Spatial Patterns and Environmental Drivers of Search And Rescue Incidents in Yosemite National Park

Introduction

Search and Rescue (SAR) incidents are a major operational challenge in large wilderness areas, especially in national parks with complex terrain. Yosemite National Park is one of the most active parks in the United States for SAR operations, often responding to hundreds of incidents each year.¹ Past research from Koester’s Lost Person Behavior and Paul Doherty’s work in Yosemite Search and Rescue (YOSAR) has shown that SAR is fundamentally a spatial problem—where someone is last seen, how they move through the landscape, and what environmental factors influence both risk and rescue outcomes.

Much of the existing research focuses on why SAR incidents occur in certain areas and how terrain or human behavior contributes to patterns of risk. Koester’s database has been widely adopted for SAR teams to help estimate where different categories of lost people are most likely to travel or be found.² However, these global averages do not always translate well to parks with highly specialized terrain. Yosemite National Park contains steep granite walls, deep glacial valleys, and extensive trail systems that constrain or redirect movement across the landscape (Figure 1). Doherty’s research specifically highlights how terrain, elevation gradients and accessibility shape both where incidents occur and how search teams should respond. Similar GIS-based SAR research has used historical incident records, environmental variables and probability mapping to identify where incidents are more likely to occur. This project builds on that work by applying spatial statistical tools to evaluate environmental predictors of SAR incident density across Yosemite.³ 

In this project, I focus on whether SAR incidents in Yosemite show meaningful spatial association with key environmental and built features. Rather than describing where incidents occur, the goal is to test specific spatial relationships using clustering methods, global and local regression, and exploratory spatial analysis. These tools help evaluate how variables such as elevation, slope, distance to trails and incident density contribute to the spatial patterns of Search and Rescue incidents across the park.

Research Questions

1. Are SAR incidents in Yosemite spatially clustered, or are they randomly distributed?
2. Are SAR incidents spatially associated with environmental characteristics such as elevation, slope and trail proximity?
3. Does a spatially varying model (GWR) provide additional local insight beyond a global  model (OLS) for understanding SAR patterns?

Methods

Data Sources

All SAR incident data came from Paul Doherty’s publicly available YOSAR datasets, which include georeferenced incident records from 2001–2011 and missing-person case data from 2000–2011.⁴ These datasets consist of mapped incidents and missing-person locations, each containing coordinate data and descriptive attributes.

Environmental variables were compiled from several sources. A 30-meter digital elevation model (DEM) was downloaded from the OpenTopography Global Datasets interface, and slope was derived from the DEM using standard surface analysis tools.⁵ Trail and trailhead datasets were accessed through the National Park Service (NPS) Open Data Portal.⁶ Distance to trails and trailheads was calculated using Euclidean distance, meaning the values represent straight-line distance rather than actual travel distance along the trail network. Kernel density estimation (KDE) was generated from the full incident dataset to visualize areas of higher incident intensity.

Data quality was generally high, though some preprocessing was required. The SAR incident dataset included n = 1,957 mapped incidents. These incidents were aggregated into n = 218 hexagons, which served as the analysis units for the OLS and GWR models. Environmental rasters were resampled to match the DEM resolution, and all datasets were projected into a consistent coordinate system (NAD 1983 UTM Zone 11N) to ensure alignment during analysis. NAD 1983 was used because it remains common in many National Park Service and legacy GIS datasets, which helped maintain consistency with the source data and reduced unnecessary reprojection between datasets.

Data Preparation

Hexagonal Grid Construction

A uniform hexagonal grid was created to standardize spatial units across Yosemite National Park. Each hexagon covered approximately 5.48 km², providing a consistent spatial framework for aggregating incident counts and environmental variables. Hexagons were selected because their low perimeter-to-area ratio can reduce bias from edge effects, while their consistent neighboring structure makes them useful for summarizing spatial patterns across a continuous landscape.⁷

Spatial Joins

SAR incident points were spatially joined to the hex grid. This produced an incident count variable representing the number of incidents within each hexagon. Additional joins assigned environmental attributes—including elevation, slope, distance to trails, distance to trailheads—to each hexagon. Kernel density estimation (KDE) was used as an exploratory visualization of incident concentration rather than a predictor in the OLS and GWR models. Because the GWR model was run at the hexagon level, local coefficient estimates were based on the spatial distribution of these 218 hexagonal analysis units rather than the individual incident points.

Variable Standardization

Because the predictor variables operate on different scales (meters, degrees, and density values), all continuous variables (except incident counts) were Z-score standardized. Standardization helped stabilize the regression models and ensured that coefficients were comparable across variables.

Quality Checks

Several quality checks were performed throughout preparation:

• Re-ran spatial joins after checking for incomplete or noisy incident records
• Verified that all layers used the same projection
• Confirmed that environmental rasters aligned correctly
• Resolved join issues that initially caused OLS residual tests to fail

Statistical Analysis

1. Global Moran’s I

Global Moran’s I was used to test whether SAR incident density was spatially clustered, dispersed, or random across the study area. A second Moran’s I test was performed on the OLS residuals to evaluate whether the global regression adequately captured underlying spatial structure.

2. Ordinary Least Squares (OLS)

OLS regression was used to evaluate whether SAR incident density was associated with environmental variables at a global scale. The dependent variable was incident count per hexagon.

3. Geographically Weighted Regression (GWR)

GWR was used to explore whether relationships identified in the global model varied across space. After correcting data joins and standardizing all predictor variables, the model successfully calibrated using an adaptive kernel and AICc-based bandwidth selection. GWR outputs included local coefficients and local ^R2 values, which were used to evaluate whether a spatially varying model provided additional local insight beyond the global OLS model.

Software

All work was completed in ArcGIS Pro using:

• Spatial Analyst tools
• Spatial Autocorrelation (Moran’s I)
• Exploratory Regression tools
• OLS and GWR regression tools
• Kernel Density Estimation
• Geoprocessing tools for joins, projections, and raster extraction

Results

Spatial Autocorrelation

Global Moran’s I indicated that SAR incidents in Yosemite exhibited statistically significant moderate spatial clustering (I = 0.315, z = 19.37, p < 0.001; Figure 2), showing that incident density was far from random and appropriate for spatial regression. Study variables showed varying degrees of spatial structure (Table 1). Elevation, slope and incident density (KDE) all exhibited significant clustering, while ruggedness showed only weak, nonsignificant clustering. Distance to trails showed moderate clustering, and distance to trailheads was strongly clustered across the park. Taken together, these results show that the environmental variables are not evenly distributed across Yosemite, which helps explain why model performance varies by location.

Ordinary Least Squares (OLS) Regression

The global OLS model explained a substantial portion of the variation in SAR incident density (adjusted R² = 0.63). Relationships aligned with expectations:

• Elevation (positive): higher elevations had more incidents.
• Slope (positive): steeper terrain was associated with higher incident levels.
• Distance to Trails (negative): areas closer to trails had more incidents.
• Ruggedness (positive, but weaker): rugged terrain showed only mild influence.

Residual Moran’s I showed a dispersed spatial pattern (I = -0.187, p < 0.001), indicating that the OLS model removed clustered structure but still left some local variation. The residual map (Figure 3) further illustrates this spatial dispersion.

Geographically Weighted Regression (GWR) Results

Although GWR did not improve overall model fit relative to OLS, it provided useful local information by showing how relationships between SAR incidents and environmental variables varied across Yosemite. Local R² values ranged from 0.11 to 0.61. These local values are distinct from the GWR global adjusted R² (0.375), which reflects overall model fit rather than spatial variation in fit across hexagons. Model performance varied substantially across the park. Higher local R² values were concentrated in central and southeastern Yosemite, where steep terrain and dense trail networks coincide. Lower values occurred in the northern and western regions, suggesting the predictors were less effective in those areas. Figure 4 shows the spatial variation in local coefficients for each predictor variable.

Spatial Variation in Predictor Effects

Local coefficients showed that the direction of relationships was generally consistent with the OLS results but varied substantially in magnitude (Figure 4):

• Elevation: strongest positive influence in southern and southeastern regions; effects weaken or turn slightly negative in the northwest.
• Slope: consistently positive across the park, with strongest effects in the south and southeast.
• Ruggedness: small but positive in central and southeastern areas; near zero elsewhere.
• Distance to Trail: largely negative, indicating incidents occur closer to established trails.
• Distance to Trailhead: weak and spatially inconsistent, reflecting its minimal influence in the global model.

Collectively, GWR shows that SAR incidents are most strongly associated with steep, high-elevation terrain near established trails, but the intensity of these relationships varies geographically.

GWR Model Diagnostics

GWR global adjusted R² (0.375) was lower than the OLS adjusted R² (0.63), reflecting the tradeoff between local flexibility and overall model fit. Diagnostics indicated appropriate model calibration:

• Global R² = 0.486
• Adjusted R² = 0.375
• AICc = 2092.3
• Effective Neighbors = ~100 (automatically optimized)

Even though GWR did not outperform OLS overall, it was still useful because it showed where the environmental relationships were stronger or weaker across the park. These insights highlight areas where environmental risk factors are most strongly associated with incident density and may support more geographically targeted SAR planning.

Discussion

The goal of this study was to evaluate whether environmental variables help explain the spatial distribution of Search and Rescue (SAR) incidents in Yosemite National Park. Results from the spatial autocorrelation analysis, the global OLS model, and the Geographically Weighted Regression (GWR) all point to a consistent pattern: SAR incidents are not randomly distributed. Instead, elevation, slope and distance to trails meaningfully influence where incidents tend to occur.

Environmental Predictors and their Influence on SAR Patterns

Across all analyses, elevation and slope emerged as the strongest predictors of SAR activity. The OLS model showed clear positive relationships, and the GWR maps demonstrated that these effects were strongest in the central and southeastern regions of the park. These areas are characterized by steeper, higher-relief terrain, where the model indicated higher incident density. The consistency of these results suggests that elevation and slope are key environmental factors shaping SAR density.

Distance to trails showed a generally negative relationship, indicating that incidents tend to occur closer to established trail networks. This aligns with the idea that visitor movement is concentrated along trail corridors, which increases exposure in those locations. GWR results also showed that this relationship was weaker and more spatially variable than slope or elevation, consistent with the smaller global effect observed in the OLS model.

Ruggedness played a comparatively minor role. Although the global model identified a modest positive relationship, the GWR results showed that the effect varied across the park and was generally weaker than that of elevation or slope. This suggests that while rougher terrain  contributes somewhat to incident patterns, its influence is less consistent.

Spatial Variation in Model Performance

The GWR local R² results revealed substantial spatial variation in model fit. High local R² values in the central and southeastern regions of Yosemite indicate areas where environmental variables were more effective at explaining SAR patterns. In contrast, northern and western regions showed much lower local R² values, suggesting that environmental factors alone provide a less complete explanation of incident density in these areas. This highlights that while environmental variables matter, their predictive strength varies across the landscape.

Model Performance and Limitations

The OLS model performed reasonably well given the scope of the study, while GWR added interpretive value by showing where relationships varied locally. The OLS model explained approximately 63% of the variation in incident density, and the dispersed spatial pattern in the residuals indicates that the global model removed clustered structure but still left some local variation. GWR added value by showing where relationships were strongest and where additional variables may be needed.

Implications for SAR Management

The spatial patterns identified in this study provide useful context for search and rescue planning. Areas with high local model performance, mainly in the central and southeastern regions, represent places where environmental factors are strongly tied to SAR incident density. These regions may benefit from targeted safety messaging, enhanced trailhead signage or increased seasonal staffing.

The concentration of stronger model performance in central Yosemite likely reflects a combination of environmental and visitor-use factors, though this analysis cannot disentangle the two. Central Yosemite contains the park's steepest and most accessible high-relief terrain, which the environmental predictors capture well. Whether the elevated SAR density there is also driven by highet visitor concentration, a plausible hypothesis given the park's visitation patterns, cannot be confirmed without visitor-use data. Integrating footfall or permit data with environmental predictors would allow future analyses to separate terrain-driven risk from exposure-driven risk more cleanly.

Areas with low local R² values, however, indicate where SAR activity is less associated with the environmental variables used here. Additional social or operational factors may need to be considered when assessing risk.

Overall, environmental predictors explain important aspects of SAR patterns, but integrating these results with visitor-use data and operational records would support a more complete risk assessment for Yosemite.

Limitations

Several limitations should be considered when interpreting the results of this study. First, the SAR incident data represent reported cases from 2001-2011 and may not capture all incidents that occurred within Yosemite National Park. Unreported events or inconsistencies in historical record-keeping could influence observed spatial patterns. The dataset also does not reflect more recent changes in visitor use, trail infrastructure, or park management, which may limit the applicability of findings to current conditions.

Additionally, the analysis focused on environmental and built features, including elevation, slope, ruggedness and proximity to trails and trailheads. While these variables explain a substantial portion of spatial variation in SAR incident density, they do not account for social and behavioral factors such as visitor experience, activity type, weather conditions or seasonal patterns. Distance to trails and trailheads was measured using Euclidean distance, meaning it represents straight-line distance rather than actual travel distance along trails or across terrain. In Yosemite’s steep andcomplex landscape, this may underestimate the real effort, time, or difficulty required to reach a trail or trailhead.

The use of a hexagonal aggregation framework introduces scale-related limitations. Aggregating data to fixed spatial units may obscure fine-scale variation and introduces sensitivity to spatial resolution and zoning choices. Although hexagons provide a consistent representation of spatial patterns, results may differ under alternative spatial aggregation schemes.

Finally, while Geographically Weighted Regression can capture spatially varying relationships not shown by the global OLS model, it remains sensitive to bandwidth selection and data distribution. Because GWR estimates relationships locally, results may be less reliable in areas with fewer nearby incidents or unevenly distributed observations. GWR coefficients should therefore be interpreted as exploratory rather than causal.

Despite these limitations, the analysis provides meaningful insight into how environmental factors relate to SAR incident patterns in Yosemite and highlights opportunities for future work incorporating social, temporal and operational data.

A future version of this analysis could also translate the strongest environmental predictors into a simple SAR hazard or risk-index map. However, developing that product would require additional decisions about variable weighting, validation and how to distinguish environmental hazard from actual incident likelihood.

Conclusion

This study examined whether environmental variables help explain the spatial distribution of Search and Rescue (SAR) incidents in Yosemite National Park. Results from the spatial autocorrelation tests, global OLS regression and Geographically Weighted Regression (GWR) indicate that SAR incidents are not randomly distributed, and that elevation, slope and distance to trails contribute meaningfully to where incidents tend to occur. These findings align with prior research showing that terrain and accessibility strongly influence SAR risk and movement patterns in wilderness environments.⁸ 

While the GWR results showed that these relationships vary across the park, areas with weaker model performance suggest that social or operational factors likely play an important role as well, reinforcing that SAR risk is locally variable and not fully captured by global models alone. This is important because it shows that environmental variables can explain broad SAR patterns, but they do not fully capture the human and operational context behind individual incidents.⁹ These results help clarify how SAR incidents relate to Yosemite’s landscape and suggest that combining environmental data with visitor-use and behavioral information would improve future analyses.