A generative model for surrogates of spatial-temporal wildfire nowcasting

We evaluate the performance of the generative and the surrogate models using a recent massive fire event in California, namely the Chimney fire in 2016. The exact ecoregion of this study is shown in Table I. We use active fire data from Moderate Resolution Imaging Spectroradiometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) satellites. MODIS provides thermal observations four times a day at a resolution of about 1km ([28]). VIIRS thermal data provides improved fire detection capabilities every 12 hours  [29]. In this study, the level 2 VIIRS I-band active fire product (VNP14IMG) with a resolution of 375 m is combined with the MODIS fire products at 1km to derive continuous daily fire perimeters, using the natural neighbour geospatial interpolation method [30].

For the training dataset of the generative model and the surrogate model, we make use of an operational CA model [1], which has been tested in the Spetses fire in 1990 in Greece [1] and several recent wildfire events in California [7, 31]. As shown in Figure 1, the model uses square meshes to simulate the random spatial spread of wildfires. The use of regular square meshes reduces the computational cost for large fire events compared to unstructured meshes. Four states are assigned to represent a cell at a discrete time, i.e., unburnable, unburned, burning and burned. When a neighbouring cell is burning, the transition from unburned to burning is random following a probabiliy determined by local geological variables. The fire propagation towards 8 neighbouring cells (as illustrated in Figure 1) at a discrete time follows the probability,

where $p_{\textrm{veg}}$, $p_{\textrm{den}}$ , $p_{s}$ and $p_{w}$ are related to the local canopy density, canopy cover, landscape slope and wind speed/direction of the receiving cell, respectively [1]. These geological fields for the corresponding study areas are processed using remote sensing images of the MODIS satellite. These data are available at the Interagency Fuel Treatment Decision Support System (IFTDSS) [32]. The simulated burned area states are denoted as $\textbf{x}_{t}$ where $t$ is the time index. The outputs of the CA simulations are used as training data for the generative and the surrogate models in this study.

In this study, a set of $n_{\textrm{state}}$ state snapshots, from several CA simulations, are represented by a tensor $\textbf{X}\in\mathbb{R}^{\textrm{dim}(\textbf{x})\times n_{\textrm{state}}}$ where each column of X represents a flattened burned area state at a given time step, that is,

The empirical covariance $\textbf{C}_{\textbf{x}}$ of X can be written and decomposed as

where the columns of ${\textbf{L}}_{\textbf{X}}$ are the principal components of X and ${\textbf{D}}_{\textbf{X}}$ is a diagonal matrix with the associated eigenvalues $\{\lambda_{\textbf{X},i},i=0,...,n_{\textrm{state}}-1\}$ in a decreasing order,

For a truncation parameter $q\leq n_{\textrm{state}}$, a projection operator ${\textbf{L}}_{\textbf{X},q}$ can be constructed by keeping the first $q$ columns of ${\textbf{L}}_{\textbf{X}}$. This projection operator can be obtained by a Singular Value Decomposition (SVD) [33] which does not require the computation of the full covariance matrix $\textbf{C}_{\textbf{x}}$. For a flattened field of burned area $\textbf{x}_{t}$, the compressed latent vector $\tilde{\textbf{x}}_{t}$ can be written as

which is a reduced rank approximation to the full state vector $\textbf{x}_{t}$. $\textrm{Tr}(.)$ in Equation (5) denotes the transpose operator.

The latent variable $\tilde{\textbf{x}}_{t}$ can be decompressed to a full vector $\textbf{x}_{t}^{r}$ by

The compression rate $\rho_{\textbf{x}}$ and the compression accuracy $\gamma_{\textbf{x}}$ can be defined as:

By reducing the space dimension, the surrogate model becomes more efficient and faster to train, but it may also lead to a loss of information. Therefore, it is important to strike a balance between the dimensionality reduction and the preservation of the useful information.

Once the data compression is performed, we aim to emulate the dynamics of fire spread in the low-dimensional latent space. In this study, we aim to perform sequence-to-sequence predictions with $m_{\textrm{in}}$ time steps as input and $m_{\textrm{out}}$ time steps as output. As pointed out by [34], sequence-to-sequence predictions can decrease the online computational time, and more importantly, reduce the accumulation of prediction error. The time steps in LSTM are determined by the CA model introduced in Section II. Given a sequence of encoded variables $\tilde{\textbf{X}}_{\textrm{train}}=[\tilde{\textbf{x}}^{\textrm{train}}_{1},\tilde{\textbf{x}}^{\textrm{train}}_{2},...,\tilde{\textbf{x}}^{\textrm{train}}_{T_{\textrm{train}}}]$, the training of LSTM can be performed by shifting the initial time step, i.e.,

Different metrics, such as Mean Square Error (MSE) or Mean Absolute Error (MAE), can be used as training loss functions by measuring the mismatch between predicted and true latent variables. As for the online prediction for a given test sequence $\tilde{\textbf{X}}_{\textrm{test}}=[\tilde{\textbf{x}}^{\textrm{test}}_{1},\tilde{\textbf{x}}^{\textrm{test}}_{2},...,\tilde{\textbf{x}}^{\textrm{test}}_{m_{in}}]$, an iterative process can be carried out for long-term forecasting, that is,

In this work, 40 CA simulations are used as the training dataset for the VQ-VAE generative model. The ignition points are randomly chosen in the central zone of the ecoregion to avoid the boundary problem as shown in Figure 3. In this study, the parameters in VQ-VAE are fixed as $\beta=0.25$ (in Equation (22)) and $\alpha=0.6$ (in Equation (24)). The performance of the generative model is evaluated through two aspects, namely the realsticness of the generated fire events regarding geological variables and the improvement of the predictive surrogate model which use the generated fire events as training data. For the latter, 8 CA simulations, different from the training dataset are generated to find out if the surrogate models can correctly emulate the fire spread with unseen ignition points. For a fair comparison, two pipelines are established,

• •

  baseline: The surrogate model (including both POD and LSTM) are trained only using the 40 CA simulations in the training dataset.

• •

  proposed: 500 wildfire events generated through VQ-VAE and the 40 CA simulations are used to train the surrogate model.

The training and testing processes of the two surrogate models are illustrated in Figure 3. The performance of the two surrogate models is then compared using the test dataset of the CA simulations and satellite data of the Chimney wildfire event. In the training and the test datasets, each CA simulation consists of 16 snapshots where the time interval between two snapshots is equivalent to 6 hours in real time. Since the state is represented by integers in the CA model (see Section II), post-processing is required for generated/predicted values. Here, the threshold is chosen to be 0.4, i.e., the cells with a value higher than 0.4 are considered ’burned’. This threshold is set empirically following the previous study [7]. For simplicity, the burned area state and the geological fields (vegetation and slope) are all resized to $128\times 128$ pixels. The generative model and the surrogate model are trained on a work station with an NVIDIA RTX A6000 GPU and 48 GB Memory. As for the online generation/simulation, VQ-VAE, CA and MTT are all performed on a same labtop CPU of Intel(R) Core(TM) i7-10810U with 16 GB Memory.

Figure 4 illustrates 8 generated fire events with random ignition points. For each generated fire, 6 snapshots respectively at 12, 24, 36, 48, 60, 72 hours after the fire ignition are shown. The background color map indicates the vegetation distribution where the green color refers to high vegetation density.

The generated data present characteristics that are in alignment with observable phenomena in CA simulations. First, the burned areas (i.e., number of burned pixels) are always increasing in each generated fire event. This observation is quantified in Figure 5 (a) where we show the averaged burned pixels against the hours after fire ignition. Overall the generated (i.e., VQ-VAE) and the simulated data (i.e., CA) demonstrate concurrent patterns despite that generated fire grow slightly slower in the nascent phase. The generated fire events also exhibit a larger standard deviation against propagation time, which is to be expected in this study. The exact burned areas observed from the satellite for the Chimney fire event are slightly larger than the simulated and generated burned areas.

It can also been clearly seen from Figure 4 that the generated fires tend to burn out the cells with high vegetation density which appears to be consistent with the CA propagation function (Equation (1)). To verify this assertion, we plot in Figure 5 (b,c), the final burned area (72 hours after the fire ignition) in number of cells against the averaged vegetation density and the slope elevation around the ignition point. More precisely, the ignition point of generated fire events is obtained by calculating the barycentre of the burned area 12 hours after ignition. The vegetation density and the slope elevation are normalized to the range of $[0,1]$. There is conclusive evidence in Figure 5 that the generated fires show similar patterns compared to the CA simulations in the training dataset. Thus, the impact of vegetation and slope on the evolution of the burned area has been well understood by the generative model.

It is worth mentioning that all training data are generated with a single ignition point for each fire scenario. However, as shown in Figure 4, separate burned regions can be found in the synthetic data (especially the last fire sequence). More importantly, the growth of each burned region appears to be consistent with the reality. In fact, multiple ignition points are frequently observed in actual wildfire occurrences. This phenomena demonstrates the capability of VQ-VAE in generalizing and extending CA simulations with realistic scenarios. The averaged computational time of generating/simulating fire spread of 8 days in the ecoregion of the Chimney fire is shown in Table II. VQ-VAE result in a 5 order of magnitude acceleration, compared to the CA and MTT fire simulators [3].

In summary, VQ-VAE allows to easily enlarge the simulation datasets with high-fidelity synthetic data. It shows great potential in generating realistic fire scenarios, which can be used to evaluate the area at risk. The efficiency of VQ-VAE can also be crucial for data-demanding downstream tasks, such as surrogate model training.

We compare the surrogate model trained on both generated (500 sequences) and simulated (40 sequences) data (i.e., proposed method in Figure 3) and the one trained only on simulation (40 sequences) data (i.e., baseline method in Figure 3). The performance is evaluated on a test dataset consisting of 8 independent CA simulations and the observed snapshots of the Chimney fire event. For each sequences of burned area, the first 4 snapshots, corresponding to 6, 12, 18, 24 hours after fire ignition, are used as input for the predictive surrogate model. The latter then predict the burned area for 30, 36, 42, 48 hours after fire ignition, as introduced in Section IV. For both surrogate models, the validation dataset consists of 8 independent CA simulations, different from the training and the test data.

The evolution of the loss value (MSE) against the number of training epochs is depicted in Figure 6 (a). It can be clearly observed that, despite some oscillations introduced by the generated data, the loss of the proposed approach converges faster than baseline, and reaches a lower stable value. Some quantitative metrics are used to assess the prediction performance as shown in Figure 6 (b). For comparison purpose, we also run the CA from the burned area of 24 hours after ignition. As mentioned in II, CA is a probabilistic model, thus the re-ran simulation will lead to a different burned area as the one in the test dataset. The blue bar stands for the Relative Mean Square Error (RMSE), which represents the mismatch normalized by the exact burned area. The red bar illustrates the online prediction time and the orange line represents the Structural Similarity Index Measure (SSIM), which measures the similarity between the true burned area and the prediction. All metrics are obtained using the average score on the 8 fire sequences in the test dataset. Consistent with our analysis for Figure 6 (a), the proposed approach shows a significant advantage in terms of both RMSE and SSIM compared to the baseline. In fact, the accuracy of the proposed surrogate model is close to a re-implementation of CA with a speed-up of 4 orders of magnitude.

Two fire events in the test data are illustrated in Figure 7 and 8, respectively. In accordance with our findings in Figure 6, the proposed approach succeeds in delivering accurate predictions of the burned area. Only minor difference can be observed against the ground truth. The baseline approach, on the other hand, manages to roughly predict the progression of fire dissemination but fails in specifying the precise geometry of burned area. This is mainly due to the lack of training data. Figure 8 shows a particular case where the vegetation density is small near the ignition point, leading to a deceleration of fire spread. This phenomenon is only well understood by the proposed approach.

We also test the prediction performance of surrogate models applied on the Chimney fire event (Table I), which took place on August 13, 2016. The observed burned area is provided by the MODIS satellite as described in Section II. Since the observation data are on daily basis [7], image interpolation method proposed by [41] is applied to emulate the burned area at intervals of 6 hours. As shown in Figure 9, for both surrogate models larger area of mismatch can be noticed compared to the CA test data (Figure 7, 8). However, a substantial gain of the proposed approach can be found against the baseline. In a consistent manner, the averaged RMSE for proposed and baseline approaches are $28.4\%$ and $18.9\%$, respectively.

These numerical results convincingly demonstrate the strength of including generated data in the surrogate model to improve the robustness and generalizability when predicting unseen scenarios.

The parameter $\beta$ determines the relative weight of $\mathcal{L}_{commit}$ while $\alpha$ determines the level of additional noise when generating synthetic fire spread videos. A small value of $\alpha$ will lead to a generated video that is very similar to the input due to the reconstruction loss. When the value of the parameter $\alpha$ exceeds a certain threshold, it engenders a diminution in controllability and an increase in noise levels within the generated video, as shown in Figure 10.

On the other hand, the coefficient $\beta$ balances the weight of the commit loss. When the value is set excessively high, it will additionally introduce unrealistic noises in the generated scenarios, as depicted in Figure 10.

These experiments illustrate the necessity of making thoughtful parameter selections during the training and application of the generative model.

In order to delve deeper into the influence of the number of generated fire scenarios during the training process, we conducted experiments where the surrogate model was trained using a range of 50 to 500 generated fire videos. Subsequently, we assessed the performance of the trained surrogate model, as depicted in Figure 11.

The results clearly demonstrate that the performance of the surrogate model exhibits a noticeable improvement as the number of generated videos in the training data increases. The performance stabilizes once the number of generated videos exceeds four hundred. Notably, it is important to highlight that employing a small number of generated videos may result in a deterioration of the prediction performance.