Very large wildfires have high human, economic, and ecological impacts so that robust evaluation of their return period is crucial. Preventing such events is a major objective of the new fire policy set up in France in 1994, which is oriented towards fast and massive fire suppression. Whereas this policy is probably efficient for reducing the mean burned area (BA), its effect on the largest fires is still unknown. In this study, we make use of statistical extreme value theory (EVT) to compute return periods of very large BAs in southern France, for two distinct periods (1973 to 1994 and 1995 to 2016) and for three pyroclimatic regions characterized by specific fire activities. Bayesian inference and related predictive simulations are used to fairly evaluate related uncertainties. Results demonstrate that the BA corresponding to a return period of 5 years has actually significantly decreased, but that this is not the case for large return periods (e.g., 50 years). For example, in the most fire-prone region, which includes Corsica and Provence, the median 5-year return level decreased from 5000 to 2400 ha, while the median 50-year return level decreased only from 17 800 to 12 500 ha. This finding is coherent with the recent occurrence of conflagrations of large and intense fires clearly far beyond the suppression capacity of firemen. These fires may belong to a new generation of fires promoted by long-term fuel accumulation, urbanization into the wildland, and ongoing climate change. These findings may help adapt the operational system of fire prevention and suppression to ongoing changes. Also, the proposed methodology may be useful for other case studies worldwide.

Wildfires are important hazards and a major ecological disturbance. In
southern France, 2500 fires are reported each year over the recent period
(1994 to 2016) and burn an average of approximately 12 000 ha

For many geophysical variables and/or hazards such as rainfall, snowfall, or
river discharge, protective measures are designed to withstand an event with
a given small exceedance probability, i.e., an event that is generally much
rarer than those already observed

Yet, to date, estimating return levels (e.g., 100 ha, 1000 ha) of fires
corresponding to large return periods (e.g.,

This work aims at computing the return periods of wildfire BA in southern
France using EVT. Specifically, we question the efficiency of the new fire
policy set up in 1994 to reduce the likelihood of very large wildfires. This
policy has been based on improved prevention of fires, increased surveillance
of forests, and a massive attack on all ignitions in order to prevent fire
enlargement

This study covers an area of 80 500 km

This study area encompasses different bioclimates, different vegetation
fuels, and different levels of human activity (which generate about 95 %
of ignitions), leading to different fire activities. For this reason we
define three main homogeneous subregions based on fire activity and
bioclimatic variables, so-called pyroclimatic regions

Maps of the study area.

We use the national georeferenced fire database called Prométhée

Figure

Number of large fires (

Extreme value theory

For the GEV distribution, the quantile

For a return period

In this study, statistical inference is performed using Bayesian methods

A Bayesian analysis combines the information in the data represented by the
likelihood function with prior knowledge about the parameter. Parameter
estimation is made through the posterior distribution, which is computed using
Bayes' theorem

The likelihood function represents the conditional density of the data

The prior distribution

Location parameter

Scale parameter

Shape parameter

The joint prior distribution is

The posterior distribution

Draws from the posterior distribution

Hence, it fairly propagates the uncertainty related to parameter estimation
on the quantities of interest. However, a closed expression of the predictive
distribution can rarely be obtained, and it is often estimated using the
draws from the posterior distribution:

Likewise, the predictive density of a maximum log-BA

Numerous statistical tests aim at testing an assumption of equality between two distributions (for example the test of Kolmogorov–Smirnov). These tests are adequate when two samples are compared and when we want to test if the sampling distributions can be considered equivalent. However, it must be noticed that these statistical tests are very powerful with large samples, which means that in this case, a small difference will be considered highly significant. As a result, comparing posterior distributions with these statistical tests generally results in a rejection of the assumption of equality, even when the distributions are very similar.

As an alternative, different measures have been proposed by statisticians in
order to quantify the similarity between two distributions, or, in other
words, how much two distributions overlap (e.g., Mahalanobis distance,
Kullback–Leibler divergence). In this paper, we apply the Bhattacharyya
coefficient

For the sake of comparison with statistical tests, when this coefficient is
applied to two normal distributions

For each of the three regions PCr-1, PCr-2, and PCr-3, we collect the annual
maxima of BA. Following the methodology described in
Sect.

Acceptance rates from the Metropolis–Hastings algorithm.

Taking the mean of the posterior distributions as point estimates, Fig.

QQ plot of the fitted GEV distributions for each region (PCr-1, PCr-2, and PCr-3) and each period (1973–1994 and 1995–2016). Point estimates of the GEV parameters are obtained as the mean of the posterior distributions. The BA (ha) is indicated on a log-scale.

Posterior distribution estimates for the extreme value parameters

Comparison of posterior distribution of the GEV parameters, before
(dashed line) and after 1994 (solid line): location parameter

Table

Bhattacharyya coefficients applied to posterior densities of the GEV parameters, before and after 1994, for each region. Bold values indicate coefficients below the reference value of 0.61.

For a return period

Figure

Comparison of return levels, before and after 1994, for each region. The 90 % credible intervals are shown and median return levels are indicated in plain lines. BA (ha) is indicated on a log scale.

Bhattacharyya coefficients applied to different return levels, before and after 1994, for each region. Bold values indicate coefficients below the reference value of 0.61.

The probability of having very large fires (

Estimated probability of having very large fires (

Table

BA (ha) corresponding to different return periods (years), by area and for the recent period (1995–2016). Intervals between brackets indicate 90 % credible intervals of the corresponding return levels.

This study provides, for the first time, a model of fire return periods in
southern France, taking into account the nonstationary nature of fire activity in
space and time. EVT provides arguments in favor of the
application of extreme value distributions

It appears that very large fires (

These findings provide information for leveraging fire risk. In the most
fire-prone areas of France (Corsica and Provence), it is less and less
doubtful that several ongoing changes will create opportunities for extreme
fire events, as in many European countries

Finally, it must be remembered that, in this study, we use the occurrence and
BA of very large fires as a surrogate for extreme fire danger because no
reliable and exhaustive database provides information on the real impacts of
fire. This deserves discussion. On average, the largest fires actually have
huge impacts on humans (including fire crews) and the environment because
they are likely to have an effect on a large number of assets

Extreme fire events (i.e., very large fires generating high human, economic,
and ecological damages) are a growing issue in southern Europe and almost
worldwide. Extreme fire events have a disproportionate impact on the media
and they challenge the suppression-oriented policies because they question
our ability to control or prevent them in the long term. In France,
firefighting accounts for two-thirds of the total budget but it cannot
suppress all large fires, as demonstrated notably in 2003, 2016 and 2017

The Prométhée fire database is freely available
online (

GE developed the methodology for data analysis, carried out the analysis, and produced the results (tables and figures). He wrote the main part of the manuscript. TC conceived the study, provided the data, and wrote Sect. 4 and most of the conclusion. NE contributed to the development of the methodology and to the manuscript.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Spatial and temporal patterns of wildfires: models, theory, and reality”. It is a result of the conference EGU 2017, Vienna, Austria, 23–28 April 2017.

Irstea – UR ETGR is a member of Labex OSUG@2020. Irstea – RECOVER is a member of Labex OT-MED. Edited by: Mário Pereira Reviewed by: two anonymous referees