# Improved fire severity prediction using pre-fire remote sensing and meteorological time series: Application to the French Mediterranean area

Victor Penot, Thomas Opitz, François Pimont, Olivier Merlin

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Victor Penot, Thomas Opitz, François Pimont, Olivier Merlin. Improved fire severity prediction using pre-fire remote sensing and meteorological time series: Application to the French Mediterranean area. Agricultural and Forest Meteorology, 2025, 371, pp.110588. 10.1016/j.agrformet.2025.110588. hal-05167337

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# Improved fire severity prediction using pre-fire remote sensing and meteorological time series: Application to the French Mediterranean area

Victor Penot<sup>a,†</sup>,*, Thomas Opitz<sup>b</sup>, François Pimont<sup>c,†</sup>, Olivier Merlin<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Fire severity

Pre-fire conditions

Time series

Optical remote sensing

Weather

Fuel

## ABSTRACT

Fire severity, or how an environment is affected by fire, can be estimated over large areas using remotely sensed indices like the Relative Burnt Ratio (RBR). RBR predictions typically rely on data from a single date just before the fire. However, predicting RBR accurately in both time and space remains challenging. To improve RBR predictability, we developed new models using time series data spanning several months before the fire. These models use fuel proxies derived from optical remote sensing and meteorological data. We applied this approach to fires in the French Mediterranean area during the summers of 2016–2021. We used a Lagged Generalized Additive Model (LGAM) and a Functional Linear Model (FLM) to estimate the influence of variables up to several months before the fire on RBR. A GAM fed with immediate pre-fire predictors served as a benchmark. Training and prediction were conducted at the fire–land-cover spatial scale using a training dataset spatially independent of the test dataset. FLM achieved the best prediction accuracy on test data (R=0.68, RMSE=0.057), outperforming LGAM (R=0.60, RMSE=0.063) and the benchmark (R=0.52, RMSE=0.069). FLM accurately predicted the highest RBR values when the Normalized Difference Vegetation Index decreased faster than the average and when the Duff Moisture Code increased faster than the average over the 65 days before the fire. The 17% decrease in the RMSE of FLM predictions compared to GAM predictions shows that understanding fuel dynamics up to two months before a fire provides valuable information for ranking areas by fire severity.

## 1. Introduction

The French Mediterranean is highly fire-prone, experiencing numerous fires annually (Galizia et al., 2021). The number of fires is expected to increase due to climate change (Fargeon et al., 2020; Barbero et al., 2020; Pimont et al., 2022). Wildland fire risk combines the potential for wildfire occurrence and its expected impacts (Bachmann and Allgöwer, 2001). The occurrence and one of the expected impacts, fire size, have been extensively studied and used in prediction models, supported by relatively long observational records (Hernandez et al., 2015a; Pimont et al., 2021; Fox et al., 2018). Fire behavior has also been a focus of study (Salis et al., 2023, 2016). Another important outcome is the severity of a fire once ignited, which assesses the impact of wildfires on the environment (Key and Benson, 2005). Specifically, it quantifies the consumption of above- and below-ground organic matter by fire (Keeley, 2009). Fire severity has been measured locally through ground assessments of fire effects, such as organic matter loss, crown volume scorch, tree mortality, or post-fire twig diameter (Keeley, 2009; Jain and Graham, 2007; Miller et al., 2023). These effects are linked

to fire intensity (Keeley, 2009; Williams et al., 1998) and burning efficiency (Bountouraby et al., 2023).

Remote sensing has enabled the estimation of fire severity over large areas at reasonable costs, thanks to fire-severity indices (FSI) derived from high-resolution (10–100 m) optical imagery (Key and Benson, 2005; Miller and Thode, 2007; Parks et al., 2014a). The most popular FSI are the Normalized Burnt Ratio (NBR), which combines Near Infrared (NIR) and Shortwave InfraRed (SWIR) bands, and its derivatives: the Difference Normalized Burnt Ratio (DNBR) (Key and Benson, 2005), a measure of absolute change, and the Relative Burnt Ratio (RBR) (Parks et al., 2014a), a normalized version of the DNBR for pre-fire vegetation biomass. These indices show significant positive statistical correlations with ground measurements of fire severity (Key and Benson, 2005; Miller and Thode, 2007; Parks et al., 2014a; Keeley, 2009; Escuin et al., 2008; Soverel et al., 2010) and with radiative transfer modeling of burnt scenes (Chuvieco et al., 2006) over various landscapes (Parks et al., 2019). Specifically, RBR has shown good agreement with Mediterranean ground measurements (Viedma et al., 2020;

<footnote><sup>a</sup> CESBIO, CNES/CNRS/IRD/UPS, Toulouse, France</footnote>

<footnote><sup>b</sup> BioSP, INRAE, Avignon, France</footnote>

<footnote><sup>c</sup> URFM, INRAE, Avignon, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: victor.penot@iut-tlse3.fr (V. Penot).</footnote>
Fernández-Guisuraga et al., 2023) and performs better at detecting high severity effects across the full range of pre-fire vegetation cover (Parks et al., 2014a). In contrast, DNBR is particularly sensitive to high pre-fire biomass (Miller and Thode, 2007).

Remote-sensing-based FSI has enabled the characterization of a wide range of conditions encountered before and during fires. To understand the factors driving fire severity, many studies have used machine learning or statistical modeling to explain the variability of FSI (Viedma et al., 2020; Lecina-Diaz et al., 2014; Fang et al., 2018). Three groups of factors have been identified: fuel (structure, dominant species and physiological activity), weather (day of fire and pre-fire), and topography. These factors are described in the following paragraphs.

The status of live fuels in relation to fire severity is effectively monitored using indices derived from satellite optical remote sensing (Fernández-García et al., 2022; Costa-Saura et al., 2022), particularly the Normalized Difference Vegetation Index (NDVI) (Parks et al., 2018a; Taylor et al., 2021). NDVI uses the Red and Near InfraRed (NIR) channels and is calculated as

$$NDVI = \frac{NIR - Red}{NIR + Red} \qquad (1)$$

It is directly sensitive to green leaf biomass and is therefore used to quantify living biomass (Zhu and Liu, 2015; González-Alonso et al., 2006). Additionally, it reflects chlorophyll content. NDVI also indirectly indicates live fuel moisture content (Yebra et al., 2013; García et al., 2020; Chuvieco et al., 1999), especially in low shrubland Yebra et al. (2008), Chuvieco et al. (2004). The high revisit frequency of Landsat 7/8/9 or Sentinel-2A/B constellations allows weekly monitoring of fuel phenological stages. The spatial distribution of dominant species and fuel structure, provided by vegetation maps, helps explain fire severity. Open/closed forests and large forest classes (deciduous/evergreen and needleleaf/broadleaf/shrubland) effectively explain FSI (Viedma et al., 2020; Taylor et al., 2021; Viedma et al., 2014; Costa-Saura et al., 2022).

Weather, particularly synoptic patterns, strongly drives fire occurrence (Barbero et al., 2019; Pimont et al., 2021), fire size (Ruffault and Mouillot, 2015; Hernandez et al., 2015a,b), fire intensity (Hernandez et al., 2015a,b; Rothermel, 1972; Byram, 1959), and fire severity (Fang et al., 2015; Birch et al., 2015). Hourly conditions drive the moisture content of dead fine fuel (Van Wagner et al., 1987; Bradshaw et al., 1984; de Groot, 1987) and fire behavior (Rothermel, 1972; Byram, 1959). Mid-term to long-term conditions drive the hydric state (Bradshaw et al., 1984; Parks et al., 2014b; Taylor et al., 2021; Littell et al., 2016) and biomass production of living fuel (Parks et al., 2014b; Piedallu et al., 2019). These factors have been integrated into many specific weather indices. For instance, the Canadian Forest Fire Danger Rating System (CFFDRS) (Van Wagner et al., 1987) provides scalar indices to rate meteorological fire risk. These include the Drought Code (DC), the Duff Moisture Code (DMC), and the Initial Spread Index (ISI). The indices are calculated using only noon meteorological data: wind speed, daily cumulative precipitation, air temperature, and relative humidity (RH). Originally built to rate forest fire weather in the Canadian forests (Van Wagner et al., 1987), these codes have been shown to be particularly relevant in the Mediterranean area (Fargeon et al., 2020; Dupuy et al., 2020; Barbero et al., 2020; Ganteaume and Barbero, 2019), and are operationally used during the fire season in Canada, France, and by the European Forest Fire Information System (EFFIS).

Topography also plays an important role in fire severity. It drives active fire, particularly through the slope, which interacts with wind speed, direction, and fuel (Rothermel, 1972; Byram, 1959; Viedma et al., 2020). However, due to the mismatch in spatial scale between the decametric resolution of available slope products and the kilometric resolution of synoptic wind and RH data, this effect is difficult to account for using common large-scale weather products. Topography also interacts with living fuel. It influences vegetation type, water

availability, and biomass production at all scales (Parks et al., 2018a; Dillon et al., 2011; Holden et al., 2009).

Given the recent focus of forest managers on assessing fire severity, many studies have aimed to improve understanding of FSI variability and its prediction, especially short-term forecasting (Parks et al., 2018a; Holden et al., 2009; Fernández-García et al., 2022; Taylor et al., 2021). Although intra-fire variability is well explained (Pascolini-Campbell et al., 2022; Wells et al., 2019), predicting FSI variability across different fires remains challenging (Wells et al., 2019; Fernández-García et al., 2022; Taylor et al., 2021; Parks et al., 2018a). This predictability is assessed using a training/testing approach (Taylor et al., 2021). The dataset of fires is split into a training dataset (used to train the model) and a test dataset (different fires from the training dataset). This method checks the predictability of FSI in different places and times (test dataset) compared to the training dataset. The procedure can be repeated, or cross-validation can be used, to obtain several configurations of train-test data. This is the essential aim of fire danger forecasting.

To date, all the studies describing and predicting the observed variability of FSI have used explanatory and predictive factors that either reflect the conditions immediately prior to the fire (e.g. immediate pre-fire NDVI (Costa-Saura et al., 2022; Taylor et al., 2021)) or represent scalar summaries of past conditions (e.g. remote sensing indices z-score (Costa-Saura et al., 2022), DC). However, using knowledge of the dynamics of such factors during a time interval prior to fire could improve prediction performance. In fact, they would capture how weather dynamics influence the volume and state of biomass (growth, drying, dying) more effectively than immediate pre-fire measurements. Moreover, such functional information is based on series of measurements and could therefore also be less noisy than measurements at a single time point. To the authors' knowledge, current studies have not yet considered the temporal information provided by pre-fire time series per se, such as time-lagged scalar or temporal evolution of pre-fire conditions (e.g. spring to summer mortality/drying). Nevertheless, optical remote sensing and meteorological data are available at least weekly, making it possible to use pre-fire NDVI and meteorological index time series to predict FSI.

Statistical regression models, such as the Generalized Additive Model (GAM), have proven useful in ecology (Guisan et al., 2002; Frescino et al., 2001; Ohana-Levi et al., 2020) and fire science (Estes et al., 2017; Fassnacht et al., 2021). They can model non-linear responses, are easily interpretable, and allow for precise likelihood-based uncertainty assessment. These models can use immediate pre-fire inputs or time-lagged inputs. However, they do not account for the entire dynamics of fuel proxies and meteorological conditions before the fire. Functional data analysis (Ramsay, 2005) provides a framework for working with functional predictors, such as time series of pre-fire measurements. Scalar-on-function regressions, such as the Functional Linear Model (FLM), use functions as inputs to predict scalar values. Different approaches can represent relevant functional features of time series (Kokoszka and Reimherr, 2017; Ramsay, 2005). For instance, these models have been used to predict coastal hypoxia from remote sensing time series (Li et al., 2023), total suspended solids (oceanography) as a function of short/mid wavelength spectrum (Acar-Denizli et al., 2018), or habitat mapping (vegetation species) with NDVI time series (Pesaresi et al., 2022).

In this context, this study focuses on two research questions: (1) Is the inter-fire variability of RBR explainable and predictable using readily available ancillary (remote sensing and meteorological) data, and with what accuracy? (2) Does knowledge of the full pre-fire dynamics or time-lagged values of NDVI, DC and DMC improve RBR predictions compared to state-of-the-art approaches based on an immediate pre-fire single date? To address both issues, this study investigates how the severity (RBR) of 79 summer fires that occurred during 2016–2021 in the French Mediterranean area can be explained by different types of prediction models. The paper is structured as follows. Section 2
<figure><img src="image_4.png" /><figcaption>Fig. 1. Map of the French Mediterranean area and studied fires.</figcaption></figure>

describes the study area, the remote sensing and meteorological data used, and the models trained and tested. Section 3 presents the results obtained by the different models, while Section 4 discusses them. Finally, Section 5 highlights the main advances of this study and suggests future improvements.

## 2. Material and methods

### 2.1. Study area and fire-land cover dataset

This study investigates 79 forest fires that occurred in the French Mediterranean area between 2016 and 2021, during the summer fire season (June–September). The Mediterranean region of France features diverse forest cover and various topographic profiles (Fargeon, 2019), from the urbanized and agricultural coastal plains to the wooded hills and mountains of Corsica and the hinterland. The biogeographical region has similar characteristics (e.g. precipitation, sunshine, air temperature), with warm and dry summers and mild winters, except for the mountainous area that combines both Mediterranean and montane influences (Barbero et al., 2019). Fig. 1 shows the study area in the western Mediterranean area and the studied fire locations. The minimum, maximum, and mean fire elevation are 5 m, 1439 m, and 285 m, respectively. Fires occurred mainly during July (26 fires) and August (35 fires), while the rest occurred in June (6 fires) and September (12 fires). During the study period, the years 2016 (21 fires) and 2017 (27 fires) experienced heatwave/drought conditions (Ruffault et al., 2023; Fargeon et al., 2020).

The fire perimeters were provided by the National French Forest Service (Office National des Forêts, ONF). To focus on areas that burned naturally, all pixels within a 50 m buffer within the fire perimeter and along the fire area boundary were excluded to take into account firefighting actions. For the same reason, pixels within 100 m of roads and built areas were removed to consider pre-fire mitigation policies (fuel clearance).

Our study focuses on the scale of land-cover (LC) types. We define the observations of the response variable as the spatial intersection between the perimeter of a fire and land-cover patches of given types (Fire-LC pairs) to obtain phenologically consistent and fire-severity-related aggregates (Fang et al., 2015, 2018; Estes et al., 2017) within relatively homogeneous spatial units. The LC perimeters and classification were provided by the National French Forest Database BDForet V2 from Institut Géographique National (IGN). First, we constructed ten classes of LC based on LC structure (open, closed, shrublands) and dominant tree classes (coniferous, deciduous, mixed, shrublands). We considered only fire-LC intersections greater than 13.5 ha, resulting in a selection of 79 wildfires out of the 215 fires mapped. This led to the creation of 179 fire-land cover (fire-LC) pairs with a final filtered

<caption>Table 1</caption>

LC classes, number of fire-LC per LC class and canopy structure types. Forested area with no forest LC class is an area after disturbance (clear cut, fire). They were mapped before 2016.

<table><thead><tr><th>Land cover</th><th>Number of fire-LC pair</th><th>Canopy structure type</th></tr></thead><tbody><tr><td>Mixed closed canopy forest</td><td>10</td><td rowspan="3">Closed</td></tr><tr><td>Broadleaf closed canopy forest</td><td>24</td></tr><tr><td>Coniferous closed canopy forest</td><td>40</td></tr><tr><td>Mixed open canopy forest</td><td>12</td><td rowspan="4">Open</td></tr><tr><td>Coniferous open canopy forest</td><td>18</td></tr><tr><td>Broadleaf open canopy forest</td><td>20</td></tr><tr><td>Herbaceous</td><td>2</td></tr><tr><td>Shrublands</td><td>44</td><td rowspan="3">Shrubland</td></tr><tr><td>Closed canopy forest with no forest</td><td>7</td></tr><tr><td>Open canopy forest with no forest</td><td>2</td></tr></tbody></table>

pixel area ranging from 14 ha to 1238 ha (Table 1). These spatial intersections were used to average ancillary data and RBR. We also grouped land cover according to its canopy-structure type for further analysis. By definition, the three types correspond to the percentage of trees capable of reaching a height of over 5 meters at maturity in situ: between 10 and 40% (open forest), greater than or equal to 40% (closed forest) and less than 10% (non-forest, including shrublands and herbaceous).

### 2.2. Remotely sensed reflectance data

Sentinel-2 and Landsat -7/8 data were used to derive spectral FSI and pre-fire time series of NDVI. The joint use of Landsat -7/8 and Sentinel-2 data enhances temporal resolution. Landsat -7 Enhanced Thematic Mapper (ETM+) and Landsat -8 Operational Land Imager (OLI) provide reflectance data with a 16-day revisit period, with an 8-day shift between Landsat -7 and Landsat -8. Landsat data were downloaded from the USGS Earth Explorer platform/Landsat Collection 2 Level-2 Science Products from 2015 to 2021. At this product level, shortwave optical data are provided directly as bottom of the atmosphere reflectance at their native resolution of 30 m. Landsat -7 data were processed with the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) algorithm (Version 3.4.0) (Schmidt et al., 2013) and Landsat -8 data used the Land Surface Reflectance Code (LaSRC) algorithm (Version 1.5.0) (Vermote et al., 2016). Sentinel-2A/2B satellites provide reflectances with a 10-day revisit period, with a 5-day shift between Sentinel-2 A and Sentinel-2B satellites. Data between 2016 and 2021 were downloaded from Theia-land with a level 2A-FRE processing, corrected for atmospheric and topographic effects using the MAJA software (Hagolle et al., 2010, 2008, 2015; Baetens et al., 2019). To filter Sentinel-2 pixels spatially (see 2.1), Sentinel-2 pixels were aggregated from 10 m and 20 m to a 30 m resolution on the Landsat -7/8 grid. To do this, weighted averages for band values (fraction of the source pixel that is covered by the destination pixel) and mode for mask values (value which appears most often of all the sampled pixels) were used.

### 2.3. Spectral FSI

For each fire, FSI were computed from immediately pre-fire and post-fire overpasses of the Sentinel-2 Multispectral Imager images with a minimum frequency of clear pixels of 80%. We prioritized the closest overpass to the start (mean[standard deviation] = 6.5[5.5] days before the fire) and end (mean[standard deviation] = 7.6[7.5] days after the fire) of each study fire. The same pixel locations were used in pre- and post-fire images. We used NIR (B8 A band) and Short-Wave InfraRed 2 (SWIR2 - B12 band) to calculate the following FSI:
Normalized Burn Ratio (López García and Caselles, 1991)

$$NBR = \frac{(NIR - SWIR2)}{(NIR + SWIR2)} \qquad (2)$$

Relativized Burn Ratio (Parks et al., 2014a)

$$RBR = \frac{NBR_{prefire} - NBR_{postfire}}{NBR_{prefire} + 1.001} \qquad (3)$$

## 2.4. Sets of explanatory predictors of RBR variability

In the following sections, we describe the different variables, either functional or scalar. Table 2 summarizes all the variables initially used in all the models.

### 2.4.1. Length of time series

In order to include all the most relevant variations of explanatory variables before fires, we chose a maximum time series length of 185 days before fire for the following reasons. NDVI time series, and particularly their variations (increase/decrease), indicate the seasonal trends in active biomass (Reed et al., 1994; Zhang et al., 2003). In the Mediterranean regions, NDVI increases in spring until early summer and decreases during summer drought until September (Chéret and Denux, 2007, 2011). Since the major part of fire activity happens at the end of July, a 185-day window encompasses both spring living fuel activity and summer decrease of activity. In addition, DC and DMC reflect seasonal to monthly weather conditions (Van Wagner et al., 1987) whose trend and variations are taken into account from late winter to the summer fire season (Ruffault et al., 2018a).

### 2.4.2. Vegetation data

NDVI time series were computed from the NIR and Red bands of both Sentinel-2 and Landsat 7/8 data. Only overpass dates that provided at least 75% of clear pixels among the pixels selected to compute FSI (see 2.3) in each fire-LC pair and date were used. Band values were averaged across each fire-LC pair and date.

To be used as a variable in an FLM, time series must have the same time step and length (same total number of time steps). However, fires occurred at different times (year and day of year) and places (different Landsat/Sentinel tiles), and were variably affected by cloud cover. Consequently, Red and NIR bands, once averaged at fire-LC scale, were resampled during a period of 185 days before fire. First, we applied a band value selection for each Fire-LC. We started by deleting band values greater than the average band value (z-score greater than 3 Yaro et al., 2023), which were possibly contaminated by undetected clouds in the mask layer (Irish, 2000; Tarrio et al., 2020; Zhu et al., 2018). Then, we used smoothed B-spline interpolation as suggested in Ramsay (2005) and implemented in Pesaresi et al. (2022), with restricted maximum likelihood (REML) for automatic smoothing parameter optimization using the R package mgcv (Wood, 2011). We selected the band values whose difference from the interpolated data was not labeled as outlying according to the interquartile range criterion with a parameter of 1.5 (Hoaglin et al., 1986; Hoaglin and Iglewicz, 1987; Hoaglin, 2003). Finally, if the number of selected band values was greater than 6, we interpolated these values as before with B-splines, using a 5-day timestep. NDVI time series were computed from the smooth resampled time series of Red and NIR using the R package fda.usc (Febrero-Bande and De La Fuente, 2012) following Eq. (1).

### 2.4.3. Meteorological data and fire weather indices

In France, the SAFRAN (Système d'Analyse Fournissant des Renseignements Atmosphériques à la Neige; Analysis system providing data for the snow model) reanalysis dataset (Vidal et al., 2010) provides daily-averaged meteorological data over an 8 km grid (air temperature (average and maximum), RH, wind speed, and 24-hour cumulative rain).

We computed the codes using the CFFDRS System, using noon meteorological variables estimated with mean daily data from the SAFRAN dataset, during the 185 days preceding the fire. Air temperature was set to the maximum air temperature as in Barbero et al. (2019). DC estimates the long-term availability of water (slow-drying fuel) in soils at a depth of 10 to 20 cm and integrates a simplified expression of potential evapotranspiration. It has a classical change time of 52 days, i.e., the free moisture content of the theoretical fuel represented by DC decreases by 2/3 in 52 days under constant weather conditions (de Groot, 1987). DC depends only on the 24h-cumulative rain and the air temperature. DC may be linked to fuel water content (grass and shrub species) in the Mediterranean area (Pellizzaro et al., 2007; Viegas et al., 2001; Ruffault et al., 2018b). DMC rates water availability in mid-to-surface soil (5–10 cm) and has a change time of 12 days (de Groot, 1987). It depends on the RH, the 24h-cumulative rain, and the air temperature. Finally, ISI is a composite index that links wind speed to a hypothetical dry fuel surface layer and is linked to fire ignition, initial propagation (Van Wagner et al., 1987) and fire spread (Wang et al., 2023). It is only computed for the day of the fire. It depends on the RH, the 24h-cumulative rain, the air temperature, and the wind speed. These codes were calculated using the cffdrs R package (Wang et al., 2017).

In the Mediterranean region, rainfall mainly occurs during fall and winter, loading the soil with reserves (Limousin et al., 2012; Allard et al., 2008). Drought conditions are often observed in summer, combined with high air temperatures (Ruffault et al., 2018a). Since wet/moist conditions during the fall may influence fire activity the following year (Holz et al., 2012; González et al., 2018), we computed the cumulative rain during the fall season preceding the fire (October-December of the pre-fire year). In addition, since drought and heat wave conditions may have a persistent effect on live fuel during the following month/year (Senf and Seidl, 2021), we also computed the mean summer daily maximum air temperature (June-September) of the year preceding the fire.

### 2.4.4. Topographic data

The French National Elevation Database (BDAlti) from IGN provided a 25 m-spatial resolution digital elevation model. We decided to keep elevation and slope data, and we computed their arithmetic average within the spatial extent of each fire-LC pair.

### 2.4.5. Location data and day of year

To consider the possible temporal shifts between time series, the day of year (DOY) was also used as a scalar input variable. In the spatial dimension, location along the Mediterranean arc was shown to be a predictor variable for large fire activity (Ganteaume and Barbero, 2019; Castel-Clavera et al., 2023), occurrence (Castel-Clavera et al., 2023), and fire severity in the USA (Parks et al., 2019). Longitude and Latitude of each Fire-LC were selected as input scalar variables.

## 2.5. Models

Three model classes were implemented to evaluate the impact on RBR prediction of pre-fire times series up to 185 days before the fire events: FLM 2.5.1, GAM with scalar time-lagged predictors and GAM with only measured pre-fire inputs 2.5.2

### 2.5.1. FLM description

The FLM extends the multiple linear regression to functional predictors. Scalar-on-function regression explains a scalar output – here chosen as RBR – using functional predictors (Ramsay, 2005). As functional variables, we used DC and DMC time series as well as resampled NDVI time series (see Section 2.4.2) with a sample frequency of 5 days. Pre-fire DC and DMC were directly used without pre-processing due to their relative smoothness. Given the functional variables $k \in$
<table><caption>**Table 2**
Time series and scalar variables used as predictors of RBR.</caption><thead><tr><th>Predictor variable</th><th>Times series/Scalar</th><th>Units</th><th>Data source</th></tr></thead><tbody><tr><td>NDVI</td><td>Times series</td><td>-</td><td>Sentinel-2/Landsat-7/8</td></tr><tr><td>DC</td><td>Time series</td><td>-</td><td>SAFRAN</td></tr><tr><td>DMC</td><td>Time series</td><td>-</td><td>SAFRAN</td></tr><tr><td>ISI</td><td>Scalar</td><td>-</td><td>SAFRAN</td></tr><tr><td>Cumulative fall rainfall<br/>- pre-year fire</td><td>Scalar</td><td>mm</td><td>SAFRAN</td></tr><tr><td>Mean maximum<br/>summer air temperature<br/>- pre-year fire</td><td>Scalar</td><td>°C</td><td>SAFRAN</td></tr><tr><td>DOY</td><td>Scalar</td><td>-</td><td>-</td></tr><tr><td>Elevation</td><td>Scalar</td><td>m</td><td>BD Alti</td></tr><tr><td>Slope</td><td>Scalar</td><td>°</td><td>BD Alti</td></tr><tr><td>Longitude</td><td>Scalar</td><td>°</td><td>-</td></tr><tr><td>Latitude</td><td>Scalar</td><td>°</td><td>-</td></tr></tbody></table>

`{NDVI, DMC, DC}` and the corresponding coefficient (weighting) functions $\beta_k$, the regression equation was:

$$ RBR_i = \alpha + \int_{\delta}^{0} \beta_{NDVI}(t) N DVI_i(t) dt + \int_{\delta}^{0} \beta_{DC}(t) DC_i(t) dt + \int_{\delta}^{0} \beta_{DMC}(t) DMC_i(t) dt + LM_i + \epsilon_i \quad (4) $$

with $\alpha \in \mathbf{R}$, the intercept; $i = 1, \dots, N$, $N$ size of the sample; $\epsilon_i \sim \mathcal{N}(0, \sigma^2)$, independent for different $i$; $\delta \in [-185; -15]$ time depth (number of days before fire); $LM_i$ a linear combination of scalar predictors (see Table 2).

For each functional predictor $k \in \{NDVI, DMC, DC\}$, $\beta_k$ – the weighting function – is constructed as a smooth and interpretable function (Goldsmith and Scheipl, 2014). If $k$ is centered, then when $|\beta_k(t)|$ is relatively large it has a significant influence on the output. The increasing or decreasing influence on the output is determined by its sign (Ramsay et al., 2009).

Among the various possibilities for defining a FLM, the functional principal-component regression (FPCR) (Cardot et al., 1999) uses the functional principal component (PC) decomposition of each functional predictor. This approach provides an orthonormal functional basis with a fixed number of basis functions than are chosen to explain as much variance of predictors as possible over the definition domain $[\delta, 0]$. Each centered predictor $k \in \{NDVI, DMC, DC\}$ was linearly decomposed on this basis $(PC_{kj})_{j \in N^*} \cdot (C_{kj})_{j \in N^*}$ are the coordinates of each centered predictor in this basis, hereafter named PC-scores. The first 3 PC were used, since they represent 99%, 88%, 96% of the total variance for NDVI, DMC and DC respectively, for the fire–LC datasets when $\delta = -185$ days.

With FPCR, each coefficient function $\beta$ is written as a linear combination of the PC variables. FPCR is therefore equivalent to a standard multilinear regression model (Goldsmith and Scheipl, 2014; Ramsay et al., 2009). In this study, the expression of $\beta_k$ ($k \in \{NDVI, DMC, DC\}$) was $\beta_k = a_{k1}PC_{k1} + a_{k2}PC_{k2} + a_{k3}PC_{k3}$ with $a_{k1}$, coefficients to be estimated. Finally, the regression equation was:

$$ RBR_i = \alpha' + \sum_{k \in \{NDVI, DMC, DC\}} [a_{k1}C_{k1i} + a_{k2}C_{k2i} + a_{k3}C_{k3i}] + LM_i + \epsilon_i \quad (5) $$

Thus, nine parameters for the three functional predictors (3 PC-scores per functional variable) and eight parameters for other scalar predictors were estimated. These seventeen predictors are referred to as

the All-variable set. All computations (FLM model training, PC analysis) were implemented with the R package fda.usc (Febrero-Bande and De La Fuente, 2012).

### 2.5.2. GAM

We successively fed a GAM (hereafter called Lagged GAM (LGAM)) with point-wise time series values from DC, DMC, and NDVI in addition to static predictors. Models were evaluated separately for time-lags $\tau$ ranging from -185 to 0 with a 5-day step, following the equation:

$$ RBR_i = \alpha'' + g_{NDVI}(NDVI_i(\tau)) + g_{DMC}(DMC_i(\tau)) + g_{DC}(DC_i(\tau)) + NLM_i + \epsilon_i'' \quad (6) $$

with : $\alpha'' \in \mathbf{R}$, the intercept; $i = 1, \dots, N$, $N$ size of the sample; $\epsilon_i'' \sim \mathcal{N}(0, \sigma'^2)$, independent for different $i$; $\tau \in [-185; 0]$, time-lag (number of days before fire); $g_k, k \in \{NDVI, DMC, DC\}$, smooth function; $NLM_i$ a non-linear additive combination of scalar predictors.

As a benchmark, we trained and tested a GAM fed with measured pre-fire remote sensing data and day-of-fire DC and DMC, in addition to static predictors. Both models were fitted using a Gaussian distribution of the response variable with the R package mgcv (Wood, 2011). We used REML for automatic smoothing parameter optimization. We activated the internal variable selection to identify and remove non-relevant predictor variables (Marra and Wood, 2011).

## 2.6. Train-test procedure of the models

In this section, we describe the procedure developed to evaluate the predictive performance of the above models.

### 2.6.1. Splitting procedure for training and test datasets

Prediction of fire severity requires that the training and test datasets be independent in time and space. The entire fire–LC dataset was randomly split into a training and test dataset according to a 90%–10% ratio, considering the location and time of each fire. For a given fire, all its fire–LC pairs were either in the training dataset or in the test dataset. To increase the variability of the training dataset when the previous split was repeated, only 75% of the initial training dataset was kept (remaining fire–LC were unused) in the final training dataset.

### 2.6.2. Optimal time depth/time-lag selection and best predictor selection

For both the FLM and LGAM approaches, we employed a 10-fold cross-validation repeated 10 times for each time depth and time-lag, respectively. This approach resulted in 100 trained models, providing exactly 100 test datasets and 10 test predictions for each fire-LC and each time depth/time-lag. Practically, we randomly split the entire dataset 10 times, using the method described in 2.6.1, ensuring that each fire-LC appeared exactly once in a test dataset. Subsequently, we trained 10 different models based on the various training datasets and obtained one prediction per fire-LC. This process was repeated 10 times so that each fire-LC was predicted exactly 10 times as a test. This approach was performed for each time depth varying between -185 and -15 days and each time-lag varying between -185 and 0, with a 5-day time step, for FLM and LGAM respectively. The minimum time series length for FLM was set to 15 days to maintain consistency with the time series approach compared to the scalar approach. This decision was motivated by the average shift between pre-fire satellite overpass and fire date, which was mean[standard deviation] = 6.5[5.5] days.

For the FLM approach, given the initially high number of variables (All-variables set: 17 variables) and the comparatively small size of our dataset (179 fire-LC), we additionally chose to perform variable selection. The most relevant predictors among PC-scores and scalar variables were therefore selected. For each train/test split and each time depth, we implemented a backward variable selection algorithm based on the p-value and the Bayesian Information Criterion (BIC) (Weidberg et al., 2021; Yu et al., 2019) prior to prediction. Note that this
step was automatically performed for LGAM using the internal variable selection (Marra and Wood, 2011).

We further put into practice the optimal time depth selection for the FLM approach. We considered the Root Mean Square Error (RMSE<sub>test</sub>), computed at each time depth. This was done between the measured RBR and the predicted RBR for each of the 100 test datasets (Li et al., 2023). For every time depth $\delta \in [-180; -20]$, the average $\overline{RMSE}_{test}(\delta)$ and standard error $se_{test}(\delta)$ of RMSE<sub>test</sub>(t), $t \in [\delta - 5; \delta + 5]$, were computed. The optimal time depth $\delta_{opt}$ was defined as the maximum $\delta$ where the minimum $\overline{RMSE}_{test}$ was reached. To account for uncertainty in the choice of optimal time depth, we further computed $\delta_{min}$, the minimum time depth such that for all $\delta_{min} \le \delta \le \delta_{opt}$, we had $\overline{RMSE}_{test}(\delta) \le \overline{RMSE}_{test}(\delta_{min}) \le \overline{RMSE}_{test}(\delta_{opt}) + 1.96se_{test}(\delta_{opt})$. We symmetrically computed $\delta_{max} \ge \delta_{opt}$. We computed for LGAM, the optimal time-lag $\tau_{opt}$, $\tau_{min}$, and $\tau_{max}$ using the same methodology.

Finally, for the FLM approach only, the cumulative number of times that a predictor variable was selected for time depths in the interval $[\delta_{opt}, \delta_{max}]$ was calculated. Only variables selected at least 1 time out of 2 (both static scalar variables and PC scores), named the FLM-selected variables set, were kept.

### 2.6.3. Selection of optimal model

For all the considered FLM, LGAM, and GAM approaches, both the All-variable set and the FLM-selected variable set were used as input. For the FLM approach, when the All-variable set was used, no variable selection was performed, although we selected the corresponding optimal time depth following the procedure previously described (see 2.6.2). For the All-variable set (and if selected in the FLM-selected variable set), GAM took as input the day-of-fire DC, DMC, and ISI, the immediate pre-fire measured NDVI and the static predictors. LGAM and FLM took as input the time-lagged predictors or time series, respectively, evaluated at the optimal time-lag or optimal time depth and the static predictors.

Regardless of the modeling approach and the variable set, we employed 10-fold cross-validation, repeated 10 times. For every repetition of the 10-fold cross-validation, the predicted RBR test dataset was then evaluated against measured RBR by computing performance scores, including the RMSE and the coefficient of correlation (R). The ten R and RMSE values were averaged. For every training dataset, the same performance scores and BIC were computed and then averaged. Finally, the prediction accuracies were compared first by set of variables for a given modeling approach (GAM, LGAM, or FLM) and then between modeling approaches (GAM, LGAM, and FLM).

### 2.6.4. Exploration of optimal models

For all the models implemented herein, the prediction accuracies (RMSE, R) were also computed by canopy structure type (see Table 1) to assess group-specific performance. For FLM, all the estimated weighting functions and coefficients provided by trained models were recorded. The mean and the 95% confidence interval of the estimated weighting function $\beta$ for each functional predictor and of coefficient estimates for each scalar predictor were computed. For LGAM/GAM and every trained model, we recorded the smooth functions of each predictor as well as their effective degrees of freedom (EDF) to compute a mean value and a 95% confidence interval. An EDF is a proxy for the degree of non-linearity. An EDF of 1 is interpretable as a linear relationship. An EDF greater than 1 and lower than 2 is a slightly non-linear relationship, and an EDF greater than 2 indicates a strong non-linear relationship (Hunsicker et al., 2016; Zuur et al., 2009).

### 2.6.5. Importance of predictors

We chose to compute the importance of a variable using a permutation predictor approach. We followed the same procedure as for best model selection (see 2.6.3). However, for a given predictor, we randomly shuffled the test dataset while keeping other predictors unchanged. The variable importance was therefore computed as the relative increase in RMSE between the predicted and measured RBR, compared to the unshuffled test dataset RMSE (Kaneko, 2022; Breiman, 2001).

## 3. Results

Results of the intercomparison between the three (GAM, LGAM and FLM) RBR models are presented in Section 3.1. In Section 3.2 the importance of each predictor and their impact on model predictions are presented.

### 3.1. Model performance comparison

#### 3.1.1. Selection of predictor set and input parameters

Based on the selection methodology of 2.6.2, all the predictors kept in the FLM-selected variables set are hereafter presented. The selected functional predictors are NDVI, DMC and DC; the selected PC-scores are $C_{NDVI1}$, $C_{NDVI2}$, $C_{DMC1}$, $C_{DMC3}$ and $C_{DC2}$. Moreover, 3 out of 9 scalar predictors are selected: DOY, ISI and latitude. Predictor selection divides the number of variables in FLM models by more than half (8 out of 17). We note that all fuel proxies (NDVI, DMC, DC) were selected, while more indirect fuel proxies (elevation, slope) were not. One location predictor (latitude) was selected. Finally, meteorological variables of the year preceding the year of the fire were not selected, suggesting that the year of the fire provides more valuable information.

Fig. 2 shows the optimal time-lag and optimal time depth for LGAM and FLM respectively, for both sets of input predictors separately. When the All-variables set is used, FLM reaches a minimum RMSE<sub>test</sub> for a time depth $\delta_{opt} = -70$ days while LGAM gets a minimum RMSE<sub>test</sub> for a time-lag $\tau_{opt}$ equal to -80 days (see Fig. 2). When the FLM-selected variables set is used, FLM reaches a minimum RMSE<sub>test</sub> for a time depth $\delta_{opt} = -65$ days while LGAM gets a minimum RMSE<sub>test</sub> for a time-lag $\tau_{opt}$ equal to -25 days (see Fig. 2). Except for the LGAM built with the set of FLM-selected variables, the intervals $[\delta_{min}, \delta_{max}]$ and $[\tau_{min}, \tau_{max}]$ intersect each other. Neither the satellite's mean overpass time before fire (-6.5 days) nor the day of the fire (i.e. 0 days) fall within these intervals, suggesting a significant effect of time-lagged variables.

Whatever the model, slightly better accuracies are reached when the set of FLM-selected variables is used than when the set of All-variables is used. Fig. 3 (respectively Figure A.1) presents the boxplot of accuracy predictions (R) (respectively RMSE) separately for the All- and FLM-selected variables and for the test and training datasets. More specifically, for each of the 3 models, the median R for the FLM-selected variables set and test dataset, is equal to or greater than for the All-variables set, even if the interquartile ranges overlap, except for FLM (see Fig. 3). In addition, by comparing the test RMSE between the set of All variables and that of FLM-selected variables, GAM, LGAM and FLM significantly reduce the RMSE by 1.5%, 3.0% and 8%, respectively. Thus, variable selection allows us to build more parsimonious models, avoiding overfitting, even when automatic variable selection is activated for GAM and LGAM models. Consequently, we will hereafter consider only the (GAM, LGAM and FLM) models built with the set of FLM-selected variables.

Throughout, a substantial drop in prediction accuracy measures is observed when comparing training and test results in Fig. 3 for models built with the set of FLM-selected variables. This drop can be attributed to two interacting factors: the relatively larger number of variables and hyperparameters in all models, and the relatively small number of observations. While the decrease (increase) in R (RMSE) only reaches 0.06 (0.006) for FLM, it reaches 0.19 (0.015) and 0.23 (0.018) for LGAM and GAM respectively. Therefore, all models show overfitting, but the FLM-based approaches are least prone to overfitting, and working with FLM-selected variables further alleviates overfitting in all models. The relatively good training-based prediction scores of GAM and LGAM are misleading, and only test-based scores will be discussed in the remainder of the paper.
<figure><img src="image_5.png" /><figcaption>Fig. 2. Intervals [$\delta_{min}$; $\delta_{max}$] and [$\tau_{min}$; $\tau_{max}$] and point set in $\delta_{opt}$ and $\tau_{opt}$, respectively for FLM and LGAM, per variable set. The x-axis is the number of days before fire.</figcaption></figure>

### 3.1.2. Performance comparison of GAM, LGAM and FLM

FLM achieves better accuracies than LGAM, and both models outperform the state-of-the-art GAM. FLM reaches R=0.68/RMSE=0.057 and LGAM reaches R=0.60/RMSE=0.063, while GAM only achieves R=0.52/RMSE=0.069. Both boxplots (see Fig. 3 and Figure A.1) show that differences between models are significant. These results imply that RBR can be predicted with good accuracy at another location and time on the scale of fire–LC when considering the time series of remote sensing and meteorological data prior to a fire.

FLM obtains a lower BIC (−328) than LGAM (−322) and GAM (−313), suggesting a better compromise between parsimony and precision with regard to training. However, we emphasize that the three model classes (GAM, LGAM, FLM) each possess a relatively large number of degrees of freedom with respect to quite different data features, such that the differences in prediction performance are largely due to model structure and not only model complexity. The additional lag-parameter of LGAM leads to clear superiority over the classical GAM, and the use of the information describing the shapes of time series curves in FLM brings significant performance gains in comparison to the nonlinearities available in GAM and LGAM.

The improved accuracy of FLM over LGAM for RBR prediction is also consistently observed in the separate analysis for different canopy structure types. Table A.1 presents the R and RMSE between predicted and measured RBR, according to the canopy structure types. The best accuracies of FLM are achieved for shrublands, open canopy structure type and finally closed canopy structure type. The same order is achieved by LGAM/GAM, which have lower prediction accuracies than FLM. Remotely sensed vegetation indices such as the NDVI are sensitive to the upper visible part of the canopy, while fire is driven by and affected both understory and overstory, and so is RBR. Consistently, for open canopy forests and shrublands, the prediction is good. Conversely, accurately predicting RBR over closed canopy forests is difficult since NDVI does not capture understory information.

## 3.2. Assessing the importance of predictors and their impact on RBR predictions

We present each variable by decreasing order of importance in FLM modeling, starting with DMC 3.2.1 followed by NDVI 3.2.2, and DC 3.2.3) and ending with the scalar variables (latitude, DOY, ISI) 3.2.4.

### 3.2.1. DMC

Fig. 4 shows the importance of FLM-selected predictors (as defined in 2.6.5) per modeling approach. DMC achieves an importance in FLM of 34%) for RBR predictions. The interpretable function that illustrates this result is the estimated weighting function $\beta_{DMC}$: it reflects the temporal weighting of DMC time series of length $|\delta_{opt}|$. Fig. 5 a and

b show the estimated weighting functions $\beta$ corresponding to the time series of each predictor (NDVI, DMC and DC). The estimated weighting function $\beta_{DMC}$ positively weights DMC values that are below the pointwise mean DMC before –45 days (particularly at time –55 days), and above the pointwise mean DMC in the interval [–45;–8] days, with a strong weight at t=–20 days (see Fig. 5 a). From –8 days to the day of fire, the weight is almost zero.

The optimal time-lag of $\tau_{opt} = -25$ days in LGAM matches the time when $\beta_{DMC}$ strongly weights the high DMC values. Fig. 6 (respectively Figure A.2) presents the estimated partial effects of smoothed functions of LGAM (respectively GAM) for the FLM-selected variables. DMC reaches an importance of 16% in LGAM and provides a nearly linear and increasing smooth function (EDF=1.1). Similar partial effects of smoothed functions and a lower importance are achieved for GAM.

### 3.2.2. Impact of NDVI

In FLM, NDVI has an importance of 32% (see Fig. 4). The curve $\beta_{NDVI}$ is strictly decreasing, with positive values in the interval [−65;−20] days and negative values in the interval [−20;0] days (see Fig. 5 a). Thus, it positively weights NDVI values that are greater than the pointwise mean NDVI before –20 days, and gives almost half the weight to values that are less than the pointwise mean NDVI after –20 days. Consequently, high RBR values are achieved for NDVI time series that decrease more rapidly than the mean NDVI time series, and that have a high NDVI 65 days before the fire and a low NDVI on the day of the fire.

Given the intrinsically temporal nature of this behavior related to the NDVI dynamics and the corresponding shape of its time series, such results cannot be captured within the framework of static LGAM/GAM. Both LGAM and GAM provide a nearly linear increasing smooth function (EDF=1.1, see Fig. 6 and Figure A.2) of absolute values of NDVI at $t = \tau_{opt} = -25$ days and immediately before the fire respectively. Even if NDVI is the second most important variable in LGAM and GAM modeling, its importance is smaller than for FLM (see Fig. 4). This partly explains the gap in prediction accuracies between LGAM, GAM and FLM.

### 3.2.3. Impact of DC

Similar to DMC, DC is a meteorological code that is evaluated using the same input data (air temperature, 24h-cumulative rainfall), except that DMC also takes RH into account. DC is the third most important variable, at 11% (see Fig. 4). The estimated curve $\beta_{DC}$ is a decreasing function of time and positively weights DC values that are greater than the pointwise mean DC before –35 days and less than the pointwise mean DC after –35 days (see Fig. 5a and b).

Average DC values ([300, 700]) maintained between –65 to 0 days are linked to a high severity rate. In contrast, rapid DC increases leading
<figure><img src="image_6.png" /><figcaption>Fig. 3. Boxplots of prediction accuracy (R) per modeling approaches, variable set and dataset. The black point and the numerical value below each boxplot is the mean R.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Importance of FLM-selected variables per model.</figcaption></figure>

to high DC values on the day of the fire are linked to a low RBR (see Fig. 5a). This situation can be encountered in places where precipitation is low and/or air temperature high but without extreme conditions for several months (Van Wagner et al., 1987; Ruffault et al., 2018a). Between -65 and 0 days, every DC function is increasing, meaning there was no significant precipitation in this time interval (Van Wagner et al., 1987), and suggesting that meteorological water inputs for living fuel were low, whatever the fire considered. Given that DC change time is 52 days, this result is consistent with a low long-term soil water availability and high air temperature influencing summer living fuel activity (Piedallu et al., 2019). These results are consistent with the LGAM/GAM results, which show that DC reaches very low importance in LGAM/GAM (see Fig. 4) and partial effects are decreasing and almost zero (see Fig. 6 and Figure A.2) when DC is evaluated between -35 days and the day of the fire.

### 3.2.4. Impact of the other static variables: latitude, DOY and ISI

Latitude has an importance of 6%, 22% and 16% for FLM, LGAM and GAM respectively (see Fig. 4). Such a difference is mainly explained by the strongly non-linear influence of latitude on RBR in LGAM/GAM (EDF=4.3/3.9, see Fig. 6 and Figure A.2). Latitudes under 42°N and above 43.3°N involve low RBR, while latitudes between 42°N and 43.3°N involve high RBR. This interval encompasses the central French Mediterranean area, where the vast majority of fires occurs along the sea (see Fig. 1). Such a discrepancy in importance between LGAM/GAM and FLM suggests that either latitude is a proxy for an effect that is already accounted for through time series in FLM, or, due to the linear model, FLM is unable to capture this non-linear influence. We point out that simply including latitude as an additional nonlinear smooth effect in FLM (i.e., in a FPCR-GAM hybrid model) does not improve test-based prediction performance (R=0.67[0.053] / RMSE
<figure><img src="image_8.png" /><figcaption>Fig. 5. Time series of a) weighting functions $\beta$ for DMC, NDVI and DC variables and b) time series of DMC, NDVI and DC (bottom) separately. $t = 0$ matches the day of fire. Gray lines refer to the 100 weighting functions (top) and the 179 DMC, NDVI and DC time series per Fire-LC (bottom).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Mean partial effects of smooth functions for LGAM at $\tau_{opt} = -25$ days. y-label provide the mean EDF and its standard error. Gray lines refer to the 100 smooth functions.</figcaption></figure>
=0.059[8.1e-3]). Therefore, further studies are needed to understand this a priori area-specific behavior and the interactions between latitude and other predictor variables to possibly integrate it into an improved model.

DOY has a low importance for FLM, LGAM and GAM at 5%, -1% and 2%, respectively (see Fig. 4). For FLM, LGAM and GAM respectively, the positive coefficient estimate (0.00049) and the increasing smooth functions (see Fig. 6 and Figure A.2) show a positive correlation between DOY and RBR. We suppose that this non-biophysical predictor explains a seasonal phenomenon that neither NDVI nor DC/DMC can explain.

ISI has an importance of 4% for FLM (see Fig. 4) and shows a counterintuitive negative effect on RBR since its mean coefficient estimate is negative (-0.0012), while its importance for LGAM/GAM is almost 0. ISI is a proxy for the rate of spread without the influence of variable quantities of fuel fire (Van Wagner et al., 1987). At decametric spatial scale, wind speed (Viedma et al., 2020) or rate of spread (Viedma et al., 2014) is one of the controlling factors of FSI. In fact, at fine spatial scale, rate of spread is a function of the relative position of the pixel in relation to the advancing flame front (leading, flanking, receding, etc.). Thus, at our coarse spatial scale, Fire-LC ISI may not be consistent. In addition, as already pointed out by Taylor et al. (2021), our weather data is daily and has a resolution of 8 km, whereas fire weather conditions can vary from hour to hour and over short distances in steep terrain Viedma et al. (2020).

# 4. Discussion

## 4.1. Model predictive accuracies

In our study, we used time series of pre-fire optical remote sensing data and meteorological indices to predict fire severity (RBR). We show that the use of time series significantly improves prediction accuracy (R, RMSE) compared to the use of immediate pre-fire values or time-lagged point values. Our evaluation of prediction accuracy allows for more robust results and conclusions as the test dataset is independent in time and space from the training dataset. To date, no such study has been carried out using pre-fire time series and the test/train split evaluation procedure. Parks et al. (2018a) used the same train/test split procedure with immediate pre-fire data and scalar summaries of past conditions. With two classes of RBR (RBR < 0.298 and RBR ≥ 0.298) in the western US forests, they reached an area under the curve of 0.72. In contrast, our a posteriori classification of RBR predictions using the same classes yielded an accuracy of 98%. However, one must be very careful with this result because our dataset is not equally balanced between the two classes (90% of our Fire-LC is classified as RBR ≥ 0.298). More recently, in the Mediterranean area, Fernández-García et al. (2022) predicted DNBR at a spatial resolution of 20 m with data remotely sensed immediately before the fire and achieved a correlation (R) of 0.49 on the test dataset.

## 4.2. Optimal time depth

Our study shows that knowledge of two months (65 days) of pre-fire fuel dynamics improves fire severity index prediction. Longer or shorter time series or pointwise time values are not useful and may introduce additional noise into the prediction. This finding is consistent with studies of fire occurrence or size using similar time frames, as there is a lack of reference in the area of fire severity research. Vega-Nieva et al. (2024) found that a period of 50 days (selected from candidates in the range of 10-90 days for an accumulated fuel dryness index) was optimal for predicting fire occurrence in Mexico; Riley et al. (2013) found that metrics based on one to three months of weather data, such as monthly precipitation totals, had strong correlations with both total area burned and number of large fires. The optimal time depth of 65 days may capture live fuel moisture dynamics – as a consequence of accumulated drought and/or antecedent water balance – that have been highlighted in fire occurrence prediction (Vega-Nieva et al., 2024; Riley et al., 2013)

## 4.3. Impact of the most important predictors on RBR

We show that predictors using time series are the most important (DMC, NDVI then DC) compared to the scalar predictors. FLM modeling allows us to physically interpret the time series variations that lead to high or low fire severity.

Our results provide a better understanding of the DMC dynamics before fire. The DMC decreases logarithmically with rainfall (which is taken into account if it exceeds 1.5 mm) and is a linearly increasing function of air temperature and a decreasing function of RH (Van Wagner et al., 1987). A fast increase of DMC is hence the result of either high air temperature, low RH or both. Thus, $\beta_{DMC}$ positively weights fires subjected to strong meteorological forcing for 35 days (-55 to -20 days before the fire (see Fig. 5)), a period of time that is consistent with the DMC change time (12 days) (Van Wagner et al., 1987). FLM and LGAM show that, contrary to other studies on the activity of large fires (Barbero et al., 2019) and burnt area (Maffei and Menenti, 2019), short-term DMC values (from -8 days to the day of the fire) do not strongly influence RBR. This result is supported by the low importance (3%) of DMC in GAM (see Fig. 4). Our interpretation is that, given the DMC change time (12 days) (Van Wagner et al., 1987), this index is not able to influence the RBR in such a short time span.

Our results confirm other studies that suggest a strong positive impact of NDVI on FSI (Parks et al., 2018a; Taylor et al., 2021). Furthermore, they provide insights into the NDVI pre-fire dynamics leading to high RBR. A low $NBR_{prefire}$, which is highly correlated to pre-fire NDVI (R=0.94 in our dataset), is either the result of a low pre-fire dead/living biomass all year long, or the result of a decrease in the amount of living/wet fuel (García et al., 2020; Chuvieco et al., 2002; Yebra et al., 2013). However, $NBR_{postfire}$ is sensitive to postfire disturbances (ash, etc.) (Kokaly et al., 2007; Hudak et al., 2007; Lewis et al., 2021) which are the result of fire influence on living and dead fuel (combustion, scorching, etc.) (Jain and Graham, 2007). Consistently, since NDVI time series are a proxy for live/wet fuel (Zhu and Liu, 2015; González-Alonso et al., 2006; Chuvieco et al., 2004, 1999), NDVI that is decreasing faster than average may be the result of an increase over time in dead or dry fuel (Pettorelli et al., 2005; Brodrick and Asner, 2017), which then induces more fuel consumption (Andrews, 2018).

Other studies have established a positive correlation between short-term/day-of-fire DC values and severity (Fang et al., 2015) (only for DC lower than 180). Our results may seem contradictory. However, with the exception of 4 fires, the day-of-fire DC values lower than the average DC, ranged from 400 to 740, indicating already high values. For instance, the forest DC was above 400 at the start of the 2018 California mega-fires (Kang et al., 2023), which is consistent with (Pellizzaro et al., 2007), who have defined DC=400 as the critical value for the ignition potential of two shrub species in northwest Sardinia. More generally, studies relating DC to fuel moisture content in the Mediterranean area show that when DC values range from 600 to 800, fuels become as dry as possible, reaching a saturation level (Field et al., 2015; Pellizzaro et al., 2007; Viegas et al., 2001).

NDVI variations reflect the interaction between fuel and weather because NDVI directly measures a surface state at high spatial resolution (fuel biomass and greenness) and thus the live fuel response to meteorological forcing. The longer-term variable DC is an index that only reflects meteorological conditions, particularly drought, typically calculated from data available at coarser spatial resolution. This may explain the greater importance of NDVI compared to DC when explaining RBR, even though NDVI variations (possibly delayed) are partly a consequence of meteorological forcing. However, the fact that DC remains in the set of variables selected by FLM implies that it brings additional information that is not included in NDVI variations. This suggests that the combined use of meteorological and remotely sensed data is important in the field of fire severity prediction and, more generally, in the field of fire risk outcomes modeling. Indeed, fire risk models and indices are mainly based on meteorological data, with the exception of the Fire Potential Index (Burgan et al., 1998), which combines both information.
<figure><img src="image_10.png" /><figcaption>Fig. 7. RBR values, measured or predicted by the different models, per fire and LC.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Predictor time series for the two studied fires A (high severity) and B (low severity); see 4.3 for details. Time series of DMC, NDVI and DC per Fire-LC, and mean (all dataset) time series of DMC, NDVI, DC.</figcaption></figure>

## 4.4. Example of application to two contrasted fires

To illustrate the previous results, two fires named fire A and fire B are selected for their contrasted overall severity. More specifically, these two fires show different temporal dynamics in terms of NDVI and DC, and almost the same temporal dynamics in terms of pre-fire DMC. These examples would allow a better understanding of the important role of pre-fire time series in predicting fire severity. Fire A took place the 3rd, July 2021 (DOY=184, ISI=4.72, latitude=43.16). Its three LC classes have RBR measured values larger than the third quartile of all the dataset. Fire B occurred the 15th, June 2017 (DOY=166, ISI=4.43, latitude=43.71). It is one of the least severe fires in the dataset. Fig. 7 presents the measured RBR and the mean predicted RBR from the three (FLM, LGAM and GAM) models, for each fire-LC separately. Figure A.3 shows the measured RBR map (a), the FLM mean RBR prediction map (b), and the LC map (c) for fire A and B separately. All the models underestimate the RBR of fire A (high severity) and overestimate the RBR for fire B (low severity), for all LC classes (see Fig. 7 and Figure A.3). However, FLM achieves the best results for both fires and every LC, by reducing the absolute error committed by the best GAM/LGAM by 35 to 70%.

Fig. 8 presents the pre-fire DMC, NDVI and DC time series for each of the 6 fire-LC and the fires A and B. Due to the coarse resolution of SAFRAN data, all fire-LC of the same fire have the same DC and DMC values. For both fires, the DMC values are lower than the pointwise

mean DMC, indicating relatively low meteorological forcing prior to the fires. DC values are more contrasted. Fire B DC is very low, with values below the mean pointwise DC during the 65 days preceding the fire. Fire A DC time series have a pattern that is positively weighted by the DC weighting function: between -65 days and -30 days, DC values are higher than the pointwise mean, while DC values between -30 days and 0 days are lower than the pointwise mean (see 3.2.3). The most contrasting pre-fire temporal dynamics are found for NDVI time series. The NDVI values of the three fire-LC of fire B increase with time and are lower than the pointwise mean NDVI 65 days before the fire. For Deciduous Close and Open canopy forest, the NDVI is higher than the pointwise mean NDVI on the day of the fire, whereas Shrublands NDVI values remain lower than the pointwise mean NDVI. These temporal patterns lead to a negative impact of NDVI on RBR (see 3.2.2). On the contrary, the NDVI time series of the three fire-LC of fire A show a faster-than-mean decrease and are higher than the mean 65 days before the fire and lower than the mean (for two LC) on the day of the fire. This pattern leads to a positive impact of NDVI on RBR (see 3.2.2). Therefore, although the meteorological conditions do not clearly distinguish the RBR of fires A and B, the NDVI time series provide a better understanding of the pre-fire conditions and the contrasting RBR values between the two fires. We suggest that taking the temporal information into account explains the difference in prediction between FLM and GAM/LGAM.
## 4.5. Perspectives

Current advances in optical/thermal remote sensing over forests (Penot and Merlin, 2023) and the future thermal mission (TRISHNA) could remove the spatial limitations of meteorological indices. The high spatial and temporal resolution of thermal data would give access to site-specific estimates of evapotranspiration/water stress in conjunction with a physical model of the moisture content of live fuels (Ruffault et al., 2023). In addition, using non-linear functional models may bring valuable improvements to the results of this study. Finally, the use of physical models of fire behavior (Andrews, 2018) and high-resolution input data (Sebbar et al., 2023; Wagenbrenner et al., 2016), would bridge the gap between FSI models that operate at both coarse and fine scales, providing operational products for both land managers and fire-fighters.

## 5. Conclusion

To date, accurate prediction of remotely sensed fire severity indices, such as RBR, from pre-fire optical and meteorological data remains a challenging task. Taking into account the temporal dynamics of pre-fire fuel proxies has not yet been explored. To fill the gap, this study is based on the use of widely available pre-fire time series of remote sensing and meteorological data in FLM and time-lagged data in LGAM to predict RBR at the fire–LC scale. More specifically, the objectives are: (1) to quantitatively assess the usefulness of time series or time-lagged data in statistical models to predict RBR, (2) to assess the optimal time depth/lag and the best predictor set to predict RBR.

As a first assessment, the use of time series/time-lagged data in FLM and LGAM models, improves the results obtained by the benchmark model (GAM). In addition, a time depth of 65 days before the fire allows FLM to achieve the best prediction accuracies, while a time-lag of 25 days for RBR predictions allows LGAM to improve the GAM prediction accuracies. The two most important selected predictors are DMC and NDVI for FLM, followed by DC, which are all variables related to fuel behavior. The faster-than-average decrease in NDVI, starting from high values 65 days before the fire, leads to large RBR values: the process of drying/dying of living fuel before the fire leads to large RBR. Consistently, the DMC time series that increase faster than average and reach pre-fire DMC values larger than average, tend to induce high RBR. Thus both bottom-up fuel drying/dying and top-down early meteorological drying are strong drivers of fire severity.

Although these results provide an overview of the prediction of RBR, our study has several limitations. First, we only use general-purpose vegetation indices that are only approximations of fuel behavior, which is particularly true for fire-weather codes. The latter variables only work with coarse meteorological data and do not take into account water storage capacities in the soil. In addition, NDVI is only sensitive to the visible overstory greenness, whereas fire affects both overstory and understory, and RBR is subject to capture impacts on both. Moreover, we do not use a phenological correction in the RBR calculation, which could improve the transferability of the burn severity assessment (Parks et al., 2018b) in the future and then strengthen our conclusions. Finally, further research is needed to better characterize spatial aggregates at a finer spatial scale, and including broader fuel and meteorological conditions would allow to improve the accuracy of our predictions and the generalizability of our conclusions.

### CRediT authorship contribution statement

Victor Penot: Writing – original draft, Methodology, Investigation.
Thomas Opitz: Writing – review & editing, Methodology.
François Pimont: Writing – review & editing.
Olivier Merlin: Writing – review & editing.

### Funding

This study was funded in part by the Horizon 2020 ACCWA project (grant agreement # 823965) in the context of Marie Sklodowska-Curie research and innovation staff exchange (RISE) program.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.agrformet.2025.110588.

### Data availability

Data will be made available on request.

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