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Applied Geography

journal homepage: www.elsevier.com/locate/apgeog

Sensitivity of tsunami evacuation modeling to direction and land cover assumptions

Mathew C. Schmidtlein a *, Nathan J. Wood b

a California State University, Sacramento, Department of Geography, 6000 J Street, Sacramento, CA 95819, USA b Western Geographic Science Center, United States Geological Survey, 2130 SW 5th Avenue, Portland, OR 97201, USA

ARTICLE INFO

ABSTRACT

Article history:

Available online 18 December 2014

Keywords:

Least cost distance

Evacuation

Model sensitivity

Tsunami

Anisotropy

Although anisotropic least-cost-distance (LCD) modeling is becoming a common tool for estimating pedestrian-evacuation travel times out of tsunami hazard zones, there has been insufficient attention paid to understanding model sensitivity behind the estimates. To support tsunami risk-reduction planning, we explore two aspects of LCD modeling as it applies to pedestrian evacuations and use the coastal community of Seward, Alaska, as our case study. First, we explore the sensitivity of modeling to the direction of movement by comparing standard safety-to-hazard evacuation times to hazard-to-safety evacuation times for a sample of 3985 points in Seward's tsunami-hazard zone. Safety-to-hazard evacuation times slightly overestimated hazard-to-safety evacuation times but the strong relationship to the hazard-to-safety evacuation times, slightly conservative bias, and shorter processing times of the safety-to-hazard approach make it the preferred approach. Second, we explore how variations in land cover speed conservation values (SCVs) influence model performance using a Monte Carlo approach with one thousand sets of land cover SCVs. The LCD model was relatively robust to changes in land cover SCVs with the magnitude of local model sensitivity greatest in areas with higher evacuation times or with wetland or shore land cover types, where model results may slightly underestimate travel times. This study demonstrates that emergency managers should be concerned not only with populations in locations with evacuation times greater than wave arrival times, but also with populations with evacuation times lower than but close to expected wave arrival times, particularly if they are required to cross wetlands or beaches.

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Introduction

Tsunami hazards threaten coastal communities throughout the world. Of particular concern are waves that could inundate low-lying areas within minutes after being generated by a local source, such as offshore earthquakes. Evacuations from local tsunamis likely will be self-initiated and pedestrian-based due to the short time scale and likely damage to road networks from the initial earthquake. Following the life loss witnessed during recent tsunami disasters (e.g., 2004 Indian Ocean, 2009 Samoa, 2010 Chile, and 2011 Tohoku), there have been considerable efforts to model pedestrian evacuations out of tsunami-hazard zones (e.g., Laghi, Cavalletti, & Polo, 2006; Jonkmann, Vrijling, & Vrouwenvelder,

* Corresponding author. Tel.: +1 916 278 7581. E-mail addresses: schmidtlein@csus.edu (M.C. Schmidtlein), nwood@usgs.gov (N.J. Wood).

2008; Yeh, Fiez, & Karon, 2009; Johnstone, & Lence, 2012; Wood & Schmidtlein, 2012, 2013). Maps of travel times to safety based on pedestrian-evacuation modeling help emergency managers understand where successful evacuations may be possible and where vertical-evacuation strategies may be warranted.

One approach to model pedestrian evacuations has focused on generating spatial surfaces that represent the minimal costs in travel across a landscape. Cost heuristics used in previous way-finding modeling have varied, such as shortest path length (Dijkstra, 1959; Wood & Schmidtlein, 2013), simplest path (Duckham & Kulik, 2003), and least risk paths (Vanclooster et al. 2014). Least-cost distance (LCD) models based on shortest path algorithms are generated typically as a function of land surface slope, land cover type, and travel speed assumptions. Recent tsunami-related efforts have improved how slope is included in the modeling by incorporating the directionality of movement; for example, Wood and Schmidtlein (2012) demonstrate how isotropic assumptions (constant slope regardless of travel direction)

http://dx.doi.org/10.1016/j.apgeog.2014.11.014

0143-6228/© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

consistently underestimated the travel times for safety out of tsunami-hazard zones compared to an anisotropic approach for slope calculations that reflected the direction of movement.

A related, yet unexplored, question in LCD modeling is how well the direction of movement is characterized in the actual least-cost-surface computations. LCD models use approaches based on Dijkstra's (1959) algorithm for finding the minimum length path between two points. This approach can be used in raster contexts to find the minimum distance from a given origin cell to all remaining cells in the study area. In order to generate an evacuation time map for the entire tsunami hazard area, this standard approach would require a separate LCD analysis to be run for each individual cell in the hazard zone. Laghi et al. (2006) proposed that a more computationally efficient approach would be to treat the safe zones as the origins, and calculate the time it would take to move from these safe areas to each cell in the hazard zone, in effect reversing the direction of the LCD analysis. Subsequent pedestrian-evacuation modeling efforts (e.g., Wood & Schmidtlein, 2012) followed this approach in their anisotropic LCD models, and used a reversed direction look up table to represent the impact of slope on travel times, since the model LCD search direction was the opposite of actual pedestrian travel direction (from safety to hazard, rather than from hazard to safety). Although reversed direction modeling

is conceptually satisfying, we are not aware of any efforts to determine the sensitivity of the LCD modeling and subsequent travel-time maps to this assumption.

In addition to examining the effect of slope anisotropy on LCD models, another unexplored model-sensitivity question relates to how travel costs are assigned to land cover categories. Currently, travel constraints due to landcover variations are expressed through speed conservation values (SCVs; Laghi et al. 2006) that represent the percent of maximum travel speed that a pedestrian would be expected to have on a given land cover. Because no consistent, empirically based relationship between land cover and travel speeds could be identified in the literature, current land cover SCVs used by Wood & Schmidtlein, 2012 are based on differences in the amount of energy used to move across different land cover types (Soule & Goldman, 1972). This is an oversimplification of the actual processes which relate land cover to pedestrian evacuation speeds and it is unclear how sensitive model results are to fluctuations in land cover SCVs.

The objective of this paper is to explore the sensitivity of pedestrian-evacuation time modeling to assumptions made in characterizations of the path of movement and in the landcover surface. These lead to two distinct research questions. First, do modeled evacuation times differ depending on the direction of

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Fig. 1. Study area of Seward, Alaska, including (A) Seward's location in Resurrection Bay, Alaska, (B) Seward's location in the State of Alaska, (C) a 2005 image of downtown Seward including lines noting a maximum tsunami-hazard zone (black line) and potential inundation caused by submarine landslides (white line), (D) land cover in Seward based on a manual interpretation of 2005,1-m resolution, RGB-band orthorectified IKONOS imagery, and (E) slope based on a 2009 5-foot (1.5 m) LiDAR-derived digital elevation model of the area (elevation and imagery from Kenai Peninsula Borough GIS Division, 2013).

movement used to estimate those times (safety-to-hazard vs. hazard-to-safety search direction)? Second, how sensitive are modeled evacuation times to variations in land cover SCVs? We explore these questions using a case study of Seward, Alaska, a coastal community that suffered substantial losses from the 1964 Mw 9.2 Good Friday earthquake and tsunami (Fig. 1). With the 50th anniversary of the 1964 disaster, there have been recent efforts to evaluate evacuation potential to future tsunamis in Seward (Wood, Schmidtlein, & Peters, 2014); therefore, geospatial data representing elevation, landcover, and hazard zones were readily available. This community was also attractive for exploring model sensitivity because of its compact size and varied land cover.

Our paper is organized as follows. In Section "Study area", we briefly review the study area with its tsunami hazard context. In Section "Baseline estimate of pedestrian travel times", we give a basic overview of Wood and Schmidtlein's 2012 model, used to estimate pedestrian evacuation times. In Section "Sensitivity of LCD model to path direction", we analyze the first research question by comparing travel times using reversed directions (i.e., safe zone to sites in the hazard zone) to evacuation times for a sample of points within the hazard zone to the safe zone. In Section "Sensitivity of LCD model to land cover SCV assignment", model sensitivity due to land cover characterizations is assessed using a Monte-Carlo simulation approach. In Section "Conclusions", we discuss the implications of all results for local emergency managers in the context of their efforts to develop effective tsunami preparedness and evacuation plans. This research furthers the application of evacuation modeling for risk-reduction efforts by discussing the influence of data and modeling assumptions on estimated travel times to safety. Improving our ability to model pedestrian evacuation times will help emergency managers develop risk-reduction strategies that will save lives from future tsunamis.

Study area

Seward, Alaska is a small port town (2010 population: 2,693, US Census Bureau 2012) on the ice free shores of Resurrection Bay (Fig. 1A). Its location on the seismically-active Pacific Ocean basin (Fig. 1B) has made it susceptible to tsunamis from a number of distant earthquake sources, such as Chile (1960, 2010), Samoa (2009), Russia (1952, 2006) and Japan (2011), and from local earthquake related to the Alaska-Aleutian megathrust zone (1946, 1964) (NOAA National Geophysical Data Center/World Data Service for Geophysics 2012). Seward's largest and most destructive tsunami waves in modern history resulted from submarine landslides and seismic tsunamis triggered by the 1964 Mw 9.2 Good Friday earthquake from the Alaska-Aleutian zone. The combined effects of the earthquake, landslides, and tsunami waves killed 12 people in Seward, as well as destroyed or severely damaged approximately 95% of the industrial base and 15% of the residences (Lander, 1996; Lemke 1967). Future tsunami hazards in Seward are associated with distant earthquakes (e.g., the 2011 Tohoku event that originated in Japan), local earthquakes associated with the Alaska-Aleutian megathrust zone, or local landslides (Suleimani, Nicolsky, West, Combellick, & Hansen, 2010). For our Seward case study, we use the maximum tsunami-hazard zone (Fig. 1C) from Suleimani et al. (2010), which is based on multiple earthquake scenarios similar to the 1964 Good Friday earthquake, instead of a specific tectonic scenario. We did this in order to capture the full extent of potential inundation related to tectonically generated waves since inundation extents from individual scenarios had subtle variations due to inherent uncertainties in seismic source parameters. Land cover in the study area is primarily a grid of impervious surfaces (e.g., roads, parking lots, and buildings), a mix of heavy and light brush within the grid, and a coastline covered in

dirt, gravel, and unconsolidated shoreland (Fig. 1D). The area is relatively flat, with most slopes along primary travel routes less than 5° (Fig. 1E). Greater slopes are associated with areas of brush and the unconsolidated shore.

Baseline estimate of pedestrian travel times

To examine LCD model sensitivity to inputs and assumptions, we first generated a baseline travel-time evacuation surface for Seward. The baseline anisotropic LCD model for Seward was implemented in ESRI's ArcMap 10.1 software, following methods described in greater detail in Wood and Schmidtlein (2012). This approach used the following four sets of data:

• A 2009 5-foot (1.5 m) LiDAR-derived digital elevation model of the area (Kenai Peninsula Borough GIS Division, 2013) used to derive slope, coupled with a lookup table based on Tobler's (1993) hiking function that converts slope to SCVs;

• A land cover surface, which was derived from a supervised and manual classification of 2005, 1-m resolution, RGB-band orthorectified IKONOS imagery (Kenai Peninsula Borough GIS Division, 2013) in ERDAS IMAGINE and then reclassified into SCVs (Table 1) as the inverse of terrain energy coefficients discussed in Soule and Goldman's (1972);

• Safe zones towards which pedestrians could evacuate based on buffers of a maximum tsunami-inundation zone modeled by Suleimani et al. (2010); and

• A pedestrian travel speed assumption of 1.1 m/s, which reflects a slow-walking speed considered appropriate for a mixed population (US Department of Transportation 2009).

To generate the pedestrian travel-time surface, the inverse land cover SCV surface, elevation, and inverse reversed direction Tobler slope table were entered into ESRI's anisotropic Path Distance tool, with the safe zones serving as the origin locations. The results of this model were then multiplied by the inverse pedestrian evacuation speed, and the resulting evacuation times were converted into minutes. Fig. 2 shows the baseline model evacuation times and demonstrates how locations in the small-boat harbor and along the adjacent waterfront have the greatest travel times to safety of 5—15 min. Arrival times for waves associated with the maximum tsunami hazard zones are approximately 30 min (Suleimani et al. 2010); therefore individuals in these locations may have enough time to evacuate from tectonically generated tsunamis, providing the evacuation models correctly estimate pedestrian travel times and at-risk individual do not delay during an evacuation. The remainder of this article focuses on examining model sensitivity;

Table 1

Land cover classes and assigned speed conservation values.

Land cover class Terrain energy coefficient categories (Soule & Goldman, 1972) Speed conservation value (SCV)

Water No Dataa

Buildings No Dataa

and fences

Impervious Asphalt 1.0000

Grass Dirt Road 0.9091

Dirt/Gravel Dirt Road 0.9091

Light Brush Light Brush 0.8333

Heavy Brush Heavy Brush 0.6667

Wetlands Swampy Bog 0.5556

Sand Hard Sand 0.5556

Shore Hard Sand 0.5556

a "No Data" values were used to note areas where travel is not allowed and were used in calculations instead of zero values due to conventions of the Path Distance tool.

however, additional information on population distributions in Seward as function of travel time out of hazard zones can be found in Wood et al. (2014).

Sensitivity of LCD model to path direction

To assess how well the reversed direction LCD approach matches a normal LCD analysis, a regular sample of 3985 points with non-zero evacuation times was drawn from the baseline pedestrian evacuation model. These points were drawn at the intersection of every eighth row and column of land cover raster grid cells for the majority of the study area. Because of the relatively limited extent of wetland and shore land cover in the study area, samples were taken in these areas at the intersection of every fourth row and column of grid cells. A separate anisotropic pedestrian evacuation model was run for each point. The same input data were used to generate these models as were used for the baseline model, with two key differences. First, in each instance, the given sample point was used as the origin for the model. Second, because the direction of LCD search in these models matched the direction that pedestrians would be evacuating in (from hazard to safety), the reversed direction slope SCV table was replaced by one based on the normal Tobler hiking function. This meant that the SCV for travel across two pixels in the hazard-to-safety models (hereafter called the normal direction) matched those for the safety-to-hazard model (hereafter called the baseline model).

The 3985 anisotropic LCD surfaces represent the shortest evacuation times from the given origin points to all other cells in the study area. The next step was to use these surfaces to derive the least cost path and its associated time from each point to the closest location in the safe zone. This was done by entering the evacuation time surfaces along with their associated backlink rasters into ESRI's Cost Path tool, with the safe zones entered in as the destinations. Backlink rasters contain values of 0 through 8, which define the direction along the least cost path from a cell to its source (ESRI, 2013), and are used to reconstruct the least cost path from an origin to a given destination (zeros indicating source cells, 1 indicating travel to the cell to the right, 2 to the lower right, and continuing in the same pattern clockwise). The final step in the analysis was to find the difference between the baseline model evacuation times and the sampled normal direction evacuation times.

Descriptive statistics for the baseline model travel times, normal direction model travel times, the total difference between the two approaches, and the proportional difference between the two approaches for each sample location are shown in Table 2. Fig. 3 shows the distribution of the total and proportional differences between the baseline and normal direction models (Fig. 3a and b, respectively). While the maximum values for both the total and proportional differences are fairly large, the total differences have a relatively small median value of 0.53 min. The median value of 0.22 for the proportional differences is relatively small as well, considering the relatively short times to evacuation in the study area. In almost every case, the baseline evacuation model also tends to slightly overestimate the standard-direction model evacuation times.

A regression analysis suggests a very strong and statistically significant relationship between the baseline model and normal-direction evacuation times (R2 = 0.976, p < 0.0001). Scatterplots showing comparisons of baseline model evacuation times and normal direction model suggest that total differences between the baseline and normal direction model evacuation times increase as baseline model evacuation times increase (Fig. 4a, b) and that the

Fig. 2. Modeled travel time to safety in minutes, assuming a slow-walking speed of 1.1 m per second.

Table 2

Summary statistics for sample points in the path-of-direction sensitivity analysis.

Measure

Safety to hazard travel times (baseline model, minutes)

Hazard to safety travel times (normal direction model, minutes)

Difference between baseline and normal direction models for travel time (minutes)

Proportion difference between baseline and normal direction models

Minimum Median Mean Maximum

0.02 3.23 2.43 14.84

0.02 1.77 2.53 12.2

-0.0002 0.53 0.71 3.85

-0.0002 0.22 0.23 0.63

2000 -,

1000-,

1500 -

1000 -

0 12 3 4 Travel time from safety to hazard minus travel time from hazard to safety (minutes)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 Proportional difference in travel time from safety to hazard minus travel time from hazard to safety (minutes)

Fig. 3. Histograms of the (a) difference between the two directional scenarios, and (b) the proportional difference between the two directional scenarios.

proportional differences are greatest when baseline model evacuation times are shortest (Fig. 4c).

Results suggest that while reversing the direction of the LCD search in the anisotropic pedestrian evacuation model does not result in identical evacuation times, it does lead to a very close approximation. The largest differences between evacuation times are in areas where baseline model times are the highest and the greatest proportional differences are in areas where evacuation times are the lowest. In other words, the highest proportional differences result from small variations in areas with low evacuation times.

Sensitivity of LCD model to land cover SCV assignment

A Monte Carlo based uncertainty analysis was performed to determine the sensitivity of the anisotropic LCD model to changes in land cover SCVs. The uncertainty analysis began with the random generation of a set of 1000 land cover SCV coefficients. Each set

contained four SCVs, one for each of the unique SCV applied to the non-impervious surface land cover categories used in the evacuation model scenarios (Table 1). Non-varying SCVs of 1 for impervious surfaces were added to this set of 4 randomly varying SCV to represent a constant maximum travel speed on these surfaces, and the SCV for water and buildings was set to "No Data" to preclude evacuation across these surfaces. Values for each varying SCV were generated using the truncnorm package in the R statistical package (Trautmann, Steuer, Mersmann, & Bornkamp, 2014; R Core Team 2014) following a truncated normal distribution with a mean value matching the base model SCV for the land cover types and all values falling between 0 and 1 (representing potential travel speeds between 0 and 100% of the model's base evacuation speed). Standard deviations of 0.10 (representing a 10 percentage point change in travel speed) were used as the standard deviations to generate the SCVs for the wetlands, shore and heavy brush land cover types. The distribution of SCVs for both the light brush and grass, dirt, gravel land cover categories (with base values of 0.8333 and 0.9091,

Travel time to hazard from safety (minutes) ~ Travel time to hazard from safety (minutes) Travel time to hazard from safety (minutes)

Fig. 4. Scatterplots comparing travel time to hazard from safety with (a) travel time to safety from hazard zone, (b) the difference between the two directional scenarios, and (c) the proportional difference between the two directional scenarios.

respectively) were substantially truncated due to their proximity to the maximum allowed value (1), so larger standard deviations of 0.113 and 0.14 were used respectively to generate these distributions in order to ensure comparable variance in the generated distributions of SCVs across all land cover categories. Fig. 5 shows density curves for the generated SCV values for each land cover category. The results of a Levene's test for homogeneity of variance (F = 0.35;p = 0.79) found equal variances in generated SCVs between the land cover groups. Land cover data were then reclassified into land cover SCV surfaces using the randomly generated SCV values, and these were then input, along with all other relevant data, into the anisotropic LCD model to create 1000 Monte Carlo scenario pedestrian evacuation time surfaces.

The impact of changing land cover SCVs on model performance was then assessed by analyzing the variations in evacuation times between these 1000 evacuation scenarios. This analysis proceeded in three sequential steps that help us to understand various questions about model performance relevant to local emergency managers. First, we assess how robust the model as a whole is to changes in land cover SCVs. Second, we look at local variations in model performance within the study area. Finally, we use a combination of descriptive statistics and spatial regression models to assess factors contributing to local model performance. The methodology used in each stage in this analysis is described in the following three sections, followed by a larger discussion in the conclusions section that integrates all analysis results and their implications for local emergency managers.

Overall model performance

Ideally, an analysis of overall model performance would involve a comparison of modeled evacuation times to known evacuation times throughout the study area. Lacking such a measure, we assume that if the base model SCVs are approximately correct, then the accuracy and precision of the model can be understood by looking at the distribution of the differences between the base model and the Monte Carlo scenarios. Following Tate (2012), we calculate the mean local absolute value of the differences between Monte Carlo scenario times and the baseline scenario times (matching the standard anisotropic scenario). The median value of these differences is taken to represent the overall accuracy of the model, and the median absolute deviation is used to represent the overall precision. In other words, if there is a low median difference between the base scenario and the Monte Carlo scenarios, this means that changes in SCV on average result in minimal changes to evacuation times, and that the baseline model has a fairly high accuracy. If the median absolute deviation for the differences between the base scenario and the Monte Carlo scenarios is low, this means that changes in land cover SCV leads to limited variability in evacuation times, suggesting that baseline model precision is high.

The distribution of the mean differences between the base scenario and the Monte Carlo scenarios suggests that the base model is fairly accurate (Fig. 6). The median of this distribution is 0.10 min, or about 6 s, and the median absolute deviation is 0.05 min, or about 3 s. Both values are relatively low, suggesting that the overall model has fairly good accuracy and precision and that the overall base model is fairly robust to changes in land cover SCV.

Local model performance

Tate (2013) describes three additional measures that can be used to describe local variations in uncertainty resulting from changes in land cover SCV. The first measure, uncertainty magnitude, is a measure of the width of the 90% confidence interval of the Monte

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Base SCV

667 0.8333 0.9091

Land Cover Type

□ Dirt, grass, or gravel Light bmsh

□ Heavy brush

Wetlands or unconsolidated

0.0 0.2 0.4 0.6 0.8 1.0 Speed Conservation Value (SCV)

Fig. 5. Distribution of randomly generated, speed conservation values for grass, dirt, and gravel; light brush; heavy brush; and wetlands, sand, and shore land cover.

Carlo scenario evacuation times for each pixel (Fig. 7a). Areas with high 90% confidence interval widths have a higher magnitude of uncertainty. While there are higher magnitudes of uncertainty around the dirt and gravel areas at the southern end of the small boat harbor, as well as the wetland areas directly to the north of the lagoon, the remainder of the study area has a relatively low magnitude of uncertainty (Fig. 7a).

The second measure, uncertainty precision, is the local coefficient of variation for the Monte Carlo scenario evacuation times (Fig. 7b). Lower values for this measure indicate higher levels of model precision. Fig. 7b shows pockets of more precise estimates to the west of the small boat harbor, and along the southern edge of the alluvial fan in areas that are primarily classified as impervious (Fig. 1D). Areas of model imprecision include the wetland area directly north of the lagoon, at the southern end of the study area, and in many small areas abutting the safe zone that are classified as a mix of dirt, gravel, and grass.

The final measure, uncertainty bias, is found by subtracting the local median evacuation times of the Monte Carlo scenarios from the baseline scenario evacuation times (Fig. 7c). Positive values indicate that the base scenario may be overestimating evacuation times, while negative values indicate that the base scenario may be

£ 200

Median value (0.1)

0.0 0.2 0.4 0.6 Minutes

Fig. 6. Histogram of the average deviation of Monte Carlo hazard-to-safe scenarios from base safe-to-hazard scenarios.

Base minus median travel times (minutes)

□ -0.60 to -0.45

□ -0.45 to -0.3

□ -0.3 to -0.15

□ -0.15 to 0.0 I—I 0.0 to 0.06

Fig. 7. Maps of local uncertainty measures derived from the Monte Carlo scenarios including (a) uncertainty magnitude, expressed as 90% confidence interval scenario results where higher values indicate a greater magnitude, (b) uncertainty precision, expressed as the coefficient of variation of scenario results where higher values indicate lower precision, and (c) uncertainty bias, expressed as base evacuation times minus the local median of scenario evacuation times where positive values indicate overestimates and negative values indicate underestimates in travel times.

underestimating evacuation times. By far the dominant observable trend is that while overall bias remains relatively small (with the largest biases of about 35 s), negative values (or possible underestimates) dominate almost all of the study area. For the areas with high uncertainty magnitude and bias (e.g., the dirt and gravel areas on the south side of the marina), emergency managers may wish to assume slightly longer evacuation times than indicated by the base anisotropic evacuation scenario.

Influences on local model performance

The local uncertainty maps in Fig. 7 provide information that may be helpful to emergency managers as they seek to better understand and make decisions based on modeled pedestrian evacuation times. The maps also suggest that there may be systematic influences that are affecting the performance of the anisotropic LCD pedestrian evacuation model. For example, Fig. 7a suggests that high uncertainty magnitude may be related to higher evacuation times (e.g. the dirt and gravel area south of the small boat harbor), that lower uncertainty precision may be associated with smaller evacuation times (e.g. in areas close to the safe zone, Fig. 7b), and as

previously noted, larger negative biases occur in areas of higher evacuation time (Fig. 7b). The area of high uncertainty magnitude and low precision north of the lagoon may indicate that the presence of wetlands and heavy brush (Fig. 1D) may also be influencing model uncertainty. Values of these local uncertainty measures were therefore compared to baseline model evacuation times and local land cover on a pixel by pixel basis to see if they were indeed systematically related to model uncertainty.

Relationships between baseline model evacuation times and the local measures of uncertainty can be seen in the hexplots shown in Fig. 8. Hexplots are useful substitutes for scatterplots when the number of points displayed in a scatterplot is so large that the patterns in the data are obscured by overprinting of point symbols. This issue is addressed in hexplots by dividing the space of the plot into a hexagonal tessellation, and shading each hexagon based on the number of observations that fall within its delineated area. We can interpret a hexplot similarly to a scatterplot, but rather than looking for patterns in the location of points, we instead look for patterns based on the shading of the hexagons. In all three hexplots, darker colors indicate that more points occurred within a particular cell, and lighter colors indicate fewer.

The most striking relationships evident in these hexplots are the positive linear relationships between base model evacuation times and uncertainty magnitude (Fig. 8a) and a negative linear relationship with uncertainty bias (Fig. 8c). While no linear relationship is evident between evacuation times and local precision (Fig. 8b), the patterns in the plot suggest there may be a more complex indirect non-linear relationship. Spearman's correlation coefficients were calculated to further analyze these relationships, and they confirmed relatively strong correlations between base evacuation times and both uncertainty magnitude and bias (rs = 0.68 and rs = -0.63, respectively), but a weaker correlations for uncertainty precision (rs = -0.39).

Boxplots showing the relationships between land cover and the local measures of uncertainty are shown in Fig. 9. We see a fairly meaningful difference in uncertainty magnitude for the wetlands and shore land cover category (Fig. 9a). This result seems consistent with the relationship between uncertainty magnitude and higher evacuation times in that most shore and wetland land cover will occur in areas closer to the shore, and therefore at a greater distance from the safe zone. It also helps to explain why high uncertainty magnitude values were found in the area north of the lagoon (Fig. 7a). While this area had relatively low evacuation times (Fig. 2) and was located near the safe zone, it had a wetlands land cover type (Fig. 7a).

The relationship between local precision and land cover type showed that substantially better precision occurred in areas with impervious land (Fig. 9b). Low coefficient of variation (CV) values for impervious surfaces are unsurprising and are likely an artifact of the analysis design used, given that SCVs for this land cover type were held constant. Values for uncertainty bias were predominantly negative across all land cover categories, with larger negative values overall for the wetlands, shore and grass, dirt, gravel categories (Fig. 9c). While these typically small, negative biases may have a limited practical significance in this study area, with its relatively constrained hazard zone, a continuation of this trend in a more extensive tsunami evacuation zone could result in more substantial underestimates of evacuation times for wetlands/shore land cover areas.

To further explore the influence of land cover on local uncertainty measures, a series of spatial regression models were created. The number of pixels in each land cover category crossed by the base model least-cost evacuation paths to the safe zone were found for each of the previously described 3985 sample points. Table 3 gives descriptive statistics on the total length (in pixels), base evacuation times, and the number of pixels from each land cover category crossed by these least cost evacuation paths. These values

show that while most evacuation paths crossed at least some pixels from the impervious; light brush; and grass, dirt, gravel land cover categories, far fewer paths crossed pixels with wetlands, shore or heavy bush land covers.

The counts of pixels crossed by land cover type for each path were then compared to the local uncertainty measures found at each of the sample points, with the number of pixels in each land cover category crossed by the least-cost evacuation paths as the independent variables, and each local measure of uncertainty used as a dependent variable in one of three separate spatial regression models. Spatial weights for the regression models were generated using the GeoDa software package (Anselin, 2013), with the 8 nearest neighbors to each point constituting the neighborhood. The actual spatial regression modeling was then conducted with the spdep package (Bivand, 2014) in R. Ordinary least squares modeling was first used to fit each of the three regression models, and Moran's I tests revealed highly significant (p < 0.001) spatial clustering in each model's residuals. No problematic multicollinearity issues were found in these models, with Variance Inflation Factor values for all independent variables in each model falling below 1.6. Diagnostic plots (residual and quantile—quantile) were used to assess additional model assumptions. We continued with our analysis despite finding both normality and heteroscedatiscity problems both because these issues do not affect estimation of slope coefficients, and also because the extreme statistical significance of model results.

Following procedures described by Anselin (2003, 2005), a spatial simultaneous autoregressive error model was run for each regression to address the statistically significant spatial clustering of model residuals. Table 4 shows the pseudo-R2 values and independent variable slope coefficients for the three spatial regression models.

Examining the results of these regression models allows us to understand how the land cover surfaces along the entire modeled evacuation path influences local uncertainty, rather than just the land cover found at the point from which evacuation would occur. A number of interesting patterns emerge from this examination. All land cover types lead to increases in uncertainty magnitude, and all types except heavy brush lead to negative uncertainty bias (underestimates of base evacuation times). And while impervious surfaces tended to improve uncertainty precision, all other land cover types lead to less precision.

In addition to being the only land cover type that improved uncertainty precision, the impervious category had the least impact on both uncertainty bias and magnitude. But as addressed earlier, this is to be expected given how the SCVs for impervious land

ôj -0.6

Base evacuation time (minutes)

Base evacuation time (minutes)

Base evacuation time (minutes)

Fig. 8. Hexplots showing the relationships between base model evacuation times and various local uncertainty measures, including (a) magnitude, (b) precision, and (c) bias. Darker hexagons indicate areas in which a greater number of observations fall, and lighter hexagons indicate fewer.

Impervious Wetlands, Heavy shore brush

Light Grass, dirt, brush gravel

Impervlous Wetlands, Heavy shore brush

Impervious Wetlands, Heavy Light shore brush brush

Fig. 9. Boxplots showing the relationship between land cover and various local uncertainty measures, including (a) magnitude, (b) precision, and (c) bias. The bottom and top of the boxes represent the first and third quartiles and the dark line represents the median. The solid vertical lines connected to the boxes are drawn to the furthest point that is within 1.5 times the distance between the first and third quartiles. The dotted lines indicate the total range of the observations.

covers were held constant in this analysis. The only land cover with an impact on local precision as strong as impervious was the wetlands, shore category, but this category lead to the most substantial loss of precision. The wetlands, shore category was also noticeable in that it made the strongest contribution to both uncertainty bias and magnitude. This meant that crossing wetlands, shore land cover types lead to the largest increases in all local uncertainty measures of all the land cover types with SCVs varied in this analysis. Finally, while most slope coefficients were significant in each model, the land cover category that seemed to have the least significant relationship with the measures of local uncertainty was heavy brush, with significance of p = 0.03 in the local bias model, and of p = 0.50 in the local precision model.

Taken together, this allows us to extend our understanding of the influence of land cover on uncertainty in modeled evacuation times. First, local uncertainty magnitude and precision will be worse in areas that traverse a greater number of wetlands, shore areas. These influences again can be seen in the lagoon area northwest of the small boat harbor, where the dominance of wetland land cover in the evacuation paths leads to worse uncertainty magnitude and precision than we see in other areas with similarly short Euclidean distances to the safe zone. Additionally, both uncertainty magnitude and negative bias are greater in areas with higher evacuation times farther from the safe zones.

Conclusions

Pedestrian-evacuation modeling can be an effective tool for identifying areas where evacuations are unlikely and vertical-evacuation strategies may be warranted. Before communities commit limited resources to risk-reducing mitigation efforts, it is imperative that they have a clear understanding of the limitations and robustness of the modeling. This paper sought to explore the sensitivity of pedestrian-evacuation modeling to assumptions

made in characterizations of the how evacuation direction is represented in the shortest-path modeling algorithm and in the land cover surface costs. Based on our analysis, we reach several conclusions that bear on future applications of LCD modeling to estimate travel times to safety out of tsunami hazard zones (or any other sudden-onset hazard).

A strong, direct relationship between baseline model evacuation times and normal direction evacuation times (Fig. 4, Table 2) suggest that while the safety-to-hazard approach does not replicate travel time values from a hazard-to-safety approach, it is a reasonable representation, particularly when considering the dramatic reduction in processing time involved in generating one anisotropic least cost surface instead of a separate least cost surface for every pixel in the study area. Differences between the safety-to-hazard (baseline model) and hazard-to-safety (normal direction) models were greater than or equal to zero for 98.9 percent of sample points. Negative differences were only seen for 1.1 percent of the sample points, all of which had very short evacuation times (of 1.2 min or less) and had normal direction times at most 0.01 s greater than base model evacuation times. This suggests that while it is possible that the baseline model can slightly underestimate evacuation times, it is far more likely to result in over-estimates. Although the baseline model does result in biased evacuation times, the bias seems to be a solidly conservative one that would result in residents having slightly more time than estimated, which is the preferred bias from a risk-reduction perspective.

Low values for both the median and median absolute deviation of the average differences between the base evacuation scenario and the Monte Carlo generated scenarios suggest that the aniso-tropic LCD evacuation model is not very sensitive to changes in land cover SCV. While this does not provide assurance that the evacuation times are correct, as an empirically measured relationship between land cover type and evacuation speed would, it does suggest that the model is performing well and increases confidence

Table 3

Descriptive statistics of length, evacuation time, and land cover pixels crossed for sample least cost evacuation paths.

Minimum 1st Quartile Median 3rd Quartile Maximum

Evacuation 2 31 62 129 420

Path Length

Base Evacuation 0.02 1.23 2.43 4.64 14.84

Time (minutes)

Minimum (proportion) pixels 1st Quartile (proportion) Median (proportion) pixels 3rd Quartile (proportion) Maximum (proportion)

per evacuation path pixels per evacuation path per evacuation path pixels per evacuation path pixels per evacuation path

Impervious 0(0%) 3 (6.1%) 18 (36.4%) 75 (69.7%) 300(100%)

Wetlands, shore 0(0%) 0(0%) 0(0%) 0 (0%) 53 (77.9%)

Heavy brush 0(0%) 0 (0%) 0 (0%) 2 (1.4%) 20 (100%)

Light brush 0(0%) 2 (4.7%) 9 (13%) 22 (27.1%) 70 (100%)

Grass, dirt, gravel 0(0%) 5 (10.5%) 17 (28.2%) 36 (56.3%) 255(100%)

Table 4

Pseueo-R2 and independent variable slope coefficients for spatial regression models.

Local uncertainty Uncertainty Uncertainty

bias magnitude precision

Nagelkerke pseudo-R2 0.98 0.99 0.87

Impervious -0.0001** 0.0023*** -0.0004***

Wetlands, shore -0.0021*** 0.0191*** 0.0004***

Heavy brush 0.0004* 0.0084*** 0.0002

Light brush -0.0003*** 0.0085*** 0.0001*

Grass, dirt, gravel -0.0017*** 0.0096*** 0.0001***

Statistical significance at *p < 0.05, "p < 0.01, ***p < 0.001.

in the modeled results. The use of energy coefficients as a surrogate for empirically based land cover SCV is still an oversimplification, but results suggest that if they are even relatively close to representing the true relationship between land cover type and pedestrian speeds, we are likely to see useful results from the model.

Spatial patterns in, and relationships between, the local measures of uncertainty (magnitude, bias, and precision) suggest that the areas that had the greatest magnitude of uncertainty were also where we tended to see the largest underestimated base model evacuation times. Knowing both that there was less certainty in evacuation times in these areas, as well as that evacuation times may be underestimates, may suggest that emergency managers would be wise to plan on longer evacuation times for these areas than indicated by the model. Comparing these local measures of uncertainty to base model evacuation times and study area land cover revealed systematic influences on model uncertainty. Areas with higher evacuation times and evacuation paths that crossed more wetlands or unconsolidated shoreland were more likely to have a higher magnitude and worse precision of uncertainty, and greater underestimates in evacuation times.

Overall, these results suggest some caution is warranted in interpreting results with higher evacuation times (where they may be a greater magnitude of uncertainty), and where there is wetland or shore land cover (where there may be a greater magnitude of uncertainty, as well as a potential for underestimates of evacuation times). This information may help to inform how the results of the analysis may be used by emergency managers, particularly if at-risk individuals must cross wetland or shore land cover areas to reach safety.

A continuing limitation in the anisotropic LCD evacuation model is the lack of an empirical basis for the land cover SCV. Even if the Soule and Goldman (1972) energy coefficients adequately represented the influence of land cover on evacuation speeds, the land cover types that they include were developed in areas of different land cover than any current implementation of the anisotropic LCD evacuation model. This means that in each instance, analysts must essentially arbitrarily decide which of the existing coefficients will be assigned to which land cover type. While the sensitivity analysis suggests that the model will perform fairly well as long as the energy coefficient proxies that are currently being used are reasonably close to reality, empirically derived values based on actual land cover conditions and at-risk individuals would be ideal.

Acknowledgments

This study was supported by the United States Geological Survey (USGS) National Geospatial Program and the USGS Land Change Science Program. Mara Tongue of the USGS, Eric Tate of the University of Iowa, and four anonymous reviewers gave insightful reviews of the manuscript. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the US Government.

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