Tag Archives: Kernel Density Estimation

Spatial variation of economic losses resulting from a joint earthquake/tsunami event: An application to Seaside, OR

Question

What is the spatial variability of economic value of buildings as well as losses resulting from a joint earthquake/tsunami event? How does this spatial variability relate to independent earthquake and tsunami events, as well as the intensity of the hazard?

The purpose of this analysis was to consider the spatial variability of initial economic value, as well as economic losses resulting from a joint earthquake/tsunami event. The losses were deaggregated by hazard (earthquake only, tsunami only, joint earthquake/tsunami), as well as intensity of the event (100-year, 250-year, etc.).

Tool and approach

Two methods were implemented to evaluate the spatial variability economic value and losses: (1) interpolation via kernel density, and (2) a hotspot analysis using the Getis-Ord Gi* statistic. The economic losses were determined using a probabilistic earthquake/tsunami damage and loss model. This model implements Monte-Carlo methods to estimate the expected economic losses following an earthquake/tsunami event. For this application, 10,000 simulations were ran, from which the average loss at each building was computed for earthquake only, tsunami only, and a joint earthquake/tsunami event.

Description of steps

The average losses at each building resulting from the earthquake/tsunami loss model were added as an attribute to a GIS shapefile. Two methods to evaluate the spatial distribution were considered:

  1. Interpolation via kernel density: Spatial interpolation was performed using a kernel density estimate. A kernel with a size proportional to the value of the attribute under consideration (in this case economic value/loss) is placed at each data point. A map is then created by taking the sum of all kernels. The kernel radius and shape can vary to produce different results. In this analysis, a quartic kernel was utilized with a radius of 200 meters. The interpolation was performed using the built in interpolation feature in QGIS 3.
  2. Hotspot analysis using the Getis-Ord Gi* statistic: Hotspot analysis was performed using the Getis-Ord Gi* statistic. This statistic results in a p-value and z-score at each attribute, providing insight into whether the null-hypothesis can be rejected (in this case, spatial randomness). As such, features with a small p-value and a very large (or very small) z-score indicate that the null can be rejected (or that the data is not spatially random). Consequently, applied across an entire spatial dataset, the hotspot analysis identifies statistically significant clusters of high (or low) values. The hotspot analysis was performed using the available Hotspot Analysis plugin for QGIS 3.

Description of results

The results of the analysis are shown in Figure 1. The columns correspond to interpolation and hotspot analysis respectively. The first row shows the building values, whereas the second shows the economic losses resulting from a joint earthquake/tsunami event (2,500-year return period).

Areas of high economic value and losses can be easily observed from the interpolation analysis. Here, areas of red correspond to larger damages. Similarly, statistically significant clusters of large (and small) damages can be observed from the hotspot analysis. Again, red corresponds to a statistically significant hot spot (e.g. a cluster of large values and losses), whereas blue corresponds to a statistically significant cold spot (e.g. a cluster of small economic values and losses).

A large concentration of economic value is centrally located along the coast, and is due to the presence of resorts and condominium complexes. This area is observed from both the interpolation and hotspot analysis. Interestingly, more clusters are observed from the hotspot analysis as opposed to the interpolation. This could be explained by the scaling of the interpolation. In this case, the red regions correspond to a maximum value of $20M. If this value was reduced by half, more areas of high concentration would be observed.

The hotspot analysis provides insight into statistically significant clusters of high and low values, as opposed to single points of high values; however, when comparing interpolation and hotspot analysis, it should not be neglected that the results of the latter are visually more difficult to observe. This is due to the discrete nature of the Getis-Ord Gi* statistic (e.g. each point corresponds to a p-value and z-score, as opposed to the continuous surfaces of interpolation). This results in polygons that are shaded according to confidence levels.

Figure 1: Comparison of interpolation and hotspot analysis for both initial building value and economic losses

In addition to the initial value and economic losses resulting from the 2,500-year earthquake/tsunami event, interpolated maps were deaggregated based on hazard (earthquake only, tsunami only, combined) as well as intensity of the event (return years 100, 250, 500, 1,000, and 2,500). The results are shown in Figure 2, where each row corresponds to the hazard, and each column to the intensity of the event. Furthermore, the total economic losses to all buildings in Seaside were determined based on hazard and intensity (Figure 3).

Figure 2 shows that the economic losses are spatially consistent across Seaside for the 100-year event, and begin to exhibit spatial variability as the intensity increases. Losses begin to accumulate for the 250-year event near the center of Seaside, and it can be seen that the earthquake is the primary driving force. Similar trends are observed for the 500-year event. The 1000- and 2500-year events begin to see significant tsunami losses that are not as spatially concentrated as the earthquake losses, but are more evenly distributed along the coast. Figure 3 shows that the tsunami losses begin to dominate for the 1000-year event.

Figure 2: Earthquake and tsunami hazard deaggregated by hazard and intensity

Figure 3: Total earthquake and tsunami damages across Seaside, OR

Critique

Both the interpolation and hotspot analyses have limitations. As previously mentioned the hotspot analysis can be aesthetically challenging. Additionally, difficulties may arise in communicating the confidence levels to community planners and resource managers who may not have a statistical background.

Similarly, spatial interpolation via kernel density has its own limitations. As there are subjective options when performing the interpolation and viewing the results (e.g. radius, color scheme, and maximum values), the resulting maps could easily be deceiving. Figure 4 shows the same data but use of a different radius to define the kernel. It can be seen that the map on the right appears more severe than the map on the left. The practicality of a spatial interpolation map ultimately depends on the GIS analyst.

Figure 4: Comparison of interpolation resulting from different kernel radii.

Deaggregation of infrastructure damages and functionality based on a joint earthquake/tsunami event: an application to Seaside, Oregon.

Research Question and Background

The Pacific Northwest is subject to a rupture of the Cascadia Subduction Zone (CSZ) which will consequently result in both an earthquake and tsunami. While all communities along the coast are vulnerable to the earthquake hazard (e.g. ground shaking), low lying communities are particularly vulnerable to both the earthquake as well as the subsequent tsunami. Completely mitigating all damage resulting from the joint earthquake/tsunami event is impossible, however, understanding the risks associated with each hazard individually can allow community planners and resource managers to isolate particularly vulnerable areas and infrastructure within the city.

The city of Seaside, Oregon is a low-lying community that is subject to both the earthquake and tsunami resulting from a rupture of the CSZ. The infrastructure at Seaside can be divided into four components: (1) buildings, (2) electric power system, (3) transportation system, and (4) water supply system. Similarly, the hazards can be viewed jointly (both earthquake and tsunami), as well as independently (just earthquake or tsunami).

Within this context, I’m particularly interested in looking at how the spatial pattern of infrastructure damage and functionality is related to individual earthquake and tsunami hazards via ground shaking and inundation respectively. Furthermore, I’m interested in looking at how these spatial patterns change as the intensity of the hazard increases.

Description of Dataset

The dataset I will be analyzing consists of two components: (1) spatial maps, and (2) infrastructure damage and functionality codes. Part of this analysis will be merging these two components to spatially view the infrastructure damage and functionality.

The spatial maps consist of:

  1. Building locations (represented as tax lots)
  2. Hazard maps: earthquake ground shaking and tsunami inundation hazard maps

The infrastructure damage and functionality codes implement Monte-Carlo methods to probabilistically define damages, losses, and connectivity. The four infrastructure codes consist of:

  1. Buildings: expected damage and economic losses to buildings.
  2. Electric power system: a connectivity analysis of each building to the electric substation. There is one electric substation within Seaside.
  3. Transportation system: a connectivity analysis of each building to critical infrastructure. Critical infrastructure at Seaside consists of two fire stations and one hospital.
  4. Water supply system: a connectivity analysis of each building to their respective pumping station. There are three water pumping stations within Seaside, and each building is assigned to a single pumping station.

Hypotheses

I hypothesize that the infrastructure damage is not spatially variable for the earthquake hazard, however it will be for the tsunami hazard (e.g. distance from coast). The relative damages due to tsunami will also increase as the intensity of the hazard increases.  That is, for small events, the damages will be dominated by earthquake, whereas for larger events, the damages will be dominated by the tsunami.

Approaches

While color-coordinating tax-lots based on economic losses provides a means to visualize damages throughout a study region, I am interested in learning about kernel density estimation and hot spot analysis to identify vulnerable regions (not just individual buildings). I am also interested in learning about different spatial network analysis methods, as only connectivity analyses within the infrastructure networks (electric, transportation, and water) have been considered so far.

Expected outcome

I’m hoping to produce maps showing how damages and economic losses relate to both joint hazards (earthquake and tsunami), as well as independent hazards (just earthquake or tsunami). I would also like to produce maps showing the connectivity of individual tax-lots to critical infrastructure. Furthermore, I would like to investigate visualizing both the economic losses and connectivity analysis through color-coordinating tax-lots, kernel density estimation and hot-spot analysis.

Significance

The ability to spatially isolate vulnerable areas will allow community planners and resource managers a means to better prepare mitigation plans. Deaggregating the damages and losses by infrastructure and hazard will isolate the relative importance of each, and can assist in mitigation measures. For example, identifying that the earthquake is the dominating force in producing building damages within a specific region, planners and resource managers can support retrofit options for homeowners within that region.

Level of preparation

  1. Arc-info: novice
  2. ModelBuilder and/or GIS programming in Python: Although I haven’t done GIS programming in Python, I am highly proficient in Python and am comfortable working with GIS data. Learning how to merge python and GIS should not be difficult.
  3. R: novice
  4. Image processing: novice
  5. Other relevant software: I’m proficient in QGIS.