Accounting for fuel in fire danger forecasts: the fire occurrence probability index (FOPI)

A new fire danger index is proposed to overcome one of the most important limitations of current fire danger metrics. The fire occurrence probability index (FOPI) combines the Canadian fire weather index (FWI) with remote observations of vegetation characteristics to better predict landscape flammability. The FOPI is designed to improve fire danger predictions in all fuel-limited environments where fire is driven by the short-term drying of intermittently-available fuel. The FOPI considerably outperforms the FWI in arid biomes while remaining comparable to the FWI where fuel is abundant.


Introduction
Wildfires are the result of the combined action of weather and fuel availability [1,8]. In forested areas, weather is the most relevant element to fire [3]. As fuel is abundant all year around, persistent droughts are crucial controlling factors. Conversely, in fuelscarce biomes, like savanna, the occurrence of fire is triggered by intermittent fuel availability and its short-term superficial drying [30]. While there is consensus that the most violent fires happen where fuel is in abundance and that weather is the controlling factor [7,26,48], surface fires in fuel-limited environments generate large-scale burning and trigger widespread pollution episodes conducive to severe health impacts [6,38]. Savanna is the largest biome, covering more than 50% of all land, and is the landscape that experiences the most widespread fire activity with 50% of all ignitions recorded [12]. The total biomass emitted into the atmosphere from African savanna fires equals 10% of carbon net primary production [31], constituting more than half of the total global burnt area [5,21,49].
Despite their relevance to global fire activity, landscape changes and fuel availability are not considered in the calculations of indices employed in fire early warning systems. A variety of fire danger rating systems are used around the world. The Canadian Forest Fire Danger Rating System is used in Canada [51], the National Fire Danger Rating System is used in the USA [11], the McArthur Forest Fire Danger Index is used in the eastern parts of Australia [35], the Forest Fire Behaviour tables were developed for use in Western Australia [46], and a variety of fire danger indices are used in Southern European countries [52]. Most of them are based on the assumption of a spatially and temporally constant fuel load and only consider weather as a driver for the establishment of fire danger conditions [3,14,15,36,43].
The reason for this simplification is historical as fire danger models were developed for local applications and often calculated at human-operated stations where weather measurements were collected and fuel status could be observed [29]. This was also at a time when continuous and globally available fuel monitoring was unavailable. Since then, there has been a steady improvement in our monitoring capabilities. Optical sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS) have been collecting the leaf area index (LAI) and the fraction of absorbed photosynthetic active radiation (fPAR) for the last 20 years. Two L-band microwave sensors have been performing systematic observations of vegetation optical depth (VOD) which is directly related to the total above-ground biomass (AGB) [44]: the Soil Moisture and Ocean Salinity (SMOS) satellite [27], launched by the European Space Agency (ESA) in November 2009, and the Soil Moisture Active Passive satellite [16], launched by NASA in January 2015. LAI, fPAR and VOD are now available in quasi-real time on a roughly weekly revisiting time, providing global information on total vegetation biomass, canopy density and greenness. Admittedly, these parameters do not directly provide the amount of biomass available for burning as the detected signal often integrates live and dead fuel mass as well as plant moisture content. Yet, they display a promising relationship with fuel load. For example, VOD observations from the SMOS sensor, transformed into AGB estimates, are a good proxy for dry-matter released during fires [13] and are a valuable predictor to identify high ignition probability from the lightning forecast [9,12]. Similarly, LAI measurements have been employed to derive fine fuel measurements in desert grassland, where they have been shown to explain 75% of the variation of the available biomass [24].
The progress made in remote sensing instruments, and the focus of many recent and planned satellite missions in collecting observations of the soil-vegetation interaction, provides an opportunity to also improve fire danger modelling. This work therefore attempts to improve fire danger prediction by suggesting a new combined index to forecast landscape flammability. The fire occurrence probability index (FOPI) is derived using either VOD or LAI measurements as a proxy for fuel load, and the fire weather index (FWI) as an indicator of fire weather. The new fire danger index, which is derived from the FWI, provides a similar ability to the FWI in forested areas but, by applying a dynamical fuel mask, highly improves the correlation of the FWI with observed fire activity in fuel-limited environments.

Data and methods
To understand the link between fuel, weather and fire, a data cube is created for 2020, collocating fuel indicators, FWIs and recordings of fire activities. The dataset is then split into 80% training and 20% testing, using a random sampling generator. The training dataset is employed to analyse under which landscape and weather conditions fire activity was observed and to derive the FOPI analytical formulation. The independent dataset is instead used to assess the new flammability index performances in predicting fire activity. More than 9 million points are used in the training and 3 million points in the validations. The dataset is composed of collocated, FWI, VOD, LAI and measures of fire activities expressed as burned areas (BAs) and active fires (AFs). The remainder of this section describes in detail the data used.

Fuel indicators
Two vegetation-related remote measurements are used in this study as a proxy for fuel: the LAI and the VOD. Both LAI and VOD (as a precursor of AGB), are identified as essential climate variables by the Global Climate Observing System working group [47] and are therefore likely to be considered a priority in the upcoming earth observing missions [42].
LAI and VOD measure different aspects of the vegetation. LAI is a dimensionless quantity that characterizes plant canopies. Defined as the total area of leaves per unit ground area, it directly relates to the amount of visible radiation that can be intercepted by plants [55]. VOD, instead, is a measure of the extinction affecting the microwave radiation when propagating through the vegetation canopy [40]. Unlike LAI, VOD measurements are not affected by the presence of clouds, which obstruct remote observations in the visible part of the solar spectum and are also less sensitive to the presence of water in the atmosphere. Despite these advantages, the use of microwave observations implies a relatively coarse spatial resolution for VOD (⩾10 km) as a result of the low energy of the emissions when compared to what is achievable for LAI (⩽1 km). Despite LAI and VOD being measured using different wavelengths, studies have shown that there is a strong correlation between them [22].
In the last 20 years, different satellite missions have been measuring LAI and VOD using both active and passive instruments [17,18]. Discrepancies among instrument outputs have also been highlighted, which could affect the homogeneity of the long term record available for these essential climate variables. Yet, as the scope here is to identify areas of available fuel with respect to barren soil, differences across missions are deemed to provide a variability smaller than the information signal of interest. This implies that the derived analytical formulation for the FOPI should be platform independent, leaving the user the chance to adopt any of the available data sets. For the scope of this analysis, we use a dataset for LAI from the product MOD15A2 of MODIS, which is an eight-day composite with a spatial resolution of 1 km on a sinusoidal grid [28,39]. VOD retrievals are from the 2LSM product of the ESA's SMOS mission [2] which is provided on a 25 km grid around 3 h after acquisitions. Data are collected on a daily time window and processed using a ten-day moving window average to obtain global coverage. Fields are also interpolated to a 0.5 • regular grid using bilinear interpolation.

Fire Weather Index (FWI)
Fire danger models quantify the effect weather has on landscape flammability. These models describe how short-term and long-term variations in atmospheric temperature, humidity, precipitation and wind affect fuel moisture content and, consequently, the likelihood that a fire can develop and sustain itself, if ignited. The FWI developed in Canada is adopted here, mostly for its widespread use in both operational and scientific communities [10,14,15,35,54]. FWI was derived for a specific woodland fuel bed meaning a globally invariant fuel density, fuel depth, fuel load and burning characteristics are assumed. In this analysis, global FWI daily values for 2020 are calculated from weather forecasts using the ECMWF operational prediction system, as described in [15]. Values from the original octahedral forecast model grid O1280 (9 km) are interpolated over a regular 0.5 • grid using bilinear interpolation.

Fire activity
Global fire activity is monitored remotely, either by observing BAs or AFs. AFs are detected through temperature anomalies in quasi real time from several instruments, including MODIS, visible infrared imaging radiometer suite (VIIRS), and Sentinel3 which are equipped with the 3.7 µm channel which displays a strong signal from a fire's radiant energy [53]. BAs are surfaces which have been sufficiently affected by fires to display significant changes and are usually images post-processed from visible acquisitions [37]. BA derivation is often aided by information on AFs and techniques for perimeter recognition. Due to the more complex processing, BA products become available with substantial delays so they are not generally used in global real time applications; however, they are considered a benchmark estimation of global fire activity [4].
Despite BA and AF providing similar information there are substantial differences between the two products [45] and they are likely to grossly underestimate fire activity globally [41]. It was found that [23] many AFs are observed for pixels without BA observation and, vice versa, there are no AFs detected in pixels that are classified as burned. It was reported in [13] that, globally in 2020, there were almost 40% cases in which a recorded AF was not matched by a BA observation. To take into account the substantial uncertainties in the detection of fires globally, in this study both BA and AF are used as a proxy for fire activity. AFs are from Collection 6 MODIS MOD/MYD14 products [19,20] and daily data are grouped and counted into a 0.5 • regular grid to provide the total number of observed AFs over a 2500 sq km surface. BAs are instead from a multisensor product provided by the ESA Climate Change Initiative [41]. Version v5.1 is processed using a twophase algorithm, where MODIS hotspots and nearinfrared reflectance are combined [32]. The gridded product is at a 0.25 • resolution and this is further processed by a cumulative aggregation to the 0.5 • regular grid of the other data sets.

Definition and analytical derivation
The FOPI is defined as the ratio of fires occurred per simultaneous occurrence of weather and fuel conditions (figure 1). The FOPI expresses a probability that a fire is detected (if an ignition occurs) when certain conditions are met. Similarly to the FWI, the FOPI is a measure of flammability but establishes a stronger link between the landscape status, the weather and past fire activity. The FOPI analytical formulation is derived with a data driven approach using a parametric nonlinear least squares fit over the training dataset (80% of the sample) extracted from the data collected in 2020. The mathematical expression for FOPI is given in equation (1) with the best fitting parameter given in table 1.
The optimised FOPI fit is provided in figure 2 as a bivariate surface that peaks at high FWI (⩾200) and at values for VOD or LAI at around 0.6. Figure 1 and its best fit counterpart (figure 2) also show that there is a clear range of values for fuel, which maximises the chance a fire can develop and sustain itself, given FWI is high enough. Interestingly, the strength of this relationship depends on the variable chosen to be a proxy for fuel load and how fire occurrence is detected. Even if the total number of detected fires is the same when either using BA or AF, more fire events fall into fewer VOD/FWI than LAI/FWI joint categories. This means that VOD is potentially a more suitable predictor of fire detection. Another aspect worth noting is the capability of BAs to act as a proxy for fire activity when compared to AFs. Despite a known large underestimation of BA caused by a failure to detect small fires which do not leave a visible scar to the ground, they have a substantially larger number of cases at high FWI. AFs can similarly suffer from missing detection due to poor satellite sampling, cloud masking and high vegetation interference [25] but are also affected by substantial over-detection in certain areas due to spurious signals from reflecting surfaces [53]. For this reason AFs are generally recognised as less accurate than BAs as a method to detect fire activity. While all parametric combinations are given in table 1, the recommendation is therefore to adopt the formulation that uses VOD and BA.

FOPI interpretation
The FOPI aims to improve the FWI applicability in fuel-limited environments by reducing FWI values in regions that either have very little fuel to burn or where the landscape is too moist to sustain fires. To this end, FOPI identifies those combinations of FWI and VOD/LAI values that have previously resulted in detected fire activity (see figure 3). The higher the fire activity detected in the past, the higher the FOPI value for that combination, the more severe the prediction of the landscape flammability. By construction, FOPI is bounded to values between 0 and 1 which ease its interpretation in terms of probability of occurrence. Nevertheless, as for other fire danger metrics, high values of FOPI do not guarantee a fire will start as this is conditioned by the occurrence of an ignition.
To understand how the weather and fuel components contribute to the FOPI, it is important to examine terms A and B of equation (1)    A VOD of 0.6 marks the maximum of this regime and larger values of VOD will indeed result in a decrease of the FOPI. While this seems counter-intuitive, it is due to the nature of VOD which is not only affected by the amount of biomass present but also its moisture content [44]. Therefore, higher VOD values are due not only to an increase in organic matter, but also to its moisture content. According to the analysis presented, when VOD is larger than 1, vegetation becomes too moist and there is a decrease in its probability of burning.
When f = f 0 , the term exp ) 4 reduces to 1 and FOPI is controlled exclusively by term A. When this happens, fire weather is extreme and a fire activity could be intense unless fuel is too wet to burn (VOD>>1). While this situation is theoretically possible, FWI being an open-ended index, values of FWI around f 0 = 200 are never recorded in vegetated areas (they can occur in dry deserts like the Sahel). This means that FOPI numerical values will almost never reach 1 in real cases. More typical values of FWI = 20 will produce FOPI ranging between 0 and 0.6, depending on the available fuel. Higher values of FWI at around 50 will be able to push FOPI to 0.9, if fuel is available.

Results of FOPI performances
The ability of FOPI is benchmarked against FWI, looking at the improved performances of this index to correlate with fire activity globally. The analysis is conducted both globally and stratified per dominant biome (here grouped in forest, savanna, and agriculture, as in [50], see also figure S1 in supplementary material). The analysis that follows is performed using the independent data set drawn from the 2020 data cube, which was not used to derive the best fitting parameter of equation (1).

Correlation with fire activity
To quantify how FOPI and FWI correlate with observed fire activity, linear correlation heat maps are provided for all data in the test dataset and for subsets classified according to the different biomes. Figure 5 confirms that, globally, FWI is a weak predictor of fire activity [15]. At most, in forested areas, correlation reaches 0.2. Correlation declines to 0.06 in fuellimited biomes. Globally, FOPI performs better as it largely improves fire detection in savanna. FWI and FOPI are, as expected, highly correlated with each other (90% correlation in forests and up to 70% globally) but their relationship with fuel (either VOD or LAI) is substantially different. FWI as a drought indicator anti-correlates with both VOD and LAI (up to −0.48). The FOPI shows a much less pronounced linear correlation due to the in-built exponential relationship expressed by equation (1) and visible also in figure 4(a). It is also interesting how the observed variables, namely AFs, BAs, LAI and VOD, correlated with each other. It is confirmed that AFs and BAs have a weak correlation at 0.37 globally. Not always large, BAs are matched with a high number of AFs [13]. LAI and VOD are instead well correlated with each other but they are not linearly correlated to AF and BA, confirming that fire activity only happens in a restricted interval of VOD/LAI values.

Forecast skill
The receiving operating characteristic (ROC) curve which marks hit rate (HRs) versus false alarm rate (FAR) for a set of thresholds, compares the ability of the FOPI and the FWI to discriminate between fire and non-fire events ( figure 6). It provides a measure of potential usefulness in operational forecasts when the decision regarding intervention is often a tradeoff between the costs associated with missing an event and intervening over too many false alarms [33]. For an index with perfect detection of fire activity, the curve would travel from bottom left to top left of the diagram in figure 6, then across to top right. In this case, HRs equals 1 and false alarm equals 0 is consistently achieved for all the possible thresholds. For an index with no ability the curve would travel through the diagonal. In this case, using the index to detect fire activity is equivalent to the chance of flipping a coin. In between these two extremes lies the skill of the prediction, with the area under the ROC curve (AUC) regarded as an overall metric of performance.
If we only consider the area under the curve, the FOPI mostly beats the FWI, however, the difference is not statistically significant for the agricultural biome when a bootstrap analysis is performed on 1000 subsamples randomly drawn from the whole dataset. The analysis of the shape of the curve helps us to understand how the system performs and its discrimination capacity. Looking at the global performances ( figure 6(a)) the best threshold for the FWI is at 25 when the HRs are greater than the false alarms. At higher values (FWI = 50) the proportion of HR and Figure 5. Correlations among all variables that contribute to the FOPI derivations. FWI is a weak predictor of fire activity (correlation between 0.06 and 0.2) while FOPI performs better as it largely improves fire detection in savanna. FWI and FOPI are highly correlated with each other (90% correlation in forests and up to 70% globally). Active fires and burned areas have a weak correlation at 0.37 globally. Also, LAI and VOD are well correlated with each other but they are not linearly correlated with AF and BA, confirming that fire activity only happens on a restricted interval of VOD/LAI values.
FAR is identical, meaning that the forecast cannot discriminate between fire and no fire. This loss of skill can almost totally be attributed to the poor performance in the savanna biomes ( figure 6(d)). Here, high FWI often cannot correspond to an event, due to fuel scarcity which is not accounted for in the FWI formulations. Thus, at FWI = 50, in 50% of cases a fire will occur and in the other 50% it will not. As the FOPI is correctly taking the fuel availability into account, it is able to greatly improve the accuracy of the detection in this biome. As expected, the FOPI and FWI perform similarly in forested and agricultural areas where fuel is in abundance and weather is a key driving factor.

Forecast reliability
The ROC results are very encouraging, however, ROC is conditioned on when an event is forecast and does not provide an insight into how sharp or reliable the fire danger index is, when it comes to (a) forecasting a no event and (b) correctly forecasting the frequency of occurrence of rare events [34]. One of the recognised limitations of the FWI is that it flattens asymptotically at very high values of flammability [54]. The implication of this asymptotic behaviour is visible in figure 7 where the forecast reliability for the FOPI and FWI are compared. Forecast reliability compares the frequency at which an event is forecast with the observed occurrence frequency. A good forecasting system for fire activity will predict extreme fire danger values only very few times in a year, and this will be matched with a high probability of a fire occurring. On the contrary, a good forecasting system in most cases will predict very low fire danger and this will correspond to low probability of detecting a fire. When this happens we say that the forecast is reliable because it is able to discriminate between event and no event. If we look at the performances of the FWI and FOPI from this perspective, figure 7(a) shows that doubling from 25 to 50 implies a substantial increase in the possible occurrence of a fire (probability of a fire detection increases from 18% to 38%). However, this is not the case when doubling from 50 to 100 (probability of a fire detection decreases from 38% to 24%). Indeed, above 50 any further increase in FWI does not correspond to an increased probability of an event occurring; conversely, the stochastic nature of fire ignition might even reduce the total number of events (like in savanna). Unlike the FWI, the FOPI shows a clear correlation between low forecast frequency and the occurrence of fires. Indeed, FOPI ⩾0.9 occurs in only 2% of cases globally but, when this happens, in 80% of cases it is matched by an observed fire.

Fire events in 2020 and FOPI predictions
There was no lack of catastrophic fires in 2020. The year started with New South Wales in Australia declaring the third state of emergency in six months due to what will be remembered as the most devastating fire season in the country's bushfire history. The 2019-2020 Australian summer, since then named Black Summer, produced hundreds of fires, mainly in the southeast of the country, which burnt an estimated 14.3 million hectares of landscape and destroyed over 3000 buildings, killing at least 34 people. It also produced immense ecological and financial losses and led some endangered species to extinction. At its peak (in January 2020), air quality dropped to hazardous levels in all southern and eastern states and the smoke could be detected across the South Pacific Ocean to Chile and Argentina. As fires were getting under control in Australia, large fires affected the west of the US continent and were particularly costly in Arizona and California. More than 1.5 million hectares of Californian landscape burned, claiming at least 40 lives and causing the destruction of more than 7000 structures. Based on the extent, length and impact the fires had, 2020 is still considered the worst year for West Coast fires in U.S. history.
To provide an idea of how the FOPI could help the localization of critical fires in real time fire monitoring, figure 8 shows the calculated FOPI and FWI for three of the days when fires raged in South East Wales, Arizona and California. The localization of the actual fires is performed through the recorded BAs and a map of observed VOD is also provided to interpret the differences between FOPI and FWI. From the examples in all three events, FOPI is better correlated with the ongoing fire activity. FOPI's more localised outcome stems from its capability of masking out areas of insufficient fuel load. Most local authorities are informed of fuel conditions and would be able to exclude areas where fires are not likely to occur despite high FWI. However, the use of the FOPI is certainly a great improvement in global systems aiming to provide an overview of fire danger worldwide. These system are often used at face value without expert interpretation, which can restrict areas in need of further monitoring.

Summary and conclusion
For years, fire danger rating systems have been a cornerstone of fire management agencies ′ tools to preemptively identify critical areas. Among others, the FWI is widely used thanks to its ease of implementation [10,14] and its correlation with fire activity in forested areas. Still, several studies have highlighted the limited performances of this and similar metrics in fuel-limited ecosystems where fire is driven by the short-term superficial drying of intermittently available biomass. Not accounting for the actual fuel available for burning is one of the most important limitations that hinder the meaningful usability of the FWI in savanna-type ecosystems [15].
The proposed FOPI overcomes part of the limitations that characterise the FWI. In particular, there are two innovative aspects in the FOPI formulations. The first aspect is that, by combining the FWI with remote observations of vegetation characteristics, it provides a framework to account for real-time fuel availability. As an immediate benefit, the FOPI limits unrealistic high values registered in desert areas where fire activity is hindered. It also allows us to retain a memory of previous burning before vegetation recovery takes place. The second advantageous aspect of the FOPI is that it expresses a probability of fire occurrence based on previous observations. The FOPI, by explicitly taking into account the burning history of a given landscape, allows for landscape susceptibility to be considered.
The FOPI formulations were derived using two different metrics for fuel load; VOD and LAI verified against BA or AF products. There is a clear indication that VOD, which is an integrated measure of biomass and its moisture content, is a better predictor to identify fire occurrence, when compared to LAI. Also, it was highlighted how fire activity is better described through the use of BAs rather than AFs, as it shows a much higher correlation with fire danger.
The FOPI is shown to greatly outperform the FWI in all fuel-limited ecosystems while still retaining a comparable ability to the FWI where fuel is in abundance. Unlike the FWI, the FOPI includes the probability of a fire occurring increasing as the index value becomes rarer. This means that while FOPI values of around 1 are very rarely observed in the record, when they are, they are associated with a high probability of fire occurrence. In summary, the FOPI index provides an advancement to monitor fire danger globally and, to some extent, to create a real time link with the available fuel in fire danger forecasts. The use of the ten-day running mean VOD implies that the FOPI can be issued as a medium-range forecast (one to five days in advance) by applying the same map. The usability of the FOPI in extended-range forecasts will, however, require the development of a predictive model for VOD and this is the next step of this research.

Data availability statement
The data used in this study are available through the 'Fire data cube for 2020' repository hosted on Zenodo https://doi.org/10.5281/zenodo.6779756.