Daily values of FWI covering the period from January 1979 to September 2017 were computed according to the procedure described by Wang et al. (2015). For each pixel, the grand average of FWI for all days of the period 1979–2016, hereby denoted FWI‾, was also computed. The spatial distribution of FWI‾ (Fig. 2) shows a general tendency to decrease with increasing latitude, which reflects the same behaviour of the surface temperature field. The spatial distribution is also consistent with the land cover (Fig. 1), the forested areas tending to be associated with lower values FWI‾. Other factors such as topography and proximity to the sea are also relevant, the values of FWI‾ tending to be lower over the mountains and along the coast. For each pixel p of the MSG NPP grid and for each day d of the study period, the anomaly FWIpd* was defined as FWIpd*=FWIpd-FWI‾p, where FWIpd is the FWI value for pixel p and day d day, and FWI‾p is the grand average of FWI for that pixel. Use of anomalies instead of values of FWI aims at reducing all the above-mentioned factors that regionally affect FWI over Mediterranean Europe. Given that FWI is defined at 12:00 local standard time (LST), use of anomalies also mitigates the impacts associated with the delay in solar time (1 h every 15∘ towards the east) given that all meteorological fields are defined at 12:00 UTC (DaCamara et al., 2014).

Daily energy released by fire at a given pixel was computed by integrating the radiative power recorded by SEVIRI in that pixel throughout the considered day. Since the data are sampled every 15 min, the daily energy, E (in gigajoules), for each pixel p and day d may be estimated as Epd=0.9×∑k=196FRPkpd, where index k indicates the sequence of 15 min images for each day, FRPkp is the fire radiative power (in megawatts) in pixel p of image k and the 0.9 factor converts the result into GJ.

Considering the calibration period (2004–2016), the static probability of exceedance of a given threshold E of daily energy released by fires at each pixel p was estimated by counting the total number of daily fire occurrences in pixels with the same land cover type as p (Fig. 1) located inside a cell centred in the considered pixel with initial size δ=0.7∘ in latitude and longitude. The size was then successively enlarged by increments of 0.05∘ until the maximum size of 20∘ was attained or the total number of events reaches 200. When denoting by Sp(δ,E) the total number of daily fires inside a cell of size δ centred at p and with released energy exceeding E, the probability of exceedance x is estimated as PpE|0=Spδ,ESpδ,0, where Spδ,0 is the number of all observed daily fire events (i.e. with energy exceeding zero). As suggested by the notation employed, PpE|0 may be viewed as a conditional probability, namely the probability that the daily energy released by fires at pixel p is greater than E provided that an ignition has occurred in that pixel. The rationale for this procedure is that the static probability of exceedance is expected to present smooth spatial variability over pixels with the same land cover type, while steep changes are to be expected among the different land cover types.

Following DaCamara et al. (2014), the statistical distribution of daily released energy, E, is modelled using the “peaks-over-threshold” (POT) approach (Pickands, 1975).

The POT approach uses the GP distribution as a model to assign probabilities to the exceedances of E over a predefined threshold, i.e. to values ΔE=E-Emin (with E>Emin), where Emin is a prescribed minimum value (de Zea Bermudez and Kotz, 2010). The GP cumulative distribution function of exceedances ΔE is GΔE|α,σ=1-1+ασΔE-1α, where α and σ are the shape and scale parameters. The value of the minimum threshold Emin is obtained by plotting the sample mean of the values exceeding successive thresholds against the respective thresholds, the chosen value being such that the dependence becomes linear for values greater than the chosen one (Coles, 2001). The shape (α) and scale (σ) parameters of the GP distribution are then estimated using the maximum-likelihood method (Grimshaw, 1993).

The obtained model, hereafter referred to as the null model, may be improved by incorporating daily anomalies, FWI*, and static probabilities, P(E|0), as covariates of the scale parameter in the GP distribution using a feedforward artificial neural network. The network is trained using the Levenberg–Marquardt algorithm (Hagan and Menhaj, 1994). Daily probabilities are then given by GΔE|α,σN=1-1+ασNΔE-1α, where σN=σNFWI*,P(E|0) is the trained neural network model using FWI* and P(E|0) as inputs and providing the corresponding scale parameter σ as an output.

Performance of the new alternative model, hereafter referred to as the daily model because of its dependence on daily values of FWI*, is compared against the respective null models by using the standard likelihood ratio test (Neyman and Pearson, 1933), which is based on statistic Λ, defined as Λ=2ln⁡L′-ln⁡L, where L and L′are the likelihood functions of the null and the daily models, respectively.

Classes of fire danger are defined, based on values of probability of exceedance and of the respective deviations from the expected value. The rationale is that large fires tend to occur in pixels of high probability of exceedance or of large positive deviation from the expected value for a given day of the year and location. For each pixel p and day d, the probability of exceedance G is evaluated using Eq. (5), and the respective anomaly A is computed by subtracting the average of all values of probability of exceedance for that pixel and day of the year over the period 1979–2016. As shown in Fig. 3, five classes of fire danger (conventionally named “low”, “moderate”, “high”, “very high” and “extreme”) are then defined by setting five partitions in the domain G versus A (delimited by dashed lines) by means of four curves (γ0, γ1, γ2, γ3) defined as follows: γ0:A≡0,0≤P≤1andγii=1,2,3:A=eln⁡PnPnP,Pn≤P≤1, where Pn are break points estimated from fire events according to the following criteria: (1) the first break point is set to 0 so that the “low” class of fire danger encompasses all cases where the probability of exceedance is below average (A<0); (2) the four break points are equally spaced; and (3) the classes “very high” and “extreme” should have about the same number of fire events.

It may be noted that the adopted approach to calibration differs from other common methods like those based on logistic regression and threshold setting that were mentioned in the Introduction. The present approach, based on a partitioning of the space of probability versus probability anomaly by exponential type functions, was motivated by the distribution of the daily energy released by observed fire events in that space during the study period (Fig. 13).

Assessment of performance of the daily model is based on a systematic comparison of the distributions of events among classes of fire danger for different ranges of energy released by fire with the corresponding distributions when using classes produced by other products, namely those from EFFIS and the LSA SAF. In the case of EFFIS, six classes are defined by means of a set of break points in FWI that are set up using historical records of large fire events of more than 500 ha of burned area (San-Miguel-Ayanz et al., 2012). The six EFFIS classes are here reduced to five by combining the “very low” and the “low” classes. In the case of the LSA SAF product, the definition of the five classes is based on break points in FWI anomalies that are defined based on information of a probabilistic model of exceedances of active-fire duration (DaCamara et al., 2014). Given that classes from the daily model are based on probabilistic information about exceedances of energy released by fires, when comparing against EFFIS and LSA SAF products, the daily model is expected to provide a better discrimination of events among classes from the point of view of energy released, particularly for the most severe classes.

The validation of the daily model is performed for the January–September 2017 (validation) period, by comparing the distributions of daily fire events among classes of fire danger with those obtained for the calibration period (2004–2016). Two severe events that took place during the validation period are also examined, namely the fires at Pedrógão Grande-Góis and near Marseille in southeastern France, which were already mentioned in the Introduction. The study of the Pedrógão Grande-Góis event focuses on the second day of the event (18 June 2017) because no satellite measurements are available on the starting day due to the presence of clouds and thick smoke. The event took place within a context of extremely high temperatures, with values of up to 40 ∘C registered at the nearest station and relative humidity as low as 20 %. Besides killing 64 people, the fire involved more than 1000 fire fighters and destroyed almost 500 buildings, and a continuous patch of more than 42 000 ha burned in one week. In the case of the fire episodes near Marseille, two large fires that started on 24 July 2017 and burned more than 3000 ha are analysed, with the study focusing on the day after the onset because of the recorded high values of released energy during that day. As mentioned in the Introduction, several other episodes occurred in the area during that week, more than 2000 fire fighters were deployed and more than 10 000 people had to be evacuated.

Figure 4 shows the monthly median values of daily energy released by fires at each pixel. The distributions represent the whole calibration period (2004–2016) and reveal an absolute maximum of 114 GJ in August and an absolute minimum of 52 GJ in May. All monthly distributions are positively skewed and the annual cycle of interquartile range presents a very similar behaviour to that of the median, with the monthly values of the former presenting an absolute maximum of 309 GJ in August and an absolute minimum of 117 GJ in May. This behaviour is to be expected since fire events with low values of released energy are less conditioned by meteorological factors and are therefore likely to occur throughout the year, whereas fire events releasing high values of energy depend on favourable weather conditions that are more frequent in the summer months. It is also worth noting that monthly values of the median for the validation period (January–September 2017) are larger than the corresponding values for the calibration period in all months, thus stressing the fire-prone year of 2017.

The spatial distribution of energy released by wildfires was analysed by adding up for every pixel in the study area the daily values of released energy recorded during the calibration period (2004–2016). As shown in Fig. 5, a large patch of high values of total released energy may be identified over the northwest of the Iberian Peninsula, with the highest values located in the forested lands of central Portugal. An elongated patch of high values may also be identified along the Mediterranean coast of Africa, with the highest values occurring in the forested areas of Morocco, Algeria and northern Tunisia. A patch of high values is also noticeable in Greece. Other patches, albeit reaching less high values of total released energy, may be identified in central Europe, in Bulgaria and Romania, in southern Italy, and in Sicily and Sardinia.

The distributions of daily released energy per pixel for the three considered types of vegetation cover/land use (Fig. 6) show that pixels covered by forests have the largest values of both the median and the interquartile range, followed by shrubland and cultivated areas. Differences among the distributions for the three land cover types were assessed by means of the two-sample Kolmogorov–Smirnov test (Massey, 1951); for each pair of the three considered distributions, the null hypothesis that the distributions are identical is rejected with a p value lower than 0.0001. These results are in agreement with the findings by Moreira et al. (2011), Fernandes (2013) and DaCamara et al. (2014) pointing out that within the Mediterranean basin long-lasting and intense fire episodes are more frequent in forests and shrubland than in cultivated areas.

Probability of exceedance of daily energy per pixel released by fires was computed over the study area according to the procedure described in Sect. 3.3. Statistical models of exceedance were then built as described in Sect. 3.4, starting by adjusting a GP model to the sample of daily values of energy exceeding a prescribed threshold (null model) and then improving the null model by using static probability and FWI anomaly as covariates of the scale parameter (daily model). In order to reduce false alarms, the computation of daily energy per pixel (which characterizes each fire event) was restricted to days where the maximum value of confidence of FRP was at least 99 %.

Classes of fire danger were defined following the procedure described in Sect. 3.5, i.e. by plotting, for the whole study area during the calibration period, each value of daily energy Epd released on day d at pixel p (Fig. 13). As expected, there is an increase in occurrence of higher values of released energy with increasing probability of exceedance G and anomaly A. The horizontal line γ0 separates the “low” class from the remaining ones. This class contains 1269 events that represent only 8 % of the total amount of 15 752 events. The remaining classes are delimited by curves, (γ1, γ2, γ3) defined by break points P1,P2,P3=(0.103,0.206,0.309). As prescribed in the procedure, break points are equally spaced by steps of 0.103, and the “very high” and “extreme” classes contain about the same number of events, i.e. 5408 and 5443, representing 34 and 35 % of the total amount, respectively.

A better insight into the characteristics of the daily model's five classes of danger may be obtained by stratifying the occurrences into three ranges of energy released by the fire events, namely below 2000 GJ, between 2000 and 10 000 GJ, and above 10 000 GJ. As shown in Table 1 (“daily model” subtable), within the cases of the lowest range (< 2000 GJ), 59 % are distributed between the “high” (26 %) and “very high” (33 %) classes, while the intermediate range (2000–10 000 GJ) presents a steep increase in frequency from “low” to “extreme”. An even steeper increase is observed for the upper range (> 10 000 GJ), for which the “low” and “moderate” classes contain 1 % of the cases and the “extreme” one concentrates 72 % of the events in that layer.

As mentioned in Sect. 3.6, the performance of the daily model is assessed by comparing the distributions of events among the classes of fire danger for the three ranges of energy with those obtained when using the LSA SAF and the EFFIS products (Table 1, “LSA SAF” and “EFFIS” subtables). Differences are particularly notable in the upper energy range (> 10 000 GJ), especially for EFFIS classes where events spread in all classes and the “very high” and “extreme” classes only contain 70 % of the cases, whereas for the daily model and the LSA SAF they contain 98 and 85 %, respectively. However, in the case of LSA SAF classes, the modal class is the “very high” and not the “extreme” as in the daily model. Similar differences, although less prominent, may be observed among the three products in the intermediate energy range (2000–10 000 GJ). The modal classes are the “extreme” for the daily model and the “very high” for the LSA SAF and EFFIS, with the modal frequency being the highest (46 %) for the daily model, followed by the LSA SAF (45 %) and EFFIS, where the frequency (33 %) is quite low and equal to that of the next class below. Finally, the lower energy range (< 2000 GJ) also presents differences among the three products, namely in the frequency of events in the “low” and “moderate” classes, which represent 21 % of the events in the daily model and only 9 and 7 % for the LSA SAF and EFFIS, respectively. The different features of the classes from the three products ultimately translate into different values of probability of a fire event releasing a given amount of energy in the case of a given class danger. For instance, using results presented in Table 1, the conditional probability of having a large release of energy (> 10 000 GJ) given “extreme” danger is 898/5443= 16.5 % and 481/3066= 15.7 % for the daily model and the LSA SAF, respectively, and is only 511/4384= 11.7 % for EFFIS. Similar features are presented by the conditional probability of having a small release of energy (< 2000 GJ) given “low” danger, with values of 984/1269= 77.5 % and 180/217= 82.9 % for the daily model and the LSA SAF, respectively, and only of 135/207= 65.2 % for EFFIS.

Differences obtained among the three products point out the better performance of the daily model if the aim is to have information about the probability of occurrence of an event releasing a large amount of energy. This result is not surprising since the daily model was specifically designed for such purpose. Estimates of probability by the LSA SAF product are closer to those by the daily model than the ones by EFFIS because the LSA SAF relies on duration of active fires inside each pixel and day, which is a better proxy of energy released by fires than records of fire events with more than 500 ha of burned area. We nevertheless acknowledge that it is not a straightforward exercise to translate the six danger classes defined by EFFIS into a five-class scheme such as those of the LSA SAF and daily model approaches.

As described in Sect. 3.6, model validation involves applying the daily model to the validation period (January–September 2017) and analysing results obtained for the two severe events of Pedrógão Grande-Góis (Portugal) and Provence (France). It is important to note that, contrasting to the calibration period where meteorological data were obtained from ERA-Interim reanalysis, ECMWF's operational 24 h forecasts are used during the validation period. The overall coherence of reanalysis data makes them especially appropriate to calibrate the daily model, but forecast information has to be used for operational application. Results obtained in the validation period therefore reflect the effects of applying the procedure to an independent dataset as well as those due to using forecast information instead of reanalyses.

As shown in Table 2, during the validation period, the obtained distributions of events among classes of fire danger are similar to those obtained in the calibration (Table 1, “daily model” subtable). The distribution of events for the lowest range (< 2000 GJ) is shifted toward the more severe classes of fire danger, with the modal class being the “very high” one, with 42 % of the events, and the “extreme” class containing 39 % of the cases. The intermediate range (2000–10 000 GJ) is slightly shifted towards the more severe classes of fire danger, with the modal class being “extreme”, with 57 % of the events, and the “very high” class containing 37 % of the cases, a figure very close to the one obtained in the calibration period (38 %); likewise, as gotten in calibration, the highest jump in relative frequency is from the “high” to the “very high” class (5 to 37 %). In the highest range (> 10 000 GJ) no cases are observed in the “low” and “moderate” classes; as found in calibration, the modal class is “extreme”, containing 76 % of the events (72 % in calibration), with the remaining 24 % (26 % in calibration) belonging to the “very high” class.

The percentage of fires for the “very high” and “extreme” classes is shifted toward the more severe classes (38.6 and 48.7 %), a feature that may be attributed to the fact that up to September, according to information at the EFFIS site, the accumulated burned area in 2017 is more than 600 000 ha, more than 2.5 times the 2008–2016 average of about 224 000 ha. This may also explain the virtual absence of episodes in the “Low” class (8 of 1972 total events).

Results obtained for the two 2017 case studies of Pedrógão Grande-Góis (Portugal) and Marseille (France) are summarized in Fig. 14. The figure is subdivided into two main vertical panels, the left one corresponding to Pedrógão Grande-Góis and the right one to Marseille. For each event a map covering the study area is presented on the top, showing the geographical distribution of values of P(2000|200) for Pedrógão-Góis and of anomaly values of P(2000|200) for Marseille. At the bottom of each panel, on the left hand side, there is a map showing the geographical distribution of classes of danger and the location of active fires detected over the region affected by the fire event; finally, on the right hand side, there is a diagram presenting the distribution of active fires detected in the domain G of P(2000|200) versus respective anomalies A. In the case of Pedrógão Grande-Góis, it is worth noting that on 18 June 2017 the area surrounding the fire events is covered by a patch of values of P(2000|200) exceeding 0.7 (top frame) over a background of lower values covering most of the Mediterranean basin. Pixels inside the area of interest (black boxes) are mostly classified as “extreme” danger of fire (lower left frame), and active fires detected (reaching up to 5000 GJ of released energy) are within or very close to the border of the partition classified as “extreme” fire danger in the domain of P(2000|200) versus anomaly A (lower right frame). The fire episodes near Marseille (Fig. 14, right panel) took place within an area conspicuously characterized by values of anomalies A as high as 0.3, which are higher than the surrounding values and much higher that the values observed in the majority of pixels over the Mediterranean basin. As in the case of Pedrógão Grande-Góis, the fire events near Marseille (reaching up to 10 000 GJ of released energy) are located within an area classified as being of “extreme” danger of fire or near the border between the “extreme” and “very high” classes (lower left frame). There is however a difference between the two events that is worth mentioning. In the case of Pedrógão Grande-Góis, pixels where active fires were observed are classified as or near “extreme” fire danger because of the high values of P(2000|200), whereas in the case of Marseille that is mostly because of the high values of anomaly A. These two examples justify the adopted rationale of defining the classes of fire danger in the space P(2000|200) versus anomalies A.