CSIRO PUBLISHING
www.publish.csiro.au/journals/ijwf
International Journal of Wildland Fire 2009, 18, 983–991
Spatial and temporal extremes of wildfire sizes in Portugal (1984–2004) P. de Zea BermudezA , J. MendesB , J. M. C. PereiraC , K. F. TurkmanA,E and M. J. P. VasconcelosD A Departamento de Estatística e Investigação Operacional (DEIO) and Centro de Estatística e Aplicações
da Universidade de Lisboa (CEAUL), University of Lisbon, PT-1749-016 Lisbon, Portugal. Superior de Estatística e Gestão de Informação (ISEGI), New University of Lisbon, PT-1070-124 Lisbon, Portugal. C Deparment of Forestry and Center for Forest Studies, Instituto Superior de Agronomia (ISA), Technical University of Lisbon, PT-1349-017 Lisbon, Portugal. DTropical Research Institute, PT-1300-344 Lisbon, Portugal. E Corresponding author. Email:
[email protected] B Instituto
Abstract. Spatial and temporal patterns of large fire (>100 ha) incidence in Portugal over the period 1984–2004 were modeled using extreme value statistics, namely the Peaks Over Threshold approach, which uses the Generalized Pareto Distribution (GPD) as a model. The original dataset includes all fires larger than 5 ha (30 616 fires) that were observed in Portugal during the study period, mapped from Landsat satellite imagery. The country was divided into eight regions, considered internally homogeneous from the perspective of their fire regimes and respective environmental correlates. The temporal analysis showed that there does not appear to be any trend in the incidence of very large fires, but revealed a cyclical behavior in the values of the GPD shape parameter, with a period in the range of 3 to 5 years. Spatial analysis highlighted strong regional differences in the incidence of large fires, and allowed the calculation of return levels for a range of fire sizes. This analysis was affected by the presence of a few outlying observations, which may correspond to clusters of contiguous fire scars, resulting in artificially large burned areas. We discuss some of the implications of our findings in terms of consequences for fire management aimed at preventing the occurrence of extremely large fires, and present ideas for extending the present study. Additional keywords: Generalized Pareto Distribution, Peaks Over Threshold method.
Introduction In many fire regimes, a small number of very large fires is responsible for most of the area burned and for the social and environmental damage caused (Strauss et al. 1989; Niklasson and Granström 2000; Díaz-Delgado et al. 2004a). Therefore, large wildfires are a relevant public policy issue (Dombeck et al. 2004), especially considering that the frequency of occurrence of extremely severe fire weather may increase as a consequence of global warming (Flannigan et al. 2001; Fried et al. 2004; Moriondo et al. 2006). Large fires are, from various perspectives, qualitatively different from small fires. Large fires tend to occur under specific, relatively uncommon synoptic meteorological conditions, typically involving combinations of high temperatures, prolonged drought and strong winds (Moritz 1997; Beverly and Martell 2005; Pereira et al. 2005; Crimmins 2006; Trigo et al. 2006). They display extreme fire behavior patterns and spread mechanisms not observed in small fires, such as crowning, horizontal roll vortices, spotting by firebrands, and fire whirls (Pyne et al. 1996). Fighting very large fires is qualitatively different from fighting small fires, because the range of options for controlling large fires is drastically reduced, in comparison with the © IAWF 2009
diversity of options available for initial attack. The degree of organizational complexity required for fighting large fires scales up non-linearly and logistical aspects predominate over tactical considerations (Pyne et al. 1996). The ecological effects of large fires also may differ qualitatively from those of smaller events. For example, in plant communities dominated by species with limited dispersal abilities, pre-fire vegetation may be unable to recolonize the interior of the fire-affected area (Romme et al. 1998; Turner et al. 1998; Rodrigo et al. 2004). The objective of the present study is to model spatial and temporal patterns of incidence of large fires in Portugal, over the period 1984–2004, using extreme value theory. The reason for using extreme value theory is that the distributions that provide the best fit to a complete fire size dataset are not necessarily the same that best fit the tail of the fire size distribution, which ought to be the object of interest when analyzing extreme fire sizes. We believe that such a study will contribute to understanding whether the fire regime is changing over the years and if so, what causes such changes. The understanding of the spatial variation in large fires will contribute to an optimal allocation of firefighting resources. 10.1071/WF07044
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Previous extreme value analysis of fire size data relied on the concept of extremal fire regime (EFR), i.e. a time series of the largest annual fire observed in the study area (Moritz 1997; Beverly and Martell 2005), and fitted those data using the Generalized Extreme Value (GEV) distribution. Moritz (1997) analyzed the EFR recorded at Los Padres National Forest, California (1911–91), finding no shift in regime owing to improved fire suppression capabilities and confirming the strong role of climate as a forcing mechanism for large fires. Beverly and Martell (2005) used the GEV to characterize dry spell extremes, or runs of consecutive days with little or no rain, and fire size extremes in the Boreal Shield ecozone of Ontario. They concluded that dry spell events above 15 days in length were associated with 76% of large fires compared with only 33% of small fires. Dry spell lengths associated with large fires were also significantly longer, compared with those associated with small fires. Díaz-Delgado et al. (2004b) constructed an EFR dataset for Catalonia, NE Spain (1975–98) and determined that the largest fire of the year was responsible for a mean annual percentage burned area of 40%, but did not attempt to model the dataset with extreme value distributions. Other authors used the Peaks Over Threshold (POT) (Adamowski et al. 1998; Katz et al. 2005) approach to model the size distribution of large fires. Alvarado et al. (1998) fitted distributions of large fires in Alberta, Canada, (1961–81) with a left-truncated Pareto distribution, considering a 200-ha minimum size threshold (480 fires) and the upper onepercentile fire size (215 fires). The POT approach was also used by Ramesh (2005) for extreme wildfires in the USA, over the years 1825–2000. He used the GEV distribution and a semiparametric smoothing technique to model the trend in extreme values over time. However, his small sample size resulted in overly broad confidence bands and inconclusive results regarding the significance of possible trends. We agree with Alvarado et al. (1998) that, in modeling wildfire sizes, the event of interest should be fires with sizes exceeding a high threshold rather than the maximum size, which strongly suggests using the POT method rather than the GEV model. The POT approach also has the benefit of using a larger portion of the available data, resulting in more precise inference on large fire regimes.
Fig. 1. Geographical regions: 1, Minho and Douro Litoral; 2, Trás-osMontes and Alto Douro; 3, Porto; 4, Beira Interior; 5, Beira Litoral, Estremadura and Ribatejo; 6, Lisbon; 7, Alentejo; 8, Algarve.
Data and methods Study area The study area corresponds to mainland Portugal (see Fig. 1), located between 37 and 42◦ N latitude and between 6 and 10◦W longitude. Geographical stratification of the study area represents a compromise between the Portuguese Forest Service standard procedure of organizing statistical fire data by administrative units, and the natural regions classification of Portugal due to Albuquerque (1985). The 18 administrative districts of Portugal were grouped into eight geographical units that closely approximate the 12 natural regions, based on similarities of climate, topography, vegetation, land use, population density and fire incidence, namely number of fires and area burned. The following description of vegetation, land cover and land use is based on Nunes et al. (2005). Forests and woodlands cover over one-third of the study area. Maritime pine (Pinus pinaster) stands are located mainly in the northern half of the country. Blue gum (Eucalyptus globulus) plantations are abundant all
along the western half of Portugal, and in a few more interior areas, in the central and southern parts of the study area. Evergreen oak woodlands predominate in the southern half of Portugal. Cork oak (Quercus suber) woodlands are the main woody land-cover type in south-western Portugal, whereas holm oak (Quercus rotundifolia) predominates in the south-east. These woodlands are managed as agro-forestry systems. Shrub understoreys are common in all of these four main forest and woodland types. In maritime pine and blue gum stands, the main understorey shrub genera are gorse (Ulex sp.) and heath (Erica sp. and Calluna sp.). Cistus ladanifer and Cistus salvifolius dominate the understorey layer in evergreen oak woodlands (DGF 2001). The aboveground biomass of the shrub layer ranges from ∼10 t ha−1 in maritime pine stands to 7.5 t ha−1 in blue gum plantations and cork oak woodlands, and is lower (∼5 t ha−1 ) in holm oak woodlands (Silva et al. 2006). Shrublands cover approximately one-quarter of the study area, and are located mostly in the northern third and in the SE parts of the country. The most widespread
1 2 3
4 5
6 7
8
Spatial and temporal extremes of wildfire sizes in Portugal (1984–2004)
shrub formations in Portugal are dominated by the genera Cytisus (Legume family, Fabaceae) and Cistus (Rockrose family, Cistaceae). Cytisus spp. dominate old-field succession and post-fire succession in areas formerly occupied by pine stands. In the northern third of Portugal, the most abundant shrubs are from the genera Erica and Calluna (Heather family, Ericaceae), Ulex, Cytisus and Pterospartium (Legume family, Fabaceae), and Cistus (Pena and Cabral 1996). In the central part of the country, Cytisus and Cistus shrublands remain dominant. Heather shrublands predominate at the highest elevations, at Serra da Estrela (up to 2000 m), whereas garrigue-like shrublands of Quercus coccifera andThymus spp. are found in limestone areas (Pena and Cabral 1996). In the southern half of Portugal, especially in the SE, there are broad areas of Cistus ladanifer shrublands, Limestone areas are also typically covered by a Quercus coccifera garrigue. In very restricted areas, maquis-type formations of tall shrublands can be found, mainly composed of strawberry tree (Arbutus unedo), wild olive tree (Olea europaea) and arborescent Quercus coccifera (Pena and Cabral 1996). The biomass of shrublands is a function of stand age and can reach 30– 35 t ha−1 , occasionally more, in old stands (∼30 years). More commonly, aboveground biomass of shrublands in Portugal is ∼10–15 t ha−1 , and lower in areas with a short fire return interval (Silva et al. 2006). In the most densely forested areas, located in central Portugal, fire return intervals are in the range of ∼50 years. In areas where forests and shrublands co-occur, fire return intervals are much shorter, in the range of 20–25 years, because shrublands are periodically burnt to stimulate the growth of palatable vegetation (Oliveira 2008). Agricultural areas occupy one-third of the area of Portugal and, although present throughout the entire country, are more abundant in the coastal plain of central Portugal, along the main river valleys, and in the SE part of the country. In central and northern Portugal, land ownership is very fragmented, and the agricultural landscape is a fine-grained mosaic of small parcels of diverse crops, vineyards and olive groves. The agricultural landscapes of south-eastern Portugal are more extensive and homogeneous, dominated by dryland farming of cereal crops, mostly wheat. Here, stubble burning is declining as a land management practice, and wildfires are also uncommon in the managed understorey of evergreen oak woodlands. Thus, fire return intervals are in the range of centuries, at the regional level (Oliveira 2008). Data The data consist of 30 616 size records of wildfires larger than 5 ha, observed in Portugal between 1984 and 2004. Fire perimeters were mapped from Landsat 5 Thematic Mapper and Landsat 7 Enhanced Thematic Mapper satellite imagery, with 30-m spatial resolution, to a geographical scale of 1 : 100 000 (Pereira and Santos 2003). Approximately 170 satellite images, acquired annually after the end of the summer fire season, were analyzed over the 21-year period. The resulting annual burned area maps form the basis for the National Fire Danger Map that the Department of Forestry, Instituto Superior de Agronomia, updates annually for the Portuguese Forest Service (Pereira and Santos 2003). We found that, during the exceptional fire season of 2003 (Trigo et al. 2006), several large fires coalesced into huge, continuous fire scars. It is infeasible, using post-fire-season Landsat
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imagery, to split these composite fire scars into their individual components. Field data, from the Forest Service and the Civil Protection Service, were also found inadequate to accomplish this task, owing to geographical or temporal inaccuracies and missing information. Thus, work is in progress using daily satellite imagery, at 1-km spatial resolution, to unravel these cases. However, this issue will not be addressed in this paper. Models for extreme events Let X denote the size of a wildfire with distribution function F(x). Our objective is to make inferences on the probability that a fire size will exceed a large value, that is, on the tail probability 1 − F(x) for a sufficiently high value of x. Extreme value theory provides statistical models and inferential methods for the tail of a probability distribution. If {Xi }, i = 1, 2, . . . are independent and identically distributed (iid) random variables, then the maximum Mn = max(X1 , . . . , Xn ) suitably normalized converges, as n → ∞, to one of the three extreme value distributions – the Weibull, the Gumbel or the Fréchet. F is then said to be in the max-domain of attraction of one of these distributions. The three distributions can be reparameterized to the GEV distribution. Because of this asymptotic justification, the GEV model is often used as a model for maxima of blocks, such as annual maxima, to estimate tail probability. However, this method does not use the data efficiently because many large observations that could be used in the inference are ignored. This is a major problem, particularly when inference has to be made on short historical datasets. A more efficient method is the POT approach, which is a likelihood-based inference on the excesses over a suitably chosen high threshold. In this method, not only the largest observations, but all the observations above a sufficiently high threshold are used in the inference. The Generalized Pareto Distribution (GPD) is then used to model the distribution of supra-threshold values. The use of the GPD to model excesses is justified by the fact that, under fairly general conditions, a distribution function F(x) is in the max-domain of attraction of the GEV if and only if the excesses over a sufficiently high threshold (u) have GPD (Pickands 1975). Hence, the tail of the conditional distribution is characterized by the GPD model: x −1/k P(X > x + u|X > u) = 1 + k σ where σ > 0, k ∈ (−∞, ∞) and 1 + k σx > 0. Here σ is the scale parameter and depends on the chosen threshold u. The shape parameter k is invariant relative to the selected threshold. This is known as the threshold stability property of the GPD. The choice of the threshold is critical and has to reconcile the availability of a sufficient amount of data for statistical estimation and the theoretical justification. Thus, it is generally chosen sufficiently high so that the excesses follow approximately a GPD distribution, and low enough to have a sufficient number of excesses for statistical inference. For instance, Du Mouchel (1983) suggests choosing u as the 90th sample quantile of the distribution. Various graphical techniques are reported in the literature to assist in the choice of u. A usual procedure is to plot the estimator of k, for instance the maximum likelihood estimator, as a function of u (or as a function of the number of upperorder statistics). The plot is then analyzed in order to detect the
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1200 800 400 0 6
7 8 9 Log(area)
10
4
6 8 Log(area)
10
8
8 6 4 2
6 4 2 0
0 0
Fig. 2.
2
Pareto quantiles
Exponential quantiles
5
20 000
40 000 Area
60 000
5
6
7 8 9 Log(area)
10
11
Histogram, boxplot (top row), exponential and Pareto Quantile plots (QQ-plots) (bottom row) of the fire sizes above 100 ha.
zone where the estimator has a stable behavior in terms of bias and variance. For an extensive study of asymptotic extreme value theory and its statistical applications, see for example Embrechts et al. (1997), Beirlant et al. (2004) or Coles (2001). For a review of methods to estimate the parameters of the GPD, see de Zea Bermudez and Kotz (2006). Once the peaks over the fixed threshold u are estimated, the tail of the distribution P(X > z) for large z = x + u can be calculated from the relationship: P(X > x + u) = P(X > u)P(X > u + x|X > u) Here, P(X > u) is often estimated in an ad hoc manner by the ratio of the number of observations above the level u to the total sample size. A common and easy way to assess any extreme event is the N-year return level. The N-year return level for annual maxima is the quantile that has the N−1 probability of being exceeded in a particular year. Thus, if x represents the size of an annual maximum, the N-year return level xN can be calculated by solving the equation: 1 P(X > xN ) = N When dealing with data on excesses over a threshold, there will be a random number of excess observations each year, and the above formula for the N-year return period can be adjusted to: P(X > xN ) =
1 Nn
where n is the average number of excesses above the threshold in each year.
The Portuguese fire data was analyzed in three consecutive stages. First, the GPD was fitted to the complete dataset, disregarding the temporal and the spatial structures. Second, separate GPDs were fitted to each year in order to quantify the temporal variation that might exist in extreme wildfires. Finally, the large fire sizes for each of the eight regions were modeled. Prior to the modeling, appropriate thresholds were selected for each region. Note that choosing a different threshold for each region corresponds to adding a third (location) parameter to the GPD model. Results The histogram and the boxplot of the log-transformed fires sizes above 100 ha are presented in Fig. 2 (top row). The right-skewed asymmetry of the distribution, which is evident from looking at the plots, clearly reflects the heavy-tailed characteristics of the fire size distribution. Some descriptive statistics for the data are presented in Table 1. Again, the range of the data, as well as the empirical quantiles, clearly reveals the extreme behavior of the Portuguese fire sizes. The exponential distribution is a Pareto distribution with shape parameter k = 0 and is in the max-domain of attraction of the Gumbel distribution. Therefore, it is often used as a benchmark to compare relative tail heaviness. The exponential and the Pareto Quantile plots (QQ-plots) for the fire sizes above 100 ha are shown in the bottom row of Fig. 2. The linearity of the Pareto QQ-plot, as compared with the exponential one, clearly shows that a heavytailed distribution, such as the Pareto distribution with positive shape parameter, can adequately be fitted to the excesses above 100 ha.
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Table 1. Descriptive statistics of the data QP represents the empirical quantile with probability P Fire sizes above 5 ha Minimum 5.00 Q0:80 70.45 Fire sizes above 100 ha Minimum 100.00 Q0:80 486.70
Q0:25 10.31 Q0:90 156.73
Median 20.45 Q0:95 309.11
Mean 91.44 Q0:99 1080.38
Q0:75 53.61 Q0:995 1662.94
Maximum 66 070.63 Q0:999 4651.17
Q0:25 138.21 Q0:90 816.88
Median 211.41 Q0:95 1298.38
Mean 468.76 Q0:99 3854.24
Q0:75 401.75 Q0:995 5772.91
Maximum 66 070.63 Q0:999 20 967.27
10 6
Pareto quantiles
Log(area)
8
6
4
2
4
2 0 1984
1987
Fig. 3.
1990
1993 1996 Year
1999
2002
Boxplots of the (annual) fire sizes.
Temporal variation The boxplots of the annual log-transformed data are presented in Fig. 3. The median and quartiles of fire sizes over the years do not seem to be very different. However, they show marked differences in terms of the large observations. Fig. 3 indicates that 1988 and 1997 produced relatively fewer extreme fires than the other years, whereas 2003 and 2004 produced particularly extreme fires. The almost perfect linearity of the Pareto QQ-plots for each year suggests that the Pareto model is valid for excesses of each year, when studied separately. Fig. 4 contains the Pareto QQ-plot for 1995. In order to assess whether the extreme wildfire sizes have some temporal structure, a GPD was fitted to each one of the 21 annual fire sizes that exceed 100 ha. The probability-weighted moments estimates (Embrechts et al. 1997) of the model parameters are given in Table 2 for u = 100 (all the models presented in the present paper were fitted using the R package evir 1.5). Although these estimates are different over the years, a quick visual check of these estimates (see Fig. 5) does not seem to indicate an increasing (or decreasing) trend in the fitted extreme value distributions. We avoided formal statistical tests owing to the reduced size of the series (21 observations).
2
4
Fig. 4.
6 Log(area)
8
Quantile plot (QQ-plot) for 1995.
Note that the estimates exhibit a significant jump in 2003 that may be partly due to four very large observations. If these observations are taken out of the analysis, then we obtain kˆ = 0.70 and for σˆ = 237 at the threshold u = 100 (these values can be compared with the ones presented in Table 2). It is very clear that these observations are very influential and if they correspond to clusters of fires rather than individual fires, they will eventually overestimate the fire risk. The shape parameter is a very good indicator of the tail heaviness of the underlying fire size distribution. For example, if k < 0.5, then the fire size distribution is consistent with a distribution having a finite mean and variance; if 0.5 ≤ k < 1, it is coherent with a distribution having a finite mean but infinite variance, whereas if k ≥ 1, then the fire size distribution is compatible with a distribution having infinite mean (for the relationship between the existence of moments and the maxdomains of attraction, see Embrechts et al. 1997). It is clear from Table 2 that over the years, Portuguese fire size distributions often show heavy-tailed behavior. This fact will be more evident in the Spatial analysis section, where we look at the spatial variation of fire size extremes. Fig. 6 represents the percentage of the total land burned owing to large fires over the years. The first series at the top represents
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Table 2. Estimated shape (k) and scale (σ) parameters over the years Year kˆ σˆ Year kˆ σˆ
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
0.282 121.0
0.521 138.6
0.676 102.7
0.575 128.4
0.222 97.0
0.367 162.7
0.598 128.0
0.642 156.1
0.737 65.4
0.599 145.1
0.227 170.3
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
0.695 112.4
0.453 135.6
0.162 80.2
0.492 190.6
0.555 101.2
0.471 162.2
0.626 87.6
0.413 161.0
0.851 246.6
0.707 176.5
1990
1995 Year
Percentage of burned area above the quantile
1.0
Estimate of k
0.8
0.6
0.4
0.2
Q0:95 Q0:995
80
60
40
20
0
0.0
Fig. 5.
1990
1995 Year
1985
2000
Estimated values of k and σ for the 21 years.
the percentage of area burned by fires above the 95% annual quantile, whereas the bottom series represents the percentage of area burned by fires above the 99.5% annual quantile. Visual analysis of Fig. 6 suggests that the relative importance of the large wildfires along the 21 years does not indicate trend-like movements (the only relevant aspect is the ‘jump’ that can be observed in 2003). Spatial analysis Owing to the dominance of higher fuel loads and more flammable vegetation types, rugged topography, higher population density and fire-dependent land-use practices, it is reasonable to expect spatial variation of fire size distributions. Fig. 7 displays boxplots of the log-transformed data within each region. These plots show that the distributions (for all regions) are strongly asymmetrical to the right, indicating that the regional data exhibit heavy-tailed behavior. The boxplots show that fire regimes in regions 1, 2, and 3 are very similar and the largest fires are mostly observed in regions 4, 5, 6, and 8. The linearity of the eight Pareto QQ-plots also strongly suggests the use of Pareto distribution for the excesses, for all the eight regions. Fig. 7 is such an example. Table 3 contains the best-fitting GPD models together with the chosen thresholds for each of the regions. The most adequate thresholds were chosen by using the sample mean excess
Fig. 6.
2000
Percentage of annual area burned by large wildfires.
10
8 Log(area)
1985
6
4
2
1
Fig. 7.
2
3
4 5 Region
6
7
8
Boxplots of the eight regions of Portugal.
functions, semi-parametric estimation techniques, as well as bias-variance reduction techniques (see Embrechts et al. 1997). All the models contained in Table 3 fit the data well. The assessment of various model validation techniques (not presented in
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Table 3. GPD models with threshold (u) and estimated shape (k) and scale (σ) parameters and their confidence intervals (CI) for the eight regions Region 1 2 3 4 5 6 7 8
Threshold
kˆ
95%
CI
σˆ
95%
CI
250 250 250 500 500 250 100 100
0.49 0.33 0.47 0.51 0.65 1.19 1.05 1.64
0.26 0.19 0.16 0.37 0.40 0.70 0.42 1.00
0.73 0.47 0.79 0.64 0.91 1.68 1.67 2.29
181 226 196 403 558 127 46 85
132 187 122 339 397 68 17 37
229 264 270 467 718 187 75 133
Table 4. Estimated quantiles and their confidence intervals (CI) for the eight regions Region
Qˆ 0:995
95%
CI
Qˆ 0:999
95%
CI
1 2 3 4 5 6 7 8
788 1017 864 2241 3545 1060 535 17 668
682 917 697 1999 2784 734 328 4975
946 1148 1164 2564 4939 1931 1556 99 106
1887 2029 2038 5432 10 820 6399 2638 247 864
1416 1675 1385 4332 6766 2903 861 28 190
2971 2647 4263 7361 22 130 29 604 2890 99 106
the present paper, but available on request) confirm the quality of the model fit. Spatial analysis of the fire size extremes clearly shows the heavy-tailed behavior of the fires sizes. The estimated shape parameters for all the regions are above 0, which indicates that the underlying fire size distributions are in the max-domain of attraction of the Fréchet distribution. Regions 4 and 5 indicate fire size distributions with finite mean but infinite variance, whereas regions 6, 7 and 8 are consistent with fire size distributions having infinite means. Region 8 is particularly extreme and this may be due to the composite fire scars explained in the Data section. Extreme quantiles (P = 0.005 and 0.001) of the models referred to above are shown in Table 4. These quantiles can be compared with the empirical ones, and, except for regions 7 and 8, there seems to be a very good agreement. In Table 5, we give the projected return periods of very large fires that are beyond the range of the observed data. The return period can be calculated as the expected number of fires (m) or the number of years before a fire of large large size occurs. As, on average, there are 1458 fires per year (over 21 years), we can give this return period in terms of years by dividing m by 1458. can be given in several different ways; here, we fix the return periods at 1, 10, 25 and 50 years (and the corresponding expected number of fires m) and report the estimated quantiles for each of the regions. It is possible to extract some very useful information from Table 5; for example, a wildfire in region 1, resulting in 7283 ha of burned land, can occur with a probability of 0.000 07, on average once in 14 580 fires or approximately once in 10 years. Similarly, we can get the value of the return level corresponding to a fixed return period. For example, in region 2, the return
level that corresponds to the return period of average 10 years is 5545 ha. Note that region 8 has the highest estimated return levels for a given return period. Possible outliers in 2003 that took place in regions 6 and 8 are basically responsible for these very large values. We do not report return levels in these regions owing to their unrealistic nature. Extreme fire regimes in these regions should be further analyzed in order to split these fire clusters. Discussion and conclusions The size distribution of fires larger than 100 ha observed in Portugal between 1984 and 2004 was modeled with the GPD. Graphical analysis of a 21-year time series of GPD shape (k) and scale (σ) parameters does not indicate any annual trend-like movements. However, graphical representation suggests a cyclical behavior of extreme fire sizes, with a frequency of 3 to 5 years, although a longer time series may be needed to assess the robustness of this pattern by using formal statistical procedures. If it really exists, it is more likely to result from post-fire vegetation response dynamics than from meteorological or anthropogenic factors. Post-fire vegetation recovery at rates compatible with these cycles has been documented in Portugal by Fernandes and Botelho (2003), Simões (2007) and Pereira et al. (2008). Years with very large fires also tend to have extensive total burned areas, which act as fire-breaks during subsequent years, on a time frame comparable with that of the cycle apparently detected. The well-known pattern of concentration of a large proportion of total annual area burned in a small number of very large fires (Strauss et al. 1989) is quite evident in our dataset. In 14 out of 21 years, 5% of the largest fires were responsible for over 50% of
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Table 5. Return levels for the eight regions m, the expected number of fires or number of fires before a large fire occurs m 1458 14 580 36 450 72 900 1458 14 580 36 450 72 900 1458 14 580 36 450 72 900 1458 14 580 36 450 72 900
Probability
Year
Region
Quantile (ha)
Region
Quantile (ha)
0.00069 0.00007 0.00003 0.00001 0.00069 0.00007 0.00003 0.00001 0.00069 0.00007 0.00003 0.00001 0.00069 0.00007 0.00003 0.00001
1 10 25 50 1 10 25 50 1 10 25 50 1 10 25 50
1
2276 7283 11 478 16 168 2363 5545 7657 9736 2450 7556 11 713 16 289 6707 22 353 35 841 51 163
5
13 769 62 743 114 114 179 268 9853 150 539 447 634 – 3924 43 455 113 641 235 237 454 585 – – –
2
3
4
the total area burned, and in 5 of those years, 0.5% of the largest fires burned more than 25% of the area. During the exceptional 2003 fire season (Trigo et al. 2006), the top 5 and 0.5% of the largest fires burned 66.2 and 35.6% of the total area affected by fires respectively. This concentration of area burned in extreme events, which typically burn under very severe fire weather conditions, creates enormous difficulties for fire suppression activities. If years with several very large fires tend not to occur in consecutive years, this may reduce the logistic and financial burdens on the firefighting infrastructure. The geographical pattern of extreme fire size mimics that of total area burned in Portugal (Pereira and Santos 2003; Pereira et al. 2006) in most regions. However, the Algarve and Alentejo regions of southern Portugal, which had moderate to low fire incidence during the study period, experienced extremely large fires (by southern European standards) in 2003. The POT analysis allowed for the estimation of regional return levels for fires of various sizes. The estimates for Alentejo and Algarve are unrealistic and appear to have been strongly influenced by the presence of inordinately large fire scars, resulting from the coalescence of distinct fire events, mostly during 2003. The return levels estimated for the remaining regions clearly reveal the need to improve the effectiveness of fire prevention in Portugal. Extended attack suppression activities appear unsuccessful at reducing the incidence of very large fires. Specifically, improved initial attack effectiveness and the construction of a network of strategically placed shaded fuel breaks may contribute towards reducing the frequency of occurrence of very large wildfires in Portugal. Our results, based on the POT method, improve on similar results based on the GEV model, as shown by the narrow confidence intervals reported for estimated model parameters (Table 3) and quantiles (Table 4). We intend to expand the analysis presented herein in various ways. The clusters of merged fire scars, which generate unrealistically large events, will be split into their individual components, using higher temporal resolution satellite imagery. The time series of data will be extended to the period 1975 to 2005, at the expense of increasing the minimum fire size threshold to 35 ha, because of the need to rely on lower spatial resolution Landsat Multi
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Spectral Scanner (MSS) imagery for the years 1975–83. This ought not to be a problem, given our large fire size threshold of 100 ha. The role of climatic correlates of large fire occurrence will be explored, using fire weather indices such as the Canadian Fire Weather Index (FWI) Seasonal Severity Rating (SSR) (Van Wagner 1987). Finally, analysis of the corrected and extended database will be performed at a more disaggregated geographical level, based on the 18 administrative districts, or on the 21 forest planning regions of Portugal. Acknowledgements This work is partially supported by Fundação para a Ciência e para a Tecnologia, POCTI and Research project PTDC/MAT/64353/2006. We thank two anonymous referees and the associate editor for their careful reading of the manuscript and for their suggestions.
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Manuscript received 27 February 2007, accepted 8 April 2009
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