Utilizing MODIS remote sensing and integrated data for forest fire spread modeling in the southwest region of Canada

Accurate prediction of fire spread is considered crucial for facilitating effective fire management, enabling proactive planning, and efficient allocation of resources. This study places its focus on wildfires in two regions of Alberta, Fort McMurray and Slave Lake, in Southwest Canada. For the simulation of wildfire spread, an adapted fire propagation model was employed, incorporating MODIS datasets such as land surface temperature, land cover, land use, and integrated climate data. The pixels were classified as burned or unburned in relation to the 2011 Slave Lake wildfire and the initial 16 days of the 2016 Fort McMurray wildfire, utilizing defined starting points and the aforementioned specified datasets. The simulation for the 2011 Slave Lake wildfire achieved an weighted average precision, recall, and f1-scores of 0.989, 0.986, and 0.987, respectively. Additionally, macro-averaged scores across these three phases were 0.735, 0.829, and 0.774 for precision, recall, and F1-scores, respectively. The simulation of the 2016 Fort McMurray wildfire introduced a phased analysis, dividing the initial 16 days into three distinct periods. This approach led to average precision, recall, and f1-scores of 0.958, 0.933, and 0.942 across these phases. Additionally, macro-averaged scores across these three phases were 0.681, 0.772, and 0.710 for precision, recall, and F1-scores, respectively. The strategy of segmenting simulations into phases may enhance adaptability to dynamic factors like weather conditions and firefighting strategies.


Introduction
Forest fires, with their sudden and devastating nature, pose immense threats to both natural ecosystems and human communities.Over the past century, exhaustive research efforts have been devoted to unraveling the intricate temporal and spatial dynamics of these formidable disasters, aiming to develop effective preventive and control measures.Amid the multitude of factors investigated, the analysis and modeling of forest fire propagation have taken center stage for various institutions and experts.The surge in computational power has fueled efforts to simulate the dynamics of wildland fires and their spread across landscapes.These models and algorithms utilize graphics and animation to visually depict the advancement of forest fires, delivering invaluable insights to fire management teams (Martinez-de Dios et al 2008, Vásquez et al 2021).By incorporating key factors like forest flammability, weather variations, and terrain characteristics, these simulations enable managers to devise efficient fire suppression strategies, mitigating the disastrous consequences of forest fires on the environment and human lives (Rui et al 2018, Qiao et al 2018, Ahmed et al 2020, Ahmed and Hassan 2023).
In Canada, there is a growing sense of concern over the escalating frequency of forest fires and the expanding areas affected by them in recent decades, despite advancements in fire suppression capabilities and increased coverage (Ricci et al 2021).Moreover, there are observable indications of the forest fire season starting earlier, ending later, and lasting longer.These occurrences significantly challenge the ability of fire management agencies to accurately allocate the necessary resources for effective fire suppression (Podschwit and Cullen 2020).The primary drivers behind these changes are believed to be weather change, specifically the rising temperatures, and the heightened human activities in forested areas, which are altering fire weather patterns and study was limited due to cloudy and rainy weather conditions.The authors highlighted the significance of data preprocessing for remote sensing images, as the quality of preprocessing directly impacted the accuracy of the analysis conducted using the remote sensing data.They emphasized the need to consider a three-dimensional spreading model for forest fires (Qiao et al 2018).(Huang et al 2020) proposed a new data-driven model that combines reference-based image segmentation for vegetation density estimation with fire heat conduction modeling.The authors utilized top-view images captured by unmanned aerial vehicles, which offered various advantages such as flexibility, safety, affordability, and convenience compared to traditional parameter collection methods.By applying their image processing algorithm, Huang et al were able to obtain the true distribution of vegetation density, which was then integrated into the probabilistic fire spread modeling.Their model incorporated factors such as terrain slope, vegetation density, and wind, and the adjustable parameters could be easily learned from experiments.The model was designed to be adaptable to forests with mixed vegetation and diverse geographical and climate conditions.To validate their model, the authors evaluated its performance by comparing the predicted fire spread with actual fire propagation data from the California Rim fire in 2013 (Huang et al 2020).
The objectives of this study are centered on creating wildfire spread models for the province of Alberta, Canada.The study focused on analyzing two major wildfires: the Slave Lake wildfire, which transpired from May 15, 2011, to May 22, 2011(Government of Canada 2023), and the Fort McMurray wildfire, which occurred between April 30, 2016, and June 1, 2016 (Government of Canada 2023).From May 15 to May 22, 2011, Alberta, Canada, witnessed forty-nine wildfires in the North-Central region.This event is notable in Canadian history.An uncontrollable wildfire originating in Slave Lake prompted a state of emergency in the Municipal District of Lesser Slave River No. 124 and nearby communities.Slave Lake endured significant damage, with 374 buildings destroyed and 52 sustaining damage.Roughly 7,000 residents were evacuated, leaving 735 individuals and families without homes.Other areas, including High Prairie, Little Buffalo, Red Earth Creek, Loon Lake First Nation (FN), Whitefish Lake FN, and Woodland Cree FN, reported 59 buildings destroyed and 32 damaged.Various oil companies, such as Penn West Petroleum, Exall Energy Corp., and Canadian Natural Resources Ltd., ceased drilling operations, suspended production, and evacuated their staff from the affected region.Canadian National (CN) Railway also suspended services in the area.The number of evacuees reached approximately 12,055 by May 19.The estimated total cost of damages surpassed $500 million.This event underscored the importance of preparedness and mitigation strategies to prevent future disasters (Pujadas Botey and Kulig 2014, McGee et al 2015, Public Safety Canada 2023).
The Fort McMurray wildfire, also known as the Wood Buffalo or Horse River wildfire, occurred in May 2016 and ignited on May 1.It expanded across a total area of 589,995 hectares of land.The fire crossed provincial borders, extending from Alberta to Saskatchewan, and was brought under control on July 5, 2016.This event led to the largest evacuation ever recorded for a Canadian wildfire, with 88,000 residents forced to leave their homes on May 3, 2016.The fire resulted in the loss of 2,400 homes and businesses.The overall estimated damages, including personal and commercial losses, amounted to $6 billion, with insured losses reaching approximately $3.6 billion.Consequently, the Fort McMurray wildfire holds the distinction of being the most expensive natural disaster in Canadian history (Tan et al 2018, Mamuji and Rozdilsky 2019, Public Safety Canada 2023).
In this research, a combination of remote sensing data, integrated climate data, and terrain information was utilized to simulate and accurately identify the distribution of burned and unburned pixels within a fire-affected region.A modified cellular automata algorithm was employed to forecast the spread of forest fires.The successful validation of this adapted algorithm emphasized its critical significance as an invaluable tool for making crucial emergency decisions in fire management.It also can aid FireSmart regulations by assessing wildfire risk, evaluating the impact of mitigation measures, optimizing resource allocation, assisting in evacuation planning, promoting public awareness, and informing policy development.These models provide data-driven insights to enhance the effectiveness of regulations and ensure the safety of wildfire-prone communities.

Study region
The primary focus of our research was to develop a model for analyzing the propagation of wildfires in the province of Alberta, Canada.Spanning an area of 438,063 square kilometers, Alberta is geographically situated between 55 and 60 degrees north latitude and shares its border with the Northwest Territories (Stralberg et al 2018).This study specifically investigated two significant wildfire events: the Slave Lake wildfire, which occurred from May 15, 2011, to May 22, 2011(Government of Canada 2023), and the Fort McMurray wildfire, which took place from April 30, 2016, to June 1, 2016 (Government of Canada 2023).For reference, figure 1 provides a visual representation of these two regions of interest.

Data
The weather data for this study were collected from two different sources.The Township Data Viewer website of the Agriculture and Irrigation Department (Goverment of Alberta 2020a) was the first source, which provided interpolated daily average relative humidity (%) and wind speed (m/s) for each township in the region.The second source was the Current and Historical Alberta Weather Station Data Viewer website of the Agriculture and Irrigation Department (Government of Alberta 2020b), which provided daily average wind speed (m/s) and wind direction (degrees) for each township.
The research incorporated various remote sensing datasets, including Land Surface Temperature (LST), and Land Use/Land Cover.Specifically, the study utilized the Moderate Resolution Imaging Spectroradiometer (MODIS) products, which consisted of MODIS LST-Day (MOD11A2, v061), MODIS LST-Night (MOD11A2, v061), MODIS Land Cover Type-1 (LULC) (MCD12Q1, V061), and MODIS Burned Area Monthly Global (MCD64A1, v061).The spatial resolution of the daily MODIS LST-Day/Night dataset used in the study was 1km (Wan et al 2006).In contrast, the spatial resolution of the remaining datasets, MCD64A1 (Giglio et al 2018) and MCD12Q1 (Sulla-Menashe and Friedl 2018), was 500 m.To ensure the accuracy and reliability of the results, several preprocessing steps were undertaken.Cloudy pixels, which could introduce inaccuracies, were effectively identified and masked out using the pixel quality band provided within the MODIS data product.
Additionally, the Canadian Digital Elevation Model (CDEM) was utilized to calculate the slope (Government of Canada 2023).This dataset, part of Natural Resources Canada's (NRCan) altimetry system, supplied elevation information that contributed to the fire spread modeling.All MODIS products were obtained from the Google Earth Engine (GEE) platform.The starting points for each wildfire were derived from the Government of Alberta datasets (Government of Alberta 2024).These initial points were then slightly adjusted to align with the MODIS Burned Area Monthly Global dataset, MCD64A1.

Data preparation
Using the coordinates of township centers, each daily climate variable weather dataset was converted into geoimages.A framework that is accessible as follows was used to process these geo-images and remote sensing data further:  (c) Upscaling: By employing splines, the resolution of each 3D matrix was enhanced, thereby ensuring that every one of the 60 slices within the matrix could accommodate data with a spatial resolution of 100 meters.
(d) Final separation: Each enhanced 3D matrix was divided into 60 geo-images, where each image corresponded to a specific time step and possessed a spatial resolution of 100 meters.
Figure 2 visually represents the step-by-step process described above, depicting the transformation of data from the initial stage to the resulting separated geo-images, each with a 100-meter resolution.

Forest fire spread model
The intrinsic feature of Cellular Automata (CA), termed 'locality,' signifies that the state update of each cell depends on the conditions of its neighboring cells.This characteristic aligns effectively with forest fire systems (Rui et al 2018).CA consists of four components: X represents the multi-dimensional space of the CA, where each cell possesses properties denoted as X = (x 1 , x 2 ,K,x m ), with m indicating the dimension of the cell space.S denotes a finite set of states, allowing each cell to be in only one state at any given time.N defines the neighborhood template for each cell, such as Moore or Von Neumann neighbors (Wolnik et al 2017).f represents the state transition function, which can be deterministic or probabilistic based on the neighboring cells.The fundamental essence of the entire system lies within the state transition rules, denoted as where t k+1 = t k + Δt = L = t 0 + kΔt.These parameters capture various aspects of a forest fire, including factors like the rate of spread, flame length, direction, intensity, and duration.These characteristics are influenced by local factors such as vegetation type, humidity, heat, terrain, wind speed, and more.By describing a system as interactions among numerous local cells, the CA approach effectively models complex global behaviors.Additionally, the CA space can seamlessly integrate with GIS data that represents diverse environmental conditions and fuel properties, facilitating their inclusion in the simulation.Moreover, the model can incorporate other empirical equations or rules (Sun et al 2012, Rui et al 2018).
R 0 is a crucial parameter in fire dynamics, representing the initial rate of fire spread when there is no wind and the fuel conditions are spatially uniform.It measures the flammability of fine fuel particles under various scenarios.The fuel bed's physical and chemical properties, closely tied to vegetation type, arrangement, and fuel moisture, significantly influence the rate of initial fire spread.Both direct and indirect effects of these factors impact R 0 .For dead fuel, environmental conditions like air temperature, wind speed, relative humidity, and precipitation mainly influence its moisture content, which, in turn, correlates strongly with R 0 and fire combustion intensity.In contrast, the moisture content of live fuel (from forests or herbaceous plants) is less affected by external conditions since it is regulated by biological processes and seasonal changes.During simulation, the moisture content of live fuel remains constant unless manually adjusted.The proposed method incorporates fuel moisture's impact on the initial fire spread rate (R 0 ) in the Wang Zhengfei model (Wang 1992), which characterizes the rate of fire spread in a fuel field with homogeneous conditions, excluding wind and topography effects (Sun et al 2012).R 0 can be calculated as follows, , 1 0 where • The constant values used in this study were obtained from (Wang 1992).Specifically, these constants are as follows: a = 0.03, b = 0.05, c = 0.01, and d = 0.3.
• T represents the temperature measured in degrees Celsius.Specifically, in our case, it refers to the LST Day/ Night values.
• The wind level, denoted as W, is calculated using the formula ( ) = W v Int 0.836 2 3 .Here, v represents the wind speed in meters per second (m/s), and Int denotes rounding to the nearest integer value.
• RH represents the relative humidity, and it is expressed as a percentage.
The Rate of Spread (ROS) equation within the Wang Zhengfei model (Wang 1992) is a result of extensive field experiments and comprehensive statistical analysis of historical fire observations (Sun et al 2012).This equation takes into account various factors such as wind, slope, and the spatial distribution of forest fuel.By considering these influences, the model formulates the one-dimensional ROS of the fire front, both in the downwind and upslope directions.The time correction coefficient K r was introduced by Rui et al (2018) to enhance the alignment between simulated and actual time.This version of the Wang Zhengfei model coefficient is available as follows (Rui et al 2018): where R 0 was defined in (1), and cos , which accounts for the impact of wind on fire spread, considering the angle j between the wind direction and fire spread direction.
, which incorporates the effect of slope, where θ represents the slope and g indicates the direction of the hill (1 for uphill, -1 for downhill) (Rui et al 2018).
• Combustible index, K s , represents the flammability of the vegetation present in the specified region which is available from table 1.The compilation of this table involved utilizing the fuel types from the Canadian Fire Behavior Prediction (FBP) system (Taylor and Alexander 2018, Wotton et al 2009), along with the original combustible index data obtained from the Zhengfei velocity model (Wang 1992).The allocation of fuel types was determined by factors such as vegetation type, tree species, crown closure, stand height, and various other characteristics.
• K r is a time correction coefficient that was introduced to ensure better alignment between simulated fire spread and actual fire behavior.K r is adjusted based on differences in time and location between the simulated and actual fires.If the simulated fire occurs earlier, K r is reduced; if the actual fire occurs earlier, K r is increased.
To implement our forest fire spread cellular automaton algorithm, we utilize a 100-meter grid image of the study area as the cell space.This choice aligns with the resolution commonly found in publicly downloadable remote sensing data.Each pixel in the grid denotes a specific cell state, which can be categorized as follows: In the simulation of forest fire propagation, a cellular automaton proves to be a highly effective method.The approach entails the application of a rule by which neighboring cells, capable of being ignited, transition to a state of 2 when they are adjacent to a burning cell.This rule serves to facilitate the comprehensive modeling of fire spread throughout the entire forest (Wang 1992, Mao 1993, Sun et al 2012, Rui et al 2018).The simulation is advanced discretely, permitting the determination of the fire's state at a subsequent time t k+1 = t k + Δt, relying on the fire's state at the preceding time t k and a constant time increment Δt.
1 1 1 , D = t mL R max with (m < 1), t k = t 0 + kΔt, J T represents the transpose of row matrix J, m is the step size factor which determines how fast the algorithm can simulate (Rui et al 2018), L = 100 represents the cell size, and R max signifies the maximum value of R. The forest fire spread model can be summarized in figure 3.

Accuracy metrics
The evaluation of the model's performance encompassed the application of several key accuracy metrics, namely precision, recall, F1-score, and overall accuracy (Powers 2011, Dastour et al 2022, Dastour and Hassan 2023).These metrics are expounded upon below:

TP TN TP FN FP TN Overall Accuracy
, 8 where True Positives (TP) refer to the number of instances correctly predicted as 'Unburned', while True Negatives (TN) represent the number of instances correctly predicted as 'Burned'.The initial fire spread rate for both wildfires was calculated using datasets for modeling, LST Day, wind speed, and relative humidity from the first day of each wildfire.These datasets were prepared in accordance with the methodology explained in section 2.3.1.1 1 1 , and J T denotes the transpose of the row matrix J.The symbol θ represents the slope, while g signifies the direction of the hill, with a value of 1 denoting uphill and -1 denoting downhill.

Results
The simulation of the forest fire spread for each wildfire was performed based on these datasets using the adapted Wang Zhengfei model.In our experiments, the minimal influence of m was observed when the spatial resolution of 100 m was considered; however, a slightly better alignment with the true values was observed when using a smaller value for m, as opposed to a larger one (e.g., 0.99).These results were found to be consistent with the findings of Rui et al (2018).For the Slave Lake wildfire, which took place from May 15, 2011, to May 22, 2011, a time correction coefficient of K r = 0.1 was employed to adjust the model's calculations and account for specific characteristics of that wildfire.On the other hand, the Fort McMurray wildfire, occurring between April 30, 2016, and June 1, 2016, required a different time correction coefficient of K r = 0.001 to accommodate the unique fire spread dynamics observed during that event.
For the 2011 Slave Lake wildfire, the propagation dynamics of the wildfire were simulated using two starting point points throughout the entire period.With regard to the 2016 Fort McMurray wildfire, the initial 16-day duration was divided into three modeling phases.The first model encompasses the period extending from the ignition of the wildfire until Day 3. The second model encapsulates the temporal span from Day 3 to Day 6, while the third model encompasses the interval spanning Day 6 to Day 16.In the context of the first model, a singular initial point was utilized to replicate the propagation dynamics of the wildfire.Conversely, for the subsequent two models, the antecedent wildfire stage was utilized as the initial condition.For instance, in the case of the model simulating the evolution of the wildfire from Day 3 to Day 6, the commencement state was delineated based on the actual status of the wildfire as of Day 3.
Figure 4  Figure 5 presents confusion matrices corresponding to the four panels of figure 4.These matrices offer an evaluation of the forest fire spread models by showcasing the interplay between predicted and actual values of burned and unburned pixels: In the case of the 2011 Slave Lake wildfire (figure 4(a)), the fire spread model exhibited inaccuracies in simulating the spread in areas where the fire needed to transition from lower to higher elevations.Specifically, the regions situated in the southwest of both starting points, which are at higher elevations, were not reached by the simulations, indicating a potential limitation in the model's capability to capture fire propagation under such terrain conditions.Furthermore, from figure 1, it was observed that the fire spread was relatively lower in areas characterized by low vegetation density, such as Woody Savannas and Savannas.These regions, with sparse vegetation cover, experienced less extensive fire propagation in comparison to areas with denser vegetation.In table 2(a), insights into the 2011 Slave Lake wildfire spread model's performance were provided.The 'Unburned' class precision at 0.995 showed accurate unburned area classification, while the 'Burned' class precision at 0.474 was lower.This aligned with figure 5(a)ʼs confusion matrix, indicating accurate unburned predictions but fewer true positives (6145) and more false positives (6274) for burned instances.The 'Burned' class had a recall of 0.668, capturing 66.8% of actual burned areas, with an F1-score of 0.555 balancing precision and recall.Using macro averaging to calculate the average performance across all classes yielded an F1-score of 0.774.However, considering the imbalanced class proportions, with 708,826 pixels (98.67% of the total) classified as 'Unburned' and 11,794 pixels (1.33% of the total) as 'Burned', the weighted average metrics resulted in a precision of 0.989, a recall of 0.986, and an F1-score of 0.987.
The assessment of the 2016 Fort McMurray wildfire, spanning from ignition to Day 3, was detailed in table 2 (b), providing valuable insights into the model's performance during this initial phase.Notably, precision values for the 'Unburned' class reached 0.999, showcasing accurate unburned area categorization.However, the 'Burned' class precision achieved a comparatively lower value of 0.316.This alignment with figure 5(b)ʼs confusion matrix underscored the model's precision in predicting unburned cases, while also revealing fewer true positives (6,145) and more false positives (6,274) for burned instances.The macro-averaged F1-score for this experiment achieved a value of 0.673.Addressing the imbalanced class distribution, with 2,639,365 pixels (99.80% of the total) classified as 'Unburned' and 5,335 pixels (0.20% of the total) as 'Burned,' the weighted average metrics resulted in a unified precision, recall, and F1-score of 0.997.Extending the analysis to the period from Day 3 to Day 6 of the 2016 Fort McMurray wildfire, as highlighted in table 2(c), the 'Unburned' class precision was 0.980 while the 'Burned' class precision was 0.460.This concurred with figure 5(c)ʼs confusion matrix, showcasing accurate unburned predictions but highlighting fewer true positives (88,379) and more false positives (103,836) for burned instances.The 'Burned' class exhibited a recall of 0.645, capturing 64.5% of actual burned areas, while maintaining an F1-score of 0.537 to balance precision and recall.The experiment yielded a macro-averaged F1-score of 0.753.Accounting for the imbalanced class proportions, encompassing 2,502,393 pixels (94.81% of the total) categorized as 'Unburned' and 136,972 pixels (5.19% of the total) as 'Burned,' the weighted average metrics yielded a precision of 0.953, a recall of 0.942, and an F1-score of 0.947.Subsequently, evaluating the model's performance during the later phase of Day 6 to Day 16 of the 2016 Fort McMurray wildfire, as portrayed in table 2(d), encompassing 2,289,100 pixels (86.55% of the total) categorized as 'Unburned' and 213,293 pixels (8.06% of the total) as 'Burned,' the weighted average metrics yielded a precision of 0.924, a recall of 0.861, and an F1-score of 0.883.The macro-average F1-score for this experiment was 0.704 Subsequently, an evaluation of the model's performance during the later phase, spanning from Day 6 to Day 16 of the 2016 Fort McMurray wildfire, is presented in table 2(d).The macro-averaged F1-score for this experiment was 0.704.This phase encompassed 2,289,100 pixels, constituting 86.55% of the total, categorized as 'Unburned,' and 213,293 pixels, making up 8.06% of the total, categorized as 'Burned.'The weighted average metrics in this context yielded a precision of 0.924, a recall of 0.861, and an F1-score of 0.883.climate data.However, certain limitations were identified upon closer analysis of the results.In the simulation of fire spread for the 2011 Slave Lake wildfire, inaccuracies were observed in areas necessitating elevation transitions, particularly in the southwest regions characterized by higher elevations.Furthermore, regions with lower vegetation density, such as Woody Savannas and Savannas, exhibited less extensive fire spread compared to areas with denser vegetation.
In the context of the 2016 Fort McMurray wildfire, the model was employed to simulate the wildfire's behavior over terrain characterized by a relatively consistent topography, which differed from the earlier simulation.Furthermore, the analysis of the wildfire's initial 16 days was divided into three phases: from Ignition to Day 3, the subsequent phase from Day 3 to Day 6, and the final phase spanning Day 6 to Day 16.In the context of simulating the propagation of wildfires during these periods, it is advisable to carefully examine observations pertaining to regions marked by low vegetation density for possible inaccuracies.Notably, there were areas on both the northwest side and the east side (proximate to Gordon Lake) of the region where the simulation may not be capable of predicting the extent of potential wildfire propagation due to the presence of low-density vegetation between the active wildfire and the unburned zones.Moreover, several small areas on the northeast side of the map, which were identified as burned areas in the MODIS data, could not be predicted by the model potentially due to their coverage by Savannas and their greater distance from the main wildfire.
Breaking down the simulation of a wildfire into several phases, each built upon the actual values from the preceding phase could offer several advantages that can significantly enhance accuracy compared to simulating the entire period solely from a few initial starting points.In our experiment, dividing the simulation into three phases offered a more nuanced portrayal of the wildfire's evolving dynamics.Wildfires are inherently dynamic, influenced by fluctuating weather conditions, topographical features, and firefighting strategies.By segmenting the simulation, the model can become more adaptable to these evolving factors, allowing it to capture the distinct phases of fire spread more accurately.This continuity in the simulation strengthens the model's capacity to mirror the true progression of the fire as it unfolds over time, and it facilitates the integration of near real-time data and live observations for practical applications.
The limited availability of data, particularly in relation to critical environmental factors such as temperature, wind speed, and relative humidity, presented a notable challenge in striving for forest fire spread modeling.These variables carried significant importance in influencing fire behavior and intensity, rendering them essential inputs for precise prediction models.Through the methodology described in this article, it was possible to interpolate the necessary datasets at a resolution of 100 meters.The interpolation process, it can be argued, played a crucial role, as it potentially facilitated the integration of the forest fire spread model for the region of interest.Additionally, the presented forest fire spread model as presented might yield valuable insights and could serve as a supportive tool in wildfire management decision-making.However, it is important to acknowledge that this model may have inherent limitations in terms of its ability to account for real-time firefighting interventions or the influence of natural events.Such factors could potentially lead to disparities between projected and observed outcomes during wildfire events.Natural occurrences like precipitation and firefighting strategies involving the application of fire retardants, water, and the creation of firebreaks might potentially alter fire behavior by reducing fuel availability and impeding fire advancement.Consequently, there exists the possibility that actual fire behavior might differ from the predictions generated by the model.

Conclusion
The simulations of two significant wildfires, the 2011 Slave Lake wildfire and the initial 16 days of the 2016 Fort McMurray wildfire, using a forest fire spread model, have provided valuable insights into the complex dynamics of wildfire propagation.The utilization of various physical characteristics, including slope, land cover, land use, remote sensing, and climate data, contributed to the simulated models.In the context of the 2011 Slave Lake wildfire simulation, precision, recall, and F1-score achieved weighted averages of 0.989, 0.986, and 0.987.Additionally, macro-average scores for precision, recall, and F1-score, computed across the 'Burned' and 'Unburned' classes, were 0.735, 0.829, and 0.774, respectively.
Inaccuracies in predictions of fire spread were observed in regions with elevation transitions, particularly in the southwest areas with higher elevations.Moreover, regions exhibiting lower vegetation density demonstrated comparatively constrained simulated fire spread in contrast to areas with denser vegetation.These factors collectively contributed to the observed inaccuracies.The simulation of the 2016 Fort McMurray wildfire provided a comprehension of fire dynamics throughout its initial 16-day progression.Conducting a phased analysis, where the period is divided into Ignition to Day 3, Day 3 to Day 6, and Day 6 to Day 16, the resulting average values (across these three phases) for weighted average precision, recall, and F1-scores were 0.958, 0.933, and 0.942, respectively.Additionally, the average of macro-averaged scores across these three phases stood at 0.681, 0.772, and 0.710 for precision, recall, and F1-scores, respectively.Areas marked by low vegetation density presented hurdles for precise predictions, particularly along the peripheries of the northwest, east, and northeast sectors.The approach of segmenting the simulation into phases, building upon actual values from preceding phases, could be beneficial in capturing the evolving dynamics of wildfires.By incorporating real-time data and live observations, this methodology can enhance accuracy and adaptability to fluctuating conditions.
This study contributes to our understanding of wildfire dynamics and propagation.We recognize that refining such models remains an ongoing endeavor.The foundation laid by this research offers a roadmap for enhancing our predictive capabilities, even in the face of challenges arising from limited data availability and the ever-changing nature of wildfires.As we strive to manage and mitigate the impact of these natural phenomena, the insights gleaned here will undoubtedly guide future advancements in wildfire prediction and management strategies.

Figure 1 .
Figure 1.Study region: (a) the map of Canada displays the locations of two wildfires examined in this study, (b) the Fort McMurray wildfire, occurring between April 30, 2016, and June 1, 2016, and (c) the Slave Lake wildfire, which took place from May 15, 2011, to May 22, 2011.The background images for both parts (b) and (c) were created using the MCD12Q1.061MODIS Land Cover Type Yearly Global 500 m Type-1.Part (b) shows the land cover for the year 2016, while part (c) corresponds to the year 2011.

( a )
Initial data acquisition: A dataset of 60 matrices was compiled, encompassing 30 images that were acquired or generated using climate data prior to the initiation of the wildfire, and an additional 30 images acquired or generated after the wildfire had commenced.The datasets had a daily temporal resolution.(b) Imputation of missing values: From the set of 60 two-dimensional matrices, a three-dimensional matrix was formed.Prior to upscaling, the missing values within the dataset were handled using 1D and 2D splines (Truong and Sarfraz 2018) in both the spatial xy direction and the temporal direction.The temporal direction pertains to a 1D array consisting of 60 elements, aligning with the 60 matrices present in the dataset.

Figure 2 .
Figure 2. Framework designed for the imputation of missing values and upscaling of geo-images.(a) Initial Data Acquisition, (b) Imputation of Missing Values, (c) Upscaling, and (d) Final Separation.In part (a), missing data points are indicated by red cells.
positives (TP) by the sum of true positives and false positives (FP).It focuses on the quality of positive predictions.Recall, also referred to as sensitivity or true positive rate, assesses the coverage of positive samples for a particular class.It is calculated by dividing the true positives by the sum of true positives and false negatives (FN).Recall emphasizes the model's ability to capture positive samples.The F1-score combines precision and recall using the harmonic mean, providing a balanced measure that considers the trade-off between them.It is particularly valuable when dealing with imbalanced positive and negative samples.Overall accuracy evaluates the proportion of correctly classified samples across all classes.It takes into account true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN).Macro average calculates the average performance across all classes, assigning equal weight to each class.It computes the mean precision, recall, and F1-score across all classes.Weighted average calculates the average performance across all classes, considering the support (number of samples) for each class.It computes the weighted mean precision, recall, and F1-score based on the support of each class (Powers 2011, Dastour et al 2022, Dastour and Hassan 2023).The accuracy test for the forest fire spread model of the 2011 Slave Lake wildfire involved the utilization of May 2011 data from the MODIS Burned Area Monthly Global dataset.Likewise, for the forest fire spread model of the 2016 Fort McMurray wildfire, the accuracy test employed May 2016 data from the MODIS Burned Area Monthly Global dataset.In the case of the forest fire spread model for the 2016 Fort McMurray wildfire, the accuracy test only considered the burned pixels during the initial 16 days of May 2016 as the true values.On the contrary, for the forest fire spread model of the 2011 Slave Lake wildfire, all burned pixels from the entire month of May 2011 were used as the true values.These burned pixels served as the reference data for evaluating the accuracy of the model.

Figure 3 .
Figure3.The forest fire spread model utilized in this investigation is hereby summarized.The rate of fire spread R is calculated based on several factors, including the initial fire spread rate R 0 , the wind coefficient K j , the terrain factor K θ , the Combustible index K s , and the time correction coefficient K r .Within this context, the vector [ ] = J 1 1 1 , and J T denotes the transpose of the row matrix J.The symbol θ represents the slope, while g signifies the direction of the hill, with a value of 1 denoting uphill and -1 denoting downhill.
presents a visual comparison between real observations and model predictions for pixels affected by fire (burned) and those unaffected (unburned).The figure is divided into four panels: (a) showcasing the 2011 Slave Lake wildfire, (b) depicting the initial stage of the 2016 Fort McMurray wildfire (from Ignition to Day 3), (c) illustrating the subsequent stage of the 2016 Fort McMurray wildfire (from Day 3 to Day 6), and (d) representing the final stage of the 2016 Fort McMurray wildfire (from Day 6 to Day 16).
(a) the 2011 Slave Lake wildfire; (b) the initiation phase of the 2016 Fort McMurray wildfire (Ignition to Day 3); (c) the subsequent phase of the 2016 Fort McMurray wildfire (Day 3 to Day 6); and (d) the concluding phase of the 2016 Fort McMurray wildfire (Day 6 to Day 16).Table 2 presents classification reports, providing an overview of precision, recall, F1-score, and support metrics for the 'UnBurned' and 'Burned' classes, which align with the four panels depicted in figure 4. Additionally, it includes overall accuracy, macro average, and weighted average measures.The breakdown of the table is as follows: a classification report for (a) the 2011 Slave Lake wildfire; (b) the initial phase of the 2016 Fort McMurray wildfire (from Ignition to Day 3); (c) the subsequent phase of the 2016 Fort McMurray wildfire (from Day 3 to Day 6); and (d) the conclusive phase of the 2016 Fort McMurray wildfire (from Day 6 to Day 16).The metrics within the classification report closely correspond to the respective confusion matrices displayed in figure 5, offering insights into the performance of the forest fire spread models throughout the 2011 Slave Lake wildfire and the three temporal stages of the 2016 Fort McMurray wildfire.

Figure 4 .
Figure 4.The forest fire propagation model was employed to simulate the 2011 Slave Lake wildfire and the first days of the 2016 Fort McMurray wildfire.The simulation outcomes are depicted in Panels (a)-(d), which provide a visual comparison between the actual observations and the model's predictions for burned and unburned pixels: (a) the 2011 Slave Lake wildfire; (b) the initial phase of the 2016 Fort McMurray wildfire (Ignition to Day 3); (c) the subsequent phase of the 2016 Fort McMurray wildfire (Day 3 to Day 6); and (d) the final phase of the 2016 Fort McMurray wildfire (Day 6 to Day 16).The initiation points in Panels (a) and (b) are denoted by white circles, while Panels (c) and (d) represent the wildfire's initial state on Day 3 and Day 6 respectively, using a blue color scheme.The background was generated utilizing the CDEM.

Table 1 .
Fuel void space and coefficient of fuel arrangement influenced by K s .
Conversely, False Negatives (FN) indicate the number of 'Unburned' instances that were incorrectly classified as 'Burned,' and False Positives (FP) indicate the number of 'Burned' instances that were erroneously identified as 'Unburned' (Powers 2011, Dastour et al 2022, Dastour and Hassan 2023).The results section presents a table summarizing the accuracy metrics discussed earlier.Precision, a performance measure, evaluates the accuracy of positive predictions for a specific class by dividing the true