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P.M. Fernandes et al. 2010. Testing the fire paradox: is fire incidence in Portugal affected by fuel age
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dominated by shrubland where fire is a tool routinely used in traditional land management. The
existing spatial and temporal information can thus be analyzed to detect relationships between
fuel age and fire incidence. Our objective is to analyze contemporary fire history data to
determine how fire recurrence, hence fuel age, relates with burn probability in Portugal.
2. Methodology
The study area is the entire Portuguese mainland, 89 x 10 3 km 2 . The analysis of burn probability
was based on all wildfire events with an area equal to or larger than 10 ha occurring in Portugal
from 1998 to 2008, i.e. during a 11-year period. We used the mapped fire history of the
Portuguese Forest Service and GIS software to process the spatial information. Fire recurrence
maps were created for each year under analysis, fire recurrence being the number of fires
experienced by each 625-m 2 pixel (25 x 25 m) since 1975. For the area within each individual
fire perimeter we have determined an area-weighed mean fire recurrence and the corresponding
fire return interval (FRI). Then we used survival analysis by fitting a two-parameter Weibull
function to the FRI distribution based on maximum likelihood. We have modelled FRI from
individual fire events, rather than from patches defined by their unique fire history, because the
former offers the possibility of assessing if the time-dependency of burn probability changes
with fire size, i.e. with weather conditions.
A fire interval distribution can be described in a cumulative form, F(t), the probability of fire
occurrence before or at time t, and as a probability density, f(t), which reflects the frequency of
burning in a given time interval (e.g. Moritz 2003; Moritz et al. 2009):
F(t) = 1-exp[-(t/b) c ] (1)
f(t) = (ct c-1 /b c ) exp[-(t/b) c ] (2)
where t > 0, b > 0 and c ≥ 0. Parameters b and c have ecological meaning. The scale parameter
(b) has the dimensions of time and is the typical fire return interval (FRI) that will be surpassed
36.79% of the time. The shape parameter (c) is dimensionless and describes the change in fire
probability through time. The negative exponential distribution is a special case of the Weibull
model that corresponds to c = 1. The probability of burning increases with time when c > 1,
increasing linearly when c = 2 and exponentially when c > 2. Vegetation types that are
simultaneously fire-prone and fire-dependent are expected to have high c values (Polakow et al.
1999) and c > 4 qualifies a fire regime as highly age-dependent (Moritz 2003). The Weibull
median fire-free interval (MEI) gives a probabilistic estimate of fire-return intervals for
asymmetrical fire interval distributions (Grissino-Mayer 1999). The “hazard of
burning“ function λ(t) gives the instantaneous probability of a fire occurring in a specific time
interval and is useful to measure how time since the last fire event affects the subsequent
likelihood of burning:
λ(t) = ct c-1 /b c (3)
Data was truncated to consider only those fires whose majority of pixels had burnt at least twice
since 1975, thus reducing the existing asymmetry that otherwise would have biased parameters
b and c (Moritz 2003); note that fire incidence in Portugal was quite low before the 1970s. The
Weibull model was fitted separately to two sub-divisions of Portugal − northern and centraleastern
(N-CE) and central-western and southern (CW-S) − mainly on the basis of their relative
fire incidence, high in N-CE and relatively low in CW-S (Verde and Zêzere 2010).
Forest Landscapes and Global Change-New Frontiers in Management, Conservation and Restoration. Proceedings of the IUFRO Landscape Ecology
Working Group International Conference, September 21-27, 2010, Bragança, Portugal. J.C. Azevedo, M. Feliciano, J. Castro & M.A. Pinto (eds.)
2010, Instituto Politécnico de Bragança, Bragança, Portugal.