1 Introduction

Vegetation fires occur extensively in Africa. Given the impacts of biomass burning on carbon pools, land cover change and atmosphere, there is a need to accurately assess the spatial and temporal distribution of burning, in order to reduce uncertainties in estimates of burned biomass and pyrogenic emissions (Barbosa et al. 1999a; Dwyer et al. 2000a; Tansey et al. 2004).

Satellite data have been used to provide estimates on burned area extent at the global and continental scale (Barbosa et al. 1999a, b; Roy et al. 2002; Silva et al. 2003; Tansey et al. 2004; van der Werf et al. 2006). The study by Barbosa et al. (1999a, b) was the first attempt to quantify burned areas at the continental level. The large area affected by fire and the level of uncertainty in the estimates of burned area extent motivate the scientific community to produce more accurate estimates and develop improved classification algorithms using new satellite sensors. According to recent estimates of the Global Burned Area 2000 initiative, 64% of the area burned in the year 2000 was located in Africa (Tansey et al. 2004). Africa and Australia burned most frequently during the 1997–2004 period, with tropical savannas accounting for approximately 80% of global burned area (van der Werf et al. 2006).

Anthropogenic, climatic and vegetation factors control the spatial location and pattern of burned areas, which in turn influence the spectral detectability and accuracy of burned area estimates derived from satellite data (Eva and Lambin 1998; Laris 2005; Pereira 2003; Sá et al. 2007). At a local scale, the spread of fire depends on (Archibald et al. 2009; Bond 1997; Dwyer et al. 2000b): fuel type and amount, which in turn depend on soil and climate; weather conditions conducive to fuel drying; source of ignition; presence of herbivores, competing with fires for the available herbaceous fuels; and landscape management, which can affect the occurrence and extent of fires (van Wilgen and Scholes 1997).

In the savanna biome, fuel availability and fire frequency increase with mean annual rainfall (van Wilgen and Scholes 1997). In grassy fuels, fire frequency depends on the availability of herbaceous vegetation in any particular year, which in turn depends on rainfall; in forest fires, fire frequency is determined by the rate of fuel accumulation and time since last fire. For example, in the arid savannas of Etosha in Namibia, the number of fires is closely related with the rainfall of the preceding 2 years (Bond 1997). When rainfall reaches levels that will support evergreen forests, fire depends on the rate of fuel accumulation and becomes rare because the fine dead fuels have a discontinuous cover, and the prolonged moist periods do not facilitate fire spread (Bond 1997, van Wilgen and Scholes 1997). A large part of southern hemisphere of Africa experiences a climate in which there is a prolonged dry period every winter. This coincides with the distribution of savannas, shrublands and grasslands. The arid stretches of this region burn infrequently, because vegetation cover is too sparse to carry a fire across the landscape (Palmer and Hoffman 1997). In dense humid forests, burned areas are small and scattered, and the presence of fires is usually associated with logging and forest clearings (Eva and Lambin 2000). In the northern hemisphere of Africa, fire activity starts at high latitudes (14–12°N), mainly located in the Sudano-sahelian regions, proceeding with the dry season towards the Equator (Palmer and Hoffman 1997). In West Central Africa, most early season fires take place in croplands/mixed croplands and are related with agricultural practices (Clerici et al. 2004). As latitude decreases, the distribution of fires follows the forested ecosystem at the southern woodlands of the savanna belt. There are several motivations for anthropogenic ignitions, such as land preparation for cultivation, honey collection, charcoal making, hunting, to control pests, and either to drive animals or to attract them later to the regrowing grass on burned areas (Frost 1996). In some areas, lightning may be the dominant form of ignition, but it is generally concentrated in the early part of the wet season when the fuels are still moist (van Wilgen and Scholes 1997).

Thus, with such diverse and complex determinants of fire occurrence, a continental-scale analysis of African pyrogeography is useful to help to clarify the contribution of key fire–environment relationships. Using geographically weighted regression (GWR), our expectations were that: (1) GWR would describe fire–environment relationships significantly better that ordinary least squares regression (OLS); (2) the localized regression coefficients developed for the environmental variables would exhibit significant non-stationarity and (3) an examination of spatial patterns of the GWR regression coefficients would help to clarify relationships between fire incidence and environmental factors that might not have been evident with OLS regression. This research provides new insights into some of the factors that characterize fire regime and the relative importance of these across the African continent. This will contribute to improve estimates on the extent of the fire-affected areas through the integration of non-stationarity into fire-vegetation models and to get better estimates of continental biomass burning and atmospheric emissions derived from vegetation fires. Additionally, it uncovers the problem of considering global coefficient estimates to study ecological phenomena that display intrinsic spatial variation, producing uncertainties in models used either for exploratory or predictive purposes.

2 Data and methods

2.1 Data and hypotheses

The following data surfaces were derived for the analysis (Table 1).

Table 1 Summary of data types and derived variables used in modelling analysis (refer text for details)
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Half-degree tile: data surfaces were compiled with respect to a common set of 0.5° tiles, covering sub-Saharan Africa (Olson et al.2001). The selection of this spatial resolution is a good compromise between the amount of data to be processed and the ability to detect local patterns of fire regimes at the continental scale. Some variables have lower spatial resolution than the 0.5° tile but these were the best available, concerning the environmental factors selected. Grid cells intersecting non-burnable areas (deserts, cities and water bodies) were removed using the Global Land Cover 2000 database (Mayaux et al.2003). Analysis was carried out between approximately 20°N–35°S latitude and 20°W–50°E longitude.

Fire Incidence: the response variable (Eq. 1) was derived from the data set on the distribution of burned areas of Africa and covers the 8-year period of 1981–1983 and 1985–1991 (Barbosa et al.1999a). Burned areas from 1984 were not included in the analysis due to processing problems of data. Fire incidence (FI) is a deviance between each cell mean burned area (a) and its expected value (b × A/B):

$$ {\text{FI}} = a-b \times A/B \, $$
(1)

where b is the cell area, A an B are constants representing the mean burned area in sub-Saharan Africa for the 8-year period and the extent of the study area, respectively (Fig. 1).

Fig. 1
figure 1

Fire incidence (FI) in sub-Saharan Africa, derived from the burned area data set, covering the 8-year period 1981–1983 and 1985–1991 (Barbosa et al. 1999a). Negative values of FI represent observations with burned area values lower than the expected, considering the whole study area and period of analysis. The study area is south of the Sahelian acacia savanna ecoregion northern boundary (Olson et al. 2001)

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Population: the effect of population density over fire incidence is not clear because increasing human densities could be predicted both to increase the incidence of fire (altering ignition regime) and to decrease the extent of fire by reducing fuel continuity (Archibald et al. 2009). Population density in 1990 at a spatial resolution of 2.5 arc-min was extracted from the Gridded Population of the World dataset (Center for International Earth Science Information Network and Centro Internacional de Agricultura Tropical 2005; available at http://sedac.ciesin.columbia.edu/gpw/).

Agriculture: the relationship between agriculture and fire incidence is expected to be globally negative, but it may be locally different because a large number of the fires in Africa are set deliberately as a land management practice. The data sets on cropland area proportion for the 1980s and 1990s (Ramankutty and Foley 1999) at the spatial resolution of 0.5° were obtained from the Global Land Use Database Center for Sustainability and the Global Environment (SAGE; available at http://www.sage.wisc.edu/mapsdatamodels.html).

Livestock: animals reduce the amount of grass available for fire consumption; thus, a negative relationship with fire incidence is expected. This data set aggregates predicted values of the density of cattle, sheep and goat for the year 2004, at 0.05° of spatial resolution (Wint and Robinson 2007; available at http://www.fao.org/Ag/AGAInfo/resources/en/glw/home.html).

Vegetation: the hypothesis tested is that vegetation cover is positively related with fire incidence, particularly with the herbaceous cover, given the annual renewal and drying of this type of vegetation. On the contrary, the absence of both vegetation (bare soil) and tree cover is expected to be negatively correlated with fire incidence. Proportional estimates of land cover were derived from the Vegetation Continuous Fields 500 m MODIS 44B product from the year 2001 (Hansen et al.2003; available at http://glcf.umiacs.umd.edu/data/vcf/description.shtml).

Net primary productivity: terrestrial primary production is positively related with the total amount of available vegetation for fire consumption. These data were derived from the AVHRR Global Production Efficiency Model (GloPEM), covering the time period from 1981 to 1991, at a spatial resolution of 8 km (Prince and Goward 1995; available at http://glcf.umiacs.umd.edu/data/glopem/).

Precipitation and temperature: a measure of precipitation seasonality was derived calculating the coefficient of variation of the monthly total precipitation. High precipitation seasonality indicates the existence of a dry season for which the preceding wet season may create conditions for vegetation growth, subsequent drying and availability to burn. Thus, a positive relationship with fire incidence is expected. The temperature data set was used to compute the mean maximum temperature during the three driest months. High temperatures create conditions for vegetation to burn if fuel moisture is low, so it is expected to be positively related with fire incidence. Both data sets were derived from the Climate Research Unit (CRU) Global Climate Dataset, and they correspond to mean monthly data for the 1961–1990 period, at a spatial resolution of 0.5° (New et al.1999; available at http://www.ipcc-data.org/obs/get_30yr_means.html).

Soil water: it is positively related with vegetation growth thus with fire, since lack of water accessible to the root system prevents vegetation growth. However, excessive surface water keeps downed dead fuels moist, preventing them from burning. Thus, it may be expected locally different signs of the relationship with fire incidence. The data set corresponds to the distribution of the total plant-available soil water storage capacity of the rooting zone, on a 1° global grid, available from the International Satellite Land-Surface Climatology Project, Initiative II Data Archive (Hall et al.2005; available at http://islscp2.sesda.com/ISLSCP2_1/html_pages/islscp2_home.html).

Lightning: in some areas, fires may be ignited by lightning strikes, so a positive relationship with fire incidence is expected. The product is a 0.5° global grid of total lightning bulk production, expressed as a flash rate density. A polynomial expression was used to calculate the fraction of the strikes which reach the ground (Price and Rind 1993). The data set is from the Global Hydrology Resource Center, with space-based lightning observations obtained from the lightning imaging sensor (LIS) (available at http://thunder.nsstc.nasa.gov/data/).

The Pearson product-moment correlation coefficient matrix of the explanatory and response variables was calculated, computing a t-test corrected for spatial autocorrelation (rDut, Dutilleul et al. 1993). Correlation coefficients between explanatory variables above 0.5 and non-significant relationships with the response variable were used as criteria to remove variables from the analysis.

2.2 Geographically weighted regression (GWR)

Standard non-spatial regression analysis is based on an assumption that the relationship between dependent and predictor variables is spatially stationary. Spatial autocorrelation (spatial dependency) and heterogeneity (spatial non-stationarity) are two aspects of spatial variability (Anselin and Griffith 1988). In a positive spatial autocorrelation, closer objects are more similar than those that are further apart, and the opposite in the negative spatial autocorrelation case (Legendre 1993). Stationarity is a property of the modelled relationship rather than the data and refers to the tendency for any relationship to vary spatially (Osborne et al. 2007).

Relationships between fire incidence and the explanatory variables were derived using ordinary least squares (OLS) and geographically weighted regression (GWR). Since OLS is extensively used, we briefly describe here the theoretical background only for GWR. A detailed description of GWR is given by Fotheringham et al. (2002) and other recent studies (Shi et al. 2006; Wang et al. 2005).

The underlying assumption of the global OLS regression model is that the relationship under study is stationary (i.e., independent from the spatial location), and thus the estimated parameters remain constant over space. However, this assumption may not be valid and many relationships between environmental variables and their associated response often vary spatially (Foody and Cutler 2003; Foody 2005; Li et al. 2002). GWR uses the location of each observation and allows model parameters to vary in space, using this information to test for and explore spatial non-stationarity (Brunsdon et al. 1998; Foody 2004; Fotheringham et al. 2002). Thus, GWR allows local rather than global parameters estimates and the model is written as (Eq. 2):

$$ y = \beta_{0} \left( {\mu ,\nu } \right) + \sum\limits_{j = 1}^{p} {\beta_{j} (\mu ,\nu )X_{j} + \varepsilon } $$
(2)

where \( \left( {\mu ,\nu } \right) \) denotes the coordinates of the samples in the space, and j denotes the number of explanatory variables. The contribution of each observation to the GWR analysis at a specific location is dependent on its geographical distance from that location, with distant observations weighting less than those nearby.

The estimated coefficients are a function of the bandwidth of the spatial kernel used, i.e., the radius or the number of observations around each point included in the weighting matrix (Brunsdon et al. 1998). Bandwidth controls the distance-decay in the weighting function and indicates the extent to which the resulting local calibration is smoothed (Fotheringham et al. 2002). Selection of the weighting function and optimal bandwidth were accomplished by minimizing the corrected Akaike information criterion (AIC), which indicates how close a regression model approximates reality, and it accommodates for differences in the number of degrees of freedom in the models compared (Akaike 1981; Burnham and Anderson 2002; Fotheringham et al. 2002). Thus, with this parameterization, the bandwidth is the same for all the covariates and the result is the best fitted model.

Analysis was performed using the GWR (version 3.0) software package (Fotheringham et al. 2002). Comparison between the OLS and GWR models tests the null hypothesis that GWR represents no improvement over the global model. Instead of using the stationarity index (IQR/(2 × SE); Fotheringham et al. 2002) to test the significance of spatial variability in local coefficient estimates, this was formally tested using a Monte Carlo permutation test. The former is an “ad hoc” test, which in this particular study would not be feasible because given the large number of observations, the SE would be rather small as a result. The GWR output also allows mapping the distribution of coefficient estimates of the explanatory variables and their local statistical significance, using a t-test.

A controversial question when analysing outcomes of ecological research has been whether the increase in Type I error under repeated testing should be taken into account or not (Moran 2003). The calibration procedure in GWR uses the same data set to calibrate models at each spatial location. Thus, there is a certain degree of dependency between the models, which inflates the t statistics and associated hypotheses tests (Byrne et al. 2009). Páez et al. (2002) also discuss the problem of highly spatially dependent tests and the need to improve the control on the family-wise error rate (the probability of rejecting one or more true null hypotheses). The most common method to address this error type has been the application of the sequential Bonferroni adjustment (Rice 1989). However, this method has several flaws, namely the concern with the general null hypotheses that all null hypotheses relative to the estimated coefficients are simultaneously true, which argues for rejecting this method in ecological studies (Moran 2003; Perneger 1998). If one is willing to redefine the problem in terms of the false discovery rate (the expected fraction of incorrectly rejected hypothesis), the Benjamini and Hochberg (1995) approach could be particularly useful (De Castro and Singer 2006). However, this method does not take into account the multiple dependent tests. In this case, the Benjamini and Yekutieli (2001) approach may be applied, and a simple Bonferroni style adjustment for dependent tests has been developed by Byrne et al. (2009). The family-wise error rate (\( \xi_{m} \)) for testing hypothesis about GWR model coefficients at \( \xi_{m} \) or less is achieved by selecting (Eq. 3)

$$ \alpha = {\frac{{\xi_{m} }}{{1 + p_{\text{e}} - {\frac{{p_{\text{e}} }}{np}}}}}$$
(3)

where p e is the effective number of parameters, n is the total number of observations and p is the number of parameters in each model. In most applications, p e will be much less than the maximum number of parameters (np) and so a significant gain in statistical power is expected when using this approach (Byrne et al. 2009). This approach avoids the large sacrifice of statistical power associated with the Bonferroni correction, introducing a dependency parameter which is a function of the effective number of parameters, an output of the GWR program.

2.3 Spatial autocorrelation

Analysis of clumping of model residuals (clusters of over or underprediction) may indicate the presence of non-stationarity and thus cause misspecification of a global model (Diniz-Filho et al. 2003; Jetz et al. 2005). Therefore, another indicator of the improvement in a GWR model when considering non-stationarity into models is a reduction in spatial autocorrelation of the residuals (Kupfer and Farris 2007; Zhang et al. 2005). Moran’s I spatial autocorrelation is one of the most commonly used coefficients to measure the similarity between samples for a given variable as a function of spatial distance (Cliff and Ord 1981; Legendre 1993). Under the null hypothesis of no spatial autocorrelation, I has an expected value near zero for large n, with positive and negative values indicating positive and negative autocorrelation, respectively (Cliff and Ord 1981).

3 Results

3.1 Model selection

A bivariate correlation matrix was computed considering the data sets: population density (PD); agriculture proportion (AG); livestock density (LD); herbaceous, bare soil and tree cover proportions (HP, BP and TP, respectively); net primary productivity (NPP); precipitation seasonality (PS); mean maximum temperature of the three driest months (T max); soil water (SW); and number of lightning strikes (L). From these, only L had a non-significant correlation with fire incidence (FI) (rDut = 0.013, P = 0.286, n = 6,296). BP and TP were removed from analysis because they had correlation coefficients with other variables higher than 0.5. Due to its high correlation with the response, HP was selected to represent the vegetation layer. NPP was also excluded because of its correlation with PS (rDut = −0.56, P = 0.001) and a lower correlation with the response than the PS covariate. Thus, the selected variables were PD, AG, LD, HP, PS, T max and SW. Their spatial distribution is shown in Figs. 2 (anthropogenic variables) and 3 (vegetation and climatic variables).

Fig. 2
figure 2

Spatial distribution of the group of anthropogenic variables: PD (a), AG (b) and LD (c) represent population density, agriculture proportion and livestock density, respectively. White areas correspond to unprocessed data, and the dashed line is the Sahelian acacia savanna ecoregion northern boundary

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Fig. 3
figure 3

Spatial distribution of the vegetation and climatic variables group: HP, PS, T max and SW represent herbaceous proportion, precipitation seasonality, mean of the maximum temperature of the three driest months and soil water, respectively. White areas correspond to unprocessed data, and the dashed line is the Sahelian acacia savanna ecoregion northern boundary

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There is a clear indication of population activity related with agriculture and livestock practices, e.g., in Ethiopia, Nigeria, Kenya and Uganda. Agricultural activity covers a large extent, especially in the eastern part of the continent (Fig. 2b). In Sudan, Ethiopia, Kenya and Tanzania, domestic animals appear to be the main contributors for the family economy (Fig. 2c).

The distribution of HP (Fig. 3a) shows a very similar pattern to the observed FI (Fig. 1), especially in the northern hemisphere. In the southern hemisphere, other factors than HP may be potentially related to FI, especially in north-eastern Angola and in the southern Democratic Republic of Congo (D.R.C.). In this region, T max (Fig. 3c) and SW (Fig. 3d) have high values favourable for vegetation growth, which promote fire occurrence. PS (Fig. 3b) shows a latitudinal gradient approximately divided by the equator, with precipitation variability increasing with increasing aridity (high values are found near the Sahara and the Namibia desert) and decreasing in very humid areas, particularly near the equator, where climate is typically aseasonal.

4 OLS

The global OLS linear regression model output is presented in Table 2 (7 covariates and 6,296 observations).

Table 2 Estimate, standard error (SE), T value and variance inflation factor (VIF) for each parameter of the OLS model, considering the 6,296 observations
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Despite the variables having different measurement units, we are not concerned with the effect of each variable over fire incidence (magnitude of the coefficient) but only with its global sign and significance, given by the T value statistic. Livestock density is the only coefficient not statistically significant. However, the model accounts only for about 57% of the variation in fire incidence. Variance inflation factor (VIF) values are below 1.5, indicating the absence of collinearity problems. Only the precipitation seasonality coefficient showed a counter-intuitive global signal for its relationship with fire incidence, indicating that local factors influencing the response may be hidden.

5 GWR

The purpose of fitting the GWR models to data was mainly to explore the different spatial patterns of the fire–environment relationships. Thus, there was no concern in having a separate data for model calibration and evaluation.

Table 3 shows the GWR models fitted to data according to the selected groups of factors affecting fire incidence (climate, vegetation and anthropogenic), with the corresponding adjusted R 2 and AICc values. All models were fitted using a Gaussian kernel and have the same bandwidth of 323 observations accomplished by minimizing the AICc. The Monte Carlo approach revealed that all the relationships and explanatory variables were non-stationary with a level of significance of 0.1%.

Table 3 Univariate and multivariate GWR models considering the seven explanatory variables: population density (PD), agriculture proportion (AG), livestock density (LD), herbaceous proportion (HP), precipitation seasonality (PS), mean of the maximum temperature of the three driest months (T max) and soil water (SW)
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Univariate local models indicate that HP is the covariate best related with FI, with the highest R 2 (0.76) and the lowest AICc, even more important than the multivariate sub-model of anthropogenic variables (PD, AG and LD). From this group, AG has the most significant relationship with FI. Among the climate variables, PS also explains moderately well (R 2 = 0.71, and the second lowest AICc of the univariate models) the variability of FI. Although AG and PS have the same R 2 value, the latter is a better explanatory variable of FI, due to its lower AICc value. The sub-model with the three climate variables performs better (R 2 = 0.78) than the one with the anthropogenic variables (R 2 = 0.74). Though the sub-model with the most significant covariates from each group of factors is less complex than the seven-variable model (with an R 2 = 0.83 and the second lowest AICc value), the latter was selected not only because it accounts for the highest R 2 (0.87) and has the lowest AICc but also because it could give additional insights into fire–environment relationships.

In the GWR model output (Table 4), the F test indicates that the GWR model is a significant improvement on the global model for the fire incidence data. There is a decrease in the AICc and an increase of the adjusted R 2 from 0.57 in the OLS model to 0.87 in the local model. The number of data points in the local sample size used to estimate the parameters was 323 (corresponding to approximately 5% of the total number of observations), so a reasonable smoothing is expected with this bandwidth.

Table 4 Output summary of the GWR local model
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R2 varies spatially over the entire study area (Fig. 4a). Only 29% of the local models have an R2 value below 0.57 (R2 of the OLS model), and almost half (45%) have an R2 above 0.75. Most of the significant intercept values are negative (Fig. 4b).

Fig. 4
figure 4

Spatial distribution of the coefficient of determination R 2 (a) and intercept parameter estimates (b) of the different local GWR models. Estimated values of the intercept are statistically significant at a level of confidence above 95%

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All GWR parameter coefficients were tested for significance according to the family-wise error rate calculated from Eq. 3 (α = 0.000168, for an ξ = 0.05). All the coefficients have spatially variable positive and negative estimates, indicating non-stationarity of the relationships with fire incidence (Figs. 5, 6).

Fig. 5
figure 5

Spatial distribution of the local GWR coefficients relative to the anthropogenic variables: population density (PD), agriculture proportion (AG) and livestock density (LD). Coefficient estimates are statistically significant at a 95% or above level of confidence

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Fig. 6
figure 6

Spatial distribution of the local GWR coefficients relative to the vegetation and climatic variables: herbaceous proportion (HP), precipitation seasonality (PS), mean of the maximum temperature of the three driest months (T max) and soil water (SW). Coefficient estimates are statistically significant at a 95% or above level of confidence

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A broad area has more than three statistically significant variables (Fig. 7a), and HP coefficient estimates cover the largest area of most significant variable, followed by the intercept, which prevails in the southern hemisphere (Fig. 7b).

Fig. 7
figure 7

Number of significant variables (a) and the most significant variable (b) for each of the local GWR models. PD population density; AG agriculture proportion; LD livestock density; HP herbaceous proportion; PS precipitation seasonality; T max mean of the maximum temperature of the three driest months; SW soil water

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When considering non-stationarity into models, GWR model standard residuals display a spatial random pattern of local areas of FI underestimation against the clustered pattern observed in OLS model residuals (Fig. 8). The calculated global Moran’s I value was reduced from 0.61 in the OLS model to 0.17 with GWR. This lower value is a consequence of the more dispersed pattern of clusters of negative spatial autocorrelation. The correlogram of model residuals also illustrates the reduction of spatial autocorrelation with the local approach (Fig. 9).

Fig. 8
figure 8

Standard residuals derived from the OLS (a) and GWR (b) models

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Fig. 9
figure 9

Correlogram of OLS and GWR model residuals displaying the changes in Moran’s I as a function of spatial distance

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6 Discussion

In southern hemisphere Africa, fire incidence has values of burned area above the expected, especially in Angola, southern D.R.C., Zambia, Mozambique and Tanzania (Fig. 1). However, fire incidence is much higher north than south of the equator. This distinct pattern may derive to some extent, from the burned area classification algorithm used by Barbosa et al. (1999b). That algorithm included a criterion of post-fire land surface albedo decrease, which may have a threshold too high to detect burns in semi-deciduous forests and woodlands of the southern hemisphere (Govaerts et al. 2002). The amplitude of the decrease of the surface albedo between burned and unburned areas depends on the pre-fire vegetation spectral characteristics. Trees have an albedo value lower than dry grass (Govaerts et al. 2002), thus reducing the spectral contrast between burned areas and the surrounding land cover types. As a consequence, the reduction of the albedo from pre- to post-fire vegetation is higher when the pre-fire vegetation is mainly composed of dry grasses, which are more reflective. Furthermore, the arid regions of the south-western and southern Africa do not promote vegetation growth, and consequently the reduced amount of charcoal produced by a fire may not be sufficient for burnt scar detection by low spatial resolution sensors.

There are some factors not adequately captured in the OLS model (R 2 = 0.57). The variability explained by the seven-variable GWR model increased to 86%. Its lowest value of AICc and the F test suggest that the local model is a significant improvement on the global model for the FI data (Table 4). According to the different local R 2 values (Fig. 4a) and the fact that only 29% of these values are below the OLS R 2 value, the GWR model did not simply distribute the model’s explanatory power spatially but provided a better explanatory ability. The null hypothesis that the GWR model represents no improvement over a global model is rejected. Thus, the relationship between fire incidence and all the selected variables is non-stationary, i.e., we can find spatially different relationships in magnitude and sign.

Exploring the fitted GWR models, none of the variables explain the low fire incidence in the region encompassed by Namibia, Botswana and South Africa (Figs. 1, 7). The reason for this poor fit is that fire is rare in the arid regions of the west and interior of southern Africa due mainly to less fire prone vegetation (amount and type), which is a response to climate, wildlife herbivory and extensive pastoralism (Bond 1997). Consequently, there is no burned area spatial pattern to model, and given the underlying homogeneity of the environment factors, fire incidence is nearly constant and will hardly be explained by any actual geographical variable. Several factors may affect the burned area detection, namely the complex spatiotemporal patterns of burned scars that may cause them to remain undetectable by low spatial resolution data sets (Laris 2005; Silva et al. 2005).

Human influence (Fig. 5) shows a general negative relationship with fire incidence, with magnitude effects locally different, as visible in a broad area north of the equator. The increased density of agricultural settlements, use of fuelwood for fire and higher domestic herbivore (Hoffman 1997) reduce the amount of vegetation available for burning and on the other hand may break the landscape continuity and prevent fire spread. In some areas, the positive relationship may be due to the lack of natural vegetation contiguity and availability of less fire prone fuels. Also, some federal fire suppression activities have been leading to catastrophic fires in contrast with traditional fire practices which may prevent large late-season fires (Butz 2009; Laris 2005). The multivariate models (Table 3) enhance the importance of considering different factors in explaining fire incidence variability. The single best fire incidence related variable is herbaceous proportion (Figs. 6a, 7b). This derives from the fact that in many savanna fires, most combustion takes place in the grass layer. High surface area-to-volume ratio and low moisture content during dry periods make them excellent fuels (van Wilgen and Scholes 1997).

The signal of the relationships between precipitation seasonality and soil water with fire incidence varies spatially (Fig. 6b, d), reflecting the geography of mean annual precipitation. Negative parameter coefficients of PS are mainly observed in a wide area of the northern hemisphere and in Angola, because the proximity to arid areas increases PS but decreases FI, since fuel becomes insufficient to support the spread of fire. Fires also become rare when rainfall reaches levels that will support evergreen forests, and the prolonged moist periods (lower PS) do not facilitate burning also decreasing fire incidence (e.g., in the middle-south of D.R.C). Soil water is related to precipitation, soil drainage and plant growth. In areas with high precipitation such as D.R.C., vegetation is less susceptible to fire due to higher plant moisture content, inducing an inverse relationship between SW and FI (especially north of the equator and in Mozambique). In climatically drier areas, SW is important for vegetation growth and availability for fire consumption, resulting in a positive relationship with FI. Positive values of T max coefficient estimates (Fig. 6c) are especially found where water is not a limiting factor. Higher temperatures favour vegetation growth, and during the dry season, vegetation easily dries supporting the occurrence of larger fires, thus a positive effect over fire incidence.

7 Conclusions

This study contributed towards understanding the pyrogeography of sub-Saharan Africa by spatially modelling fire–environment relationships and the relative importance of such drivers at the continent level. Introducing non-stationarity into fire-vegetation models may contribute to a better understanding of fire regimes, which is needed to predict their consequences in terms of vegetation and continental climate change.

At the moment, this is the first application of GWR to study fire regime, and it provided new insights into localized controls on fire incidence that were not evident when using a global model and thereby helped to demonstrate the value of examining the non-stationarity of regression coefficients. Within this context, this study fulfilled the stated initial expectations. The fire–environment relationships are better described using local than a global model given the spatial variation of the regression coefficients. A recent study (Archibald et al. 2009), using data only for 1 year and applied to southern Africa, also enhances the importance of considering a local approach to evaluate the drivers of burnt area. Other studies also stress the importance of considering non-stationarity and use GWR as a tool to assist in model development to improve our understanding of several spatial processes as species diversity and other biogeographical patterns (Foody 2004; Zhang and Shi 2004; Osborne et al. 2007). The search for additional environmental variables may be more appropriately through an analysis of the spatial patterns in the parameter estimates derived from a local technique such as GWR (Foody 2004).

We concluded that the occurrence of fire is primarily dependent on climate, directly through weather conditions that enable fires to spread, such as temperature and moisture, and indirectly through plant productivity, which supplies fuel load to sustain fire. However, this fuel load is also dependent on local patterns of human influence which should be taken into account if we are concerned with fire regimes. Herbaceous cover has a very significant relationship with fire incidence, and climate variables are more important than anthropogenic variables in explaining fire incidence. Human activities have here an indirect effect over fire incidence through the amount and spatial distribution of vegetation available for burning. Precipitation seasonality revealed local patterns of contrary effects over fire incidence that would have been missed in a global regression analysis. Improved understanding of local fire–environment relationships, in terms of signal and magnitude, contributes towards highlighting areas of potential inaccuracies in available burned area maps and to elucidate the geography of environmental and anthropogenic fire correlates. Also, the significance of the intercept over a large area of southern Africa suggests a problem of model misspecification, which can derive from the need of higher spatial resolution burned area cartography. Thus, it is important to reanalyse African pyrogeography using the recently available MODIS burnt area product (Roy et al. 2005).