Dedah Ahmed-Babou
email: dedah.ahmed-babou@ird.fr

Hervé Demarcq
email: herve.demarcq@ird.fr

Beyah Meissa

Nicolas Bez
email: nicolas.bez@ird.fr

Portfolio of distribution maps for Octopus vulgaris off Mauritania

Keywords: Spatiotemporal distribution data, Maps portfolio, temporal dynamics, Octopus vulgaris

This study introduces the concept of portfolios of distribution maps, which consist of the reduced set of empirical orthogonal maps that best explain spatial biomass distributions of a given species over time. The approach is demonstrated for the distributions of common octopus (Octupus vulgaris) off Mauritania over the last thirty years. The maps in the portfolio are the subset of empirical orthogonal maps that allowed to recover 60% of the spatiotemporal biomass distribution variance and whose temporal weights were significantly correlated with abundance. For octopus during the hot season, one single map explained half of the overall variance of the distribution data, while during the cold season, the portfolio of octopus distribution maps consisted of four maps, with the temporal weights of the second map being negatively correlated with upwelling intensity six months before. The size of each portfolio represents the number of distinct spatial patterns describing octopus spatial distributions. Assuming that specific but hidden processes

Introduction

Ecological monitoring and information systems are increasing worldwide. They are key to providing long-term observations, which are particularly important for reference point determination and investigating tipping points and regime shifts. Aside from their maintenance, one of the main challenges associated with these monitoring systems is how to extract scientific knowledge. For example, how to detect spatial patterns that are persistent in time from large sets of georeferenced observations and how to evaluate their temporal stability in conjunction with abundance variability.

This study aimed to develop a generic approach for summarizing the overall spatiotemporal information of a long time series of spatial distributions into a portfolio of distribution maps with two elements, one time-dependent and the other, possibly low dimensional, space-dependent. The approach is based on min-max autocorrelation factors (MAF) [START_REF] Switzer | Min/max autocorrelation factors for multivariate spatial imagery[END_REF] that can be seen as an extension of empirical orthogonal functions (EOFs, Lorenz, 1956;Wikle et al., 2019) to deal with the presence of spatial structure in the data. MAF have been widely applied in ecology (e.g. [START_REF] Petitgas | Analysing Temporal Variability in Spatial Distributions Using Min-Max Autocorrelation Factors: Sardine Eggs in the Bay of Biscay[END_REF][START_REF] Solow | Detecting change in the composition of a multispecies community[END_REF]Woillez et al., 2009). However, MAF were initially designed to filter out smallscale noise from a set of images. The percentage of variance explained by the selected factors is thus unknown. A recent paper by [START_REF] Bez | Empirical Orthogonal Maps (EOM) and distance between empirical spatial distributions. Application to Mauritanian octopus distribution over the period 1987-2017[END_REF] suggested that MAF can be appropriately reformulated into Empirical Orthogonal Maps (EOMs) that order the factors according to the percentage of variance explained. The aim of the study by [START_REF] Bez | Empirical Orthogonal Maps (EOM) and distance between empirical spatial distributions. Application to Mauritanian octopus distribution over the period 1987-2017[END_REF] was to identify the main spatial patterns that shape the dynamics of a stock. The present work defines how the EOMs are formulated and selected to construct a portfolio of maps consisting of a set of maps describing the main spatial patterns governing the biomass distribution of a species. It then investigates the mutual temporal fluctuations of the elements of the portfolio.

The ideas developed in this paper are illustrated for common octopus (Octopus vulgaris) off Mauritania over the past thirty years. Octopus represents a key species of the Mauritanian marine ecosystem both in ecological terms [START_REF] Boyle | Cephalopod populations : Definition and dynamics[END_REF][START_REF] Caddy | The cephalopods: Factors relevant to their population dynamics and to the assessment and management of stocks[END_REF] and in economic terms. It accounts for more than 70% of cephalopod landings and one third of demersal catches [START_REF] Khallahi | Aménagement des ressources halieutiques et gestion de la biodiversité au service du développement durable[END_REF]. In 2019, octopus generated 71% of total export value ($360 million) of fishery products (Société Mauritanienne de Commercialisation Des Poissons "SMCP", 2020).

The current management and conservation of octopus is based on biological and ecological knowledge, in particular its short lifespan of 12 to 14 months [START_REF] Guerra | Fitting a von Bertalanffy expression to Octopus vulgaris growth[END_REF][START_REF] Hernández-López | Age determined from the daily deposition of concentric rings on common octopus (Octopus vulgaris) beaks[END_REF][START_REF] Mangold | New data on reproductive biology and growth of Octopus vulgaris[END_REF], its rapid growth (Domain et al., 2000;[START_REF] Mangold | Octopus vulgaris[END_REF][START_REF] Sanchez | Growth of octopus (octopus vulgaris) males and females under culture conditions[END_REF], its high fecundity of 100,000 and 500,000 eggs laid by female (O'dor et al., 1978) and its sedentary lifestyle [START_REF] Hatanaka | Studies on the fisheries biology of common octopus off the northwest coast of Africa[END_REF][START_REF] Caverivière | Observations on the influence of temperature on the length of embryonic development in Octopus vulgaris (Senegal)[END_REF]. Octopus reproduce only once; males die after mating and females after hatching of offsprings. Therefore, it is essential to ensure a sufficient proportion of the stock has the chance to reproduce to ensure stock renewal. The sedentary nature of the species implies the need for spatialized management to limit the effects local depletion by fishing and thus creates the need for a good knowledge of its spatiotemporal distribution. In Mauritanian waters, two biological rest periods of 1-2 months each have been implemented each year for all demersal fisheries since 2008. These two rest periods reflect the existence of two annual octopus cohorts with distinct spawning seasons [START_REF] Hatanaka | Studies on the fisheries biology of common octopus off the northwest coast of Africa[END_REF][START_REF] Bez | Empirical Orthogonal Maps (EOM) and distance between empirical spatial distributions. Application to Mauritanian octopus distribution over the period 1987-2017[END_REF]. The variability in abundance of this species is mainly a consequence of recruitment fluctuations that are partly dependent on environmental conditions, especially the intensity of upwelling [START_REF] Caverivière | Observations on the influence of temperature on the length of embryonic development in Octopus vulgaris (Senegal)[END_REF][START_REF] Otero | Bottom-up control of common octopus Octopus vulgaris in the Galician upwelling system, northeast Atlantic Ocean[END_REF] and on the two spawning periods taking place under distinct environmental conditions [START_REF] Faure | The importance of retention processes in upwelling areas for recruitment of Octopus vulgaris: The example of the Arguin Bank (Mauritania)[END_REF].

Since 1982, a dedicated monitoring system has been developed to support scientific advice to octopus management bodies [START_REF] Gascuel | Decline of demersal resources in North-West Africa : An analysis of Mauritanian trawl-survey data over the past 25 years[END_REF]. It is based on regular scientific surveys with standardized sampling protocols providing information on octopus spatial distributions through time. Using these data, persistent spatial patterns or tipping points of change in spatial distribution can then be tracked. In this study, the portfolio of octopus distribution maps in Mauritanian waters was characterized using data from 63 scientific surveys covering the period 1987-2019. The size of the portfolio is discussed as a potential proxy for ecosystem resilience.

Materials and methods

Scientific monitoring surveys

Between 1987 and 2019, the Mauritanian Institute of Oceanographic Research and Fisheries (IMROP) performed 97 scientific demersal bottom trawl surveys on the continental shelf. However, only 63 surveys covered the entire continental slope and were therefore kept for analysis in this study (Figure 1a). The sampling protocol was standardized over the entire period and followed a stratified random protocol based on three latitudinal strata (Figure 1). The mean number of hauls was 102 hauls per survey (min = 57, max = 205, but only four exceed 121 hauls), equally distributed in each strata. The survey area was divided into five bathymetric strata (<30m, 30-80m, 80-200m, 200-400m and 400-600m). The sampling covered very coastal areas due to the probable presence of coastal demersal species. The depth covered ranged from 10m to around 600m. The area of the Banc d'Arguin National Park (PNBA) was not covered by the sampling because it is a marine protected area closed to motorized fishing. The observations consisted of the octopus densities expressed in terms of number of individuals per square meter obtained by dividing the catches by the surface of the area swept by the trawl. These were considered as indicator of abundance assuming that gear catchability remained constant. More details on these data are available in [START_REF] Gascuel | Decline of demersal resources in North-West Africa : An analysis of Mauritanian trawl-survey data over the past 25 years[END_REF], [START_REF] Meissa | Assessing stocks in data-poor African fisheries: A case study on the white grouper Epinephelus aeneus of Mauritania[END_REF] and [START_REF] Meissa | Overfishing of marine resources: Some lessons from the assessment of demersal stocks off Mauritania[END_REF].

For each survey, haul positions were randomly selected and mutually independent. The hauls were thus not performed at the same locations each year. However, the method used in this study required that the observations are located at the same positions (regular or not in space) during the entire time series. In order to fulfill this requirement, the data were kriged on a 0.1° x 0.1° grid covering the sampling area before analysis (341 grid cells). Kriging allows estimating the mean octopus density within each grid cell (Chilès and Delfiner, 2000), provided that there were enough hauls in the vicinity. Variogram models were fitted, survey by survey, to the empirical variograms (for the sake of parsimony they are not shown). The input data for the analyses were thus 63 kriging maps and the corresponding abundance indices.

A time series of upwelling strength over the same period was built from a monthly dataset of the meridian component (North-South) of composite wind speeds over the Mauritanian zone, 50 to 100 km from the coast. This proxy is considered the best proxy linearly linked to the upwelling index for a North-South oriented coast [START_REF] Demarcq | Coastal upwelling and associated retention indices derived from satellite SST. Application to Octopus vulgaris recruitment[END_REF], which is the case for the study area.

A spatialized time series of seasonal average sea surface temperature (two maps per year, one for the hot season and one for the cold season) on the same spatiotemporal grid as the survey data was built from the National Oceanic and Atmospheric Administration (NOAA) database (NOAA, 2020).

Four climatic seasons are generally distinguished in the Mauritanian zone [START_REF] Dobrovine | La ZEE mauritanienne et son environnement géographique géomorphologique et hydroclimatique[END_REF]. A cold season from January to May, a cold-warm transition season from June to July, a hot season from August to October, and a hot-cold transition season from November to December. For this study, these four seasons were aggregated into two main seasons of five and seven months respectively: a hot season from June to October, including 28 of the 63 available surveys and a cold season for the rest of the year (November-May), including the remaining 35 surveys (Figure 1).

The precise timing of the surveys within each season was opportunist rather than following a predefined sampling protocol. The temporal spreading of the surveys was however of the same level in each season (similar coefficients of variation; Figure 1). A portfolio of maps was considered for each season. All the calculations were performed in R using the package RGeostats (MINES ParisTech / ARMINES (2022)).

Setting up the portfolio

A portfolio is defined as a selection of relevant empirical orthogonal maps (EOMs). Below the definition of EOMs is recalled and the method to select those included in the portfolio is explained.

Building EOMs

The workflow for creating empirical orthogonal maps [START_REF] Bez | Empirical Orthogonal Maps (EOM) and distance between empirical spatial distributions. Application to Mauritanian octopus distribution over the period 1987-2017[END_REF] is depicted in Figure 2. EOMs are a variation of min-max autocorrelation factors [START_REF] Switzer | Min/max autocorrelation factors for multivariate spatial imagery[END_REF], where the factors are ordered according to their percentage of contribution to the total input variance. The first EOM explains most of the input variance, and so on down to the last EOM that explains little of the input variance.

We denote 𝑥 𝑖 , 𝑖 = 1, … , 𝑆 the geographical positions of the 𝑆 grid nodes that were systematically informed (isotopy) at time 𝑡 𝑗 , 𝑗 = 1, … , 𝑇, with 𝑇 being the number of input maps(𝑆 = 341, 𝑇 = 63). Input data can be formatted as an 𝑆 × 𝑇 matrix denoted by 𝑍 = 𝑍[𝑖, 𝑗] = 𝑧(𝑥 𝑖 , 𝑡 𝑗 ) where each line in Z corresponds to the time series of the value of a given grid cell. Computing EOMs consists of two sequential PCAs. The first PCA, which is nothing but an EOF based on 𝑍, produces an 𝑆 × 𝑇 matrix, denoted 𝑌, with 𝑇 uncorrelated columns 𝑦(•, 𝑡 𝑗 ):

∑ 𝑦 𝑆 𝑖=1 (𝑥 𝑖 , 𝑡 𝑗 ) • 𝑦(𝑥 𝑖 , 𝑡 𝑗′ ) = 0 ∀𝑗 ≠ 𝑗′ (1)
In the spatio-temporal context, each column of Y is a set of georeferenced points, i.e. a map, uncorrelated to each other.

The absence of correlation refers to pointwise correlations, therefore, to the absence of correlation between map values for the same geographical point.

The second PCA aims at building 𝑇 new factors 𝐹 𝑗 (x i ) = 𝐹(x i , 𝑡 𝑗 ), 𝑗 = 1, … , 𝑇, without mutual spatial correlation for a given spatial distance 𝑟 (the unit spatial lag corresponds to the grid cell size of the input maps), that is, with the following null scalar products:

∑ [𝐹(𝑥 𝑖 , 𝑡 𝑗 ), 𝐹(𝑥 𝑖 + 𝑟, 𝑡 𝑗′ )] 𝑆 𝑖=1 = 0 ∀𝑗 ≠ 𝑗′ (2)
This second PCA is based on the eigen-decomposition of the matrix of variogram and cross-variogram values between standardized EOFs from the first PCA. Finally, we obtain a set of 𝑇 new maps called empirical orthogonal maps (EOMs) ordered by decreasing percentage of explained variance. This realizes the decomposition of the initial spatiotemporal variables 𝑧(𝑥 𝑖 , 𝑡 𝑗 ) into a product of two elements, one element purely spatial made up of the EOMs 𝐹 𝑘 (𝑥 𝑖 )

and the other element made up of their temporal weights 𝜓 𝑘 (𝑡 𝑗 ).

𝑧(𝑥 𝑖 , 𝑡 𝑗 ) = 𝑚(𝑡 𝑗 ) + ∑ 𝜓 𝑘 𝑇 𝑘=1 (𝑡 𝑗 ) • 𝐹 𝑘 (𝑥 𝑖 ) (3)
where 𝑚(𝑡 𝑗 ) is the average abundance of the input map for time tj. The weights measure the importance of a given EOM for explaining the survey time series. In other words, the initial set of maps is decomposed into a weighted linear combination of maps without correlation at short scale (blue box in Figure 2). At this stage, the decomposition is performed with no loss of information. EOMs can be computed for raw or standardized maps. The pseudo-algorithm provided in supplementary material highlights the main steps for computing EOMs when the first PCA is applied to standardized maps.

The signs of the values of the EOMs and their weights are conventional. Therefore, the interpretation of EOMs and their weights must be established jointly. For example, the interpretation of an EOM whose weights are all negative in the decomposition is strictly equivalent to its symmetry with respect to 0 when taking the symmetry of both the EOM and its weights.

By construction, EOMs are mutually uncorrelated for distance 0 and distance r. Assuming that they are also orthogonal for all distances implies that they are fully spatially orthogonal, and that they can be considered as basis for map decomposition. This assumption could be of concern if we were interpolating (i.e. kriging) several EOMs obtained from irregular points in space. In such a case, rigorous interpolation should be done by cokriging the different EOMs.

In this study, interpolation was done before the decomposition and we were simply taking linear combinations of the interpolated input maps. Thus, two contrasting situations can be considered: "interpolate first and decompose then" (as in the present case study) where the assumption has no consequence, and "decompose first and interpolate then", in which case, co-kriging should be recommended to provide a spatially interpolated version of the EOM.

Building the portfolio

The selection of EOMs for the portfolio is based on two nested steps (dashed orange box in Figure 2). In step one, as it is standard practice in PCA analyses, the number of selected EOM is set to ensure a sufficient part of the variance of the input maps is retained. In the present work, we selected the Q EOMs explaining at least 60% of the input variance.

The 60% threshold is arbitrary. It is a compromise between complexity (i.e. the number of EOMs) and explained variance. In our case study, beyond 60% the number of factors increased considerably without a significant gain in explained variance.

In step two, among the Q EOMs from step 1 only those are retained whose spatial patterns are connected to the population dynamics of the stock, that is their temporal weights 𝜓 𝑘 (𝑡 𝑗 ) are correlated with abundance. This is achieved using three complementary criteria. The first criterion is a statistically significant linear correlation between the EOMs' weights and abundance (test level 5%). The second criterion is based on a multivariate time series analysis using autoand cross-correlograms to identify EOMs whose weights vary smoothly over time (auto-correlogram of weights) and in a consistent manner with regards to the temporal variation of abundance (cross-correlogram between weights and abundances). For this, a linear model of co-regionalization (Chilés and Delfiner, 2000; [START_REF] Goulard | Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix[END_REF] consisting of a nugget effect and a linear part is fitted to the empirical correlograms. This allows modeling and quantifying in a consistent manner the random part and the temporally structured part of the correlations. EOMs to be retained have a small random part (small percentage of nugget effect in the respective auto-correlograms). The third criterion is based on maximizing the covariation in time between abundance and EOM weights. This criterion is evaluated using the slopes of the cross-correlograms between weights and abundance. In linear models of coregionalization, the (absolute) value of the slope of the cross-correlogram must be smaller than the square root of the product of the slopes of the two auto-correlograms (Chilès and Delfiner, 2009). Thus, the third criterion is that the ratio between the slope of the cross-correlograms and this upper limit is near one. The final selected set of P EOMs (P≤Q) constitute the portfolio of maps summarizing the spatial dynamics of the species for a given season (Figure 2). Note that when a portfolio is made up of several maps, their temporal joint dynamic is accessible through the auto-and the cross-correlograms that were used for the selection of the EOMs entering the portfolio.

For each of the two seasons, this methodology is used to build portfolio for octopus and for SST separately.

Climatology

A climatological spatial distribution pattern can be obtained computing weighted averages of the P maps in the portfolio:

𝑧 ‾ 𝑃 (𝑥 𝑖 ) = 𝑚 ‾ + ∑ 𝜓 ‾ 𝑘 𝑃 𝑘=1 •𝐹 𝑘 (𝑥 𝑖 ) ∑ 𝜓 ‾ 𝑘 𝑃 𝑘=1 (4)
where 𝜓 ‾ 𝑘 is the mean temporal weight of the P selected EOMs such that:

𝜓 ‾ 𝑘 = 1 𝑇 ∑ 𝜓 𝑘 𝑇 𝑖=1 (𝑡 𝑗 ), 𝑘 = 1, . . . , 𝑃 (5)
and where 𝑚 ‾ is the mean abundance:

𝑚 ‾ = 1 𝑇 ∑ 𝑚 𝑇 𝑖=1 (𝑡 𝑗 ) (6)

Results

Portfolio of distribution maps for the hot season

The hot season is the main octopus breeding period (June to October). The first EOM alone restored 47% of the variance of the observed abundance data (Figure 3), and the first three EOMs recover 60% of the initial variance.

Amongst them, only the first one was finally selected, the two others ones being not sufficiently correlated with abundance, both statistically and temporally (small coordinate values in Figure 3), and having poorly organized temporal evolutions (small feature size in Figure 3).

The hot season's portfolio thus consists only of the first EOM, which is characterized by a north-south gradient, with a high-density area in the north (especially in its wide part), a moderately dense area in the center, and a low density area in the south (Figure 4 , left). The temporal evolution of the weights of the first EOM shows three different phases.

There is a sharp decrease over the first five years followed by stability at low level for about 15 years and then a slightly higher level. Most of the signal describing the spatial distribution of octopus abundance is represented by this pattern.

This distribution pattern provides information on space occupancy of octopus during this season. It summarizes the historically known pattern of octopus distribution with decreasing abundance from north to south. The years where this pattern had a large weight were years of high octopus abundance during the hot season such as the beginning of the study period. The spatial distribution represented by this EOM is linked to the main breeding season of the species, which takes place at the end of the hot season (September-October). During reproduction, octopus seems to display an affinity to milder water temperatures, which occur to the North of the study area (Figure 5, left).

Portfolio of distribution maps for the cold season

During the cold season the spatio-temporal complexity and thus the size of the portfolio was larger than during the hot season (Figure 3, right). No single EOF spatial pattern was found to be dominant. Indeed, the first EOM explained only 14.7% of the variance of the input distribution data, while the first nine EOMs restored 60% of the variance. Four of these top nine EOMs, respectively the 1st, 3th, 4th and 5th, were linked to the spatiotemporal dynamic of the observed mean gridded survey abundance (density). Their weights depicted significant temporal cross correlation with mean abundance. Together, the four finally selected EOMs to build up the portfolio represented 35.4 % of the initial spatiotemporal variance.

The spatial pattern of the first EOM for the cold season was similar to that of the hot season, characterized by an overall north/south gradient with a slightly different temporal evolution (Figure 4, left). However, this EOM showed a denser abundance off the northern area with a more pronounced southward expansion of moderately dense areas. The second EOM of the portfolio (EOM3) indicated a higher abundance in the center with a concentration of abundance south of Nouakchott and two lower density areas in the far south and off the Banc d'Arguin. The EOM4 displayed across-shelf gradient patterns, opposing low density coastal areas to denser offshore areas, particularly in the north and center but also, to a lesser extent, in the south. The last EOM in the portfolio (EOM5) showed two hot spot areas in the north and center. This spatial pattern reinforced, in the north, the spatial pattern of the first EOM but complemented it in the central and southern zones.

Given the criteria used for their selection, i.e. correlation with abundance, the EOMs selected for the portfolio had similar long-term temporal variations in their weights (Figure 4, right). The weights decreased at the beginning of the period, then flattened and slightly increased during 2010-2015. This pattern was reflected in the slope of the respective correlograms (Figure 6). However, as indicated by the (quasi systematic) absence of nugget effects in the crosscorrelograms, their fluctuations at short temporal scales were not correlated (Figure 6). A noticeable exception concerned the short term negative cross-correlation between EOM1 and EOM3. This reflected the opposite fluctuations of the empirical time series in the middle of the period.

The model used in this study quantified the joint temporal dynamics of the EOMs of the portfolio and mean seasonal abundance. It decomposed their mutual temporal correlation into two parts: a nugget effect and a slope. The nugget effect quantified short-term joint fluctuations (e.g. the average variations between two consecutive cold seasons). The slope characterized long-term (multi-annual) joint evolutions. In this context, a change in the overall correlation can be due to either short or long-term processes, or both. However, by construction, the EOMs of the portfolio have been selected because they shared long-term dynamics with that of abundance. By consequence, it remains that within the portfolio the various levels of correlation between EOM weights and abundance rely strongly on the short term. This was consistent with the strong correlation found between EOM' weights and abundance and the value of the nugget effect (Figure 6). In particular during the cold season, the weights of EOM3 were the most strongly correlated to abundance of octopus specifically because, in addition to the fact that they shared similar long-term variations, their short-term fluctuations were also correlated. The cross-correlogram between EOM3 and abundance was indeed proportional to the auto correlogram of abundance (Figure 6). This means that the residual from the regression of the weights of EOM3 against abundance was pure noise, i.e., residuals with no temporal auto-correlation (self-krigeability;

Chilès and Delfiner, 2012). In practice, this means that the weights of EOM3 were proportional to abundance over time with some uncorrelated noise (Figure 7). The third EOM represents thus a central spatial pattern of the spatiotemporal dynamic of octopus. It explained around 7 % of the spatial distribution of octopus that is density dependent.

The climatological spatial pattern associated with the cold season was characterized by two dense areas rather offshore in the northern zone and coastal in the central zone (Erreur ! Source du renvoi introuvable.). A northern zone off Cape Blanc had its epicenter located between the bathymetric lines of 80 and 200m. A second zone was found south of the Cap Timiris (in the middle of the central zone) with an extension to a bathymetric level close to that of the northern zone.

The weights of the EOMs that were part of the portfolio were not statistically different (Student p-value = 0.008) for surveys carried out in December and in March (Figure 9). The ranges of fluctuation and the mean densities appeared smaller for December surveys. However, for the two instances where a December survey was followed by a March surveys the following year, the evolutions of the weights were mixed up (increasing for EOM5, decreasing for EOM3, one increasing and the other one decreasing for EOM1 and EOM4).

During the cold season, the two months with the largest number of surveys were December and March (Figure 1b).

Although not significant, the temporal weights for EOM 1 to 5 were larger in March compared to December (Figure 9). March was the month used for analyzing relationships with the upwelling intensity index. Correlations with the upwelling index for the same month (i.e. considering EOM weights during the months of the surveys and the upwelling indices for the same month during the period 1987-2019) and with a time lag of one to seven months before showed similar behavior for each of the EOMs of the portfolio. The correlation is significantly negative only for EOM3 for a 6 months delay (5% level test; Figure 10 left). The upwelling indices in September belonged to the lower part of the interval of fluctuation and corresponded to low upwelling intensity [START_REF] Balguerías | On the identity of Octopus vulgaris Cuvier, 1797 stocks in the Saharan Bank (Northwest Africa) and their spatio-temporal variations in abundance in relation to some environmental factors[END_REF]. The eight instances available for this study (octopus survey in March and upwelling index available six months before) covered the full range of possible values observed in September from 1988 to 2019. In particular, they were not distributed in the tails and hence did not represent a particular situation.

Discussion

The approach of portfolios of distribution maps proposed in this paper relies on a set of criteria to select the empirical orthogonal maps to be included in the portfolio. These criteria may be case specific and it is hard to avoid subjective choices. First, similarly to any PCA analysis, one has to choose a threshold for the variance to be explained by the set of selected maps. For a target value of 60% of explained variance, it can happen, as in our case that three and nine maps can be enough for summarizing spatial distributions of octopus in two seasons. The aim of the study being to identify the spatial patterns which were correlated with abundance, we then selected those EOMs whose weights had significant temporal cross-correlations with abundance. This resulted respectively in one and four spatial patterns in each seasonal portfolio explaining 47% and 35 % of the overall variance observed over the past thirty years. In other words, this analysis demonstrated for the first time that half of the information brought by the initial twenty-eight maps recorded between 1987 and 2019 during the hot season could be summarized by a single distribution map whose temporal evolution increased and decreased with octopus abundance. During the cold season, the situation was more complex and the variability could be less easily reduced. Four maps madee up the portfolio for that season and their recombination based on their respective weights allowed recovering only a third (35%) of the initial variance. There was thus a more clear and persistent signal for connecting spatial pattern and stock abundance during the hot season, and thus more possibilities for efficient spatial planning during this season.

Despites its importance for explaining the overall variance of the distribution maps observed during the cold season, EOM2 was not selected for the portfolio. Its weights were too variable over time and not sufficiently correlated with abundance, both in the short and in the long term (Figure 3). In other words, EOM2 represented a spatial pattern that was important for explaining the variance of the original set of distributions (hence its rank in the decomposition) but without temporal coherence and without connection to abundance. EOM2 was symptomatic of a coastal hotspot of abundance south of Cap Timiris (Figure 11) that pulses at random from time to time without contributing much to the abundance. The portfolio of the cold season explained not more than a third of the overall variance, which indicates that the spatial distribution of octopus during the cold season were highly variable and poorly linked to abundance variations.

The derived climatology aimed at representing the average spatial distribution of octopus over the study period accounting for the effects of abundance variations on the spatial distribution. The two seasonal climatologies based on one map for the hot season and on the average of four maps weighted by their average weights for the cold season, showed similar spatial patterns (not shown). This confirms the known yearlong persistence of a gradient of octopus density from north to south [START_REF] Pease | Fisheries of Mauritania[END_REF] whose intensity is related to abundance (stronger in years with higher densities). However, during the cold season, abundance tended to be more offshore with a secondary area of distribution in the middle of the Mauritanian EEZ. The fact that the portfolio was larger during the cold season could be linked to an affinity to optimal water temperatures.

The spatio-temporal decomposition of the time series of thirty-four SST maps covering the period 1986-2020 for each season provided interesting insights on the spatial distribution of octopus and on the two portfolios generated in the present study. First, during the hot season, 88% of the variance of the SST input maps was represented by a single map. During the cold season, the signal was more blurred. Four maps were needed to recover 67% of the variance (the first one incorporating 38%). This difference in number of maps was similar to the difference between the two portfolios obtained for octopus even though the levels of variance explained by the portfolio (48% and 35%) were notably smaller than the percentage of variance explained by the first x EOMs of SST (? %). Second, the main spatial patterns in both seasons was a north-south gradient. However, the gradient did not mean the same thing in both seasons.

According to the literature, an optimal window for octopus would likely be centered on 21°C (Villanueva, 1995). The observed mean SST was around 24°C and 19.5°C during the hot and the cold seasons respectively so that the optimal window is respectively below and above the mean during the two seasons. Values around 21°C corresponded to negative areas in SST EOM1 for the hot season (Figure 5). More precisely, the SST in the northern area of EOM1 during the hot season represented an area that was -2°C below the seasonal average. Weighted by 1.5 in the decomposition of the true SST distributions, this area was thus precisely where one finds systematically SST values around 21°C during the hot season. There was thus a very strong match between octopus densities and SST main spatial patterns during the hot season. In the cold season, this gradient was complemented by other patterns accounting for more than 10% each, that were consistent with the patterns observed in the octopus portfolio (more southern, more offshore). Indeed, given the mean SST, the optimal window, if relevant, corresponded to positive areas in the main maps. In particular, the fourth most important pattern presented in the cold season time series corresponded to a clear and strong westwards cross-shelf gradient that can be connected to a similar medium signal found in the octopus portfolio.

The fact that the arrangement of maps in terms of the percentage of variance explained (EOM) strongly matched the arrangement based on the strength of their spatial structures (MAF) is worth mentioning (Erreur ! Source du renvoi introuvable.). The situation could be that the EOMs explaining most of the variance could be maps without spatial structure, i.e. with hot spots appearing here and there from EOM to EOM. This would be the case for systems with strong spatiotemporal fluctuations and poor persistence of their spatial distribution over time. In this study, the maps explaining the most of the variance of octopus spatial patterns are indeed also those with the strongest spatial structures.

In an ideal situation, one would work with a regular spread of scientific surveys over time. This was not the case in the present study as the timing of the surveys was somewhat opportunistic. For instance, during the cold season, surveys took place mainly in December (N=10) or in March (N=10) and April (N=8). However, the weights of the EOMs were not associated with specific months and their differences were not statistically significant. Therefore, the four EOMs selected for the portfolio of the cold season (November-May) were considered together as the set of principal spatial patterns that best summarized octopus spatiotemporal distributions during that season. However, the analysis of the joint temporal dynamics of the weights of the different EOMs highlighted the particular characteristics of EOM3.

While all EOMs of the portfolio shared their long-term trends with that of abundance, the short-term (i.e. year-to-year) variations of the weights of EOM3 were also correlated with abundance. EOM3 represented thus a major spatial pattern of the spatiotemporal dynamics of octopus. It captured a part of the spatial distribution of octopus that is density dependent. The particular role played by EOM3 was reinforced by the analysis of the correlation with the upwelling intensity index. Amongst the four EOMs making up the portfolio of the cold season, this was the only one whose temporal weights showed significant correlation with the upwelling index when considered six months before. Even though to be interpreted with care given it was based on only eight observations, this result is interesting. While the phenology between upwelling and primary and secondary productions is well documented, the demonstration of a delayed impact on octopus distribution is new. The March surveys caught individuals that weight on average one kilogram (data not shown). These individuals mostly correspond to pre-spawning adults of 9-10 months. They come from the spawning that took place around May the year before. Given the duration of larvae and para-larvae developments [START_REF] Otero | Reproductive cycle and energy allocation of Octopus vulgaris in Galician waters, NE Atlantic[END_REF], Domain et al., 2000), the end of the pelagic phase for these individuals falls around August-September. Thus September during which upwelling is usually not intense (Figure 10), coincides with the period of settlement for the individuals spawned in May. Our results suggest that the less intense the upwelling is in September, the more spatially concentrated the octopus recruitment is in the following March, with highest occurrence of octopus off the coast in the central Mauritanian ZEE as indicated by the spatial pattern of EOM3 (Erreur ! Source du renvoi introuvable.).

The present study suggested that a portfolio of distribution maps and in particular its size can provide novel insights.

During the hot season, only one EOM was needed to summarize the set of observations for octopus compared to four EOMs for the cold season. The two seasons are of similar durations (five and seven months respectively) and surveys data were spread across both. Thus, the difference in portfolio size between the two seasons is not attributable to variations in the timing of the monitoring. Instead, the difference in map portfolio size could be considered a consequence of a real difference in the spatial dynamics of octopus during the two seasons. The portfolio size quantified the effective number of spatial patterns of octopus seasonal distributions. It was reduced to a single spatial pattern during the hot season in the present study. In contrast, the spatial distribution of octopus during the cold season was a mixture of four principal maps, with the importance (weight) of one being strongly related to the fluctuation of abundance.

Ecological considerations arising from portfolio size can be of two kinds. Portfolio size measures the complexity of spatial occupancy patterns and the associated complexity of possible external parameters governing them over time.

On the one hand, a large portfolio can characterize systems where one process governing biomass distribution can decrease without impacting the overall system if other processes offset it. On the other hand, systems associated with a small portfolio size have fewer buffer effects and could be more sensitive to external changes (putting all the eggs in one basket is risky). Following these lines, a general perspective of this work could be to quantify the size of many species distribution portfolios and relate them to knowledge about the resilience of the ecosystem the species belong to. 22 25 28

Figure 2

 2 Figure 2 Workflow of the method. Upper blue block: building T different EOMs from a set of T maps. Lower orange block: selecting the P EOM entering the portfolio. In this case, the Q-first EOMs explain a given percent of the overall variance. Amongst them, the second EOM is not retained as its weights are not sufficiently correlated to the temporal fluctuations of abundance.

Figure 3

 3 Figure 3 Criterion used to define the distribution map portfolio for octopus in Mauritanian waters for the hot (left) and the cold (right) season. The inset panels represent the percentage of variance explained when including progressively more and more EOMs. The threshold of 60% was used for selecting the candidate EOMs for building the portfolio. The main graph shows the position of EOMS with respect to their relationship with octopus abundance.The x-axis corresponds to the correlation between EOM weights and abundance (the closer to +/-1, the better). The y-axis represents the relative values of the slopes of the cross-correlograms between each EOM weights andabundance, with respect to the maximum possible value (the closer to +/-1, the better). The size of EOF numbers is inversely proportional to the percentages of nugget effect in the auto-correlograms of the EOMs' weights (the larger the better). The EOMs that allow recovering 60% of the input variance are indicated in red and connected for better visibility.

Figure 4 Figure 5 .

 45 Figure 4 Portfolio of octopus during the hot (left -red) and the cold (right -blue) seasons over the entire study period. Each plot is made of an EOM with the temporal evolution of its weights, smoothed by a loess method with a span parameter value of 0.5 and associated 95%-confidence interval. Pie chart indicate the percentage of variance explained by the EOM (arrows represent the cumulative percentage of variance explained by the current EOM and the previous ones and the percentage of variance explained by the portfolio). The EOMs that were not selected for the portfolio are represented in grey.

Figure 6

 6 Figure 6 Analysis of the temporal dynamics of the principal spatial patterns (EOM 1, 3, 4, 5) and of the abundance for the cold season. Diagonal panels: auto-correlograms; Lower triangle panels: cross-correlograms. For all panels, the x-axis represents time lags in years (from 0 to 30 years) and the y-axis represents correlations. The horizontal black dashed line is at 1. For off diagonal panels, the horizontal dotted lines represent the correlations. The panels of the last line concerns the cross-correlograms of EOM weights with abundance and the auto correlogram for abundance (last panel). The horizontal red dashed lines represents the correlation between EOM weights and abundance. The linear model of coregionalisation is represented as a continuous line (nugget effect + slope). The

Figure 9 Figure 10

 910 Figure 9 Portfolio for the cold season. Distribution of the EOMs' weights as a function of the EOM numbers for March and December surveys. The weights for the surveys carried out in March (N=10) are represented in black. The weights for surveys performed in December (N=10) are given in red. The average values are superimposed. For the two instances where a December survey is followed by a March surveys three months later, the evolutions of the weights are represented by doted segments.

Figure 11 .Figure 12

 1112 Figure 11. Left: Empirical Orthogonal Map EOM2 of octopus for the cold season. This EOM was not selected for the portfolio. Right: temporal evolution of its weights smoothed by a loess method with a span parameter value of 0.5 and associated 95%-confidence interval.

Funding

No funding

Conflict of Interest statement

No conflict of interest.

Author Contributions Statement

DAB and NB conceived the ideas, analysed the data and led the writing of the paper. HD and BM contributed critically to the draft. All authors gave final approval for publication. 20 Villanueva, R. 1995. Experimental rearing and growth of planktonic Octopus vulgaris from hatching to settlement.

Canadian Journal of Fisheries and Aquatic


Jacky Fayad

Lucile Rossi

Nicolas Frangieh
email: frangieh_n@univ-corse.fr

Carmen Awad

Gilbert Accary

François-Joseph Chatelon

Frédéric Morandini

Thierry Marcelli

Valérie Cancellieri

Dominique Cancellieri

Dominique Morvan

Antoine Pieri

Gilles Planelles

René Costantini

Sofiane Meradji

Jean-Louis Rossi

Numerical study of an experimental high-intensity prescribed fire across Corsican Genista salzmannii vegetation

Keywords:

This paper reported a high intensity experimental fire conducted during a field-scale experiment on a steep sloped terrain (28 • ) as part of a winter prescribed burns campaign managed by the local firefighter service in the north-western region of Corsica. The rate of spread (ROS) of fire, measured using UAV cameras (thermal and visible), was evaluated at 0.45 m/s. The experiment was numerically reproduced using a completely physical 2D model, namely FireStar2D, and the comparison with the experimental measurements mainly concerned the fire ROS and the heat fluxes received by three distant targets placed at the end of the plot. The results analysis shows that the considered fire has a wind-driven regime of propagation with a fire intensity higher than 7 MW/m. The numerical results are in fairly good agreement with the experimental measurements, within 11% difference for the ROS and 5% for the heat fluxes, validating consequently the relevance of the numerical approach to tackle such high-intensity wildfires. Despite the unfavorable wind and humidity conditions for fire propagation (U = 1.67 m/s and RH = 82%), this experiment confirms that such fire can exhibit a dangerous behavior due to the steep slope of the terrain.

Introduction

Wildfires represent the main cause of natural capital damage in Mediterranean regions and one of the main drivers of landscape. There are five regions over the world that present a Mediterranean climate: the Mediterranean basin, California, Chile, South Africa and Australia (the South and South-West). These zones occupy almost 2% of Earth surface. The Mediterranean climate is characterized by a high seasonality that can be summarized as hot, dry summers, and mild wet winters [START_REF] Di Castri | Mediterranean-type Shrublands of the World[END_REF]. Changes in climatic and weather conditions are one of the major reasons for the increase in wildfire risk [START_REF] Benson | Chapter 2 climatic and weather factors affecting fire occurrence and behavior[END_REF][START_REF] Sommers | Synthesis of Knowledge: Fire History and Climate Change[END_REF]. In recent decades, Mediterranean regions tend to be warmer and drier [START_REF] Mariotti | Long-term climate change in the Mediterranean region in the midst of decadal variability[END_REF], and has experienced frequent heat waves [START_REF] Russo | Top ten European heatwaves since 1950 and their occurrence in the coming decades[END_REF]. Moreover, studies have shown that the region around the Mediterranean Sea has been identified as one of the most vulnerable regions around the world to climate change [START_REF] Giorgi | Climate change hot-spots[END_REF]. So, Mediterranean climate conditions are prone to fire ignition and propagation in a very flammable vegetation [START_REF] Ganteaume | Understanding future changes to fires in southern Europe and their impacts on the wildland-urban interface[END_REF][START_REF] Ganteaume | What causes large fires in Southern France[END_REF] with a longer wildfire season. It is generally recognized that these conditions constitute one of the major sources of increasing forest fires risk [START_REF] Jolly | Climate-induced variations in global wildfire danger from 1979 to 2013[END_REF][START_REF] Castro Rego | Forest Fires -Sparking Firesmart Policies in the EU[END_REF] and burned area [START_REF] Cary | Comparison of the sensitivity of landscapefire-succession models to variation in terrain, fuel pattern, climate and weather[END_REF]. In the next century, global temperatures are expected to be warmer than current levels and severe droughts more frequent [START_REF]Evolving Risk of Wildfires in Europe -the Changing Nature of Wildfire Risk Calls for a Shift in Policy Focus from Suppression to Prevention[END_REF]. Thus, the Mediterranean regions will potentially be more affected by wildfire risk [START_REF] Jolly | Climate-induced variations in global wildfire danger from 1979 to 2013[END_REF]. The last years witnessed many high-intensity forest fire incidents caused mainly by the heat wave and the extreme drought conditions [START_REF] Castro Rego | Forest Fires -Sparking Firesmart Policies in the EU[END_REF]. For instance, the catastrophic fires of 2018 summer in Greece [START_REF] Xanthopoulos | A tale of two fires and a seaside tragedy[END_REF], fanned by strong wind and high temperature, grew rapidly destroying houses and reaching the sea and it posed a risk to the safety of a large oil refinery. The severe fires of Portugal (2007), southern Italy (2005), and Greece (2003) are further examples high intensity forest fire incidents. Other 2 extreme fires could blaze during winter, caused by the early melting of winter snows and the late rains in the fall season. The cold-weather wildfires are becoming more common during the last years, such as the recent winter wildfire in Colorado that occurred in December (2021). In general, extreme fires are very dangerous since their behavior is unpredictable and uncontrollable [START_REF] Balbi | Modelling of eruptive fire occurrence and behaviour[END_REF]. This type of fires can be characterized by a high rate of spread (ROS), by spotting fires, or by a sudden change of fire behavior [START_REF] Alexander | Calculating and interpreting forest fire intensities[END_REF] as well as by a high fireline intensity that could exceeds the 10 MW/m, the threshold beyond which a fire becomes erratic and uncontrollable [START_REF] Tedim | Defining extreme wildfire events: difficulties, challenges, and impacts[END_REF]. Therefore such fires constitute a threat for the population, assets, and natural values, resulting in important negative socio-economic and environmental impacts [START_REF]Evolving Risk of Wildfires in Europe -the Changing Nature of Wildfire Risk Calls for a Shift in Policy Focus from Suppression to Prevention[END_REF][START_REF] Tedim | Defining extreme wildfire events: difficulties, challenges, and impacts[END_REF]. Hence, Mediterranean region is in a new wildfire context because fire risk is likely to increase substantially in the future, and extreme catastrophic wildfire events could occur more frequently. The real problem here is that these extreme wildfire events tend to overwhelm suppression efforts. Thus, this new context requires adapted policies to shift the focus from suppression to prevention, as called by the Sendai Framework for Disaster Risk Reduction 2015-2030 [START_REF] Undrr | Sendai Framework for Disaster Risk Reduction 2015-2030[END_REF].

Wildland fire suppression and prevention requires a good knowledge of the physical mechanisms governing fire behavior (ignition, initial development, spread). Therefore, local measurements of fire dynamics in field-scale experiments of wildland fires are highly useful. This is true either for understanding the mechanisms driving fire spread that result in the observed macroscopic behaviors or in terms of providing comparison points for numerical tools, such as detailed physics-based fire models. Wide variety of experimental and numerical studies on wildfire behaviour exists in the literature. For instance, Finney et al. [START_REF] Finney | A study of flame spread in engineered cardboard fuelbeds: Part I: correlations and observations[END_REF] performed wind tunnel laboratory fires spreading through laser-cut cardboard while Frangieh et al. [START_REF] Frangieh | Wildfires front dynamics: 3D structures and intensity at small and large scales[END_REF] investigated these fires later on using a CFD Physical model; Liu et al. [START_REF] Liu | Effect of slope on spread of a linear flame front over a pine needle fuel bed: experiments and modelling[END_REF] studied the effect of slope on spread of a linear flame front over a pine needle, experimentally and numerically, at laboratory scales; Awad et al. [START_REF] Awad | Fuel moisture content threshold leading to fire extinction under marginal conditions[END_REF][START_REF] Awad | Numerical study of the moisture content threshold under prescribed burning conditions[END_REF] studied numerically and experimentally at small scale the moisture content threshold of extinction; Viegas et al. [START_REF] Raposoa | Analysis of the jump fire produced by the interaction of two oblique fire fronts: comparison between laboratory and field cases[END_REF] investigated experimentally junction fire, at laboratory and small field cases, where these results were compared also to a previous wildfire and later on simulate the evolution of this kind of fires where reproduced numerically using CFD based numerical models [START_REF]Advances in forest fire research[END_REF]; Marsden-Smedley et al. [START_REF] Marsden-Smedley | Fire behaviour modelling in tasmanian buttongrass moorlands ii. Fire behaviour[END_REF] performed a burning program, based on experimental and prescribed fires in order to develop fire behaviour prediction models; Xavier et al. [START_REF] Silvani | Fire spread experiments in the field: temperature and heat fluxes measurements[END_REF] investigated the temperature and the heat fluxes of experimental field fires spreading through small flat parcels; Bulter et al. [START_REF] Butler | Observations of energy transport and rate of spreads from low-intensity fires in longleaf pine habitat -RxCADRE 2012[END_REF] reports the fire intensity rate of spreads of low-intensity fires spreading in longleaf pine. The idea of citing these studies, is to point that most of the experimental studies were carried out for laboratory scale and/or small terrain (flat or with moderate slope) and under moderate wind speed resulting consequently in a low ROS and low fire intensity; not to mention that most of them focus on specific aspects of fire behavior. This could be justified as follows: on the one hand, despite the considerable progress that has been made in the characterization of wildland fire spreading [START_REF] Morvan | Physical phenomena and length scales governing the behaviour of wildfires: a case for physical modelling[END_REF][START_REF] Frangieh | Numerical simulation of grassland fires behavior using an implicit physical multiphase model[END_REF][START_REF] Morvan | A 3D physical model to study the behavior of vegetation fires at laboratory scale[END_REF], experimental field-scale fires remain extremely problematic in terms of security and fraught with numerous difficulties. Such fires are often subject to the vagaries of the weather and variations in the vegetation and land topography [START_REF] Owen | ASHRAE Handbook: Fundamentals[END_REF]. The interaction of these, and even with the fire itself, can result in seemingly capricious behavior. On the other hand, attempting to obtain direct measurements of the characteristics of such fires with pre-positioned instrumentation is similarly beset by practical problems, including being in the right location at the right time, safely, to make useful observations and measurements of critical quantities during the fire propagation. Consequently, obtaining repeatable conditions in the field is challenging, often requiring a large number of replicate experiments to reduce statistical error, which is costly and difficult to achieve. Therefore, relevant experimental data on high-intensity wildfires is of paramount interest and experiments at the field-scale are highly valuable.

In this context, the main objective of this study is to present experimental data of a fire carried out at large scale field, having an important slope, resulting in a high fire intensity. This field-scale experiment has been conducted at the north-western region of Corsica during a prescribed fire campaign in March 2021, where prescribed burnings are commonly used in Corsica [START_REF] Silvani | Fire spread experiments in the field: temperature and heat fluxes measurements[END_REF]. In order to understand and investigate the different phenomena encountered in this type of fires, the experimental results are compared to the prediction provided by a complete physical model, namely FireStar2D [START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF]. FireStar2D is employed to assess the fire front dynamics, in particular to accurately evaluate the

Nomenclature

C p

Vegetative fuel specific heat (J/kg. K) C p0

Ambient air specific heat (J/kg. K) fire intensity, which is always a challenge for field-scale experiments. In addition, the rate of spread and the heat fluxes received by three distant targets placed at the end of the plot are also examined and compared to the experimental data. Consequently, these data could contribute to a better understanding of these fires and serve to validate numerical models for this fire category.

In the next section the experimental method is thoroughly described, followed by the modeling approach that was used. Then, the experimental results are detailed as well as numerical results in two separate sections. Finally, an analysis and a discussion of the relevance and the significance of these results are presented.

Experimental method

Site description

In order to obtain field-scale data, a fire spread experiment was carried out as a part of a winter campaign of prescribed fires conducted at the north-west coast of Corsica (France), in March 2021. The experimental site is located 10 km from the sea, in an uneven terrain (42 • 32 ′ 38 ′′ N, 8 • 58 ′ 07 ′′ E) at 990 m above sea level and facing eastnortheast (Fig. 1a), and it was selected based on two criteria. First, the plot has a steep slope in order to generate high intensity fire close to wildfire conditions; the average slope of the terrain is 28 ± 2 • . This value was obtained by precisely measuring the coordinates of five points positioned 25 m apart along the centerline of the plot, namely poles 1, 2, 3, 4 and thermocouple 1, as shown in Fig. 1b. The coordinates of these points were determined using a high-precision Global Navigation Satellite System (GNSS). Second, the plot has a roughly homogeneous vegetation with high vegetation cover (coverage >90%). The vegetation was mainly composed of 0.6 m high mountain shrubs (Genista salzmannii) with few fuel discontinuities. The vegetation plot to be burned was in the shape of a rectangle, about 30 m wide and 130 m long along the main slope direction.

General overview of the experimental protocol

The limits and orientation of the vegetation plot (30 m × 130 m) were chosen according to the main slope direction to favor a high intensity fire. The experimental protocol was developed to investigate the main thermal properties and behavior of a fire. Thus, pre-fire vegetation samplings were done to measure the FMC, and measuring devices have been deployed in the field (Fig. 2). Six heat flux sensors and four thermocouples were placed in the vegetation free area to record the radiant/ total heat fluxes and air temperature, respectively. Two video cameras were located on the sides to investigate the flame geometric characteristics. The fire front propagation was also recorded from above using a drone-mounted Visible-IR camera. The wind properties and ambient conditions were also recorded using a portable weather station. A linear ignition was performed at the bottom of the plot resulting in an upslope fire spreading.

Characterization of the vegetation and meteorology

As mentioned previously, this site was selected for the apparent structural homogeneity of its vegetation, mostly composed of Genista salzmanniin, whose thermo-chemical properties (such as specific, yield, and pyrolysis heats) can be found in literature [START_REF] Leroy-Cancellieri | Evaluation of wildland fire smoke plume dynamics and aerosol load using UV scanning lidar and fire-atmosphere modelling during the Mediterranean Letia 2010 experiment[END_REF]. On the other hand, other physical properties, such as the FMC, the packing ratio, the fuel height, and the fuel-load density are specific to the geographic area and depend on weather conditions. Fuel height was evaluated by averaging 20 different measurements of the distance between the ground and the average top of the vegetation. Fuel characterization was carried out by fuel sampling and applying a destructive inventory using a cube methodology [START_REF] Cohen | From the vegetation to the inputs of a fire model: fuel modelling for wildland-urban interface management, Warm Int. Work[END_REF]. Before ignition, samples of dead and live fuel elements with diameters less than 6 mm (assumed to mainly contribute to fire spread) were collected in double-seal plastic bags. For the FMC determination, the collected samples were considered as consisting of a single fuel type, thus the reported FMC corresponds to an average value covering both the dead and the living fuels. The FMC was calculated based on a dry weight basis taking into account condensation onto the bags. Fuel samples were oven dried at 60 • C for 48 h for moisture content determination [START_REF] Awad | Fuel moisture content threshold leading to fire extinction under marginal conditions[END_REF]. Oven-dry weight of the collected material was determined after laboratorial processing and expressed in terms of fuel loading. The volume fraction (packing ratio) was then obtained by dividing the fuel load by the product of the average vegetation height and the particle density.

The Ambient weather conditions were recorded less than 50 m from the centerline of the plot (Fig. 1b). The wind velocity and direction were obtained using a two-dimensional ultrasonic anemometer (WS425, Vaisala) at 3 m above the ground to reflect the average wind acting on the fire front. The anemometer was located downhill of the vegetation plot to minimize the influence of the fire on the wind measurements. Wind data were recorded using a data logger (CR3000, Campbell Scientific) at a sampling rate of 1 Hz. Air temperature and relative humidity were monitored during fire spread using a weather meter (Kestrel 5500, Kestrel Instruments).

ROS evaluation: drones and vision technology

Given the plot width and field constraints, the ignition was conducted, slowly and unsymmetrically, starting from the left side to right side of the plot. During the experiment, the fire front propagation was recorded from above using a drone and from the side using two cameras (GoPro Hero4, GoPro Hero+) located on the ground. The drone used was DJI M210 with a Zenmuse XT2 camera featuring both a FLIR longwave infrared (7.35-13.5 μm spectral band) camera and a visual camera, with resolutions of 3840 × 2160 and 640 × 512 pixels respectively. The drone was located at a height of about 100 m, which allowed top shots of the fire spread across the whole vegetation plot. In order to simplify the video tracing of the fire front location, four poles were placed, before ignition, on four equidistant reference points (~25 m apart) as shown in Fig. 1b. These points were also used to evaluate the plot slope. The ROS was then determined by recording the times at which the fire front had crossed each reference pole; this allowed the evaluation of the ROS when the fire had reached a steady state propagation.

Heat flux measurement

The total and radiant heat fluxes emitted from the flame front during the fire spread were measured with 3 pairs of Medtherm transducers (16H and 64 Series, Medtherm Corp, Huntsville, AL, USA) located uphill on the vegetation free area. A sapphire window was added to the radiant heat flux transducer to eliminate the convective heat being transferred to the sensing area. These transducers were calibrated by the manufacturer in the range 0-200 kW/m 2 and had a response time less than 0.25 s. Thus, experimental studies have shown that a maximum total heat flux of 112 kW/m 2 could be reached ahead of the fire front [START_REF] Silvani | Fire spread experiments in the field: temperature and heat fluxes measurements[END_REF]. The radiant and total heat flux transducers had a view angle of 150 • and 180 • , respectively. They were oriented towards the fire and in the slope direction (Fig. 3). The pairs of heat flux transducers were fixed on 0.5 m high supporting rods located at 6, 11, and 16 m from the upper limit of the vegetation plot. Air temperature was also recorded using K-type thermocouples with a 2.5 μm-diameter grounded junction. Four thermocouples were also fixed on supporting rods located at 1, 6, 11, and 16 m from the upper limit of the vegetation plot (Fig. 2). The heat flux gauges and thermocouples were plugged into a power-supplied data logger (CR3000, Campbell Scientific) buried 0.3 m into the ground to protect it from the fire. Extension cables of the sensors were insulated by Teflon coating and aluminum foils (Fig. 3). They were buried into the ground up to the data logger. The analogue signals from all transducers were recorded at a sampling rate of 1 Hz.

Modeling and numerical method

In order to test the relevance of numerical simulation in the case of high-intensity wildfires, a simulation was carried out using a completely physical 2D model, namely FireStar2D. Indeed, having an important fire-front width in this present case allows good predictions using Fire-Star2D model that assumes an infinite ignition line. In addition, this 2D model was validated from calculations carried out at different scales for homogeneous fuel beds and was compared to experimental results as well as to empirical and semi-empirical models [START_REF] Awad | Fuel moisture content threshold leading to fire extinction under marginal conditions[END_REF][START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF][START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF]. FireStar2D model appears to be suitable for operational works since it provides valuable results and requires much less simulation time compared to the 3D model version.

The mathematical model used in FireStar2D is based on a multiphase formulation [START_REF] Grishin | Mathematical Modeling of Forest Fires and New Methods of Fighting Them[END_REF], it consists in a first step in space-averaging the conservation equations (energy, mass, momentum …) governing the behavior of the coupled system formed by the vegetation and the surrounding atmosphere. This averaging is performed on elementary control volumes including both the gaseous phase and the solid phase (the vegetation). Thus, the model consists of two parts that are solved on two distinct grids. The first part consists of the equations governing the reacting and turbulent flow of the gas mixture of fresh air and the gaseous products resulting from the degradation of the solid fuel (by drying, pyrolysis, and heterogeneous combustion) and the homogeneous combustion in the flaming zone. The second part consists of the equations governing the state and the composition of the solid phase subjected to an intense heat flux coming from the flaming zone. Therefore, the rate of fire spread, and more generally, all variables characterizing fire behavior (flame geometry, fire intensity, etc.) are obtained from the resolution of the balance equations governing the various interactions occurring between the vegetation, the surrounding atmosphere, and the flame [START_REF] Grishin | Mathematical Modeling of Forest Fires and New Methods of Fighting Them[END_REF][START_REF] Hanson | The potential and promise of physics-based wildfire simulation[END_REF]. The details of FireStar2D model have been thoroughly described in previous publications, and the reader is invited to consult references [START_REF] Awad | Numerical study of the moisture content threshold under prescribed burning conditions[END_REF][START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF][START_REF] Morvan | Modeling the propagation of a wildfire through a Mediterranean shrub using a multiphase formulation[END_REF][START_REF] Morvan | Wildfire behavior study in a mediterranean pine stand using a physically based model[END_REF][START_REF] Morvan | Modeling of fire spread through a forest fuel bed using a multiphase formulation[END_REF] for more information about this 2D model and for a comparison with other wildfire tools available within the community.

The 2D computational domain used for the simulations was 200 m long and 35 m high (Fig. 4), and the homogeneous vegetation layer, of height e = 0.6 m and 100 m long was located 20 m from the domain inlet. The main physical characteristics of the vegetation layer are given in Table 1. The solid fuel particles were assumed to behave as a black body and a vegetation family of cylindrical shape was considered. The shape of the fuel particles is used for the description of their regression law and for the estimation of the heat transfer coefficients. Both the solid-phase and the fluid-phase grids were characterized by cells sizes below the radiation extinction length scale [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF][START_REF] Morvan | Physical phenomena and length scales governing the behaviour of wildfires: a case for physical modelling[END_REF] the vegetation given by 4/sβ, where s is the surface to volume ratio of the vegetation (m -1 ) and β is the volume fraction of the solid phase (see Table 1); this characteristic length is equal to 0.42 m in present case. This value should not be exceeded in order to avoid fire extinction especially in the case of radiation-dominated fire propagation (i.e., when the wind speed is low to moderate). Ignition was obtained by the injection of carbon monoxide at 1600 K from the ground (between 20 m and 22 m) during 5 s and with a constant velocity of 1 m/s [START_REF] Frangieh | Wildfires front dynamics: 3D structures and intensity at small and large scales[END_REF][START_REF] Awad | Numerical study of the moisture content threshold under prescribed burning conditions[END_REF][START_REF] Frangieh | Numerical simulation of grassland fires behavior using an implicit physical multiphase model[END_REF][START_REF] Morvan | A 3D physical model to study the behavior of vegetation fires at laboratory scale[END_REF]. Ignition was activated after reaching a statistically-steady profile of the turbulent boundary-layer inside and above the fuel bed [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF] which required 30 s of simulation time.

The simulation was carried out for a 10 m open wind speed U 10 = 1.98 m/s (which corresponds to 1.67 m/s at 3 m above ground by assuming a one-seventh power wind velocity profile) and for a slope angle α = 28 • . The domain inclination angle was specified through two non-zero components of gravitational acceleration: g x = -g sin(α) and g z = -g cos(α), where g = 9.81 m/s 2 is Earth gravity.

The ROS represents one of the main parameters that characterize wildland fire behavior. Using FireStar2D, the ROS is obtained from the slope of the curve of the pyrolysis front position (during the time), at the fuel-bed surface, once fire propagation had become steady. One other feature of FireStar2D, is the possibility to evaluate any characteristic of the fire at any time and any position in the computational domain. On the one hand, this model allows the evaluation of the convection and radiation heat transfer rates between the flame and the vegetation (W/m of fuel-bed width) [START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF], thus to identify the dominant heat transfer mode between the flames and the vegetation layer as well as its effect on fire behavior. On the other hand, this model allows the evaluation heat fluxes (radiative and convective) received by a target (W/m 2 ) at a given position, particularly to assess the heat fluxes recorded by the three flux meters located at the end of the plot. To evaluate the convection heat flux received by the flux meter a Newton's law of cooling [START_REF] Owen | ASHRAE Handbook: Fundamentals[END_REF], given by Eq. ( 1), was employed. In this equation, (T 0 -T a ) represents the difference between the gas mixture temperature and the target temperature (assumed to be the ambient temperature) and h conv is the convective heat transfer coefficient.

Q conv = h conv (T 0 -T a ) (1)
h conv was calculated from the correlation given by Eq. ( 2) for forced convection over the fluxmeter gauge foil assumed to behave as a flat plate, where the flow can be considered as laminar at the gauge surface even if the flame is strongly turbulent [START_REF] Silvani | Fire spread experiments in the field: temperature and heat fluxes measurements[END_REF]; L c (m) is the characteristic length that depends on the target shape (equal to the fluxmeter gauge diameter in this case), k is the thermal conductivity (W/m.K) of the gas mixture, Re is the Reynolds number based on L c , and Pr is the Prandtl number of the gas mixture.

h conv = k L c 0.664 Re 1/2 Pr 1/3 (2)
The Fireline intensity cannot be experimentally measured, but only estimated through other measured quantities. The experimental fireline intensity can be evaluated from Eq. (3) (Byram's intensity [START_REF] Byram | Forest Fire Control and Use[END_REF]), where w a is the weight of fuel consumed in the active flaming front (kg/m 2 ), and ΔH c is the heat yield of the fuel (estimated at about 18,620 kJ/kg, see Table 1). In operational conditions, the consumed fuel w a , is eval- uated from the fuel load (σ) weighted by a combustion efficiency, i.e., w a = μ σ, where μ is the percentage of the fuel weight actually consumed in the active flaming front and effectively contributed to fire propagation.

I BExp = ΔH c .w a .ROS (3)
This experimental method is often inaccurate, because it is based on visual estimation of the burned vegetation during the fire [START_REF] Alexander | Fireline Intensity, Encycl. Wildfires Wildland-Urban Interface Fires[END_REF]. These difficulties do not exist in the numerical evaluation of the fire intensity from the Heat Release Rate (HRR) given by Eq. ( 4) [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF], where ṁ (kg/m. s) is the vegetation degradation rate evaluated by the summation of mass losses due to pyrolysis and charcoal combustion where ΔH c is the vegetation heat yield (J/kg).

I BNum = ṁ .ΔH c (4)
The vegetation degradation rate is evaluated in FireStar2D [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF] from Eq. ( 3), where ẇpyr and ẇchar represent the rate of dry material pyrolysis and charcoal combustion.

N c = 2g I B ρ 0 C P0 T 0 (U 10 -ROS) 3 (6)
For a fire propagating uphill, an effective wind speed acting in the direction of fire propagation should be considered to include the effect of the slope on the fire regime [START_REF] Nelson | An effective wind speed for models of fire spread[END_REF]; this effective wind speed is given by Eq. ( 6), where w c represents the buoyant flame velocity [START_REF] Nelson | Re-analysis of wind and slope effects on flame characteristics of Mediterranean shrub fires[END_REF] given by Eq. [START_REF] Ganteaume | What causes large fires in Southern France[END_REF].

U e = U 10 + w c sinα ( 7
)
w c = ( 2g I B ρ 0 C P0 T 0 )1 / 3 (8)

Experimental results

Fuel characteristics and wind conditions

A single type of vegetation particle was considered in this study [START_REF] Leroy-Cancellieri | Evaluation of wildland fire smoke plume dynamics and aerosol load using UV scanning lidar and fire-atmosphere modelling during the Mediterranean Letia 2010 experiment[END_REF]. The vegetation characterization, described in section 2.1, resulted in FMC, e, and σ equal to 65%, 0.6 m, and 1.8 kg/m 2 respectively (Table 1).

The fire experiment occurred between 12:49 and 13:04. During this period, the average wind speed was 1.67 ± 0.54 m/s. It should be noticed that the average wind direction (60 ± 14 • ) was aligned with the main slope direction and it exhibited few fluctuations. The average air temperature and relative humidity were 6 • C and 82%, respectively.

Rate of spread

Fig. 5 shows the fire front position at different instants during the fire propagation, and Table 2 reports the time lapses taken by the fire to cross consecutive poles. For the first 22 s, just after the establishment of the ignition line, estimated at t = 12:53:30, the fire propagated with ROS equal to 1.136 m/s and then it slowed down to 0.423 m/s before reaching a quasi-steady propagation speed between the last three poles (Pole 2 -Pole 4) with a ROS equal to 0.45 m/s.

Heat fluxes and fireline intensity

Fig. 6 shows the time evolution of the radiative and total heat fluxes received by the different flux meters. Before t = 3700s, the time when fire front reached the end of the plot, flux meters were not sensitive to the heat produced by the fire. These heat fluxes outputs are later on investigated in the numerical results section.

According to Eq. ( 3), if all the vegetation was supposed to be consumed during the fire propagation, then μ = 1 and w a = σ = 1.8 kg/ m 2 (see Table 1), consequently I BExp = 15.082 MW/m. By visually comparing the plot vegetation before and after burning (see Fig. 7) the percentage of fuel weight consumed was estimated to μ ≈ 70 %; this results in I BExp = 10.5 MW/m from Eq. (3).

Numerical results

Rate of spread and heat fluxes

FireStar2D predicts a ROS of about 0.5 m/s (Fig. 8), which is in agreement within 11% difference with the experimental value.

To identify the dominant heat transfer mode between the flames and the vegetation, the time evolution of the total rate of heat transfer (by radiation and convection) between the flame and the vegetation, integrated across the whole domain, is reported in Fig. 9.

On the other hand, the radiant and the convective heat fluxes received by three vertical targets located at 6 m, 11 m, and 16 m from the end of the vegetation plot are shown in Fig. 10 (respectively P1, P2 and P3). Fig. 11 presents the radiative heat fluxes obtained numerically at different sensor's positions, along with the experimental measurements, when the fire front reaches the end of the vegetation plot. Fig. 12 reports the radiative heat flux, obtained in Fig. 11, for the three sensors at t = 183.7 s. This figure, presented at logarithmic scale, shows a quasilinear diminution of the radiative heat flux with respect to the target positions. The time-averaged ratio of the radiative heat flux to the total heat flux (i.e., convective and radiative), evaluated for the three flux meters (see Table 3), show a good agreement between experimental and numerical values within 5% difference.

Fireline intensity and fire regime

The experimental evaluation of I B is rough because of the uncertain estimation of the total fuel load consumed by the fire in Eq. ( 3). The evaluation of the fireline intensity, according to Eq. ( 4) and Eq. ( 5), once fire propagation had become steady results in I BNum = 7.665 MW/m. Using the measured U 10 value to evaluate Byram's convective number, Eq. ( 6) results in N c = 114, which indicates a plume-dominated regime. Whereas using the value of U e instead of U 10 in Eq. ( 6) gives a N c = 3.24, shifting substantially Byram's convective number toward the wind-driven fire range. The fire regime is further illustrated by Fig. 13 showing cuts of the temperature and the flow fields (streamline) in the vertical plane where the flow affects significantly the rise of the flame plumes by pushing the hot gases toward the unburned vegetation.

Discussion

Rate of spread

The transitory phase of the experimental ROS, before its establishment, could be due: first to an excess of gasoline poured to ignite the fire line (using drip torches) and second to the unsymmetrical ignition process (for safety considerations) applied in this prescribed fire. Because of this unsymmetrical ignition, fire starts moving at the departure ignition side (left side of the plot) with a higher speed than the rest of the fireline ignited progressively, but due to low wind speed conditions, the fire front was then established along the plot perimeter (see Fig. 5) to propagate after that with a quasi-steady speed of 0.45 m/s.

Concerning the 11% relative error between the experimental and the numerical values of the ROS, two factors can explain this difference: [START_REF] Di Castri | Mediterranean-type Shrublands of the World[END_REF] in the numeric simulation, a homogeneous vegetation layer was considered, which is not the case in the experiment; (2) in 2D simulations, the fire front constitutes a uniform thermal barrier, while the fire front is in reality structured as a succession of peaks and troughs, allowing for the air flow to find a way across it [START_REF] Frangieh | Wildfires front dynamics: 3D structures and intensity at small and large scales[END_REF][START_REF] Viegas | Advances in forest fire research[END_REF]. Nevertheless, an 11% error is often considered acceptable for fire spread models [START_REF] Cruz | Uncertainty associated with model predictions of surface and crown fire rates of spread[END_REF].

Heat fluxes

The experimental radiative and total heat fluxes, reported in Fig. 6, are almost equal at the early stages (for the first 100 s) for all three targets. Then, the difference between the total heat flux (Q tot ) and the radiant one (Q rad ) becomes more pronounced, which is due to the ex- istence of convective heating mechanism ahead of the fire front.

Fig. 9 shows that the convection is the main mechanism of heat transfer in this case. This is mainly due to the steep slope and the resulting thermal plume trajectory with respect to the fuel bed. Preheating of the unburned fuel mainly by convection (i.e., by direct contact with the hot gases) accelerated the fire front and led to a relatively high ROS despite the unfavorable propagation conditions. Nevertheless, even if the radiation is not the dominant heat transfer mode, it remains an important mechanism and contributes to 30% of the total rate of heat transfer received by the vegetation located ahead of the flame as shown by Fig. 9 and reported in the literature [START_REF] Cheney | Fire behaviour[END_REF].

Both the numerical and the experimental radiative heat flux reported in Fig. 10 show the same levels of the radiative flux at the different target points. The discrepancy between the experimental data and numerical evaluation of the radiative heat flux is more pronounced at position P1 (the closest to the fire front) and is mainly due to the direct contact with the flame, whereas the differences are much less pronounced at positions P2 and P3.

Table 3 shows that the contribution of the radiative heat flux received by distant targets is dominant and exceeds 93% for the two furthermost points (P2 and P3). Despite the same order of magnitude, the radiation contribution at position P2 exceeds that at position P3. This slight difference could be due to the coherent turbulence structures present near the last target (see Fig. 10) which makes it in contact with the hot gases more than P2 target. Consequently, this increases the convective heat transfer, making the radiative contribution more important at position P2 than P3.

Fireline intensity and fire regime

Fireline intensity is usually used as an index to characterize the fire intensity rating (or fire severity or the suppression difficulty), such as in Ref. [START_REF] Cheney | Fire behaviour[END_REF] where the classification was obtained for eucalypt forests. Whatever the evaluation method of the fire intensity (I BNum = 7.665 MW/m and I BExp > 10.5 MW/m assuming a percentage of fuel con- sumption greater than 70%), the considered fire falls into the category of "very high" fire severity, according to Ref. [START_REF] Cheney | Fire behaviour[END_REF] with a wind driven regime of propagation. It is worth mentioning here that the evaluation of Byram's convection number using of the effective wind U e instead of U 10 in Eq. ( 6) was required to account for fire propagation on sloped terrain. Thus, in this specific case and due to the steep slope, the flame attachment to the ground results in a wind-driven-like regime of fire propagation [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF][START_REF] Morvan | Wildland fires behaviour: wind effect versus Byram's convective number and consequences upon the regime of propagation[END_REF].

However, for this fire class, all available fuel is usually consumed, which was not the case for this fire. Fire severity and its effect on soil also depends on fire residence time [START_REF] Alexander | Calculating and interpreting forest fire intensities[END_REF][START_REF] Chatto | A Review of the Relationship between Fireline Intensity and the Ecological and Economic Effects of Fire[END_REF] which is also related to the ROS. Due to the relatively large value of the ROS obtained in this case (0.45 m/s), only partial combustion was achieved and less fuel was burned in the flaming front compared to a slower-moving fire where more fuel is consumed in the flaming front [START_REF] Burrows | Experimental Development of a Fire Management Model for Jarrah (Eucalyptus Marginata Ex Sm) Forest[END_REF]. Also, the amount of consumed fuel is affected by the FMC (especially when it exceeds 40%), where the time required for the fire to consume the solid fuel increases with the FMC [START_REF] Dahale | Effects of distribution of bulk density and moisture content on shrub fires[END_REF]. However, due to the important slope, fire moves relatively fast, and its residence time is relatively small, which does not allow reaching a high percentage of fuel consumption. This explains why not all the fuel was consumed during this fast fire propagating uphill.

On the other hand, even though the fire occurred under unfavorable propagation conditions, with relatively high fuel moisture and relative humidity (FMC = 65% and RH = 82%) and low ambient air temperature (6 • C), the fire was characterized by a fire intensity larger than 6 MW/m (according to any evaluation method). This threshold value corresponds to the transition between "high" and "very high" fire danger index [START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF]. Indeed, in a fire fighting context, this value (6 MW/m) corresponds more or less to the efficiency limit of aerial means for the direct attack of a head fire (ranging between 3 and 10 MW/m depending on the spotting activity) [START_REF] Hirsch | A review of initial attack fire crew productivity and effectiveness[END_REF]. Consequently, even if the wind speed was quite moderate (U 10 = 1.98 m/s), and the conditions were unfavorable for fire propa- gation, this experiment confirms the fact that such fire can exhibit a dangerous behavior even in winter because it occurs along a steep slope (28 • ).

Conclusions

This paper presents a high-intensity experimental fire carried out during a field-scale experiment on a 28 • sloped terrain, in the context of the winter prescribed burns campaign managed by the local firefighter service in the north-western region of Corsica. The paper describes thoroughly the used methodology as well as the collected measurements. The relevance of the numerical simulation in the case of highintensity wildfire was demonstrated by numerically reproducing this experiment, using a completely physical 2D wildfire model (FireStar2D). The ROS was evaluated both experimentally and numerically, as well as the radiative and convective heat fluxes received by three distant targets, placed at the end of the plot. Numerical predictions were in fairly good agreement with experimental results. Moreover, the numerical prediction of heat transfer received by the unburned vegetation showed that the convection was the main mechanism of vegetation preheating. The fire intensity, evaluated experimentally and calculated numerically, was higher than 7 MW/m, which places this experimental fire in the "very high" despite the unfavorable conditions of fire propagation. The analysis of the dimensional Byram's convection number N C , based on the fire line intensity, indicates that the fire regime was wind driven despite the low wind speed, and this is due to the steep slope and the resulting flame attachment to the fuel bed.

Only the global characteristics of this experimental fire were reported in this paper; other aspects, such as the shape of the fire front and temperature measurements, will be addressed in a future paper and compared to the predictions obtained from 2D and 3D numerical simulations. Also, further experimental studies are planned in the near future in order to better understand the behavior of high intensity wildfires.

Fig. 1 .

 1 Fig. 1. Experimental fire site in Corsica island: (a) location on the map; (b) view by Google earth and main GNSS measurement points.

Fig. 2 .

 2 Fig. 2. Schematic view of the experimental plot and the location of the measuring devices.

Fig. 3 .

 3 Fig. 3. Radiant and total heat flux sensors and thermocouple fixed on supporting rod and protected by aluminum foils.

ṁ = ẇpyr + ẇchar ( 5 )Fig. 4 .

 54 Fig. 4. Computational domain and boundary conditions used in the 2D simulation of the experimental fire.

Fig. 5 .

 5 Fig. 5. Infrared images of the fire front travel between equidistant positions (the green lines passing through prefixed poles) at different times taking t = 0 s at 12:49 (fire start time): (a) t = 140 s; (b) t = 242 s; (c) t = 360 s; (d) t = 422 s. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 6 .

 6 Fig. 6. Time evolution of the radiative and total heat fluxes obtained experimentally at the different target positions.

Fig. 7 .

 7 Fig. 7. Plot vegetation: (a) before burning and (b) after burning, allowing a visual estimation of the percentage of fuel consumed by the fire.

Fig. 8 .

 8 Fig. 8. Position versus time of the furthermost point of the pyrolysis front at the fuel-bed surface obtained by FireStar2D after ignition at t = 30 s.

Fig. 9 .

 9 Fig. 9. Time evolution of the convection and radiation heat transfer rates between the flame and the vegetation evaluated with FireStar2D.

Fig. 10 .

 10 Fig. 10. Temperature field and streamlines obtained numerically as the fire approaches of the three targets positions points located ahead of the fire front.

Fig. 11 .

 11 Fig. 11. Numerical and experimental values of the radiative heat flux at the different target positions when the fire front reaches the end of the plot.

Fig. 12 .

 12 Fig. 12. Numerical and experimental radiative heat fluxes at different targets positions ahead of the fire front (P1 = 6 m, P2 = 11 m and P3 = 16 m), at t = 183.7 s.

Fig. 13 .

 13 Fig. 13. Temperature field and flow streamlines obtained numerically in xz plane.

Table 1

 1 Main average properties of Genista salzmannii. < 2) are obtained in fires piloted by inertial effects (wind-driven fire), with a more important contribution of convection heat transfer[START_REF] Morvan | Wildland fires behaviour: wind effect versus Byram's convective number and consequences upon the regime of propagation[END_REF]. Byram's number is given by Eq. (6), where I B is the fire intensity, g is the gravity acceleration, ρ 0 = 1.26 kg/m 3 and C P0 = 1004 J/kg.K are air density and specific heat at the ambient temperature T 0 = 279 K, and U 10 is the 10 m-open wind velocity.

	Particle density, ρ v (kg/m 3 )	970
	Volume fraction, β	0.00309
	Fuel moisture content, FMC (%)	65
	Fuel bed depth, e (m) Fuel load, σ (kg/m 2 )	0.6 1.8
	Thermal capacity, Cp (J/kg/K) Yield heat, ΔH c (J/kg) Pyrolysis heat, ΔH t (J/kg) Surface-area to volume ratio, s (m -1 )	1648 1.8620 × 10 7 1.3917 × 10 7 3100
	Thermal emissivity, ϵ	1
	Vegetation family shape	Cylindrical

Table 2

 2 Time lapses of fire propagation between consecutive poles.

		Distance separating poles	Time lapse (s)	ROS (m/
		(m)		s)
	Ignition line -Pole 1	25	22	1.136
	Pole 1 -Pole 2	25	59	0.423
	Pole 2 -Pole 4	50	111	0.45

Table 3

 3 Time-averaged ratio of the radiative heat flux to the total one evaluated experimentally and with FireStar2D at the different target positions.

	Position	Q rad /Q tot FireStar2D	Q rad /Q tot Experiment
	1	0.796	0.845
	2	0.993	0.971
	3	0.961	0.930

Acknowledgements

This field experiment required the cooperation of many people and would not have been possible without the assistance of the Forestry Service Department of North-Corsica (SIS2B) staff who selected the site, constructed firebreaks, protected the area, conducted the burning, and carried out fire suppression when spotting occurred with the collaboration of the Corsican DFCI (Défense de la Forêt Contre l'Incendie) Group. The authors would particularly to thank firefighter Patric Botey who supported this project since its beginning.

Funding

This work was funded by the Corsican Region and the French state in the framework of the collaborative project GOLIAT (CPER: 40031).

Author contributions

Conceptualization, all the authors; methodology, Jean-Louis Rossi, Gilbert Accary, Lucile Rossi, Jacky Fayad, Nicolas Frangieh; software, Jacky Fayad, Carmen Awad, Nicolas Frangieh, Gilbert Accary, Lucile Rossi; validation, all the authors; formal analysis, all the authors; writing-original draft preparation, Jean-Louis Rossi, Jacky Fayad, Nicolas Frangieh, Carmen Awad, François-Joseph Chatelon, Gilbert Accary; writing-review and editing, Jean-Louis Rossi, Jacky Fayad, Nicolas Frangieh, Carmen Awad, François-Joseph Chatelon, Gilbert Accary; supervision, Jean-Louis Rossi, Gilbert Accary, Dominique Morvan. All authors have read and agreed to the published version of the manuscript."

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.