2.2. Model Development
 Deforestation fires are the culmination of numerous factors that drive land use decisions in Amazonia (Figure 1). Here, we focused on the climate-mediated potential for fire-driven deforestation. Figure 2 shows 10-day time series of deforestation fires and precipitation over 2003–2006 for three grid-cells. Precipitation patterns define the seasonal timing of fire activity; fires only occur during the dry-season, mostly as late season fires [Schroeder et al., 2005]. At an intraseasonal time scale, wet 10-day periods within the dry-season result in a drop of deforestation fire activity (e.g., last 10-day of August 2004 in Mato Grosso). These examples suggest that climate can dissuade human ignitions and/or influence whether these fires will be successful through direct impacts on vegetation and soil moisture (Figure 1, arrows a, b, d, f, and h). Finally, fire activity also varies significantly at inter-annual time scale: Figure 2a illustrates how drought conditions in Rondônia in 2005 increased deforestation fire potential.
Figure 1. Interactions among climate, vegetation and anthropogenic factors in the context of fire-driven deforestation. Climatic conditions govern fuel moisture following deforestation, described as the deforestation fire potential, whereas land-use decisions on the amount and type of agricultural expansion in Amazon regions ultimately determine the fire activity within periods with suitable climate for fire-driven deforestation. Feedbacks from deforestation on local climate or moisture dynamics due to fragmentation were excluded.
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Figure 2. Ten-day time series of precipitation rates (blue bars), deforestation fire detections (red stairs), and Fire Deforestation Potential (FDP, black stairs), during 2003–2006 for three 1° × 1° cells in southern Amazonia.
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 Since we aim to model the potential use of fires, independent of any deforestation projections, climate is the factor to isolate. However, factors of anthropogenic origin are also involved, and need to be taken into account to characerize climate-driven variability. First, vegetation curing is intentionally accelerated by cutting trees, preventing them from accessing groundwater (Figure 1, arrow c). Second, humans decide whether or not to burn during a fire prone climatic window. In Rondônia for example, increased fire activity in 2005 (845 deforestation fires versus 354 in 2004) may have various explanations. Economic incentives for deforestation may have been stronger in 2005 (arrows i and j), possibly aided by new infrastructure facilitating deforestation (arrows i and j). Alternatively, 2004 had a rather moist dry-season which may have limited the use of fires (through arrows a and b, and see Figure 2a), while drought conditions prevailed in 2005 [Marengo et al., 2008]. The predominant type of deforestation could also be involved (arrow k); in the state of Mato Grosso conversion to cropland involves nearly three times as many fires as conversion to cattle ranching [Morton et al., 2008]. Unfortunately, information about these anthropogenic factors is not always available at the spatiotemporal resolution required to perform satisfying statistical analyses at the scale of the Amazon. One could argue that gridded information on deforestation rates [Achard et al., 2007; Hansen et al., 2008] provide a single proxy accounting for the combined influence of these factors, and could be used to remove the fire variability due to changes in deforestation pressure rather than climate variability. A drawback of this approach is that deforestation and fires are both a cause and a consequence of each other: a lower deforestation rate may be either the cause of decreased fire activity (arrow l, unwanted variability) or its consequence if climate was too humid (arrows f, g, and h, variability under study).
 Consequently, building a fire-potential model required transforming the fire observation data to make it independent on the extent and type of deforestation. This was partially achieved by computing intra-annual fire anomalies for each grid-cell and each year, based on two assumptions:
 1. The anthropogenic will to deforest is rather constant within a year, i.e., conversion plans are decided early and do not change much over the course of the dry-season (other than for climatic reasons), and economic or political factors impacting deforestation are stable at an annual time scale.
 2. The distribution of deforestation fires within a year is mostly driven by climate, other potential drivers being considered insignificant. [Morton et al., 2008], for example, showed that the intra-annual timing of fires changes slightly with conversion type.
 Fire intra-annual anomalies were computed as:
where Fy,d is the fire activity during the 10-day period d of year y (36 10-day periods per year), and Fay,d the corresponding fire anomaly. To avoid unrealistic anomalies, we discarded 1° × 1° grid-cells with a peak fire activity of less than 10 fires in a 10-day period, and years with less than four 10-day periods with observed fires.
 To study the relationship between fire anomalies and climate, we defined two indicators of moisture conditions based on Figure 1, detailed observations of the data (as in Figure 2), and reported deforestation practices:
 1. The long-term precipitation (LTppt) variable represents the vegetation sensitivity to fires due to climate conditions on monthly timescales. This indicator captures desiccation dynamics of the slashed trees (fuels) during the dry-season, as fire efficiency increases with curing time following clear-felling of vegetation [Carvalho et al., 2001]. LTppt is calculated as follows:
where d is the current 10-day period, m the number of previous 10-day periods to be considered (the “memory” of the indicator), PPTi the precipitation at 10-day period i, and b a constant value controlling the decrease of the weight of 10-day periods with time (conditions during the most recent 10-day periods have a greater impact on LTppt). Various studies point at a delay of two to five months after the wet season to reach significant fire sensitivity [Carvalho et al., 2001; Field and Shen, 2008; Schroeder et al., 2005; van der Werf et al., 2008a]. Accordingly, we apply a memory (m) of 15 10-day periods, equivalent to 5 months. We tested a range of value for the parameter b, which we set to b = 6 by visual inspection, meaning that precipitation during the most recent 10-day period is three times as important as the oldest (15th) 10-day period in computing LTppt. Note also that LTppt does not depend on precipitation during the 10-day period under consideration, which is captured with the short-term precipitation parameter (see below).
 2. The short-term precipitation (STppt) variable, which represents the vegetation sensitivity to fires due to climate conditions over recent days. The STppt metric captures the rapid dynamics of superficial moisture due to daily weather [Holdsworth and Uhl, 1997; Ray et al., 2005; Uhl and Kauffman, 1990]. This indicator is taken as the weighted mean of the precipitation over the considered (weighting 75%) and previous (weighting 25%) 10-day period.
 For each grid cell and for each 10-day period we computed fire anomalies, LTppt and STppt. LTppt and STppt were binned into 25 equal intervals, and each fire anomaly was attributed to the observed LTppt and STppt. To strengthen the independence of the results to other sources of variability that may limit fire use even under favorable climate conditions, the fire deforestation potential (FDP) under each LTppt/STppt pair was then computed as the upper quartile (at 0.75) of the corresponding fire anomalies (Figure 3, left). These results were finally smoothed to avoid unrealistic behavior of the final model (using a classic moving window average filter and forcing a decreasing FDP along increasing LTppt and STppt), as presented in Figure 3 (right). A second metric, the annual fire deforestation potential (anFDP), is defined as the sum of all positive 10-day FDP values in a given year (negative values of FDP always result in no or insignificant fire activity). Fire anomalies as used here represent the fire climate potential, i.e., under what climatic conditions do the fires actually burn in a given year. Although raw anomalies are not quantitative, the removal of unrealistic anomalies, the use of the upper quartile, and the annual aggregation make of the anFDP metric a relevant indicator of the maximum fire activity possible during a given dry season (see section 3).
Figure 3. (left) Contour plot of the upper-quartile FDP based on climate and fire detections during 2002–2006 and (right) final model configuration after smoothing. FDP is unitless (standardized anomalies).
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 We excluded several factors in our model that influence moisture dynamics (Figure 1, arrows e and e'), including forest fragmentation [Broadbent et al., 2008; Laurance and Williamson, 2001], vegetation type and density [Saatchi et al., 2007] and soil water retention capacity [Nepstad et al., 2004]. Further, our model represents moisture conditions with two indicators based on precipitation, while temperature also modulates evapotranspiration rates. We chose not to include temperature in the model as it shows little seasonality in most tropical forests, indicating that moisture anomalies are largely a function of precipitation.