The annual area burned due to wildfires in the western United States (WUS) increased by
more than 300 % between 1984 and 2020. However, accounting for the nonlinear, spatially heterogeneous interactions between climate, vegetation, and human predictors driving the trends in fire frequency and sizes at different spatial scales remains a challenging problem for statistical fire models. Here we introduce a novel stochastic machine learning (SML) framework, SMLFire1.0, to model observed fire frequencies and sizes in 12 km

Wildfire is an important biophysical process that structures natural and anthropogenic
systems and is, in turn, affected by climate, vegetation, and humans

Individual wildfire events in the WUS are caused by the coincidence of fire-conducive hot
and arid weather in the presence of adequate vegetation and sources of ignition

Here we focus on statistical models for two important fire variables: frequency and area
burned. Broadly, these models infer the empirical relationships between observed wildfire
activity at a given spatiotemporal scale and its various climate, vegetation, and human
drivers. To account for the multiple degrees of freedom characteristic to the problem,
regression-based models tend to study the mean state relationship between wildfire
activity and its drivers by averaging all variables along spatial

In this paper, we introduce a stochastic ML (SML) model, SMLFire1.0, to estimate the
probability distributions of monthly fire frequencies and sizes in 12 km

Our modeling approach for SMLFire1.0 builds upon and extends previous methods in four
important ways: (a) unlike other ML methods based on gradient boosted trees or
quantile regression, our use of parametric distributions in SMLFire1.0, especially for
individual fire sizes, provides a straightforward way to implement uncertainty
quantification for our predictions; (b) we account for the spatiotemporal variability in
the predictors and their nonlinear interactions; (c) our model includes fire frequencies
and locations while simulating the total area burned, thus enabling projections of total
area burned for different idealized future scenarios of fuel flammability, human ignition
patterns, and fuel treatment; and (d) the combined frequency and size ML framework
serves as a single model across the entire WUS and does not require separate training for
predicting fire activity in each constituent region. While we do not explore the scenario in
detail here, the flexibility and efficiency of our ML framework also makes it an ideal
subgrid-scale parameterization scheme for the fire modules of regional-scale dynamic
vegetation models (DGVMs)

Our study region consists of all 12 km

Wildfire activity in the western United States (WUS) from 1984 to 2020.

We focus on two primary fire variables in this analysis: occurrences and sizes. Both
these variables are available in the western US MTBS-Interagency (Monitoring Trends in Burn
Severity; WUMI) wildfire
dataset

In Fig.

We consider four broad classes of input predictors – three dynamic plus one static –
aggregated to the 12 km

We select six primary climate and fire weather predictors: temperature, precipitation, vapor pressure deficit (VPD), snow water equivalent (SWE), wind speed, and lightning. Monthly climate grids for mean daily maximum temperature (

The monthly mean and maximum daily SWE variables come from the gridded National Snow and Ice Data Center (NSIDC) dataset

We leverage land type data from the National Land Cover Dataset (NLCD)

Combining the following NLCD land cover types that reflect the presence of urban areas – “developed high”, “developed low”, “developed medium”, and “developed open” – we construct a single, annual-scale human predictor, urban fraction. For more granular information of human settlements, we include the following predictors: distance from the nearest area with population density greater than 10 people per square kilometer (Pop10_dist), mean population density (Popdensity), and mean housing density (Housedensity). These predictors are adapted to annual timescales using data for 3 years – 1990, 2000, and 2010 – from the SILVIS dataset

Lastly, to incorporate the effect of topography on fire activity

Before analyzing the data with a statistical model, we perform an additional preprocessing step. To account for spatiotemporal heterogeneity of the WUS ecological landscape, we “standardize”, i.e., subtract the mean and divide by the standard deviation, all input predictors. Dynamic predictors, including all climate and most vegetation variables, at each location are standardized in time, whereas the static predictors are standardized across the entire spatial domain.

Schematic diagram illustrating the input (blue), hidden (green), and output
(purple) layers of a mixture density network (MDN) model within the SMLFire1.0
framework. While a fully connected neural network is implemented in practice, only a
partial connected one is shown here for clarity; the solid black line on the left denotes the
direction from the input to the output layer, whereas the dotted black lines represent
additional nodes and layers in the network. Also shown above the output layer are the
parameters for a two-component mixture distribution of the form given in Eq. (

Our main goal is to develop a statistical model for fire frequency and sizes as a
function of input predictors described in the previous section. Specifically, we want our
model to (a) capture the nonlinear, spatially heterogeneous interactions among
the climate, vegetation, human, and topographic variables that influence wildfire activity;
(b) rely on physical variables and be independent of location and time of year; (c) be based on parametric distributions that could be sampled using Monte Carlo
simulations for estimating the mean and parametric model uncertainty of modeled fire
frequency and sizes. While tree-based ML approaches using XGBoost (extreme gradient boosting) have shown high
performance in predicting area burned across the continental US

In SMLFire1.0, we use two mixture density networks (MDNs) to separately model the
conditional probability (henceforth conditional for brevity) distributions for fire frequency
and sizes on a monthly timescale. An MDN is a fully connected, feedforward neural
network whose output layer consists of parameters of a mixture model

We use the monthly fire counts (including zeros) in each grid cell across the WUS as the
data for our fire frequency model. In total, we consider data in about

Meanwhile, as shown previously

The conditional distributions of monthly and annual area burned (MAB and AAB
respectively) are obtained by aggregating the distribution of fire sizes for each
grid cell in an ecoregion with a fire. We compute the mean and variance for the fire
size distributions using MC simulations and formulas similar to the ones described in
Eq. (

The expressions for MAB and AAB can be schematically interpreted as follows:
assuming that the mean size of all fires at a given spatiotemporal scale

Following

In order to isolate the role of frequency in the total area burned, we first derive the AAB
using the combined GPD MDN model evaluated with observed fire frequencies
and values of input predictors corresponding to the observed locations of fires given in
the WUMI dataset. We also explore three further variations for the WUS AAB time series: first, using modeled frequencies for each ecoregion from the frequency MDN model with observed fire locations; second, with observed frequencies but input predictors
corresponding to model fire locations predicted by the frequency MDN; and third, with
both fire frequencies and locations drawn from the frequency MDN model. Since our
modeled frequencies also include smaller fires, we apply an additional time-dependent
scaling factor to account for the relative abundance of large fires (

Lastly, to obtain percentiles of the burned area distribution we require the full probability
density function defined over all grid cells with fires,

We implement our SMLFire1.0 framework using the

For model training, we hold out 1 contiguous year (which we take to be 2020, unless specified otherwise) of fires and input predictors as test data and split the monthly data from the remaining 36 years

We train our model for up to 500 epochs using the Adam optimizer with learning rate,

We define metrics for two broad purposes: enabling model selection and measuring model
performance. For the former, a straightforward choice is the value of the loss function,
given in Eq. (

Having selected a model, we characterize its performance by measuring, statistically, how
well or poorly the modeled time series fits the observed data. We use the Pearson's
correlation coefficient,

Summary of the mixture density network (MDN) architecture and performance
metrics used for modeling fire frequencies and sizes in SMLFire1.0.

Finally, we determine the optimal number of predictor variables by iteratively dropping all predictors that
do not improve overall model performance and are highly correlated (

We estimate the sensitivity of model output to input predictors using the SHapley Additive
exPlanation (SHAP) technique

A SHAP value

We visualize our results using two types of plots: a summary plot that shows the SHAP
values of the leading input predictors at each test point colored by the predictor value
alongside the partial dependence plots of two important predictors, as well as a global feature
importance plot of the leading predictors ordered according to their mean absolute SHAP
values, or

An important step in our model selection process is determining the optimal
hyperparameter configuration for each loss function. We train the frequency and size
MDNs on a subset (

The optimal hyperparameters and performance metrics for each MDN are outlined in
Table

Observed (blue) and modeled (orange) fire frequencies across the western United
States at monthly

We use an MDN trained on downsampled training data to determine the parameters of the
ZIPD for fire frequencies in each grid cell across the WUS from 1984 to 2020. MC
simulations of the parametric frequency distributions for all grid cells are aggregated to
compute the mean fire frequency and its

Goodness-of-fit metrics in terms of Pearson's correlation (

An upshot of our likelihood-based MDN model in SMLFire1.0 is the availability of
uncertainty estimates

Observed (blue) and modeled (orange) fire frequencies at monthly and
annual scales from 1984 to 2020 for ecoregions selected based on the total
number of fires and goodness-of-fit metrics. The orange shaded regions within each
subplot indicate

As in Fig.

At the WUS level, our mean modeled frequencies are in good agreement with the
total number of observed fires, exhibiting high correlations at both monthly (

SHapley Additive exPlanation (SHAP) analysis of the fire frequency MDN model outputs across the western United States.

SHAP analysis of the fire frequency MDN model outputs for different western United States' divisions:

Broadly, the trends in fire frequencies can be characterized as a competition between
three independent drivers. One, an increasing trend in climate dryness

Since our model is trained on data over the whole WUS, its performance, on average,
is better over ecoregions with a larger number of fires, such as the Middle Rockies and IM
Semidesert. On the other hand, our model performs quite poorly for regions with a low
number of total fires, where it is more likely to exhibit large interannual variations over a
baseline of very few to no fires. This behavior is evident in the plot for CH Desert in Fig.

The SHAP values for individual predictors of the frequency MDN, as well as the
partial dependence plots for two important predictors, VPD (

Among the other subdominant predictors, antecedent climate conditions play
a varying role across different divisions. Antecedent snowpack estimated using 3-month
average SWE,

We visualize the response of fire frequencies to individual predictors through the partial
dependence plots in Figs.

Observed (red) and mean modeled (teal) area burned across the western United
States at monthly (MAB)

We use MDNs trained on fires

Observed (red) and mean (teal) modeled monthly (MAB) and annual area
burned (AAB) from 1984 to 2020 for the ecoregions shown in
Fig.

As in Fig.

The introduction of a time-dependent response and a breakpoint after 2004 in our
modeling is justified through the following analysis. As indicated by
Fig.

We emphasize that the improved agreement between the CCDFs of observed and modeled sizes is not merely an artifact of the breakpoint procedure; in fact the choice of the distribution plays a critical role. Specifically, we verify this by repeating our analysis with the lognormal distribution, which has thinner tails than the GPD. In Fig. S5, we demonstrate that the CCDF of the reweighted lognormal MDN (Lognorm-Ext) underestimates large portions of the observed sizes' CCDF while being able to account for only the most extreme fires. Consequently, the combined distribution (Lognorm-Comb) is an inadequate model for the observed fire sizes over the study period.

The choice of fire frequencies – either observed or modeled – and the stochasticity in
fire locations affects both the interannual variability and total area burned of the modeled
AAB time series. Contrasting the results shown in Figs.

Using the combined GPD MDN model, our modeled MAB (

Boxplots of predicted annual area burned (AAB) for 2 extreme fire years, 2012 and 2020, for the entire western United States (WUS) (teal) and three divisions organized by their primary vegetation types: forests (green), deserts (yellow), and plains (gray). The lower and upper whiskers of each boxplot indicate the 0.5th and 99.5th percentile of the predicted AAB distribution, whereas the black line represents its median value. Also shown for reference are the observed AAB for both 2012 (red diamond) and 2020 (indigo triangle).

Our model has mixed skill in predicting large MAB and AAB during the study period. For
example, our model is able to simulate the full range of AAB variability in the Northern
Rockies, Northern Great Plains (Fig.

With these results, we can make a stronger assessment about our modeling framework: first, for almost all years in our study period, the mean of the aggregate burned-area distribution is a good approximation for the observed time series, so the only challenging part is determining the time dependence of the mean sizes of individual fires; and second, while the discrepancy between modeled and observed area burned in 2020 highlights a clear limitation of our model, can we still use it to make meaningful predictions for anomalous extreme fire years?

In Fig.

As in Fig.

SHAP analysis of the fire size MDN model outputs for different western United States' divisions:

Among the 10 input predictors of fire size shown in descending order of importance
in Fig.

We also retrain our fire size model with two different variations in the input predictors
selected for the main analysis: first with relative humidity (RH), average RH over 3
antecedent months (

Lastly, we show the responses of fire sizes to individual predictor values for all test points
at the WUS and divisional level in Figs.

We have developed a novel stochastic ML framework, SMLFire1.0, for modeling fire activity
across different WUS ecoregions. Although the fire frequency and area burned time series
simulated using this framework are in good agreement with observations at multiple
spatial and temporal scales, there are several areas of improvement across three
interconnected themes: modeling approach and architecture, vegetation, and other
potential predictors. We discuss each one of these themes in detail below.

Disentangling the various climate, vegetation, and human drivers of wildfire frequency
and sizes in the western United States is critical for developing accurate seasonal and longer-term forecasts of fire activity. In this paper, we introduced a novel stochastic ML
framework, SMLFire1.0, for estimating the parametric distributions of observed fire
frequencies and sizes in 12 km

Our main results are as follows: (a) the time series for both modeled frequencies and area burned are in good statistical agreement with the observed data over monthly and annual timescales at spatial scales from ecoregions to the whole WUS; (b) the modeled area burned successfully accounts for the interannual variability and multidecadal trends in the observed area burned in both forested and non-forested regions; (c) for anomalous extreme fire years such as 2020, the stochastic model is useful for estimating the upper percentiles, i.e., 95th, 99th …, of the total annual burned-area distribution; and (d) the cumulative observed fire size distribution is best fit by a combined GPD model with finite mean but infinite variance, which has important consequences for how resources are allocated for fuel treatment and fire containment.

We used the SHAP technique to evaluate the predictor importance for the frequency and size models at the ecoregional, divisional, and WUS scales. While VPD is the leading predictor at both smaller and larger scales, the order of subleading fire month predictors – precipitation total, mean daily maximum and minimum temperatures, moisture in large-diameter dead fuels – and the fraction of grassland cover, aboveground biomass, and topography varies across ecoregions, indicating that our model is able to generalize well across spatially heterogeneous climate, vegetation, and human gradients. Furthermore, we visualized the different functional relationships between predictor values and wildfire activity with potential interaction effects through partial dependence plots for several important predictors. Besides fire-month variables, we find that increased fire frequencies in our model are driven by a set of antecedent predictors acting at two distinct timescales across forests, deserts, and plains: a seasonal (3–4 months) scale associated with snow or precipitation drought and a cumulative longer-term (1–2 years) scale correlated with wetter conditions that promote fuel growth. Modeled fire sizes, on the other hand, are mostly sensitive to seasonal-scale antecedent conditions.

Future research directions will focus on expanding the SMLFire1.0 model framework to include a stochastic model for human ignitions, nonstationary relationships between predictors and fire activity, fire–fuel feedback over different climate and vegetation gradients, and additional finer-scale moisture and human action predictors. Moreover, we intend to incorporate SMLFire1.0 as a subgrid-scale parameterization scheme for the fire modules of a regional-scale DGVM and ESM while also benchmarking it against existing parameterizations.

The code for training and validating the SMLFire1.0 model, as well as reproducing the
figures shown in this paper, is available at

The supplement related to this article is available online at:

JB, APW, and PG conceived the study. APW, CSJ, and WDH handled the data collection and processing. JB performed the analysis and wrote the paper. All authors discussed the results and contributed to the final version of the draft.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We acknowledge initial work from Kenza Amara during an internship at Columbia University on machine learning and wildfires. We are also grateful for the critical feedback from Ye Liu and the two anonymous reviewers that improved the presentation of our results.

This work is funded by the Zegar Family Foundation and the Amazon Reseach program. Caroline Juang is supported by a Future Investigators in NASA Earth and Space Science and Technology (FINESST) (grant no. 80NSSC20K1617). Winslow D. Hansen received support from the Gordon and Betty Moore Foundation (grant no. GBMF10763), the Environmental Defense Fund, and the Three Cairns Group. Pierre Gentine's research is funded by the NSF LEAP Science and Technology Center (grant no. 2019625) and the USMILE European Research Council grant.

This paper was edited by Po-Lun Ma and reviewed by Ye Liu and two anonymous referees.