, contents, and other, as well uncertainty around first floor elevation, structure value, content-to-structure value ratio, and other-to-structure value ratio in this example are in the Table 3, Table 4, Table 5, and Table 6.

With structures, water surface profiles, and depth-damage relationship, an estimate of stage-damage with uncertainty can be computed.

Computation Steps

HEC-FDA 2.0 generates an aggregated stage-damage function by Monte-Carlo simulation process. The software calculates many iterations of the damage estimates as shown below to generate an empirical distribution of damages for each stage. The following steps are repeated each iteration of the Monte-Carlo process for different values of the variables according to the defined uncertainty distributions in the Occupancy Type data.

1. Obtain Structure Information

Attributes are retrieved from the structure inventory in Table 1 using uncertainty distributions in Table 5 and Table 6 to sample individual values for a user-defined number of iterations. A sample of structure value, content value (by way of CSVR), other value (by way of OSVR), foundation elevation, and foundation height.

2. Interpolation and Extrapolation of Stages

HEC-FDA 2.0 utilizes the user-provided index station and structure water surface profiles and extrapolates and interpolates points beneath, between, and above those provided. In this example, those generated points are below with the input values from Table 2 highlighted. See Identification of Aggregation Stages for the Stage-Damage Function for a detailed explanation of how stages are selected for the stage-damage function.

3. Compute Depth of Flooding

The water surface elevations at the locations of the structures are then converted to depths of flooding on the structures relative to the structures' first finished floor by subtracting the water surface elevation in Table 11 from the structures' sampled foundation elevations in Table 10.

4. Compute Percent Damage with Uncertainty to the Structure, Contents, and Other

The depths of flooding are then used to identify a point in the depth-percent damage functions in Table 3 and Table 4. A random sample from the uncertainty distribution of structure-percent damage, content-percent damage, and other-percent damage is sampled for each structure at every depth calculated in Step 3. The percent-damage values in this example are in Table 12.

5. Compute Economic Damages with Uncertainty for the Range of Water Surface Elevations

The sampled asset-percent damage values in Table 12 are applied to the sampled asset values in Table 7, Table 8, and Table 9 to calculate samples of lost asset value, or economic damages to the assets. Table 13, Table 14, and Table 15 show the calculated structure, contents, and other value damages.

Table 16 shows one iteration of a user-defined number of iterations of damage estimates that will be used to generate the empirical uncertainty distribution of damages for a given stage. The stages in the stage-damage function are the stages from the index point. Stage-damage functions are aggregated by impact area, occupancy type, and asset category. Asset categories are aggregated by occupancy type, and occupancy types are aggregated by impact area. Since Structure 1 and Structure 2 are both residential occupancy types, asset damages will be aggregated to their respective asset categories. All the structures in this example are in the same impact area.