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Article Type:
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Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts

Bryan Shaddy aDepartment of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California

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Deep Ray aDepartment of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California
bDepartment of Mathematics, University of Maryland, College Park, College Park, Maryland

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Angel Farguell cDepartment of Meteorology and Climate Science, San Jose State University, San Jose, California

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Valentina Calaza aDepartment of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California

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Jan Mandel dDepartment of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, Colorado

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James Haley eCooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

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Kyle Hilburn eCooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

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Derek V. Mallia fDepartment of Atmospheric Sciences, University of Utah, Salt Lake City, Utah

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Adam Kochanski cDepartment of Meteorology and Climate Science, San Jose State University, San Jose, California

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Assad Oberai aDepartment of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California

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Online Publication:
31 Jul 2024
Print Publication:
01 Jul 2024
DOI:
https://doi.org/10.1175/AIES-D-23-0087.1
Open access
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Abstract

Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in using satellites to detect fire locations further provides the opportunity to use measurements toward improving fire spread forecasts from numerical models through data assimilation. This work develops a physics-informed approach for inferring the history of a wildfire from satellite measurements, providing the necessary information to initialize coupled atmosphere–wildfire models from a measured wildfire state. The fire arrival time, which is the time the fire reaches a given spatial location, acts as a succinct representation of the history of a wildfire. In this work, a conditional Wasserstein generative adversarial network (cWGAN), trained with WRF–SFIRE simulations, is used to infer the fire arrival time from satellite active fire data. The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections. Samples produced by the cWGAN are further used to assess the uncertainty of predictions. The cWGAN is tested on four California wildfires occurring between 2020 and 2022, and predictions for fire extent are compared against high-resolution airborne infrared measurements. Further, the predicted ignition times are compared with reported ignition times. An average Sørensen’s coefficient of 0.81 for the fire perimeters and an average ignition time difference of 32 min suggest that the method is highly accurate.

Significance Statement

To initialize coupled atmosphere–wildfire simulations in a physically consistent way based on satellite measurements of active fire locations, it is critical to ensure the state of the fire and atmosphere aligns at the start of the forecast. If known, the history of a wildfire may be used to develop an atmospheric state matching the wildfire state determined from satellite data in a process known as spinup. In this paper, we present a novel method for inferring the early stage history of a wildfire based on satellite active fire measurements. Here, inference of the fire history is performed in a probabilistic sense and physics is further incorporated through the use of training data derived from a coupled atmosphere–wildfire model.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Bryan Shaddy, bshaddy@usc.edu

Abstract

Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in using satellites to detect fire locations further provides the opportunity to use measurements toward improving fire spread forecasts from numerical models through data assimilation. This work develops a physics-informed approach for inferring the history of a wildfire from satellite measurements, providing the necessary information to initialize coupled atmosphere–wildfire models from a measured wildfire state. The fire arrival time, which is the time the fire reaches a given spatial location, acts as a succinct representation of the history of a wildfire. In this work, a conditional Wasserstein generative adversarial network (cWGAN), trained with WRF–SFIRE simulations, is used to infer the fire arrival time from satellite active fire data. The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections. Samples produced by the cWGAN are further used to assess the uncertainty of predictions. The cWGAN is tested on four California wildfires occurring between 2020 and 2022, and predictions for fire extent are compared against high-resolution airborne infrared measurements. Further, the predicted ignition times are compared with reported ignition times. An average Sørensen’s coefficient of 0.81 for the fire perimeters and an average ignition time difference of 32 min suggest that the method is highly accurate.

Significance Statement

To initialize coupled atmosphere–wildfire simulations in a physically consistent way based on satellite measurements of active fire locations, it is critical to ensure the state of the fire and atmosphere aligns at the start of the forecast. If known, the history of a wildfire may be used to develop an atmospheric state matching the wildfire state determined from satellite data in a process known as spinup. In this paper, we present a novel method for inferring the early stage history of a wildfire based on satellite active fire measurements. Here, inference of the fire history is performed in a probabilistic sense and physics is further incorporated through the use of training data derived from a coupled atmosphere–wildfire model.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Bryan Shaddy, bshaddy@usc.edu
Keywords: Wildfires; Coupled models; Data assimilation; Model initialization; Bayesian methods; Deep learning

1. Introduction

Recent decades have seen increases in both wildfire frequency and severity, with parts of the western United States being some of the most impacted (Westerling et al. 2006; Dennison et al. 2014). The increase in wildfire activity is believed to be tied to global warming, with climate predictions for North America’s West Coast indicating wetter winters, drier summers, and more heat in years to come, leading to conditions conducive to large wildfires (Williams et al. 2019; Liu et al. 2010). Wildfires impact air quality, cause damage through the destruction of property and harm to health, and negatively influence atmospheric composition (Jaffe et al. 2008; Wang et al. 2021; Aguilera et al. 2021; Solomon et al. 2022). With current trends expected to continue, it is important to further the advancement of wildfire prediction models to accurately forecast wildfire spread and resulting smoke dispersion.

As climate change drives wildfires to grow larger and more intense, their interactions with the atmosphere are becoming ever more important in understanding their behavior. Large wildfires have been observed to create their own weather through strong convective updrafts resulting from the immense heat released to the atmosphere (Lareau and Clements 2017; Lareau et al. 2018). These modifications to local meteorology then feed back into the spread of the fire through the important two-way atmosphere–wildfire coupling. The importance of wildfire–atmosphere interactions has led to the development of a new generation of wildfire–atmosphere models which aim to capture these critical interactions (Bakhshaii and Johnson 2019). State-of-the-art wildfire models have also benefited from advancements in computational power, which has made it possible to run wildfire simulations with high resolution in operational settings (Kochanski et al. 2013; Jiménez et al. 2018; Mandel et al. 2019). However, issues of accumulated model errors leading to degraded forecasts still remain. Consequently, there is an interest in assimilating data from new measurement platforms into wildfire forecasts to address these issues and to allow for the use of wildfire models to accurately forecast fire spread in an operational setting.

Remote sensing capabilities have similarly advanced in recent decades. In the context of monitoring wildfire spread, there are typically two main sources of measurement data, which include airborne infrared (IR) fire extent perimeters and satellite-based active fire (AF) products. Airborne IR fire perimeters are provided through the National Infrared Operations (NIROPS) program and are generally considered to be highly spatially accurate representations of fire extent at the time of measurement (Greenfield et al. 2003). However, these measurements are typically made once a day and delays in their public availability hinder their use as a basis for data assimilation in an operational setting. Measurement of IR perimeters may also be impacted by weather or resource availability. AF satellite data products on the other hand can provide the location of actively burning regions with a higher temporal frequency of around 12 h per each low-Earth-orbiting satellite, dependent on fire location. Some of the most prevalent AF data products are provided by thermal imaging sensors onboard polar-orbiting satellites including the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Terra and Aqua satellites and the Visible Infrared Imaging Radiometer Suite (VIIRS) on board the Suomi NPP and NOAA-20 satellites. These systems provide AF detections with resolutions between 375 m and 1 km. However, even these spatiotemporal resolutions are not sufficient to directly incorporate AF data into current wildfire spread models (Schroeder and Giglio 2016; Giglio et al. 2016). Furthermore, these measurements can have artifacts from sun glint, clouds, or topography. While AF satellite data products cannot be directly used in wildfire spread models, they are a useful source for input to data assimilation algorithms which use these products and simulations from wildfire spread models to infer or initialize the state of a wildfire.

For a dynamic coupled atmosphere–wildfire spread model, the state of the system is represented by all the wildfire and atmosphere variables in the simulation. These include wildfire variables like fire position and fuel availability, in addition to atmosphere variables such as temperature and wind speed. Further, there are two types of equally useful data assimilation procedures that can be applied to these state variables. One involves using new satellite measurements to update the state variables in an ongoing simulation (Mandel et al. 2014a). The other involves using satellite measurements acquired in the initial period of the wildfire (the first 72 h, for example) to determine the initial condition for these state variables, from which a simulation may be started (Farguell et al. 2021). This problem of determining the initial condition of the state variables is the focus of our work.

In Mandel et al. (2012), it was observed that if the precise history of a wildfire during its initial spread was known, then this history could be prescribed within a coupled wildfire–weather model, thereby generating the correct initial state of both the wildfire and atmosphere variables. In other words, this history could be used to spin up the atmosphere with the right amount of heat and mass flux added at the right place and time, yielding the correct atmospheric state which is in sync with the fire state at the end of the initial phase. Thus, it was recognized that the data assimilation problem of determining the initial condition could be transformed to one of determining the history of the fire in the initial period. It was further shown that this history is succinctly represented by the fire arrival time map which contains the precise time the fire arrives at a given location (Mandel et al. 2012, 2014b). With these two key observations, the data assimilation problem reduces to the following: given satellite measurements of active fire made during the initial phase of spread, determine the high-resolution fire arrival time for this period.

Previous methods to solve this problem have used interpolation between airborne infrared fire perimeters to create higher-resolution fire arrival times with some success (Kochanski et al. 2019; Mallia et al. 2020). However, the coarse temporal frequency with which these measurements are made, along with delays in availability, limits the use of this approach in operational settings. Turning to the use of active fire satellite measurements for this data assimilation problem, a number of geospatial interpolation schemes have previously been used (Veraverbeke et al. 2014; Scaduto et al. 2020; Parks 2014). Satellite active fire detection data were utilized in Mandel et al. (2014a) to estimate the fire arrival time by penalizing the difference between the prior obtained from model results and satellite active fire detection pixels; however, this approach did not take the rate of spread into account. It was then considered to minimize the residual of a differential equation model of fire propagation [the eikonal equation ‖∇u‖=1/R, where R = R(u, x, y) is the rate of spread and u is the fire arrival time] subject to constraints derived from data; however, this approach faced numerical difficulties (Farguell Caus et al. 2018). To overcome previous difficulties, in Farguell et al. (2021), a machine learning–based method for estimating fire arrival times was developed. This method uses a support vector machine (SVM) to estimate the fire arrival time based on satellite active fire and clear ground detection pixels. The SVM method works by finding an optimal separation between the fire and no-fire locations in space and time to construct the fire arrival time. While the SVM method has provided good results, it does not incorporate any of the physics inherent to wildfire spread into estimates and further does not provide information about uncertainty, which is desirable when relying on error-prone satellite measurements. The method described in this work addresses both of these limitations.

The point of departure of the method presented in this manuscript is a probabilistic interpretation of the problem. We treat both the measured active fire pixels and the desired fire arrival time field as random vectors. The inference problem we wish to solve is one of quantifying the conditional probability distribution for the fire arrival time conditioned on a given measurement of the active fire pixels. We recognize that the measured fire pixels and the arrival time field are both high-dimensional random vectors, which makes this problem challenging to solve. To address this challenge, we utilize a conditional generative algorithm called the conditional Wasserstein generative adversarial network (cWGAN). A cWGAN relies on the expressivity of a deep neural network and the concept of adversarial loss to learn and then sample from a conditional probability distribution. Its training requires the use of samples from the joint probability distribution of the field to be inferred (fire arrival time) and the measurements (active fire pixels). We generate these by employing WRF–SFIRE to produce physically consistent fire arrival time maps, to which we then apply an approximation of the measurement operator. This approach does not require any satellite measurement data to train the network and allows us to inject the appropriate physics into the inference problem. Once trained, we apply the algorithm retrospectively to four recent wildfires in California and assess its performance by comparing its predictions with IR fire extent perimeters and reported ignition times, which are treated as ground truth. We also include predictions from the SVM-based algorithm for comparison and describe the relative benefits of the two approaches.

The remainder of this manuscript is organized as follows. In section 2, we provide a mathematical formulation for the data assimilation problem. In section 3, we describe the cWGAN algorithm used to solve this problem. In section 4, we apply this algorithm to wildfires and quantify its performance. We end with conclusions and remarks for future work in section 5.

2. Problem formulation

We let τ denote the matrix of fire arrival times whose components τij represent the fire arrival times for the ith pixel along the longitude and the jth pixel along the latitude. We assume that there are Nτ such pixels and therefore τ∈Ωτ⊂RNτ. The size of each pixel is 60 m × 60 m.

A measurement operator M may be applied which transforms τ into a coarse, sparse, and noisy measurement τ¯. That is to say, we may use the mapping M:Ωτ→Ωτ¯, which takes as input the complete and smooth fire arrival time and produces the corresponding measurement τ¯∈Ωτ¯. Since the arrival time and the measurement are defined on the same grid, Ωτ¯=Ωτ. We note that the measurement operator M may easily be approximated to produce the mapping from fire arrival time to active fires satellite measurements (see section 3b for the precise definition); however, here we are interested in the inverse problem, which maps from τ¯ to τ and is much more challenging to solve.

We recognize that a single measurement can correspond to a distribution of likely fire arrival times, and to cope with the ill-posed nature of this problem, we adopt a probabilistic approach. We let the inferred field τ and the measurements τ¯ be modeled by random variables T and T¯, respectively. Following this, we recognize that given a measurement τ¯, we are interested in learning and generating samples from the conditional distribution PT|T¯. We accomplish this through the following steps:

  1. Generate N pairwise samples of arrival times and measurements [τ(i),τ¯(i)],i=1,…,N, sampled from the joint distribution PTT¯. This is accomplished by using WRF–SFIRE (and data augmentation) to generate N instances of arrival times τ(i) and then applying the measurement operator to obtain the corresponding τ¯(i).

  2. Use these data to train the generator and critic subnetworks of a cWGAN.

  3. Use active fire satellite measurements of a wildfire as input to the trained generator to produce samples of the arrival time from the conditional distribution. Further, use these samples to generate statistics of interest, which include the pixelwise mean and standard deviation in arrival time.

In the following section, we provide a brief summary of the cWGAN. The interested reader is referred to Adler and Öktem (2018); Ray et al. (2022, 2023) for further details. Thereafter, in section 3b, we describe the generation of the training data for the cWGAN and the training procedure. Finally, in section 4, we describe the application of the trained cWGAN to four recent wildfires in California.

3. cWGANs

The cWGAN consists of two subnetworks, a generator g and a critic d. The generator g is given by the mapping g:Ωz×Ωτ¯→Ωτ, where z∈Ωz⊂RNz is a latent variable modeled using the random variable Z with distribution PZ. The distribution PZ is selected such that it is easy to sample from, such as a multivariate Gaussian distribution. The critic d is given by the mapping d:Ωτ×Ωτ¯→R.

For a given measurement τ¯, the generator g produces samples τg=g(z,τ¯),z∼PZ, from the learned conditional distribution PT|T¯g(τ|τ¯). The training of the cWGAN requires this distribution to be close to the true conditional distribution PT|T¯(τ|τ¯) in the Wasserstein-1 metric. The cWGAN is trained using the following objective function:
L(d,g)=E(τ,τ¯)∼PTT¯[d(τ,τ¯)]−Eτg∼PT|T¯gτ¯∼PT¯[d(τg,τ¯)].
The optimal generator and critic (g∗ and d∗, respectively) are determined by solving the min–max problem
(d∗,g∗)=arg mingarg maxdL(d,g).
Assuming the critic d is 1-Lipschitz in both its arguments, it is shown in Ray et al. (2023) that the g∗, found by solving the min–max problem given by Eq. (2), can be used to approximate the true conditional distribution. More precisely, for any continuous, bounded function l(τ) defined on Ωτ, and ϵ > 0, we may select a generator with a sufficiently large number of learnable parameters such that
|Eτ∼PT|T¯[l(τ)]−Eτ∼PT|T¯g∗[l(τ)]|<ϵ.
This implies that once the generator has been trained, it may be used to approximate the statistics from the true conditional distribution. In particular,
Eτ∼PT|T¯[l(τ)]≈1K∑i=1Kl{g∗[z(i),τ¯]},z(i)∼PZ.
Following Eq. (4), the pixelwise mean prediction for τ based on a given τ¯ can be computed by setting l(τ)=τ. Similarly, the pixelwise variance may be computed by setting l(τ)=(τ−E[τ])2, which proves useful for quantifying the uncertainty in our prediction.

a. cWGAN architecture

The architectures of the generator and critic used here are based on Ray et al. (2022) and are shown in Fig. 1. The generator g has a U-Net architecture which takes as input the measurement τ¯ and the latent vector z. The latent information is injected into the U-Net at various scales using conditional instance normalization (CIN) (Dumoulin et al. 2016). This allows the latent dimension Nz to be selected independent of Nτ and introduces stochasticity at multiple scales of the U-Net, thereby overcoming the problem of mode collapse which previously required the use of more complicated critic architectures (Ray et al. 2022; Adler and Öktem 2018).

Fig. 1.
Fig. 1.

Architecture of (a) generator and (b) critic used in cWGAN. The downsample, upsample, and dense blocks are described in Fig. 2.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

In the U-Net, the residual blocks used in Ray et al. (2022) are replaced with dense blocks, which have been shown to lead to superior performance while reducing the number of trainable parameters (Huang et al. 2017). Dense blocks are denoted as DB(k, n), where n is the number of subblocks in the dense block and k is the number of output features in all but the last subblock of the dense block. The generator architecture also contains downsampling blocks denoted by Down(p, q, k, n), which coarsen the resolution of inputs by a factor of p and increase the number of channels by a factor of q. The k and n listed for a downsampling block refer to the parameters of the dense block contained as a subblock of the downsampling block. Upsampling blocks are denoted as Up(p, q, k, n), where p is the factor by which resolution is refined and q is the factor by which the number of channels decreases. Again, k and n refer to the dense block included in the upsampling block. Values for k, n, p, and q used in this work are included in the schematic shown in Fig. 1.

The architecture of the critic follows that of Ray et al. (2022), with a relatively simple architecture comprising dense blocks and downsampling blocks, followed by fully connected layers which result in a scalar output. Schematics for the dense blocks, downsample blocks, and upsample blocks used here are provided in Fig. 2, with the corresponding network parameters used for this work, p = 2, q = 2, k = 16, and n = 4, also shown.

Fig. 2.
Fig. 2.

Architecture of (a) downsample block, (b) upsample block, and (c) dense block, with the values p = 2, q = 2, k = 16, and n = 4 used for this work shown.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

b. Training the cWGAN

To train the cWGAN, we begin by drawing samples of τ from the prior marginal distribution PT by performing simulations with the coupled atmosphere–wildfire model WRF–SFIRE. To each instance of τ, an approximation of the measurement operator M is applied to produce a corresponding measurement τ¯=M(τ), producing samples from the conditional density PT¯|T. This yields the pairs [τ(i),τ¯(i)] from the joint distribution PTT¯ which are used to train cWGAN.

The fire arrival times are computed from 20 idealized WRF–SFIRE simulations, each considering a 2-day fire spread over flat terrain with a uniform fuel type of brush. The initial condition used for wind in all simulations consists of a logarithmic profile up to 2 km and constant wind speed above 2 km, with wind prescribed uniformly in one direction. The initial wind profile was maintained, and the wind magnitude 10 m from the surface was varied randomly from a uniform distribution between 0 and 5 m s−1 to produce the 20 simulation results.

The simulations used an atmospheric mesh of size 128 × 128, with a resolution of 300 m, giving a domain size of 38.4 km × 38.4 km. The fire mesh was refined from the atmospheric mesh by a factor of 10, for a mesh size of 1280 × 1280 and a resolution of 30 m, with point ignitions located in the center of the domain. The highest altitude for the atmospheric model was fixed at 4500 m, and the model considered 41 vertical levels, open boundary conditions, and a fixed fuel moisture content of 18%.

The fire arrival time results from the 20 WRF–SFIRE simulations were cropped to a new grid size of 1024 × 1024, on a domain of size 30.72 km × 30.72 km. The fire arrival times were then coarsened from their initial resolution of 30 m to a resolution of 60 m, giving a final grid size of 512 × 512. Cropping and coarsening were done to reduce the size of the input to the cWGAN and consequently reduce the size of network needed for this work. Data augmentation was then performed to increase the total number of fire arrival time maps available for training. Augmentation was done by rotating the fire arrival time maps randomly between 0° and 360° about their center and then translating them within a box of size 9 km × 9 km located at the center of the domain. Each WRF–SFIRE arrival time leads to 500 augmented samples thereby generating a total of 10 000 fire arrival times τ(i). The augmentation of the fire arrival times was enabled by the rotational and translational symmetry of the simulations, which consisted of flat terrain, uniform fuel, uniform initial wind direction, and point ignition.

An approximation to the measurement operator M was applied to the samples of τ(i) to generate the corresponding measurement τ¯(i). The measurement operator was constructed to replicate the high-resolution (375 m) VIIRS Level-2 (L2) AF data in the following steps (see also Fig. 3):

  1. Coarsen τ(i) to a resolution of 375 m using nearest neighbor interpolation.

  2. Create four copies of the coarsened τ(i) and apply a distinct knowledge mask to each to randomly eliminate 50% of the fire arrival time values, setting eliminated pixels to a background value. Denote these by τj(i),j=1,…,4.

  3. Select four measurement times (ti, i = 1, …, 4) from a uniform distribution between 2 and 48 h and sort them in ascending order. Associate each ti with a τj(i).

  4. For each measurement time ti, create a time interval [ti − δ(−), ti] where δ(−) is selected from U(6,12), where U denotes the uniform probability distribution. If ti − δ(−) < 0, set it to 0.

  5. For each τj(i), set fire arrival time pixels falling within the associated time interval [ti − δ(−), ti] to ti. Set the remainder to a background value, to be assigned later.

  6. Combine the four measurements into a single consolidated measurement by selecting τ(i)=min⁡j[τj(i)] for each pixel.

  7. Eliminate three 3 km × 3 km patches with locations selected at random. Set the values in these patches to the background value.

  8. Resample back to the original size of 512 × 512 pixels and let the output measurement be denoted by τ¯(i).

Fig. 3.
Fig. 3.

Stepwise transformation of an input fire arrival time τ into an output measurement τ¯ following the eight steps of the measurement operator M.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

The critical operations for recreating the behavior of VIIRS AF measurements lie in steps 2–7 of the measurement operator algorithm, for which an explanation based on the physical measurement system follows. The overall goal of steps 2–7 of the measurement operator algorithm is to capture the behavior of polar-orbiting satellites wherein for a given location measurements are only taken 2–4 times a day and, in these measurements, areas ignited shortly prior to the measurement can be captured, as can areas ignited hours prior to the measurement that are still burning sufficiently. To achieve this, we begin by creating four copies of the fire arrival time map and applying a unique knowledge mask to each to randomly eliminate 50% of the fire pixels, simulating the sparsity of AF pixels in true VIIRS measurements (step 2). Four random measurement times are then selected, which are intended to simulate the times at which a polar-orbiting satellite might make measurements (step 3). To capture the effects of satellites detecting hotspots which may have ignited some random number of hours prior to when a measurement is made, we assign a measurement time window that begins somewhere between 6 and 12 h prior to the measurement times (step 4). Each copy of the fire arrival time map is then assigned a measurement time window, and any arrival time values falling in that measurement window get assigned the corresponding measurement time, and the other pixels are set to a background value (step 5). This simulates how an area picked up as an AF detection may have been ignited some time prior to when the measurement was made. The four measurements are then combined, taking the smallest arrival time value for each location from the four copies (step 6). Further effects of steps 2–6 are to recreate instances where VIIRS measurements may show an active fire detection that is closer to the ignition location than measurements made earlier in time. This could occur for several reasons, for example, if a cloud covered some part of the fire when an earlier measurement was made, following which another measurement captured fire in this region, leading to later arrival time values being assigned to areas surrounded by earlier arrival time values. Similar occurrences may be caused by terrain. The end result of this is a checkerboard-like pattern in the measurement images, which we often found when processing VIIRS measurements. Finally, step 7 was implemented to emulate the effect of measurement obstruction due to larger static obstacles like terrain features which could affect multiple measurements similarly. The end result of these steps is a measurement which has many of the characteristics we found to be prevalent in the VIIRS AF measurements. Figure 3 provides a visual representation of the effects of each step of the measurement operator, going from an input fire arrival time τ(i) to an output measurement τ¯(i).

Further complexity is added to the data by shifting the values in each arrival time and measurement pair [τ(i),τ¯(i)] by a random amount of time so that ignition no longer occurs at time 0, thus simulating how VIIRS only provides the time fire was detected, as opposed to directly providing an arrival time for which knowledge of the ignition time would be required. This is done by adding δ∈U(0,24)h to the arrival time and measurement pairs [τ(i),τ¯(i)]. Last, [τ(i),τ¯(i)] are normalized to be in the interval [0, 1] by dividing by 72 h, following which the background values are set to 1. The dataset was split, so 8000 samples were used for training and 2000 samples were reserved for validation (selecting optimal hyperparameters). Sample data pairs from the training dataset are shown in Fig. 4.

Fig. 4.
Fig. 4.

Sample data pairs from the training set, with true fire arrival times τ in the first row and corresponding measurements τ¯ in the second row. Here, fire arrival time values represent hours from the start of the day on which ignition occurred.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

The training of the cWGAN was tracked using a mismatch term defined as the mean 2-norm of the difference between samples of the generated fire arrival time τg=g(z,τ¯) and the true fire arrival time τ from the training set. Additional metrics tracked included the approximate Wasserstein-1 distance measured as the difference between the scalar critic outputs for the true and generated input values, τ and τg, in addition to the critic and generator losses. The cWGAN was trained in PyTorch for 200 epochs using a batch size of 5 and the Adam optimizer with a learning rate of 0.001, betas (0.5, 0.9), and a weight decay of 1 × 10−7. During the training process, the loss was observed to drop progressively up through 200 epochs, following which the mismatch term had reached an acceptably low value while also balancing consideration of training time, though the loss curve suggests that further training would result in a lower final mismatch term.

4. Results

In this section, we validate the cWGAN fire arrival time predictions for four retrospective California wildfires. Comparisons are made against high-resolution fire extent perimeters and reported ignition times. Further comparisons are made with the SVM method described in Farguell et al. (2021).

a. Test cases

The criteria for selecting wildfires for validation are as follows:

  1. Sufficient VIIRS AF measurements (for input) and at least one fire extent measurement (for validation), both within the first 48 h of the wildfire ignition.

  2. Wildfires whose extent does not exceed the domain size considered in the training data.

Following these considerations, four fires are selected for validation: Bobcat, Tennant, Oak, and Mineral. These fires occurred in California between the years 2020 and 2022. It is worth noting that while the training data for the cWGAN considered flat terrain only, this was not a requirement for the fires selected for validation. Additional information about these fires is presented in Table 1.

Table 1.

Wildfire test cases examined using cWGAN approach. For each fire, start date (UTC), approximate ignition time (UTC), approximate initial location, fire perimeter day (UTC), and fire perimeter time (UTC) are listed. Ignition times for Tennant, Oak, and Mineral are gathered from CAL FIRE reports. Ignition time for Bobcat is unavailable from CAL FIRE and has been gathered from news reports and is not used for evaluating performance.
Table 1.

b. Active fire satellite measurements

The 375-m L2 Active Fire Version 1 (Collection 1) data product from the VIIRS system on board the Suomi NPP satellite is utilized. This data product, referred to as VNP14IMG, provides day and night fire detections globally using algorithms based on the baseline MODIS product, Thermal Anomalies and Fire. Data come from roughly 6-min orbital segments created from multiple scans using input data from all five 375-m I-channels (I1-I5) and the dual-gain 750-m midinfrared M13 channel of the VIIRS system (Schroeder and Giglio 2016). Detections are provided approximately 2–4 times a day from the Suomi NPP satellite, dependent on geographic position, with locations of active fire detections provided as latitude and longitude coordinates. Confidence information is further provided for each detection, including low, nominal, and high confidence labels. The VNP14IMG data used for this work were collected from the Level-1 and Atmosphere Archive and Distribution System Distributed Active Archive Center (LAADS DAAC) hosted by NASA on 6 March 2023, 5 March 2023, 6 March 2023, and 23 February 2023 for the Bobcat, Tennant, Oak, and Mineral fires, respectively.

To preprocess VIIRS 375-m L2 AF satellite data to be used as input to the cWGAN, a domain of interest with size 30.72 km × 30.72 km which is approximately centered on a desired wildfire is selected. The domain is discretized based on latitude and longitude coordinates, and cells corresponding to AF detection locations are assigned a value based on the measurement time. Values assigned to activated cells are the number of hours since the start of the day on which ignition occurred. The measurements are then normalized using a value of 72 h, following which remaining cells are assigned a background value of 1, putting the measurements in the range [0, 1], following the format of the training data.

Measurements are further separated based on confidence level such that one version contained only high confidence detections and another version contained both high and nominal confidence detections. This results in two measurements τ¯ per fire, on which predictions may be conditioned. This was done for all measurements available within the first 48 h of a fire, being sure to assign the earliest available measurement time for cells that correspond to detections in more than one satellite measurement.

To evaluate available AF data for each of the four test cases, the preprocessed and geolocated measurements τ¯ are examined relative to available IR fire extent perimeters. Shown in Fig. 5 are two measurements τ¯ per fire, corresponding to the two confidence intervals. For each fire, one fire extent measurement made within the first 48 h after ignition is overlaid on the measurement images for comparison. The times of the perimeter measurements are indicated in the plot labels of Fig. 5 in hours and minutes (HH:MM) format from the start of ignition day.

Fig. 5.
Fig. 5.

Measurements τ¯ after preprocessing of VIIRS 375-m L2 AF data for the Bobcat, Tennant, Oak, and Mineral fires, in left to right order. The first row contains high confidence detections only, and the second row contains high and nominal confidence detections. AF detection colors indicate the measurement time, taken as the number of hours after the start of the ignition day. IR fire extent perimeters are additionally included, with measurement times listed in plot labels in HH:MM format, again as the number of hours and minutes after the start of ignition day. All measurements are geolocated, with longitude and latitude indicated.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

c. Arrival time predictions and statistics

The two measurements (high and high + nominal confidence) for each fire are used as input to the trained cWGAN. For each measurement, 200 realizations of the arrival time are generated by sampling the latent vector z from its distribution. These realizations are combined with different weights (0.2 for the high confidence and 0.8 for the high + nominal confidence, as empirically determined to be ideal) to compute the pixelwise mean and standard deviation plots of arrival times that are shown in Fig. 6. There are several interesting observations to be made:

  • The mean arrival time plots appear to smooth interpolations of the measurements shown in Fig. 5. They can be used to generate a smooth sequence of fire perimeters to initialize the state variables in a coupled weather/wildfire code like WRF–SFIRE.

  • The standard deviation plots in Fig. 6 provide a measure of uncertainty in the predictions. We observe that in some cases and in some select locations, this uncertainty is as high as 20 h, which implies that the ensemble of predictions used to generate the mean has significant differences in these regions.

Fig. 6.
Fig. 6.

(top) Weighted mean and (bottom) standard deviation of fire arrival time predictions using the cWGAN approach.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

To understand where prediction uncertainty comes from, we have examined the locations of high prediction uncertainty relative to the locations of high and nominal confidence AF detections. Figure 7 shows the pixelwise weighted prediction standard deviation for each of the four fires studied, with nominal confidence AF detections overlaid in pink and high confidence detections overlaid in dark red. We observe that the locations of highest uncertainty correspond to areas with no detections or areas with only nominal confidence detections and no high confidence detections. Instances of this include the western region of the Bobcat fire, the southernmost tip of the Tenant fire, and the southern region of the Mineral fire. These occurrences are to be expected because the uncertainty in the predictions should be larger either where there are no detections or where the detections are expected to have larger error.

Fig. 7.
Fig. 7.

Weighted standard deviation of fire arrival time predictions using the cWGAN approach, with VIIRS nominal confidence AF detections overlaid in pink and high confidence AF detections overlaid in dark red.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

It is also informative to compare the fire arrival time predictions made by the cWGAN method to those produced by the SVM method described in Farguell et al. (2021), which is also designed to predict fire arrival times from AF satellite data. The results from the SVM method, using the same set of 375-m VIIRS L2 AF data from the Suomi NPP satellite, are shown in Fig. 8. We observe that the SVM method produces islands of unburnt regions on the interior of predicted fire extents (see the Bobcat and Mineral fires), while these are absent from the cWGAN predictions. Additionally, it is noted that the SVM method does not provide any measure of uncertainty with its predictions, unlike the cWGAN approach.

Fig. 8.
Fig. 8.

Fire arrival time predictions produced using the SVM method (Farguell et al. 2021).

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

d. Spatial agreement with IR fire extent perimeters

To quantitatively assess the fire arrival time predictions made by the cWGAN and SVM methods, high-resolution IR wildfire extent perimeters provided by the NIROPS program are used as ground truth (Greenfield et al. 2003). These perimeters are obtained from infrared sensors onboard aircraft that fly over and survey large wildfires during the night. They are considered a very accurate representation of wildfire extent at the time of measurement with accuracy on the order of meters (approximately 6.3 m per pixel).

Using the fire arrival times produced for each fire by the cWGAN and the SVM methods, along with the geolocation information used when preprocessing the AF measurements, a geolocated fire perimeter is computed for any time within 72 h from the start of ignition day simply by plotting a contour of the fire arrival time at the prescribed time. The predicted perimeter is compared with the measured perimeter (see Fig. 9) by identifying the true positive pixels (burnt in both the prediction and truth), the false negative pixels (not burnt in the prediction but burnt in truth), and the false positive pixels (burnt in the prediction but not burnt in truth). These regions are marked as A, B, and C, respectively, in the figure. Using these regions, three dimensionless numbers that quantify the accuracy of a prediction are computed. These are the Sørensen coefficient (SC), the probability of detection (POD), and the false alarm ratio (FAR). They are defined as
SC=2A2A+B+C,POD=AA+B,FAR=CA+C.
All these coefficients attain values between 0 and 1. For the SC and POD, the best model yields a value of 1, whereas for the FAR, a value of 0 is ideal.
Fig. 9.
Fig. 9.

Plots comparing the predicted and measured IR fire extent perimeters. Gray pixels (labeled A) represent the true positive pixels, blue pixels (labeled B) represent false negative pixels, and red pixels (labeled C) represent false positive pixels.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0087.1

To quantify uncertainty for the POD and FAR values determined for the cWGAN predictions, we have taken the weighted mean arrival time prediction and added and subtracted the corresponding weighted standard deviation, obtaining one fire arrival time map for each which may be used to determine bounds for the POD and FAR values. Using the resulting fire arrival time maps, two fire perimeters are determined by plotting contours of the fire arrival time maps for the time corresponding to the measured IR fire perimeter, as described above. These two perimeters are then used to compute the FAR and POD values relative to the corresponding measured IR fire perimeter, giving upper and lower bounds for the cWGAN predictions in these metrics. The SC is left out of this analysis as it is a measure of how well two areas agree, and for each of the two perimeters determined by adding and subtracting the weighted standard deviation the SC goes down from that obtained from the mean perimeter, and consequently no useful bounds for the SC value are obtained.

Table 2 contains the SC, POD, and FAR values computed for the Bobcat, Tennant, Oak, and Mineral fires based on predictions by the cWGAN and SVM methods, along with bounds determined for the POD and FAR values for the cWGAN predictions. In all cases except the Tennant fire, the SC for the cWGAN method is higher than the SVM method. In the case of the Tennant fire, while the SC for the cWGAN prediction is lower than that for the SVM prediction, the values are close. From the POD values, we conclude that the SVM method performs better, indicating that the cWGAN is less likely than the SVM method to capture the full extent of the fire. On the other hand, the FAR values for the cWGAN are better than those for the SVM method in every case, indicating the cWGAN is less likely than the SVM method to suffer from false-positive errors. Of these metrics, the SC is the most critical to do well on when evaluating the accuracy of predicted fire perimeters.

Table 2.

SC, POD, and FAR values obtained for the cWGAN and SVM predictions, including bounds for the POD and FAR values determined for the cWGAN predictions based on their corresponding standard deviation. Bold values indicate which prediction scores the best in each metric.
Table 2.

e. Ignition time predictions

Both the cWGAN and SVM methods predict fire arrival times with reference to the start of the ignition day. Thus, implicitly they also generate an estimate of the ignition time for a fire, which corresponds to the smallest fire arrival time in the prediction. To determine uncertainty in the ignition time estimates, we find the pixelwise weighted standard deviation of the predicted arrival times for the ignition location, which is determined from the location of the smallest fire arrival time in the mean prediction. Using the standard deviations for the ignition locations along with the predicted ignition times, upper and lower bounds are computed for the ignition time estimates by adding and subtracting the standard deviation. These predicted ignition times and their corresponding upper and lower bounds are reported in Table 3 for the Tennant, Oak, and Mineral fires, for which the ignition times published by California Department of Forestry and Fire Protection (CAL FIRE) are available for comparison. In each case, the cWGAN method is significantly more accurate than the SVM method relative to reported ignition times from CAL FIRE. The latter appears to bias the prediction toward the time when the first satellite measurement is available, leading to an overestimate of the ignition time.

Table 3.

Estimated ignition times for the cWGAN and SVM predictions. Ignition times are reported in HH:MM format from the start of the ignition day. Upper and lower bounds determined from the mean ignition time and the ignition time standard deviation are also included for the cWGAN predictions. Ignition time offsets are further provided for the Tennant, Oak, and Mineral fires relative to ignition times reported by CAL FIRE. Bold values are used to indicate the superior ignition time predictions and offsets relative to those reported. The Bobcat fire is excluded as its ignition time is not reported by CAL FIRE.
Table 3.

5. Conclusions and outlook

In this study, a novel method for generating the early stage fire arrival time of a wildfire based on active fire satellite detections obtained from polar-orbiting satellites is developed, implemented, and tested. The method treats the satellite measurements and the desired arrival times as random vectors and solves the problem of sampling from the distribution of the arrival times conditioned on an instance of the measurement. It accomplishes this using a conditional Wasserstein generative adversarial network (cWGAN). Once the arrival time is inferred, it can be employed in a coupled wildfire–weather prediction code to spin up the atmosphere to an accurate initial state in order to make further predictions.

There are two significant desirable features of the proposed method. First, by treating the inference problem in a probabilistic way, it generates an ensemble of likely fire arrival times. These can be used to generate a mean arrival time field, which serves as the best guess. They can also be used to compute the pointwise standard deviation in the arrival time which in turn can be used to quantify the uncertainty in the arrival time prediction and therefore in the initial state of the atmosphere. Second, the method is trained with simulations generated by a coupled atmosphere–wildfire prediction model. These simulations are consistent with the physics included in this code, and through these, the generator of the cWGAN learns to produce samples of arrival times that are also close to the underlying physics.

When applied to data from four naturally occurring wildfires, the cWGAN method yielded predicted fire perimeters that were more accurate than a similar method based on the SVM. In particular, a quantitative comparison revealed that the fire perimeter predictions produced by the cWGAN method were more accurate than the SVM predictions when measured using Sørensen’s coefficient (SC) and false alarm ratio (FAR). For the cWGAN, the average SC was 0.81 and the average FAR was 0.23, whereas for the SVM, these values were 0.78 and 0.31, respectively. The SVM method performed better on the probability of detection (POD), with an average value of 0.92 compared with 0.87 for the cWGAN. The cWGAN method was also more accurate in predicting the ignition time of a fire, with an average offset of 32 min relative to CAL FIRE reports, when compared with the SVM method which incurred a average difference of 2 h and 11 min across the fires considered.

It is remarkable that the cWGAN, trained using the simulated data acquired under the idealized scenario of flat terrain, uniform fuel, and uniform wind direction, performed well when applied to wildfires where these conditions did not hold. We believe that this remarkable performance can be attributed, at least in part, to the fact that during its application, the cWGAN was never used by itself. Instead, as is the case for any data assimilation problem, it was used in conjunction with true, measured data which were acquired under the complex conditions prevailing during the wildfires. Thus, the role of the cWGAN was not to generate new fire arrival time maps from scratch, which would have required more complex and realistic training data; rather, it was to use the sparse arrival time satellite data to create a complete arrival time map. It may be useful to think of the satellite AF data as anchor points where the true solution is known (modulo some noise) and to think of the cWGAN as an algorithm that is used to interpolate between these points. Then, the role of the training data is to provide the cWGAN with enough physics-based information so that it can successfully carry out this interpolation.

In the future, we plan to train the cWGAN with more realistic training data acquired for true terrain maps. We also plan to use fields like the terrain and fuel maps as conditional fields for the generator of the cWGAN. We believe that these steps will add more accurate physics to the interpolation performed by the cWGAN and should help improve the performance of the algorithm. Potential future work also includes extending this approach to solve the data assimilation problem of correcting the current state of an ongoing wildfire with newly acquired measurements and considering the use of other conditional generative algorithms that avoid the pitfalls associated with adversarial training, like those based on diffusion maps (Song et al. 2020), for solving this problem.

Acknowledgments.

B. S. and A. A. O. gratefully acknowledge support from ARO, Grant W911NF2010050 and NASA Grant 80NSSC23K1344. D. R. acknowledges support from ARO, USA Grant W911NF2010050. K. H. was funded by NASA Grants 80NSSC19K1091, 80NSSC23K1344, and 80NSSC22K1717. J. M. was funded by NASA Grants 80NSSC19K1091, 80NSSC22K1717, 80NSSC23K1118, 80NSSC23K1344, and 80NSSC22K1405. A. K. and A. F. were funded by NASA Grants 80NSSC19K1091, 80NSSC22K1717, 80NSSC23K1118, 80NSSC23K1344, and 80NSSC22K1405, as well as NSF Grants DEB-2039552 and IUCRC-2113931. J. H. is supported by NOAA under Award NA22OAR4050672I. V. C. acknowledges support from the Center for Undergraduate Research at Viterbi Engineering (CURVE) program. The authors acknowledge the Center for Advanced Research Computing (CARC) at the University of Southern California, United States, for providing computing resources that have contributed to the research results reported within this publication. The authors acknowledge the use of HPC infrastructure at the Center for Computational Mathematics, University of Colorado Denver, funded by NSF Grant OAC-2019089.

Data availability statement.

The code for WRF–SFIRE, which has been utilized to generate the wildfire spread solutions used for training data here, is publicly available at https://github.com/openwfm/WRF-SFIRE. Information about the VIIRS active fire data product used here, along with information on data availability, is available at https://ladsweb.modaps.eosdis.nasa.gov/missions-and-measurements/products/VNP14IMG/. The code and data used for the work presented here are available at https://github.com/bshaddy/cWGAN_fire_arrival_time_inference.git.

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Cover Artificial Intelligence for the Earth Systems
Artificial Intelligence for the Earth Systems

  • Adler, J., and O. Öktem, 2018: Deep Bayesian inversion. arXiv, 1811.05910v1, https://doi.org/10.48550/arXiv.1811.05910.

  • Aguilera, R., T. Corringham, A. Gershunov, and T. Benmarhnia, 2021: Wildfire smoke impacts respiratory health more than fine particles from other sources: Observational evidence from Southern California. Nat. Commun., 12, 1493, https://doi.org/10.1038/s41467-021-21708-0.

    • Search Google Scholar
    • Export Citation

  • Bakhshaii, A., and E. A. Johnson, 2019: A review of a new generation of wildfire–atmosphere modeling. Can. J. For. Res., 49, 565–574, https://doi.org/10.1139/cjfr-2018-0138.

    • Search Google Scholar
    • Export Citation

  • Dennison, P. E., S. C. Brewer, J. D. Arnold, and M. A. Moritz, 2014: Large wildfire trends in the western United States, 1984–2011. Geophys. Res. Lett., 41, 2928–2933, https://doi.org/10.1002/2014GL059576.

    • Search Google Scholar
    • Export Citation

  • Dumoulin, V., J. Shlens, and M. Kudlur, 2016: A learned representation for artistic style. arXiv, 1610.07629v5, https://doi.org/10.48550/arXiv.1610.07629.

  • Farguell, A., J. Mandel, J. Haley, D. V. Mallia, A. Kochanski, and K. Hilburn, 2021: Machine learning estimation of fire arrival time from level-2 active fires satellite data. Remote Sens., 13, 2203, https://doi.org/10.3390/rs13112203.

    • Search Google Scholar
    • Export Citation

  • Farguell Caus, A., J. Haley, A. K. Kochanski, A. C. Fité, and J. Mandel, 2018: Assimilation of fire perimeters and satellite detections by minimization of the residual in a fire spread model. Computational Science–ICCS 2018, Y. Shi et al., Eds., Lecture Notes in Computer Science, Vol. 10861, Springer, 711–723, https://doi.org/10.1007/978-3-319-93701-4_56.

  • Giglio, L., W. Schroeder, and C. O. Justice, 2016: The collection 6 MODIS active fire detection algorithm and fire products. Remote Sens. Environ., 178, 31–41, https://doi.org/10.1016/j.rse.2016.02.054.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Architecture of (a) generator and (b) critic used in cWGAN. The downsample, upsample, and dense blocks are described in Fig. 2.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Architecture of (a) downsample block, (b) upsample block, and (c) dense block, with the values p = 2, q = 2, k = 16, and n = 4 used for this work shown.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Stepwise transformation of an input fire arrival time τ into an output measurement τ¯ following the eight steps of the measurement operator M.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Sample data pairs from the training set, with true fire arrival times τ in the first row and corresponding measurements τ¯ in the second row. Here, fire arrival time values represent hours from the start of the day on which ignition occurred.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Measurements τ¯ after preprocessing of VIIRS 375-m L2 AF data for the Bobcat, Tennant, Oak, and Mineral fires, in left to right order. The first row contains high confidence detections only, and the second row contains high and nominal confidence detections. AF detection colors indicate the measurement time, taken as the number of hours after the start of the ignition day. IR fire extent perimeters are additionally included, with measurement times listed in plot labels in HH:MM format, again as the number of hours and minutes after the start of ignition day. All measurements are geolocated, with longitude and latitude indicated.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    (top) Weighted mean and (bottom) standard deviation of fire arrival time predictions using the cWGAN approach.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Weighted standard deviation of fire arrival time predictions using the cWGAN approach, with VIIRS nominal confidence AF detections overlaid in pink and high confidence AF detections overlaid in dark red.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Fire arrival time predictions produced using the SVM method (Farguell et al. 2021).

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Plots comparing the predicted and measured IR fire extent perimeters. Gray pixels (labeled A) represent the true positive pixels, blue pixels (labeled B) represent false negative pixels, and red pixels (labeled C) represent false positive pixels.

Fig. 1.

Architecture of (a) generator and (b) critic used in cWGAN. The downsample, upsample, and dense blocks are described in Fig. 2.
Fig. 2.

Architecture of (a) downsample block, (b) upsample block, and (c) dense block, with the values p = 2, q = 2, k = 16, and n = 4 used for this work shown.
Fig. 3.

Stepwise transformation of an input fire arrival time τ into an output measurement τ¯ following the eight steps of the measurement operator M.
Fig. 4.

Sample data pairs from the training set, with true fire arrival times τ in the first row and corresponding measurements τ¯ in the second row. Here, fire arrival time values represent hours from the start of the day on which ignition occurred.
Fig. 5.

Measurements τ¯ after preprocessing of VIIRS 375-m L2 AF data for the Bobcat, Tennant, Oak, and Mineral fires, in left to right order. The first row contains high confidence detections only, and the second row contains high and nominal confidence detections. AF detection colors indicate the measurement time, taken as the number of hours after the start of the ignition day. IR fire extent perimeters are additionally included, with measurement times listed in plot labels in HH:MM format, again as the number of hours and minutes after the start of ignition day. All measurements are geolocated, with longitude and latitude indicated.
Fig. 6.

(top) Weighted mean and (bottom) standard deviation of fire arrival time predictions using the cWGAN approach.
Fig. 7.

Weighted standard deviation of fire arrival time predictions using the cWGAN approach, with VIIRS nominal confidence AF detections overlaid in pink and high confidence AF detections overlaid in dark red.
Fig. 8.

Fire arrival time predictions produced using the SVM method (Farguell et al. 2021).
Fig. 9.

Plots comparing the predicted and measured IR fire extent perimeters. Gray pixels (labeled A) represent the true positive pixels, blue pixels (labeled B) represent false negative pixels, and red pixels (labeled C) represent false positive pixels.
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