## 1. Introduction

Wildfires, which are defined as any uncontrolled fire occurring within nature landscape, such as forestlands, are one of the main concerns for the public and for forest managers. The occurrence of wildfires can be affected by various factors, including climatic conditions and other factors. Global climate is predicted to change over the next century due to increased greenhouse gas (GHG) concentration in the atmosphere [

1]. The projected climate change is likely to alter wildfire activity. Warmer spring and summer temperatures will make the fire season longer. Forests will become more combustible under the increasing temperature trend as snowpack will be melting earlier than before. Additionally, warmer and drier conditions will make trees more susceptible to diseases and pest infestations, increasing tree mortality and fire hazards [

2].

Studies have recognized that climate is a dominant driver of wildfire activity and that wildfire activity and uncertainty will intensify due to ongoing global climate change. Climate change can affect the number of wildfire occurrences and increase wildfire intensity and the length of the wildfire season [

3]. For example, warmer temperature is expected to increase lightning ignition and wildfire severity [

4]. Moritz

et al. [

5] assess global disruption in future wildfire activity using empirical analysis and Global Climate Model (GCM) projections. Dennison

et al. [

6] examine regional trends in wildfire occurrence, total burned area, and wildfire size for 1984–2011 in the Western US using burned area boundaries mapped from satellite remote sensing data. They found that the number of large wildfires has shown a significantly increasing trend in the major ecoregions of the Western US.

Although several studies have explored climate change impacts on wildfire, we intend to advance existing work in both estimating the climate-wildfire relationship and projecting the impact of future climate change on wildfire risk. We employ generalized estimating equations (GEE), a nonlinear panel data model, to take into account the bounded nature of the dependent variable, wildfire risk. Moreover, we consider both spatial and serial correlations using the autoregressive AR(1) covariance structure form. Preisler

et al. apply a spatial term in the model to account for spatial correlation and apply logistic regression to estimate the probability of large fire occurrences [

7]. However, they only focus on specific local areas, such as California and its adjacent regions. The target areas of our study are 48 US continental states. Thus, we can investigate climate effect on wildfire activity in a border area. Additionally, the GEE model provides more consistent estimates of the parameters and standard errors than a logistic regression [

8]. Unlike logistic regressions, the GEE allows for dependence within clusters so it is more appropriate for longitudinal data. Another advantage of the GEE is that, even if the correlation matrix is incorrectly specified, the estimated parameters and standard errors from the GEE can still be consistent using a robust sandwich estimator [

9]. If the correlation is correctly specified, the GEE estimator is more efficient than logistic regression. Therefore, we will provide more consistent and efficient parameter estimates under the GEE framework [

8]. We also provide statistical tests related to the GEE, although few methods exist to assess the specification of fitted marginal regression models.

This study has several objectives. First, we aim to identify the relationship between wildfire risk and climate factors such as temperature and precipitation. In addition to the climatic conditions, we also consider human and natural adaptations, as well as demographics, such as human population density. Using the panel data that reflect past variations in wildfire activity, climatic and other natural conditions, and human interventions along the climate gradient, we make it possible to incorporate human and natural adaptations into estimating the relationship between wildfire risk and climatic conditions. Additionally, climate variables are often correlated. The panel data model can alleviate the multicollinearity problem among climate variables and better control for the missing or unobserved variables [

10,

11,

12]. Because the response variable “wildfire risk” is bounded by zero and one, the standard linear panel data model is not well suited. In this case, a fractional response model is a better choice [

9,

13]. Westerling and Bryant [

14] use the Generalized Linear Model (GLM) with the logit link function to assess climate change impact in California and neighboring states. Although the logit link function addresses the issue associated with the fractional response variable, the GLM cannot appropriately take into account within group correlations [

15]. To overcome this problem, we introduce the fractional probit model, a non-linear panel data model, and the Generalized Estimating Equation (GEE) approach. The GEE is an expansion of the GLM by taking into account within group correlations [

16]. The GEE includes an additional variance component to adapt correlated data and to allow for differences among clusters [

15]. Therefore, the GEE is more appropriate than the GLM for panel data analysis. Brillinger, Preisler, and Benoit [

17] use a generalized mixed effect model (GMM) to assess wildfire risk. The GMM and GEE are the most widely used analytical techniques for longitudinal data. Even though these two models share some similar characteristics, the GEE has several advantages over the GMM because the GEE is a partial-likelihood method [

15], which makes computation easier and can be more easily applied to different distribution forms [

18].

Second, we aim to assess the impact of future climate change on wildfire risk using our regression model coupled with the future climates projected by Global Climate Models (GCMs). GCMs provide simulated future climates that reflect the responses of the global climate system to GHG emissions scenarios [

19]. We use newly updated GCMs based on the fifth phase of the Coupled Model [

1]. The new GCMs adopt the Representative Concentration Pathways (RCPs) scenarios that supersede the previous GHG emissions scenario. The RCPs are the latest iteration of the scenarios to provide time-dependent projections of atmospheric GHGs [

20]. They have several advantages. First, the GCMs based on RCPs provide more unified metric, grid, and location points. Thus, it is easier to compare one model to another. Second, these RCP scenarios are defined by their total radiative forcing pathways (cumulative measure of human emissions of GHGs from all sources expressed in Watts per square meter) and level [

1]. Thus, they use the scientifically specified term to avoid the ambiguous definition. For example, the most moderate scenario, RCP2.6, assumes the radiative forcing will peak at ~3 W/m

^{2} before 2100 and then decline.

This study not only advances the modeling approach but also reveals the impact of climatic conditions and demographics on wildfire activity and provides projections of wildfire risk under climate change. Our modeling results foster a better understanding of the linkage between wildfire risk and climatic conditions and can aid in developing more effective wildfire response strategies under climate change.

## 4. Conclusions

We apply non-linear panel data modeling to establishing a statistical linkage between wildfire risk and climatic and other factors. The model is estimated by using the GEE method. This approach takes into account of the bounded nature of the dependent variable, wildfire risk that is fractional response variable. Additionally, the panel data model can better control for missing or unobserved variables and alleviate the multicollinearlity problem associated with correlated climate variables, while incorporating natural and human adaptations into the modeling. All these represent methodological innovations in modeling climate change impact on wildfire risk. Meanwhile, we simulate the impact of climate change on future wildfire risk using our regression model coupled with the future climates projected by two GCMs under two RCP scenarios.

According to our modeling results, both climate and non-climate variables are likely to affect wildfire risk. Wildfire risk would generally increase with an increase in temperature and a decrease in precipitation. Spring, summer, and winter temperatures in particular would have a significant impact on wildfire risk with summer temperature having the largest impact. This implies that climate change could greatly intensify wildfire risk particularly in the summer, the most active and severe wildfire season, and make the wildfire season longer, extending from spring to winter. On the other hand, precipitation increases would likely reduce wildfire risk. Temperature increases coupled with human population expansion could elevate wildfire risk as humans are a major source of wildfire ignitions.

Based on the future temperatures and precipitations predicted by the GCMs, future wildfire risk would increase in almost all states. The South Central states including Texas, Oklahoma, Louisiana, Kansas would experience the highest risk increase, and the climate change impact will be more severe in the long run (2031–2050) than in the short-run (2011–2030). This calls for more effective wildfire management strategies for all states in general and the South Central region in particular.

Our simulation results on the climate change impact on future wildfire risk demonstrate considerable variations across the future climate scenarios projected by the GCMs under the different RCP scenarios. The variations could stem from several sources. First, it is the uncertainty associated with the projections of future climate. The variations in the future climates projected by different GCMs are substantial even under the same RCP scenario, which contributes greatly to the variations in our projected impact of climate change on wildfire risk. Second, our regression model indicates that temperature in general has a positive impact on wildfire risk whereas precipitation tends to dampen wildfire risk. According to the simulation results from the GCMs, changes in temperature and precipitation (in both magnitude and direction) under climate change vary tremendously from location to location. This adds to the uncertainty in projecting climate change impact on wildfire risk, particularly given the difficulty in projecting future climate on a finer scale or at the local level. Third, our regression model is estimated using seven-year data due to the unavailability of consistently recorded nationwide wildfire data. Although the spatial variations in our data compensate for the limitation imposed by the short time series, using the data of a longer time series available in the future could improve the estimation of our regression model and thus the projections of climate change impact on wildfire risk. Hence, there is a need for future studies to address these uncertainties.

This study focuses on the impact of climatic conditions on wildfire risk. Although our data and modeling approach can incorporate some human response (e.g., adaptation) to wildfire into the analysis, national wildfire policy is not explicitly included in the model. National wildfire policy can interact with wildfire risk; future studies can also explore their interaction. Additionally, to overcome the limitations of current GCMs, future studies can apply statistical downscaling models, such as Multivariate Adapted Constructed Analogs (MACA) [

33].