Natural hazard risk prediction is a multivariate and non-linear task ([27]) due to the combined role of many disaster-inducing factors. Several methods and machine learning algorithms have been employed to solve predictive analysis, such as support vector machine (SVM), artificial neural networks (ANN), and decision trees (DT). The major weakness of these algorithms is their inability to estimate each conditioning factor’s contribution to the total risk ([27]). CART decision trees are greedy. Even with bagging, the trees can have structural similarities that will result in high correlation in predictions. However, in Random Forest (RF), the trees are uncorrelated or at least correlated because learning algorithms just select a random sample of features from a random sample of variables consistent with standard Random Forest methodology ([5]). RFs are modifications of classification and regression trees (CART) algorithms ([20]). It is a supervised classification and regression method of modelling that allows growing an ensemble of trees and letting them vote for the most occurring class as the predicted class ([5]). The RF is the algorithm that is capable of estimating the contribution of each factor to the total effect ([27]). The RF has high forecast accuracy, acceptable tolerance to outliers and noise, and easy avoidance of overfitting ([27]). RF algorithm generates numerous binary trees, which are collectively called forests ([19]). In the RF, trees grow based on a bootstrap sample. For each node, random subsets of samples are selected. The “out-of-bag” error rate is calculated using samples out of the bootstrap sample ([19]). Mean decreases in accuracy and mean in the Gini are calculated in the process, which is then used to calculate the variable importance score ([19]).

Given an observation, for each tree in the model, RF predicts the outcome using a tree applied to an observation and stores the outcome as a list. If the model is a classifier, it returns the maximum count. If the model is a regression, it returns an average as depicted in Figure 2, consistent with standard ensemble learning frameworks

The RF algorithm uses a parallel ensemble method called “bagging” or bootstrap aggregation to generate classifiers. This is a method that averages multiple estimates that are measured from random subsamples of variables. A subset of observations is selected at random to form a subsample and used to train the model. The process is repeated to select the subset of samples from the original observation until the specified number of trees is reached. This process is known as bootstrapping, consistent with standard Random Forest methodology ([5]). Random Forests are built by: specifying the number of trees,

Figure 2. Random Forest process flow.

specifying the number of variables, specifying the number of features (columns) to be used in each tree. Then, for each tree: select some samples with replacement from all observations (rows), select given number of features randomly, train a decision tree with selected samples and features ([5]). Select a specified number of samples from the original dataset, which is known as bootstrap samples. Randomly select variables from the sample for each node split. An unpruned classification tree is grown for each bootstrap sample. All the trees are aggregated to predict the new label by majority votes ([1]).

Variableimportance

Mean decrease accuracy and mean decrease Gini are widely used for measuring, ranking, and selecting variable importance ([19]). Often in regression problems, the drop in the sum of squared errors, and classification problems, the Gini impurity is commonly used to evaluate node purity in tree-based models and is widely applied in Random Forest algorithms ([5]; [11]). The greater the impurity, the greater the importance of the variable, as commonly established in tree-based learning methods ([5]; [11]). The Gini impurity is computed by summing the probability of each item chosen multiplied by the probability of an error to classify that item into the correct class ([1]). The Gini impurity is obtained by the following algorithm (Equation (1)).

The Gini impurity of the parent node is higher than that of the child node ([27]). The Gini decrease of each explanatory variable is combined to estimate the total contribution of it in the prediction of vulnerability ([27]). The variable importance is calculated by the given formula (Equation (2)).

where P_k is the variable importance, m = the total number of explanatory variables, n = the total number of classification trees, t= the total number of nodes, D_Gkij = Gini decrease value of the j^th node in the i^th tree that belongs to the k^th variable. Mean-squared error (MSE) is obtained by the given equation (Equation (3)).

where ε is the mean squared error, V_observed is the variable from observed data, and V_response is the variable from the result ([17]).

Out-of-Bag(OOB)error

Each tree in the random forest is constructed from a random sample of observations, usually called bootstrap samples. The observations that are left out from constructing a tree during the classification process are called “out-of-bag” (OOB) observations, i.e., unseen data in classification (or out of bootstrap samples). Therefore, each tree is constructed from different samples from the whole dataset. The prediction for an observation made from the trees for which the observation was not used. The error rate that is estimated from these predictions is known as OOB error ([1]; [15]).

Ground observations from social media were used for training. NAPSG Foundation, GISCorps, and CEDR Digital maintained a Story Map displaying 2018 hurricane crowdsourced photos collected from Instagram, Twitter, Facebook, and online news media (https://napsg.maps.arcgis.com/apps/StoryMapCrowdsource/index.html?appid=69b95886cf8e49a3a349c9d550174a91). This is the collection of photos with a brief description of events by social media users illustrating the incidences (e.g., hurricane impact, hurricane intensity, damage, storm surge, flooding, rescue efforts, etc.) during and after the hurricane event. After careful observation of photos and their descriptions, they were classified into four different levels of severity as class vulnerability levels (categories) and assigned the numbers from 1 to 4 - 1 being the most at risk (highest vulnerability) location and 4 being the least at risk (lowest or no vulnerability) location. Within the study area, 99 locations were identified from the story map that were appropriate for training input. Similarly, emergency shelters, shelter locations designated by New Hanover County to evacuate county residents during natural disaster emergencies, including hurricanes and floods. These were considered as no-risk or least risk locations, which were assigned to 5 and 6 in the vulnerability category. More locations were identified by observing satellite imagery and flood maps during Hurricane Florence and assigned numbers from 1 to 6 vulnerability categories depending on the severity of the impact observed. A total of 273 locations were identified for input as training features. These training features with vulnerability labels are summarized in Table 1 and displayed on a map in Figure 3.

Table 1. Vulnerability categories and the number of locations for model training.

Figure 3. Training point features corresponding to Table 1 (left), and prediction polygon features (census blocks, right).

The distribution of training samples across vulnerability categories (Table 1) indicates moderate class imbalance, with fewer observations in extreme categories. This imbalance may influence model training by biasing predictions toward more frequent classes. While Random Forest is relatively robust to class imbalance due to its ensemble structure, imbalanced class distributions can still affect predictive performance ([6]). Techniques such as stratified sampling, class weighting, or balanced subsampling could further improve model reliability.

Future work will explicitly address class imbalance and evaluate performance differences across categories, particularly for extreme vulnerability levels.

Vulnerability categories (1 - 6) were assigned based on observable damage severity and contextual information from crowdsourced images, descriptions, and satellite imagery. The classification followed these general rules:

Category1(VeryHigh): severe structural damage, deep flooding, life-threatening conditions;Category2(High): significant flooding or infrastructure damage;Category3(Moderate): localized flooding or moderate disruption;Category4(Low): minimal visible damage;Category5 - 6(VeryLow): safe zones such as shelters or unaffected areas.

To reduce subjectivity, ambiguous cases were reviewed iteratively and assigned based on consensus interpretation of image evidence and contextual metadata. A subset of locations was re-evaluated to ensure consistency in labeling decisions.

These photos are powered by NAPSG Foundation, GISCorps, and CEDR Digital, a Story Map (upper left), a general map with a cluster of locations with impacted locations; the map showing the location of the damaged gas station in Wilmington, NC on 9/14/2018 (upper right), map showing location of a downed tree on a house on 9/14/2018 (lower left); location on map and an abandoned car in Wilmington, NC on 9/15/2018 (lower right).

This is a feature that represents polygons to receive the results of the predictions made by the models. Since the goal of this work is to make predictions for the vulnerability of communities, the census blocks would be ideal polygon features to predict on because census blocks are the areas that encompass small communities with distinctive geophysical and demographic similarities. New Hanover County consists of 5069 census blocks as delineated by the US Census Bureau in the 2010 census (Figure 3, right).

The vulnerability is due to one or a combination of multiple geophysical, demographic, or socio-economic conditions of people or places. These conditions, information generated regarding these conditions, and information regarding the hurricane itself can be defined as explanatory variables for hurricane disaster analysis. There is no consensus as to which factors should be given higher priority when deciding the level of vulnerability of communities from hurricanes in coastal areas ([3]). This work used a combination of geophysical, demographic, and social media-generated information as explanatory variables, as discussed in forthcoming sections.

Geophysicalvariables

1) Land use/land cover

Sentinel-2, a sensor developed by the European Space Agency (ESA), provides high-resolution (10 m) multispectral imagery for surface reflectance, which was used for land-use/land-cover (LULC) classification. The imagery was classified using a Semi-automatic Classification Plugin for QGIS version 2.18. Out of 12 Sentinel-2 spectral bands, bands 1 (coastal aerosol), 9 (water vapor), and 10 (cirrus) were excluded from the classification dataset. The imagery was classified into nine different land-use and land-cover classes: a) forest, b) ocean, c) river, d) lake/pond, e) road, f) residential, g) agricultural, h) commercial, and i) marsh. The maximum likelihood algorithm was used to classify the imagery, which calculates the probability distribution for the classes, based on the Bayesian theorem, to determine which pixel belongs to the land cover class in training ([22]). The classified output raster was then resampled to 30 m to reduce the number of pixels to synchronize with the processing ability of ArcGIS Pro, Forest-based Classification and Regression tool.

2) Elevation

Digital elevation model (DEM) dataset at 1/9 arc seconds (approximately 1 m) resolution obtained from the 3D Elevation Program (3DEP) of the USGS National Map Services (https://www.usgs.gov/core-science-systems/ngp/3dep) was used as an elevation dataset for the model. The DEM was resampled to 30 m to overcome the computational limitation of the tool. The elevation of New Hanover County ranges from 0 m to 30 m.

3) Slope

The slope tells the steepness of a raster surface. The slope was calculated in degrees using the DEM data discussed in the previous section. The planar method parameter was used, where the slope is measured as the maximum rate of change in value from a cell to its immediate neighbors. The following slope algorithm was used (Equation (4)).

where d z d x is the rate of change in the x-direction, and d z d y is the rate of change in the y-direction. The slope indicates the topographic change and variability of the surface. A lower slope means a flatter surface, which has a higher risk of flooding ([27]). The slope raster used as input is shown in the map.

4) Stream Power Index (SPI)

Stream Power Index (SPI) is a measure of the power of flowing water on the terrain surface. The higher the stream power index, the more erosion it can cause downstream. Stream power is a hydrological factor that can condition or explain how damaging the flood would be ([27]; [17]). The SPI was calculated from slope and flow accumulation raster datasets obtained from terrain analysis of digital elevation models. The percent rise slope was used to calculate SPI by the formula in the ArcGIS raster calculator (Equation (5)).

5) Normalized Difference Vegetation Index (NDVI)

Normalized Difference Vegetation Index (NDVI) measures the difference between near-infrared (NIR) and red values of wavelengths. NDVI values range from −1 to 1. Healthy vegetation has the highest NDVI value, i.e., inclined towards 1, and water is inclined towards −1. Other land cover values fall between these two extremes depending on the type, growth, soil moisture, and presence or absence of vegetation, snow, and soil roughness ([27]). NDVI of the area of interest was computed from the Sentinel-2 imagery bands, Band 4 (Red) and Band 8 (NIR), as given by the formula in Equation (6) below. NDVI input is as shown in the map.

6) Major roads

Major roads play a critical role before, during, and after natural disasters from the perspective of evacuations, rescue, and recovery needs. The more roads and the wider roads are closer to a settlement, the easier it becomes to evacuate and provide post-event assistance. As a result, the communities could become safer from the impacts of hurricanes and floods. Thus, road features can be considered marked variables to explain vulnerability prediction. Road features were obtained from the North Carolina Department of Transportation (NCDOT).

7) Water features

The NC Center for Geographic Information and Analysis distributes the major hydrography data that includes major rivers and water bodies (lakes, ponds, dams, etc.) and floodwaters. Rivers and other water features are the areas where floods surge during hurricanes and heavy rainfall. People near these water features could be in danger of being affected by floods. For this reason, this is an important addition to the list of explanatory variables of vulnerability prediction.

Demographicvariables

As shown in Figure 4, poverty, gender, race, ethnicity, age, and disability are demographic indicators of social vulnerability. Poor, women, children, people with disabilities, and aged people are vulnerable because of their inability to have access to resources that they need to protect themselves when disaster strikes and recover in the aftermath of disaster ([24]). American Community Survey (ACS) 2017 data at block group levels of age, disability, and poverty were used as demographic explanatory variables. Age groups 0 - 14 and 65 plus, the population with disability, and the population with poverty are considered more vulnerable than the rest of the population in the event of natural disasters such as hurricanes.

Figure 4. Workflow for hurricane vulnerability mapping and prediction.

Social media variables

Social media is a fundamental tool for individuals to access and disseminate real-time information regarding storm intensity, damage, safety, evacuation, and recovery during disaster events ([10]; [16]). The “tweets” variable represents the spatial presence of geotagged Twitter posts during Hurricane Florence. Specifically, the predictor was constructed as the count of geotagged tweets within proximity to each location, serving as a proxy for real-time human-reported impact intensity. Tweets were filtered using the keyword “#Florence” and restricted to geolocated posts within New Hanover County during September 14-19, 2018. A total of 65 geotagged tweets were retained after filtering.

Given the limited number of observations, this variable may be subject to spatial and sampling bias. Therefore, its influence on model performance should be interpreted cautiously. Future work will explore alternative representations such as kernel density estimation, spatial smoothing, or population-normalized tweet intensity to improve robustness.

The two-thousand decision trees parameter was found to be optimal during model construction. The predictions from regression models were made to census blocks to produce predicted vulnerability output corresponding to vulnerability levels in input training features. Explanatory variables were calculated from the distance feature and raster datasets.

Thirty percent of the training data was excluded from training the model for validation. After the model is trained, the validation data are used to predict the values of the test data; the predicted values are then compared to the observed values to provide a measure of prediction accuracy based on data that were not included in the training process.

The validation strategy employed a random 70/30 split, which may lead to optimistic performance estimates in spatial datasets due to spatial autocorrelation. In geographically structured data, nearby observations tend to share similar characteristics, potentially inflating predictive accuracy ([23]).

Figure 5. Explanatory geophysical variables: (a) land use/land cover, (b) elevation, (c) NDVI, and (d) SPI.

Figure 6. Explanatory variables: (a) slope, (b) major roads, (c) major rivers, and (d) water bodies.

Figure 7. Explanatory demographic variables: (a) poverty, (b) disability, (c) children, and (d) aged population.

Figure 8. Explanatory variables: tweets.

A more robust approach would involve spatial cross-validation techniques, such as spatial blocking or leave-area-out validation, to better assess generalization across geographically distinct regions ([26]). Due to data and computational constraints, this was not implemented in the current study; however, future work will incorporate spatial validation frameworks to provide more conservative and realistic performance estimates.

The leaf size parameter is the number of observations required to keep a terminal node without further splitting. The minimum leaf size parameter set for this regression model was 5, i.e., the tree stopped growing after it had a minimum observation of 5 at its terminal node. Tree depth means the depth of each tree in the tree. The tree depths in the forest range between 0 - 18 (this is data-driven), with having mean tree depth of five. The number of data points available to form per tree was set to 100%, and the number of randomly sampled variables for each tree was 3 (the square root of the total number of variables). The percentage of data excluded for validation for the regression model was 30.

Variable importance is a measure of how important a variable is in prediction. Complex interactions among the variables determine Random Forests. It is determined by looking at how much the prediction error increases when data for that variable is permuted while all others are left unchanged. The calculations are carried out for each tree.

Mean decrease in accuracy measures to which a variable contributes to the mean decrease in accuracy of prediction during the OOB error calculation. The variables with a large mean decrease in accuracy are more important for classification. The more the accuracy of the random forest decreases due to the exclusion (permutation) of a single variable, the more important that variable is considered. The mean decrease in Gini measures how each variable contributes to the homogeneity of the nodes. Each time a particular variable is used to split a node, the Gini for the child nodes is calculated and compared to that of the original node. Variables that result in nodes with higher purity have a higher decrease in Gini.

Mean squared error (MSE) is the average squared difference between the predicted values and the actual values. This is a measure of the quality of the model. The values closer to zero are better. In this model, the MSE for the number of trees 1000 and 2000 are 1.728 and 1.729, respectively. While doubling the number of trees, the error decreased, but not significantly for the regression model.

The percent of variation explained is the determination of the degree of relationship in the patterns of variation, or how well the variation of one variable explains the variation of the other variable. The coefficient of determination, R², is a measure of the variation explained. The higher the value of R², the higher the predictive value of the regression. In this study, R² is 0.931 from the training and only 0.610 from the validation. The percent of variation explained may vary as the number of trees parameter is changed. In this analysis, the percent of variation explained is 1.728 and 1.719 for 1000 and 2000 trees respectively, a slight increase when the number of trees is doubled, indicating that predictive ability of the model increased as the number of tree parameter has increased from 1000 to 2000, but also it appears that it did not make a remarkable difference in the ability of model to predict. The difference between training (R² = 0.931) and validation performance (R² = 0.610) suggests moderate overfitting, which is common in spatial machine learning models with complex interactions. Despite this, the model retains acceptable predictive performance on unseen data, indicating reasonable generalization ability.

Since the outcome variable represents ordered categories, additional evaluation metrics such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) would provide more interpretable measures of prediction error compared to R² alone ([11]). Furthermore, if formulated as a classification problem, performance could be evaluated using per-class accuracy and confusion matrices to distinguish between minor and major misclassification errors ([21]).

In this study, R² and MSE are reported to maintain consistency with the regression framework; however, future extensions will incorporate these additional metrics to better align evaluation with the ordinal nature of vulnerability. P-value in regression analysis measures the relationship between the change in the predictor and response variables. Higher P-values mean the response variable is insignificant for prediction, and a value as low as (or lower than) <0.05 indicates a significant relationship with the predicted outcome. P-value in this analysis is zero (0), which means that the variables used are statistically significant, having a decent relationship with the predicted outcome.

Variable importance ranked in Table 2 and Figure 9 shows the contribution of each explanatory variable to predict the vulnerability situation in the study area from Hurricane Florence using a regression model. Tweets, roads, elevation, and NDVI have the highest contribution for predicting the vulnerable communities, whereas water body, land use/land cover, slope, demographic variables, and Stream Power Index (SPI) have a moderate contribution.

Table 2. Variable importance output from the RF regression.

Figure 9. Summary of variable importance from the regression model.

The regression analysis predicted that approximately 10 percent of census blocks (482) would be classified as vulnerability level 1, approximately 47 percent (2311) as vulnerability level 2, and 31 percent (1538) as vulnerability level 3. The rest would be categorized as four or five (Figure 10).

Figure 10. Predicted categories for different explanatory variables on census blocks from the RF regression model.

Figure 10 shows vulnerability categories by explanatory variables. This shows that about 10% of the communities had the highest level of vulnerability, nearly 47 percent of the communities corresponding to the census blocks had a high level of vulnerability, about 31 percent of the communities were moderately vulnerable, and the rest, nearly 12 percent, had a low level of vulnerability to the risk associated with Hurricane Florence. It is found that the predicted map indicates that generally the areas around water bodies, including coast, rivers, and floodwaters, and lowland areas appear to have higher vulnerability compared to the areas away from them (Figure 11).

Figure 11.Predicted categories on census blocks from the RF regression model.