*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:

__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.__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.

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.

*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.

jonesjuDylan, nice analysis. Lots of information. For Ex 2, what do you want to concentrate on? I think we discussed that you might select some points which were in hotspots and cold spots of tsunami damage, and try to describe the “up-gradient neighborhood”, i.e., the building values at successive distances from that point toward the coast (i.e., the source of the tsunami). Such an analysis might reveal how the tsunami could entrain debris as it moves inland, potentially increasing the ability to do damage. Another possible analysis we discussed is how the topography (and/or buildings) between the coast and any given point might concentration or disperse the tsunami energy. This could be estimated by selecting points of interest and running some kind of effective contributing area algorithm (or combinations of elevation and slope angle) west of that point toward the coast.