PREDICTING THE OCCURRENCE OF FIRES IN AFRICA
Maria Fernanda Buitrago Acevedo
Thesis code: REG80439
Registration number: 780804-144-120
Supervised by:
Frank van Langevelde
Arnold Bregt
Aldo Bergsma
Cesar Carmona-Moreno
Thomas Groen
Chair group:
Resource Ecology Group
Laboratory of Geo-Information Science and Remote Sensing
Wageningen University and Research Centre
May 2008
Content
Summary............................................................................................................................ 7
1. Introduction................................................................................................................... 8
1.1 Background ............................................................................................................. 8
1.2 Research questions................................................................................................ 11
2. Methodology ................................................................................................................ 12
2.1 Data collection ....................................................................................................... 12
2.2 Data management ................................................................................................. 14
2.3. Data analysis......................................................................................................... 16
2.3.1 Correlations and regression analysis ........................................................... 16
2.3.2 Time series analysis........................................................................................ 17
3. Prediction of fire frequency ....................................................................................... 19
3.1. Results ................................................................................................................... 19
3.1.1 Correlations and regression analysis between fire frequency and
environmental variables ......................................................................................... 19
3.1.2. Regression models for the prediction of fire frequency (Ff) ..................... 23
3.2 Discussion .............................................................................................................. 25
3.2.1 Correlations and regression analysis ........................................................... 25
3.2.2 Models for predicting fire frequency ........................................................... 27
4. Prediction of monthly fire occurrence in South Africa ........................................... 29
4.1 Results .................................................................................................................... 29
4.2 Discussion .............................................................................................................. 33
5. Conclusions and recommendations ............................Error! Bookmark not defined.
References........................................................................................................................ 38
Predicting the occurrence of fires in Africa
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Content of figures
Predicting the occurrence of fires in Africa
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Content of Tables
Predicting the occurrence of fires in Africa
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Content of Appendixes
Predicting the occurrence of fires in Africa
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Summary
Fires are among the most important processes in shaping natural ecosystems, acting as an
evolutionary force both directly for humans, and for their environment, by changing the
ecosystem structure and biodiversity. Although the driving factors that influence the
occurrence of fires in the world are still not widely understood, current studies on the
spatial and temporal interrelations between fire, climate, and other environmental and
anthropogenic variables are the key for understanding this influence.
This research makes a spatial and temporal assessment in the African continent, of the
correlations between fire occurrence and possible explaining environmental, climatic and
anthropogenic variables, and generates some models to predict fire frequency based on
these explanatory variables. This study also makes a temporal analysis between fire
occurrence and Normalized Digital Vegetation Index (NDVI), using the monthly time
series for the period 1982-1999. Fire occurrence is derived from the weekly global burnt
surface product (GBS) generated by the Joint Research Centre of the European
Commission for a period of 17 years (1982-1999), and was used for the characterization
of fire occurrence (presence or absence) and fire frequency. This product registers the
presence or absence of fire’s scars and is based on the observations from the Advanced
Very High-Resolution Radiometers (AVHRR) on the series of meteorological satellites
operated by the National Oceanic and Atmospheric Administration (NOAA).
The explanatory variables selected for the analysis are: temperature, precipitation,
relative humidity, wind speed, land cover (MODIS product), NDVI, soil characteristics,
livestock (number of cattle, sheep, and goats), population density, growth, and elevation.
All the datasets were rescaled to 8km resolution and the averages were calculated to
analyze the correlation between individual explanatory variables and fire frequency
(weeks burned/year). Environmental variables showed the most important correlations
with fire frequency. NDVI, percentage of herbaceous vegetation, and percentage of bare
soil are the variables most strongly related with fire frequency. Climatic variables showed
weaker correlations, however, precipitation has a negative and significant correlation.
The influence of human factors in the fire activity was evaluated through variables like
livestock and human settlements. Livestock, measured as the number of cattle has a
strong correlation with fire, while number of sheep or goats has a weaker correlation. On
the other, hand human settlements were not correlated with fire frequency.
The most significant variables were used to generate models for predicting fire
occurrence. These models were calculated with bootstrapping techniques and stepwise
methods for the selection of the most important variables. Models based on few variables
like NDVI and land cover, are the most simple and significant models that can accurately
predict the phenomena (R2a=0.62).
A time analysis was developed between the monthly data of fire occurrence (presence or
absence) and NDVI for South Africa. Logistic models were adjusted between fire
occurrence of every month and the NDVI of the current month, and the 11 previous
months. These logistic models were transformed to probabilistic functions that were
compared with the real occurrence of fires. The models for every month show the real
patterns, however, the models underestimate these probabilities, due perhaps to the large
number of locations without fires in South Africa.
Predicting the occurrence of fires in Africa
7
PREDICTING THE OCCURRENCE OF FIRES IN AFRICA
1. Introduction
1.1 Background
Fires are among the most important processes of transformation in natural ecosystems, as
an evolutionary force both for humans and their environment; changing the structure and
biodiversity in many different ecosystems, particularly in savannas. These driving
factors, and the consequent transformation to different ecosystems, have significant
implications in the climate system (MacGregor 2006, Verbesselt et al 2006, William et al
2005). Historically, fires have been burning ecosystems for hundred of millions of years,
transforming and shaping global ecosystems, as well as their spatial distribution and
maintaining the structure and function of fire-prone communities such as savannas (Bond
et al 2005a, Stronach and McNaughton 1989). Fire has such an important role
modulating ecosystems, that many African plant species and animals would likely
become locally extinct without these fire processes, due to the fact that their growth and
reproduction cycles are linked to the fire regimes (Clerici 2006, Krock 2002, Lloret et al
2005).
However, the spontaneous nature of fire events and its benefits have been changing
drastically in the last century. Fire events are becoming more common and frequent in
time and space, mainly due to human influence and climate change. Fires are a threat for
several natural environments because nowadays they contribute to the decrease and
depletion of the same ecosystem resources they were benefiting for centuries (Clerici
2006, Dwyer et al 1999, Dwyer et al 2000, William et al 2005).
Fires and human communities in the African continent
Historically, fires in the African continent have had enormous economic and social
impacts, and these have been in general positive. The economy in many African countries
relies on small scale agricultural production, and fires have been used for centuries by
local communities to enhance the productivity of the land. Nevertheless, in the last
decades the intensive use of fire to enhance productivity, especially in savanna
ecosystems, has risen to a dangerous level, and combined with increased pastoralism and
hunting, has threatened biodiversity and ecosystem stability (Verbesselt et al 2006).
Human activities are partly responsible for the substantial increase in frequency and
intensity of fires in the continent, as well as timing and spatial distribution of fires,
particularly in grassland and savanna ecosystems (Dwyer et al 1999, Silva & Pereira
2005). Usually these anthropogenic fires are set during the dry seasons to remove dead
vegetation that accumulates after harvesting, and to promote new and high-quality
growth. Moreover, fires are set in order to control undesirable plants in crop areas and to
drive grazing animals to less-preferred growing areas. Even more, some governments
have promoted the regular use of fire as an important tool for grazing management and
Predicting the occurrence of fires in Africa
8
agriculture (Krock 2002, Stronach and McNaughton 1989).
Fires and biomass burning due to anthropogenic causes are responsible for drastic
changes in vegetation at global scales. It is estimated that approximately 90% of the
biomass burnt in Africa comes from savanna ecosystems, due to the increase of human
activities in those areas. In the past, lightening and other natural events were the main
causes of fires in the extensive African savannas, but nowadays these natural events are
the second major source of fires, after the newly increased human activities (Cahoon et al
1992).
Fires and savanna ecosystems
Savannas are particular ecosystems affected by seasonal and inter-annual fire regimes,
that create certain conditions for the establishment of a high diversity of plants and
animals that nowadays are becoming threatened by the increase in intensity and
distribution of fire regimes (Cahoon et al 1992). Moreover, at the global scale it is
estimated that savanna fires, caused mainly by human activities, are drastically increasing
CO2 emissions in the atmosphere. But the frequency and location of the fires, the burned
area, the interaction between fires and other biotic and abiotic factors and the further
implication over the entire system are not really known, and are still subject to research
(Cahoon et al 1992).
Savannas are one of the most productive ecosystems, with annual productivities that vary
between 1 and 12 ton of carbon per hectare per year that are constantly threatened and
changed by natural and mostly by anthropogenic fires (Grace et al 2006), moreover are
one of the largest African ecosystems, covering approximately 50% of the African
continent. At a global scale, fires in savannas contribute to almost one third of the annual
emissions from biomass burning (Andreae 2001, Silva & Pereira 2005). However, these
estimations are subjected to high levels of uncertainty due to the different methodologies
used, the scales, the calculation processes, and the variation in intensity and extent of the
fires (Silva & Pereira 2005).
Fire dynamics
There are many environmental, climatic, and anthropogenic factors that can influence the
increase in intensity, periodicity and spatial distribution of fires in the African continent.
Currently, there is a need for understanding the complex relationships between these
factors. This study examines these variables, including temperature, relative humidity,
wind speed, rainfall, land cover, soil types, altitude, latitude, animal diversity, and human
communities) for which data is available for the African continent
Climatic conditions are some of the most important factors in changes in fire dynamics.
Extreme regional weather conditions and interannual climate variability are some of the
causes of these recent changes in fire dynamics. Events such as El Niño and La Niña,
create severe droughts that can increase the number and distribution of fires, or increase
precipitation and therefore the biomass available for more intense fires (Goldammer and
Hoffmann 2001). Local climatic conditions, such as temperature, relative humidity and
precipitation are factors affecting the status of the vegetation and water availability,
which can increase or decrease biomass, and therefore the susceptibility to fires (Röder et
al 2007). In general, dry areas can allow more intense and extensive fires than more
Predicting the occurrence of fires in Africa
9
humid areas, where the fires tend to be smaller, and dispersed (Silva & Pereira 2005).
Natural vegetation cover is an environmental factor which is highly affected by human
activities, and has an important role in fire regimes, especially on the timing and spatial
distribution of fires. In savannas, fires tend to be more extensive than in dense forests
where the fires may be more intensive (Krock 2002, Silva & Pereira 2005).
Periodicity of fires is a factor that can be related to the presence of human settlements.
This effect can be especially appreciated in areas like savannas and grasslands, which are
often used by local communities as grazing pastures or for crop growing.
Prediction of fire occurrence
Accurate predictions of fire occurrence are very important at any scale, due to the
constant threat of uncontrolled fires, which can devastate vegetation, human and
economical resources. In the short term, the increase in fire events can have negative
effects such as the disruption of ecosystem processes, economic losses, and humanitarian
problems. In the long term, the increase in fire events can have consequences such as the
degradation of the stability and productivity of ecosystems and land use systems (Michel
et al 2005; Tansey et al 2004, Textor et al 1992).
Nowadays, the prediction of fire occurrence is a topic that has been studied at different
scales, covering local, regional, continental and global ecosystems, and in a multi
temporal and spatial scale. The accuracy of these predictions varies with the scale of the
remotely sensed data and the scale of the maps and outputs, which can be used for
different governmental, educational or management purposes. There are recent studies
that focus on regional and global inventories of fires, based on multi temporal sources of
remotely sensed data, with accurate products such as World Fire Atlas (WFA), with a
spatial resolution of 1 km (Boschetti 2005), and the Global Burnt Surface (GBS) with a
spatial resolution of 8 km (Carmona-Moreno et al 2005a).
Global fire maps, among others, present burnt areas at a global scale and also the
probability of fire occurrence in each pixel, which are good proxies for predicting fires in
different regions (Boschetti 2005). However, fires do not occur in different regions as
isolated events; and they occur more under certain conditions than under others, and may
be determined by a group of particular environmental, climatic or anthropogenic
variables. Therefore a deeper study in the interactions between these variables and the
occurrence of fires is still needed.
This study makes a spatial assessment of the interactions between certain ecological,
climatic, and anthropogenic variables, and the probability of occurrence of fire events.
The probability of occurrence of fire events is represented as fire frequency and was
derived from Global Burnt Surface (GBS) data of the average number of weeks with fires
per year over a 17 year period.
In addition to the spatial assessment, this study examines the occurrence of fires on a time
series basis. The time series of Normalized Digital Vegetation Index (NDVI) is a good
predictor of the status of the vegetation in a location; and therefore, we expect that fire
occurrence is highly dependent on this variable. An analysis between these two time
series can give some insights in the prediction of fires according to the status of the
vegetation in the moment of the fire event, but especially the vegetation conditions in the
Predicting the occurrence of fires in Africa
10
weeks or months before the event occurs.
1.2 Research questions
The present study aims to answer two main questions about the relationship between fire
frequency and some environmental and anthropogenic variables:
First of all, this study would like to assess which environmental or anthropogenic
variables have strong correlations with fire frequency, and therefore, which are the most
suitable predictors for the occurrence of fire events.
Secondly, this study assesses the temporal relation between the time series of NDVI and
fire occurrence, as presence or absence of fires, and evaluates if it is possible to predict
accurately the probability of fire occurrence for any month based on the time series of
NDVI.
Hypotheses
For the first question, we expect to find a high correlation between vegetation, land cover
and fire occurrence, since one of the most important factors in the frequency of fires is
the availability of biomass for fuel to be burned. We further expect climatic variables to
be the second most important factors. Precipitation induces an increase in biomass;
however more humid places, such as rain forests, can be less susceptible to fires. High
temperatures can induce fires, however, the African continent has extended deserted
areas that are not affected by fires.
For the second question, we expect to develop a regression model between the presence
or absence of fire events for every month of the year and NDVI as explanatory variable,
testing the hypothesis that the occurrence of fires in any location is related not just to the
NDVI value at the same point, but also to the NDVI values of the preceding months.
Predicting the occurrence of fires in Africa
11
2. Methodology
The methodology for this study consisted of several steps. First, we gathered the fire
occurrence data, and we searched several open internet geo-portals, to get all the
environmental, climatic and anthropogenic data that could be related with fire dynamics.
Once we gathered this data, we processed the data and homogenized all the information
to the extension of Africa, with the same scale and spatial reference. For this process we
used mainly GIS software and Python scripts.
With all the data matching together, we had all the information about fire occurrence for
every pixel in Africa, and all the variables gathered in the GIS software. All this
information was condensed in a single table that was used for the different analyses. We
used the weekly time series of fire occurrence and the bi-weekly time series of NDVI for
the time analysis. Finally we analyzed our hypotheses with statistical programs, to create
the correlations and models that best describe the relations between fires and these
variables.
2.1 Data collection
For this study, we searched all the environmental, ecological, geographical and
anthropogenic variables that could have any interaction with fire dynamics or that can
help to predict fires in the African continent. We searched for all the variables that were
available in the internet sources and the ones that were provided by the institutes
participating in this project, and that were available in the appropriate format and at the
scale of the study.
Table 1 summarizes the data used for this study, which was selected from more than 30
different variables. We included the variables that were most likely to affect fire
dynamics in Africa: variables that influence the vegetation type and biomass and
therefore the fuel to be burnt, the climatic conditions that favor the ignition of fires, and
finally the human factor that is known as one of the most important driving factors of
fires in some African ecosystems.
For this study we used two different kinds of variables: annual averages of all the
variables, and the time series of NDVI and fire occurrence. We will shortly describe the
different datasets.
Fire data
The most important variable for the analysis is the Global Burnt Surface data, which is
the fire occurrence variable that we used as the dependent variable. The GBS data is a
weekly time series for the period 1982-1999, which consist of a raster output with a
resolution of 0.07 degrees (approximately 8 km), and indicate the presence or absence of
fire in each pixel. This GBS output was generated with an algorithm primarily developed
for detecting burnt scars in Africa, therefore it is the best input to recognize the fires in
this region (Carmona-Moreno et al. 2005a). For each pixel, GBS data indicate the
presence of fire with a value of 1, and the absence of fire with a value of 0. With this
weekly data, we calculated the averaged fire frequency (Ff), as the number of weeks with
fires per year, from the 17 years time series.
Predicting the occurrence of fires in Africa
12
Table 1. Fire occurrence, environmental, climatic, and anthropogenic data.
units
Resolution
(km/degrees)
Period
Source**
presence/absence
8 / 0.07°
1982-1999
IES
NDVI
n/a
10 / 0.08°
1981-2003
GLCF
Temperature (temp)
°C
20 / 0.17°
1961-1990
CRU
Precipitation (prec)
mm/month
20 / 0.17°
1961-1990
CRU
m/sec
20 / 0.17°
1961-1990
CRU
%
20 / 0.17°
1961-1990
CRU
Land cover: trees (tree),
herbaceous vegetation (herbac),
bare soil (bare)
percentage of
coverage
0.5 / 0.0045°
2000-2001
GLCF
Soil: Cation Exchange Capacity
(cecs)
Me*/100gr
120 / 1°
2000
ISRIC
Soil: Total Extractable Bases (teb)
Me*/100gr
120 / 1°
2000
ISRIC
%
120 / 1°
2000
ISRIC
Meters above sea
level
20 / 0.17°
1961-1990
CRU
# animals/km2
6 / 0.05°
2000
FAO
5 / 0.04°
1990-2015
SEDAC
Data
Global Burn Surface (GBS)
Wind speed at 10m (wind)
Humidity (humid)
Soil: clay fraction (clay)
Elevation (elev)
Livestock: sheep, goats, cattle
Population density (pop) and
population growth (growth)
2
Inhabitants/ km
(inhab/ km2/year)
*
Milliequivalent for 100gr of soil.
All data sources are shown in the references
**
Normalized Difference Vegetation Index (NDVI)
This product from the Global Land Cover Facility (GLCF 2007) is the most important
variable for a temporal analysis with the fire data set. This dataset is a bi-weekly product
available for the period 1981-2003, with a resolution of 0.08 degrees; and is derived from
the images obtained from the Advanced Very High Resolution Radiometer (AVHRR).
Climatic data
Climatic variables have a big impact in the presence of fires, therefore we included in the
study several variables such as precipitation, temperature, humidity, and wind speed at
10 m. These variables are represented in this study for the annual averaged calculated
from the period 1961-1990, and with a resolution of 10 minutes latitude – longitude.
These data were interpolated from a data set of meteorological station means around the
world, and were available through the Climatic Research Unit (CRU 2007).
Environmental data
Land cover is one of the most important variables that can influence the presence of fires
Predicting the occurrence of fires in Africa
13
in natural ecosystems. In this study we worked with the Vegetation Continuous Fields
Collection which contains proportional estimates for 3 cover types: woody vegetation,
herbaceous vegetation, and bare ground. This global product is derived from all 7 bands
of the MODerate-resolution Imaging Spectroradiometer (MODIS) sensor onboard
NASA’s Terra satellite, and has a high resolution of 0.0045 degrees -500m- (GLCF
2007). This data was calculated for the period 2000-2001.
Some other environmental variables included are the elevation above sea level with a
resolution of 10 minutes, and some soil quantitative characteristics such as cation
exchange capacity, total extractable bases, and percentage of clay that describe the
availability of nutrients in soils and potential productivity (Batjes 2005, W.S.U 2004).
This set of variables can influence the presence of some vegetation types and therefore
the presence of fires.
Livestock and anthropogenic variables
We expect that humans have a significant influence on land use change, livestock and
anthropogenic fire ignition. Therefore, we included some variables related to the presence
of human settlements in the African continent: population density, population growth,
and livestock. The Gridded Population of the World, version 3 (GPWv3), is the most
recent product of the Socioeconomic Data and Application Center (SEDAC) for the
years: 1995, 2000, 2005; and population estimates for the years: 2010, and 2015.
Population growth was calculated from these 6 datasets. Livestock, consisting of the
actual densities per squared kilometer, for sheep, goats and cattle, were obtained from the
Food and Agriculture Organization's Animal Production and Health Division (FAOAGA).
2.2 Data management
The data was stored, transformed and managed using ArcGIS 9.2. All the models created
were stored in the model builder and some scripts were created using Python, to automate
and facilitate some processes. Figure 1 and 2 summarize the processes done to the
datasets for the two different analyses.
Fire
Climate
ASCII
to
raster
Calculate
average
Environment
Resample &
Geo-reference
Livestock &
population
Sample
Mask
Final table
Africa
Figure 1. GIS data processing for fire data and the independent variables.
Predicting the occurrence of fires in Africa
14
Monthly
average
Fire
Average
Resample &
Geo-reference
Mask
Sample
NDVI
Monthly
occurrence
Final table
South Africa
Figure 2. GIS processing for the time series data sets: fire occurrence and NDVI.
The GBS data and some other variables such as the climatic data were transformed from
ASCII to raster format. Once all data sets were transformed into raster format, the
geographic reference was evaluated and adjusted to GCS_WGS_1984, and all the data
was unified at the same origin.
Correlation and regression analysis
For the first analysis, consisting of the correlation and regression analysis between fire
and the environmental variables, the data sets that consisted of time series were averaged.
To describe the fire, fire frequency was calculated. This variable, defined as the number
of weeks of fire per year, is perhaps the most frequently used to describe fire events (Li
2002), and was calculated from the GBS seventeen-year time series.
All data sets were unified at the same resolution. Data sets were resampled to a cell size
of 0.07 degrees (approximately 8 km), equivalent to the resolution of the GBS data, in
order to have all the data in the scale of the dependent variable. The data sets were
masked to the extension of Africa.
Finally, the datasets were combined into a table, containing the coordinates of every point
and all the 18 variables used in the analysis. This table was divided into 2 datasets; 4/5 of
the data were selected randomly and stored in a table, and was used to generate the
correlations and regressions between fire and the independent variables. The last fifth of
the data was stored in a table and used in a further analysis in the validation of the
regression models.
Time analysis between fire and NDVI
The analysis of the time series of NDVI and fire occurrence was developed for a smaller
and local study area, due mainly to the high variance in climates and seasonality over all
of Africa that can bias the output and lead to a misinterpretation of the results. NDVI and
fire occurrence are variables highly dependent on seasonality and weather conditions, and
the African continent has a large extension, that covers from 37 degrees above the
equator until 35 degrees below the equator. This large extension drives into a different
seasonality at a given moment in time in the north, center or south of Africa. Therefore,
an analysis in time will give different and opposite results for all these locations.
For this analysis we selected South Africa for the regression analysis and Swaziland for
the validation. Both countries have a high variety of environments and a regular and
periodic fire regime that makes it interesting for this temporal analysis.
We calculated monthly averages for NDVI, and the occurrence of fires was registered as
Predicting the occurrence of fires in Africa
15
the presence or absence (1 or 0) for the whole seventeen-year series. All the data sets
were homogenized to the same resolution, geo-reference and extension. The information
was summarized in tables, 1 for every month, containing the fire occurrence in that
month, and the NDVI of the 12 previous months.
2.3. Data analysis
2.3.1 Correlations and regression analysis
Correlations and regressions
Scatter plots between each variable and fire frequency were drawn to analyze the
relationship between these variables. Pearson correlations were calculated between the
fire frequency and the environmental, climatic and anthropogenic variables.
Linear regression models were adjusted between the dependent variable, fire frequency,
and the 17 independent variables (climatic, environmental and anthropogenic factors).
Variables that exhibit more complex relationships than linear were analyzed with
quadratic and polynomial regressions to better describe the relations with fire frequency.
These models were adjusted with the interactions between the variables.
All the statistical analyses were using bootstrapping techniques. This statistical method
uses a technique of sampling randomly with replacement from the original sample; with
the purpose of deriving the most robust estimators of a population parameter like mean,
median, proportions, correlation coefficient or regression coefficients (Efron 1979). For
this analysis, samples of 500 records were taken, and the correlations and models were
run for 500 times. Number of runs and sample size were estimated by means of running
the model and calculating the estimates for correlation coefficients and regression
parameters, until the point that the estimators were approximately asymptotic.
Prediction of fire frequency
This study wanted to create a model for the prediction of fire frequency based on a
combination of the most significant variables from the set of 17 dependent variables.
With the analysis of the correlations and regressions between fire frequency and the
independent variables, we detected the variables that have a strong correlation with fire
frequency, and we included them in a model to predict fire frequency. Moreover, we
evaluated the most significant interactions between independent variables, and they were
introduced in the analysis to adjust the best regression model
The best models were evaluated and compared with the statistics: R2 adjusted, P-value, tvalue, multicollinearity diagnosis and Durbin-Watson (Cummins 2006). The P-values for
all the models generated after a bootstrapping method were evaluated as the proportion of
the total number of runs of the bootstrapping that have a P-value lower than 0.05.
Number of bootstrapping runs are 500, therefore a proportion of P-value of 1.0, means
that the 500 models run in the bootstrapping are significant.
Validation
The validation of the models consisted of fitting the validation models with the same set
of variables found with the original models. The coefficients of the independent variables
Predicting the occurrence of fires in Africa
16
in the validation models must fall within the confidence limits of their corresponding
coefficients in the original model. This validation will assure that coefficients of any
model can be included in these intervals and that the model is valid for any dataset in the
African continent.
A spatial validation was done, plotting the results of the different models adjusted for the
prediction of fire frequency and the real values of this variable.
2.3.2 Time series analysis
An analysis of the relationship between fire (presence or absence) and the NDVI was
developed using the monthly data in a logistic model. The logistic regression is used
when the dependent variable is a dichotomy, and the independent variables can be binary
or decimal. Logistic regression applies maximum likelihood estimation after transforming
the dependent variable into a logit variable (the natural log of the odds of the dependent
occurring or not). The logistic regression output is a model that can be transformed in a
model to estimate the probability of a certain event occurring (Dayton 1992).
The logistic curve relates the independent variable X, with the probability of having a fire
event (P). a and b are the parameters of the model.
P=
e a + bX
1 + e ( a + bX )
1
** * *** **
Pr
o
fu b a
nc bil
ti o i ty
n
Fire occurrence
Figure 3 shows the tendency of the binary variable fire occurrence with values of 0 and 1,
and the probability function adjusted, which can varies from 0 to 1.
0
*** * ** *
Figure 3. Probability function of the logistic regression (*: observations).
Logistic models were generated for each month, and scatter plots were made to analyze
the relationship between the fire event in each month and the NDVI value in the same
month and the eleven previous months. The models were evaluated with the Akaike
statistic (AIC) and the deviance of the model. Low values of deviance show a better
fitting model.
Deviance = -2log(likelihood)
Predicting the occurrence of fires in Africa
17
Validation
For the validation of the models, the datasets of fire occurrence and NDVI of Swaziland
were used. The similarities in climate, environments and geographic conditions, make
this country situated next to South Africa, the most suitable dataset to validate the South
African models. The whole surface of Swaziland in the resolution of the study compiles
290 pixels, which is enough to validate the models. The year 1992 was selected and the
information of NDVI of the current month and the 11 previous for each month in 1992
was compiled, to predict the occurrence of fires in each month.
The validation consisted of calculating for the Swaziland dataset the same logistic
regression than for South Africa, including the confidence limits for every coefficient.
The validation was confirmed, when the coefficients of the models for Swaziland are
included within the confidence intervals of the logistic model for South Africa.
Predicting the occurrence of fires in Africa
18
3. Prediction of fire frequency
This chapter summarizes the results of this study concerning the question of whether it is
possible to accurately predict fire occurrence based on a set of environmental, climatic
and anthropogenic variables. The first part of the chapter describes the relationship
between fire frequency and the independent variables used in the analysis, and explores
which set of variables has the strongest correlation with the occurrence of fires. The
second part of the chapter describes the best regression models adjusted to predict fire
frequency, and includes maps of the models’s predictions and validations of the results.
3.1. Results
Environmental variables were highly correlated with fire frequency in the African
continent. The most important variables were NDVI and vegetation cover, represented
mainly by MODIS data, while Anthropogenic variables showed less correlation with fire
frequency (Figure 4, Table 2).
3.1.1 Correlations and regression analysis between fire frequency and
environmental variables
For all the variables in the analysis, the Pearson correlation coefficient was calculated,
and linear and quadratic models were adjusted to find the model that best describes the
interactions between the data and fire frequency (Figure 4, Table 2).
b
6
4
0
2
Fire frequency
4
2
0
Fire frequency
6
a
0.1 0.2
0.3
0.4 0.5
0.6 0.7
0
NDVI
40
60
80
Herbaceous vegetation (%)
4
2
0
0
2
4
Fire frequency
6
d
6
c
Fire frequency
20
0
20
40
60
80
100
bare soil (%)
0
20
40
60
80
Trees (%)
Figure 4.(1 of 3) Scatter plots and best model for fire frequency (weeks/year) vs. environmental and
anthropogenic variables
Predicting the occurrence of fires in Africa
19
4
0
2
Fire frequency
4
2
0
Fire frequency
6
f
6
e
15
20
25
30
0
50
Temperature (°C)
250
6
4
0
2
Fire frequency
6
4
2
0
Fire frequency
200
h
30
40
50
60
70
80
1
2
Humidity (%)
3
4
5
Wind speed (m/s)
4
2
0
0
2
4
Fire frequency
6
j
6
i
Fire frequency
150
Precipitation (mm/month)
g
0
10
20
30
40
50
0
20
25
30
4
Fire frequency
6
4
0
2
15
Total extractable bases (Me/100gr)
l
0
10
2
k
5
6
Cation exchangeable capacity (Me/100gr)
Fire frequency
100
0
10
20
30
40
50
Clay (%)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Elevation (km.a.s.l)
Figure 4. (2 of 3) Scatter plots and best model for fire frequency (weeks/year) vs. environmental and
anthropogenic variables
Predicting the occurrence of fires in Africa
20
4
0
2
Fire frequency
4
2
0
Fire frequency
6
n
6
m
0
200
600
1000
0
200
Cattle (#/km2)
600
800
1000
Goats (#/km2)
4
2
0
0
2
4
Fire frequency
6
p
6
o
Fire frequency
400
0
200
400
600
800
1000
Sheep (#/km2)
0
200
600
1000
1400
Population density (inhabitants/km2)
4
2
0
Fire frequency
6
q
-5
0
5
10
15
20
25
Population growth (inhabitants/km2/year)
Figure 4. (3 of 3) Scatter plots and best model for fire frequency (weeks/year) vs. environmental and
anthropogenic variables
The variable with the strongest correlation with fire frequency is the percentage of
herbaceous vegetation (0.60). According to this high correlation coefficient, the quadratic
model fitting, and the scatter plot of the data (Figure 4b), there is a clear positive relation
between this variable and fire frequency. When the percentage of herbaceous vegetation
is low there is a low response in fire occurrence; and any progressive increase in the
percentage of herbaceous vegetation has a significant increase in fire frequency.
Bare soil had an opposite tendency to herbaceous vegetation (Figure 4c). The correlation
and the regression were negative. Increases in the percentage of bare soil correspond to
decreases in fire frequency. Low values of bare soil lead to a high fire frequency, because
low percentage of bare soils represents a high cover of trees or herbaceous vegetation that
are more inflammable. Tree cover, on the other hand, had a weak correlation with fire
Predicting the occurrence of fires in Africa
21
frequency, and although the regression analysis is significant, tree cover does not have as
strong a correlation as bare soil or herbaceous vegetation (Figure 4d).
Table 2. Correlation coefficients and best fitting models for each variable vs. fire frequency (Ff)
Correlation
coefficient
Proportion
p-value
Best fitting model
NDVI
0.32
1.0
Herbaceous
vegetation
0.60
Bare soil
Interaction
with FF
R2a
Proportion
p-value
–0.862 + 10.225ndvi – 12.8733ndvi2
0.30
1.0
1.0
0.0357 – 0.0163herbac + 0.0004herbac2
0.45
1.0
–0.47
1.0
0.9749 – 0.0099bare
0.23
1.0
Tree
vegetation
0.02
0.1*
0.3198 + 0.0485tree – 0.00072tree2
0.17
1.0
Temperature
0.18
1.0
–0.4342+0.0411temp
0.02
1.0
(Ff=)
2
Precipitation
0.21
1.0
–0.0337 + 0.0247prec – 0.00014prec
0.25
1.0
Humidity
0.13
0.9
–3.3992 + 0.1539 humid – 0.0014humid2
0.16
1.0
Wind speed
–0.23
1.0
1.0979 – 0.2393wind
0.05
1.0
Cation
exchange
capacity
0.34
1.0
0.7512 – 0.0513cec + 0.0027cec2
0.17
0.9
Total
extractable
bases
0.03
0.6
1.564 – 0.1695teb + 0.0061teb2
0.07
0.9
Clay
percentage
0.10
0.7
1.2938 – 0.0845clay + 0.00202clay2
0.07
0.9
Elevation
0.03
0.0*
0.4428 – 0.0906elevation
–0.002
0.13*
0.17
1.0
Cattle
0.32
1.0
0.3155 + 0.0047cattle – 0.0000036cattle
2
2
Goats
0.21
1.0
0.3832 + 0.0034goats – 0.0000028goats
0.08
0.9
Sheep
0.14
0.8
0.3325 + 0.0039sheep
0.05
0.9
Population
density
0.003
0.0*
0.5179 + 0.0018pop – 0.0000034pop2
0.003
0.2*
Population
growth
0.003
0.0*
0.5203 + 0.0752growth – 0.0061growth2
0.003
0.2*
* values are not significant
Fire frequency gives a hump shaped response to NDVI (Figure 4a), with a high
correlation coefficient and a significant quadratic model. Low values of NDVI, such as
deserts, have null fire frequency as expected. Slight increases of NDVI, like in
grasslands, tend to increase fire frequency, which is most frequent in the savannas. When
NDVI increases to values above 0.4, with more dense vegetation, like in forests, the fire
frequency is low again.
Climatic variables showed a weak correspondence with fire frequency, compared to the
correlations of vegetation and NDVI with fire frequency. Precipitation had the highest
correlation with fire frequency, and had a similar tendency to NDVI (Figure 4f).
Although the graphical tendency of temperature seems to show a positive correlation with
fire frequency (Figure 4e), this variable was poorly correlated with fire frequency, and
the regression was less significant and less reliable than models with other variables.
Wind speed at 10 m had a negative correlation with fire frequency. Locations with low
Predicting the occurrence of fires in Africa
22
wind speeds tend to have more fires than locations with wind speeds above 4 m/s, where
fire frequency tends to be null. Elevation was one of the variables that were not correlated
with fire frequency, and it was not possible to adjust a significant model to the data
(Figure 4l).
Cation exchange capacity (cec) is the only soil characteristic that was highly correlated
with fire frequency. Locations with low cec values tend to have low fire frequency, and
places with high cec values tend to have more frequent fires. Other soil characteristics
such as total extractable bases and clay percentage have a weak correlation with fire
frequency, although the regression adjusted for both variables is still significant.
Livestock in Africa, represented by number of cattle, goats, and sheep, has a significant
correlation coefficient with fire frequency and significant models were adjusted for each
variable. The most important variable correlated with fire frequency was the number of
cattle in every pixel: the higher the number of cattle, the higher the fire frequency. The
same positive correlation was found for number of goats and sheep, the number of goats
having a stronger correlation with fire frequency, than number of sheep (Figure 4m).
Anthropogenic variables were less correlated with fire frequency. Correlation coefficients
and the models were not significant. Pixels with high population are less susceptible to
having fires; because these events tend to occur in rural areas, where the population
density is lower (Figure 4p).
3.1.2. Regression models for the prediction of fire frequency (Ff)
Several models were created to predict fire frequency based on all the environmental,
climatic and anthropogenic variables. All models were adjusted using stepwise
techniques, and only the interactions between the variables that showed a significant
correlation with fire frequency were included to more accurately explain the dependent
variable. Table 3 shows the models with the best fit, and the most reliable models
according to the statistical values. Figure 5 shows the spatial validation of the models and
compares the real fire frequency with the three best models from Table 3.
Table 3. Best fitting models for the prediction of fire frequency (weeks with fire/year).
Model
R2a
Proportion
p-value
DurbinWatson
–0.36476 + 0.03612cecs – 0.00043goats – 0.04049herbac +
0.00033herbac2 + 0.00125temp*herbac
0.59
1.00
1.84+
–1.89025 + 0.03429bare – 0.01522herbac – 4.48672ndvi + 0.06525humid +
0.00033herbac2 – 0.00069humid2 + 0.24054ndvi*temp
0.62
1.00
1.89+
–2.28935 + 0.03458cecs – 0.02099herbac – 4.46595ndvi – 0.01905prec +
0.02610tree + 0.06872humid – 0.000345herbac2 – 6.06543ndvi2 –
0.00022tree2 – 0.00072humid2 + 0.41935ndvi*temp – 0.00094prec*temp
0.65
1.00
1.90+
1.73198 + 0.03672cecs – 8.41359ndvi – 0.00190pop + 0.01706prec –
0.02320tree – 0.00795humid + 0.39871ndvi*temp – 0.06635ndvi*bare –
0.00055temp*bare – 0.00084prec*temp
0.61
1.00
1.79+
(FF = )
+
significant values at a 95% confidence interval. Variables not autocorrelated
*cecs: cation exchange capacity, goats: number of goats, herbac: % of herbaceous vegetation, temp: temperature, prec:
precipitation, tree: % trees, humid: humidity, pop: population density, bare: % bare soil.
Predicting the occurrence of fires in Africa
23
a
b
c
d
Figure 1. Maps of fire frequency in Africa. Original fire frequency (a), and predictions (b: model 1, c:
model 2, d: model 3)
The first and the second models were the regressions done using the least number of
significant variables, nevertheless, they both have a high R-squared value and a
significant Durbin-Watson value -compared with the table of critical values (Cummins
2006)- which assures that there is no autocorrelation between the variables in the model.
These simple models can predict fire frequency in any location using a combination of
just a few variables.
The third model consists of the variables that had the most significant correlations with
fire frequency. The model has the highest R2a of the three models, the p-value is
significant, and the Durbin Watson shows that the variables are not autocorrelated.
The fourth model is also a good fit with a high R2, significant p-value, and the variables
are not autocorrelated according to the Durbin-Watson. This model was adjusted
Predicting the occurrence of fires in Africa
24
including all the variables and interactions in the stepwise analysis.
To validate the models, one fifth of the data that was not used in the models, was used to
generate a new model, using the same combination of variables. The purpose was to
determine whether each coefficient of the validation model is included within the
confidence limits of the original model or not. Appendix 1 shows the four models
adjusted, and their correspondent validation models. All coefficients of the validation
models fall within the confidence limits of the models, indicating the models are reliable
and valid for predicting fire occurrence.
3.2 Discussion
3.2.1 Correlations and regression analysis
Africa has a high diversity of ecosystems, each with different vulnerability to fires.
Savannas and grasslands that cover more than 20% of the continent, have a periodical
regime of fires, and are the land cover most affected by these dynamics, due mainly to
their location in the fire belt of Africa, and in the corridor that runs to the south of Africa
(which experiences the same fire regimes). Other ecosystems, such as bush lands and dry
forests, are also affected by fires. However, when the precipitation and the humidity
increase, and therefore the biomass (high NDVI values), these ecosystems turn into more
humid or tropical forests that are less vulnerable to fires (Lavorel et al 2007).
For this study we selected some of the most important variables to describe ecosystem
dynamics. Environmental variables such as land cover and NDVI are among the most
important and reliable variables to predict fire frequency. Climatic variables are the
second group with strong correlations, whereas anthropogenic variables cannot be used to
predict fire occurrence. Similar results were found by Dwyer et al (2004), who found that
vegetation was the most important factor for determining fire activity.
Vegetation
Land cover from the MODIS sensor is one of the most reliable sources to describe
vegetation cover at this scale. This data has a high resolution and consist of three layers
describing the natural cover of any ecosystem. This land cover data is crucial in the
analysis of fire dynamics, since the vegetation in a given location determines the fuel
necessary to start a fire (Grace et al 2006).
Herbaceous vegetation has a positive and the highest correlation with fire frequency. This
type of vegetation, which includes grasses and bushes, is one of the most important fuels
for burning, and is an accurate predictor of an area’s susceptibility to fires. This type of
vegetation dries out during the dry season, becoming a stand of dry and dead biomass that
increases the possibilities of fires in these ecosystems (Sheuyeange et al 2005).
Bare soil is a contrasting variable in comparison with herbaceous vegetation, and has a
highly significant negative correlation with fire frequency. A low percentage of bare soil
implies that the terrain is covered by grasses, bushes, or trees, and therefore there is more
fuel, and subsequently more fires. When percentage of bare soil increases the biomass
decreases and so does fire frequency, and where bare soil is the main cover (as in arid
areas or deserts) the fire frequency tends to be null.
Predicting the occurrence of fires in Africa
25
Tree vegetation is the only variable from the MODIS data that has a weak correlation
with fire frequency. We expected a strong correlation, with more susceptibility to fires in
areas with less trees, and fewer fires in dense forest (Sheuyeange et al 2005). However,
the scatter plot (Figure 4d) shows that at low tree density, there is either a higher
probability of having fires, in the case of bush lands or savannas, or there is no
probablility of fires at all, as in deserts. This ambiguous tendency makes it difficult to
create a model that describes the relationship between fire frequency and percentage of
trees.
NDVI is another important variable to describe the status of the vegetation cover, and
gives additional information about land cover. NDVI describes the greenness of the
vegetation, and can also be linked to biomass and the status of wetness or dryness of the
vegetation. Consequently, this variable is highly important and correlated with fire
dynamics (Verbesselt et al 2007).
NDVI has a unimodal relationship with fire frequency. At low NDVI values, there is little
biomass to burn. Slight increases in NDVI, to values that correspond to grasslands,
bushlands, and savannas, increases fire frequency up to a certain point. Values above 0.5
correspond to high biomass, most likely in tropical humid forests, where the frequency of
fires tends to be zero (Lozano et al 2007, Verbesselt et al 2007).
NDVI data are one of the most common sources of information about the status of
vegetation around the world. There are many geoportals that offer this data with high
temporal and spatial resolution, and so, the model based on NDVI offers an advantage in
predicting fire frequency for any time and at different resolutions (GIMMS 2007)
Climate
Climatic variables can influence the presence of fires in two ways. Firstly, climate
influences the type and quantity of vegetation, and therefore the susceptibility to fires.
Secondly, variables such as high temperatures, dry periods, or droughts, can be the
igniters of fires (Bond et al 2005b, Riaño et al 2006).
Climatic variables have shown fewer correlations with fire frequency than land cover.
These results were also found by Dwyer et al (2004), who found that climatic variables
like precipitation have a weak relationship with the number of fire detected per year.
Some climatic variables serve an important role in keeping the balance and structure of
ecosystems like savannas or grasslands, which are highly vulnerable to fire events (Bond
et al 2005b). However, the same set of variables can be found in other ecosystems rarely
affected by fires such as deserts. Therefore, climatic variables are not the only factors
dictating the presence or absence of certain ecosystems. Other factors, such as soil type or
human intervention, can also be important in maintaining the conditions that make
savannas and grasslands more vulnerable to fire events, and that create the particular
conditions for deserts in some locations of Africa.
This is the particular case for temperature, which is a variable known as being highly
related with the vulnerability to fires (Bond et al 2005b). However, in this study,
temperature was found to have a weak correlation with fire frequency, due to the
ambiguity of this variable in Africa. The same high temperatures can be found in
savannas or in deserts which have extremely different fire regimes.
Predicting the occurrence of fires in Africa
26
Elevation and soils
Elevation is a variable that has been related with vulnerability to fires, since locations at
low altitude experience higher air temperature, and subsequently a higher fire frequency
(Diaz-Delgado et al 2004). In Africa, this variable is not correlated with fire frequency.
This trend can be explained by the fact that the altitude in Africa is mainly low, and more
homogeneous than in other continents. High locations experienced few fires; however,
most of the data was from below 1500 meters above sea level (Figure 4l), where the trend
is more ambiguous, and the conditions are favorable for different types of vegetation with
different fire regimes.
Variables that define the productivity of soils can be used as proxies for fire frequency.
Soils with a high density of cations and nutrients (and therefore high potential
productivity), can support different types of vegetation that are also linked to different
vulnerabilities to fires. Rich soils are associated with highly productive ecosystems such
as savannas and grasslands, while poor soils tend to be present in deserts or in mature
ecosystems such as tropical forest (W.S.U. 2004). Cation exchange capacity (cecs) is one
of the soil characteristics that shows this tendency and has a high correlation with fire.
Poor soils, with low cecs values are associated with vegetation types that are less
susceptible to fires (such as deserts and forests), while high cecs values are associated
with savannas and grasslands which have high fire frequency. This tendency is similar for
total extractable bases, another indirect measurement of a soil’s productivity and clay
percentage; although the correlations were less strong.
Anthropogenic variables
Humans drastically influence the actual increase in fire frequency and intensity of fires in
Africa (Sheuyange et al 2005). In this study, we checked the correlation of some
variables associated with human settlements and activities with the presence of fires.
Livestock, that reflects the land use of the African savannas and grasslands is highly
correlated with fire frequency, showing that more intense use of land, related with
increases in livestock, will affect and increase the intensity and the periodicity of fires
with the purpose of adequate the land and increase productivity. African communities
regularly use fire to improve soils and vegetation conditions for maintaining livestock in
some locations as is reported by Silva & Pereira (2005) and Sheuyange et al (2005).
On the other hand, this study did not find a direct influence of human settlements on fire
frequency. Anthropogenic variables are not correlated with fire frequency. We were
expecting that fires were more likely to occur in places with less population density,
however, most of the locations in Africa are deserted and may or may not have a high
frequency of fires. Although it is well known that human factors are strong driving
factors in changing ecosystems and influencing fire frequency (Sheuyange et al 2005),
we did not find it directly, but other variables like livestock are indirect measurements of
this human influence.
3.2.2 Models for predicting fire frequency
Currently, there are no models for the prediction of fire occurrence at the scale of Africa.
Modeling of fire events, fire vulnerability, and risk has been restricted to small local
analysis, and it has not been related with environmental or other variables that can
Predicting the occurrence of fires in Africa
27
explain the presence of fires events. Most of the studies are focused on global or local
estimations of burning areas of carbon emissions (Michel et al 2005, Tansey et al 2004).
We tested whether some variables have a significant relationship with fire events, in this
case, fire frequency. If the variables that can drive the ecosystem to a status of
vulnerability to fire can be recognized, we can use them to predict fire frequency.
In this study we showed that fire frequency can be predicted with a high level of accuracy
with several combinations of variables. Figure 5 shows how accurately the models can
predict fire frequency in Africa. All the models confirm the same tendency with small
differences in the intensity. The location of fires and the fire frequency is clearly similar
to the real values.
Although the best fitting models are the ones with more variables, the simplicity of a
model that uses just four variables makes it more convenient and useful, and the
predictions it makes are comparable with the real fire frequency data. Figure 5, compares
the maps of the real fire frequency from the 17-years of observations with three of the
models adjusted. All the predictions are accurate in the locations of the fires, but, all the
models underestimate the values of fire frequency. The first model has a good fit and
some advantages in its predictions, since it is based on few variables readily available in
the scientific world. However, this model underestimates fire frequency, having values
that vary from 0 to 3.5 weeks/year, compared to the real observations, that can reach
values of 5 weeks of fire/year.
The models proposed in this study were adjusted with bootstrapping techniques and were
validated assuring their reliability and accuracy. Therefore, the final models can be
applied to any location in Africa. Moreover, these models can be easily applied, since the
variables used in this study are open sources from different geoportals. In general, these
variables are updated frequently, and are commonly used by scientists around the world
to describe and predict different ecosystems’ characteristics.
Predicting the occurrence of fires in Africa
28
4. Prediction of monthly fire occurrence in South Africa
This chapter summarizes the results of this study concerning the question of whether the
occurrence of fires of any month in South Africa could be described as a function of the
NDVI of the 12 previous months, using logistic models. To test our hypothesis, we
adjusted logistic models for predicting fire occurrence in every month of the year. These
logistic models can be transformed to a function to predict the probability of fire
occurrence in each month in South Africa, as shown in the results.
4.1 Results
450
7
400
6
350
300
5
4
250
200
3
150
2
100
50
Fire occurrence
NDVI
The fire activity in South Africa has a specific seasonality, as is shown in Figure 6 (which
shows data from the seventeen-year time series in South Africa).
1
0
0
1
2
3
4
5
6
7
8
9
10 11 12
Months
Figure 6. Averaged monthly NDVI (pink line) and Fire Occurrence (% of surface burn/month),
There is a peak in fires at the beginning of the summer season from September to
December. This peak in fire activity contrasts with the rest of the year were there are
barely any fire events, and particularly in the period between May and July, when fires
are rare.
The tendency of fire events is strongly related with the seasonality of South Africa, which
for our analysis can be divided in three periods. The first period starts at the beginning of
spring (September) and matches up with the beginning of the fires that runs until
December. In the second period, from January till April, the fire activity decreases
drastically, but keeps active in some locations. In the winter period, between May and
August, the fire activity is almost null.
Although the analysis was done for each month, we focused the analysis on the three
most contrasting months of the three periods mentioned above: February, as part of the
period of low fire activity, June, from the winter period without fires, and October, the
month with the highest fire activity. The other months show a pattern similar to the
pattern of the months selected for each period, and the results are summarized in
Appendix 1. Figure 7 shows the high contrast in the averaged fire occurrence for every
Predicting the occurrence of fires in Africa
29
pixel in South Africa for the seventeen-year period, for the three months selected for the
analysis.
a
b
c
Figure 2. Fire occurrence in South Africa. a. October, b. February, c. June.
For this analysis, we adjusted logistic models for each month, in order to predict the
probability of having a fire event in each pixel based on monthly NDVI. To generate the
models, we used the binary variable fire occurrence as a dependent variable (that
represents the presence or absence of fires in each pixel), and we used all the information
for each month in the seventeen-year period. The independent variables were the monthly
NDVI of the year related with the month analyzed. For example, for January, we adjusted
a logistic regression between fire occurrence of January, and NDVI of the same month
(January), and the 11 previous months (from February through December of the previous
year).
The models were selected using stepwise techniques, from models that used the whole
series of twelve previous NDVI months, until simpler models were obtained based on the
most significant variables, as shown in Table 4.
Table 4. Logistic models for fire occurrence (F), for each month in South Africa, based on the 12
previous NDVI values (n).
Logistic models
AIC
Fire occurrence in February
F (February) =-4.692-0.0049n2-0.0119n3+0.01078n4+0.0062n12
26242
F (February)-=-4.5561701-0.0115591n3+0.0114788n4
26947
F (February)-=-4.564485+0.0002253n4
28407
Fire occurrence in June
F (June) = -9.591-0.01n1+0.0057n3+0.0055n9-0.0127n10+0.0111n12
516.03
F (June) = -9.349174-0.007517n10+0.006146n12
529.92
F (June) = -10.101030+0.002552n12
540.56
Fire occurrence in October
F (October) =-3.496-0.00048n1+0.0049n2+0.0026n3-0.0062n4+0.0061n50.001n6+0.0029n7+0.00097n8-0.0038n9-0.0078n10+0.00063n11+0.00096n12
95494
F (October) =-3.377+0.006464n2-0.007022n10
97594
F (October) =-4.104+0.003256n2
103178
*n is the value of NDVI from January through December (1-12).
Predicting the occurrence of fires in Africa
30
The models can be transformed into the probabilistic function: P(Fire)= 1 /(1 + e − f (ndvi ) ) .
Figure 8 shows the two simplest models for each month (probabilistic function), based on
one or two NDVI months from the year.
a
b
0.9
probability of fire in February
probability of fire in February
0.012
0.0118
0.0116
0.0114
0.0112
0.011
0.0108
0.0106
0.0104
0.0102
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.01
0
100
200
300
400
500
0
600
100
200
NDVI April
100
400
NDVI March
c
d
0.0002
probability of fire in June
probability of fire in June
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
600
300
600
0.0014
0.0012
0.001
0.0008
0.0006
0.0004
0.0002
0
0
0
0
100
200
300
400
500
100
600
NDVI December
200
300
400
NDVI December
100
400
NDVI October
200
500
500
600
300
600
f
0.12
0.5
probability of fire in October
probability of fire in October
200
500
500
0.0016
0.00002
e
400
0.0018
0.00018
0.00016
300
NDVI April
0.1
0.08
0.06
0.04
0.02
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0
100
200
300
400
500
NDVI February
600
0
100
NDVI October
200
300
400
NDVI February
100
400
200
500
500
600
300
600
Figure 8. Logistic models for South Africa, for February (a,b), June (c,d), and October (e,f)
Figure 8 shows the probabilities calculated from the logistic models for February, June,
and October. On the left-hand side, the models are based on the most significant variable.
On the right-hand side, the models are based on two variables, and the lines show the
different tendencies for different values of the second month.
Predicting the occurrence of fires in Africa
31
More accurate models were created using more variables (Table 4), but simple models
including one or two variables can help to give an easier-to-use graphical interpretation
of the model.
The results of the real data, with the presence or absence of fires, and the prediction of
the models for South Africa, for the 3 moths selected for the analysis are shown in
Figure 9.
a
b
c
d
e
f
Figure 3. Fire occurrence and predictions in South Africa for the year 1992, for October (a,d);
February (b,e) and June (c,f). Top figures (a,b,c) show the real fire occurrence (1: presence of fire; 0:
absence of fire). Bottom figures (d,e,f) show the predictions of the models for probability of fire
occurrence.
For February, two models were used. The first model predicts the probability of having a
fire using just the value of NDVI of the last April, which was the most significant month
for this model. As is shown in Figure 8a, the probabilities are really low as was expected;
however, when more variables (other NDVI months) are included, results are more
accurate and show higher probabilities of fire (Figure 8b). Plotting the models with two
variables has an advantage in the interpretation of fire occurrence, because more
scenarios can be analyzed, between the two most significant variables.
The probability of having a fire in February, in a given location, can be predicted using
data from the months of March and April from the previous year (Table 4). Using the
graph or the model, if March NDVI is 400, and April NDVI is 500, the probability of
having a fire in that location in February is 3.2.
For the first period of the year, represented by February, the probability of having a fire
in a pixel is low, reaching just 0.012, when the model is based on one variable, April
NDVI (Figure 8a). When more variables are included, more scenarios can be analyzed
and the probability can reach 0.76, for some combinations of the variables: March NDVI
and April NDVI (Figure 8b).
The winter months in South Africa have a drop in NDVI values, and the fire occurrence
Predicting the occurrence of fires in Africa
32
is almost null. For months like June, the most important NDVI month to predict fire
occurrence is December of the previous year. A high NDVI value in December (as it is
normally) create conditions where there is a low probability of fires, nevertheless big
changes in December’s NDVI do not drastically change the tendency of less fires in June
(Figure 8c).
In the logistic models for the last period, represented by October which has the highest
fire probabilities, the values can reach probabilities of 0.5, which is lower than the real
magnitude of the fire season. For this season, we should expect that the probabilities and
the tendency lines (Figure 8a) were reaching values close to 1.
4.2 Discussion
The prediction of fire occurrence or the probability of having a fire has not been done at a
continental or national scale. Most of the prediction models in fire dynamics focus in
small scale events, or regional levels, and center their attention in risk or vulnerability
assessment (Lavoel et al 2007). This study develops reliable models on a national level
for the prediction of fire events based on NDVI. NDVI is a convenient variable for
prediction, since it is commonly measured on a bi-weekly basis around the world.
This study used a seventeen-year time series of fire occurrence, and NDVI, to create a
model to predict fire occurrence in anytime. For each month, a logistic model was
adjusted between fire frequency and monthly NDVI values. These logistic models can be
adapted to a probabilistic function (as shown in the methodology), to predict the
probability of having a fire in any location based on NDVI.
As suggested in the hypothesis, a peak of fire events in any month is related with NDVI.
But this relation is not linear as it was shown in the Figure 6. The presence of fire is not
linked to high values (positive correlation) or low values of NDVI (negative correlation).
For the time series analysis and as it is shown in the figure 5, we expected to have a
strong relationship between fire occurrence in a given moment and the NDVI of some
previous months. Figure 6 shows that for a given pixel in South Africa, there is a fire
when the green biomass is low. However, to have a fire in that pixel it is necessary to
have a peak in green biomass some months before the event. This high biomass dries
during the dry season, and assures enough flammable biomass to burn at the beginning of
the summer season.
In general, for South Africa, NDVI has a tendency to increase during spring (the wet
season from September to November) and keep a high biomass for the whole summer
(December-February). At the end of autumn, the NDVI starts declining until it reaches its
lowest point (around 0.28). This is at the end of the dry season when the vegetation starts
to die. After winter (dry season), when spring is coming and the temperature starts
increasing, the biomass is dry enough to start burning around August.
These fires at the end of the dry season are essential for biomass growth, because fires
affect the availability of nutrients in the soils, and therefore are the catalytic factor that
increases the growth of mainly herbaceous vegetation, bushes and grasses (MacGregor
2006, McNaughton 1989, Sheuyage et al 2005). The peak in fires goes from September
to December, and there are some fires until April. After this date, there are no fires in
Predicting the occurrence of fires in Africa
33
South Africa until the cycle starts again between August and September.
In the dry period, the biomass of bushes and grasses dries. The NDVI value only registers
the green vegetation that corresponds to trees that are less susceptible to die due to this
seasonal change. During this period, the NDVI is around 0.28, represented by the green
vegetation. When the rain season starts after the first period of fires, the productivity of
the ecosystems increases, represented mainly by the growth of grasses, herbaceous
vegetation, and the re-growth of bushes in savannas and grasslands. These ecosystems
have productivities around 7 ton per hectare per year (Grace et al 2006), that are reflected
in the peak of NDVI of 0.38,
Several models were adjusted for each month. For some months the best model is the one
including all the eleven previous months, and the current NDVI value of the month
analyzed. However, models with one or two variables are simpler and easier to use for
interpretation and prediction of fire occurrence. All the models were validated, and they
describe the probability of having a fire in that specific month with an acceptable
accuracy (see Appendix 1).
For the first four months of the year, late summer and autumn, fire behavior is similar and
low, and the NDVI is high due to the rainy season. The probabilities of having a fire in
any pixel are not higher than 0.02, and all the models are based mainly in the NDVI of
the previous April. For the whole period (January through April) the most important
explanatory variable was April NDVI. The whole period between January and April has
relatively the same high value of NDVI, therefore other models based on these months
with high values of NDVI show similar results to the model chosen here.
For the period from May till August, fires are rare and the probabilities hardly reach
values higher than 0.01. This period corresponds to the winter period and dry season,
when the vegetation dries and the NDVI drops to values around 0.28, that corresponds to
the green biomass or tree vegetation of the ecosystems that keeps alive during the dry
season.
For the summer months from September till December, the prediction of fires by the
models are higher than the previous months, but are still low compared with the real fire
occurrence (Figure 8). Since the models adjusted were significant, we expected higher
probabilities, close to the real values, which is 1 when the pixel is burnt. In the model and
in the validation these values only reach around 0.5. This underestimation by the model
can be due to the high amount of locations in South Africa without fires that could bias
the model to low probability values. Since there are not other studies using the same
methodology, we cannot completely explain this trend. Nevertheless, the prediction of the
location of fires based on the NDVI is accurate, compared with the location of the real
fires for 1992, as shown in Figure 8.
The group of summer months shows the tendency that we were expecting in our
hypothesis. For instance, fire occurrence in October is highly related with the NDVI of
the same month, and a peak in green biomass in the previous months, (in this case, the
high NDVI value in February). This peak in biomass assures enough herbaceous
vegetation that will die during the dry season, and will become potential fuel for burning.
The same tendency was found for November and December, where the model with two
variables includes the NDVI of the same month and the NDVI of the previous February.
Predicting the occurrence of fires in Africa
34
For this study, we used South Africa as a pilot country. We think that this kind of
analysis has to be done on local scale or in a country level, because these temporal
variables in a bigger scale are influenced by the seasonality of the different locations. On
a local scale, we assure that the whole study area is in the same season.
South Africa did not show the accuracy in prediction of fires that we expected. Although
this country has a regular fire regime, which varies with seasonal changes, it seems like
the periodicity is not as regular as in other countries, and it was poorly described by the
models. Nevertheless, from these models, the user can play with the different scenarios,
and predict the occurrence of fires in any place using just past values of NDVI for that
location. We think these models are a handy tool to implement in predictions of these
events or in ecosystem modeling in countries affected regularly by fires.
The strength of this South African pilot study lies in the fact that the same methodology
can be applied to other African countries; especially countries in the equatorial zone of
Africa that have large extensions of savannas with a high periodicity of fires. For these
countries an analysis of fire based on NDVI values could be a successful tool for the
analysis of fires and ecosystem dynamics and assessing vulnerability to fires in a
temporal scale.
Predicting the occurrence of fires in Africa
35
5. Conclusions and recommendations
This study aims to solve two main questions about fire dynamics. The first question was
if there are strong relations between some climatic, environmental and anthropogenic
variables, and one of the more important fire characteristics: fire frequency. The second
question was whether fire occurrence can be predicted based on the NDVI of the months
preceding the fire events.
This research had interesting findings in the relationship between fire frequency and a set
of environmental, climatic and anthropogenic variables. As suggested in the hypotheses,
the variables describing vegetation and ecosystem status are the variables most strongly
correlated with fire frequency, as vegetation is the fuel to burn. Herbaceous vegetation
that represents the biomass that dies after the dry season and that is easily inflammable,
has the strongest relationship with fire frequency.
Climatic variables were correlated with fire frequency but were less strong than the
vegetation variables. Precipitation is the variable more correlated with fire frequency,
since dry ecosystems are more susceptible to fires than the more humid ecosystems, such
as tropical forests in central Africa. Although temperature is known as having a high
influence in the ignition of fires, in this study, this correlation was less strong than other
climatic variables. In general, the correlations between climatic variables and fire were
ambiguous, because climate cannot be an isolated factor to predict fires. High
temperatures can start fires, but if there is not fuel to burn, like in deserts, the influence of
this variable is null.
Humans influence drastically the actual increase in fire frequency and intensity. In this
study, we checked the correlation of some variables associated with human settlements
and activities. Livestock that reflects the land use of the African savannas and grasslands
is highly correlated with fire frequency. Increases in livestock, will affect and increase
the intensity and the periodicity of fires with the purpose of peparing the land and
enhnacing productivity. On the other hand, variables determining human settlements,
such as population density or population growth, were not correlated with fire frequency.
The most important variables found in this analysis, NDVI, herbaceous vegetation, bare
soil, and precipitation, among others, were used to generate models to predict fire
frequency. Although all the models had a satisfactory fit according to the statistical
analysis, the simplest models are just as accurate. Models based on a few variables, such
as NDVI or MODIS data, are the most suitable for prediction, due to the fact that those
datasets are found in different free geo-portals, and these simple models can be easily
used by anyone who needs to predict fire frequency in any location of Africa.
Although fire frequency is an important variable for management purposes, many
organizations are not really interested in annual patterns, but more in the prediction of
local fire events. Our second question wanted to find local models to predict the
likelihood of fire occurrence. We used South Africa, as a pilot study, and we made the
analysis on a monthly basis. The logistic models and the probability functions generated
for every month, showed a good fit, according to the statistics. Although the models
accurately predict the location of the fires, the predictions underestimate the probabilities
Predicting the occurrence of fires in Africa
36
of fire occurrence in South Africa.
Recommendations:
Although this study gives some highlights in the nature of fires, further studies should
include other variables that were not included in this study. Although human variables are
known as some of the most important driven factors in fire dynamics, the variables that
we used in this study seemed to be not the most suitable to identify this relationship.
Perhaps, other variables or analyses can give more highlights to describe the nature of
this relationship. Concerning to human influences, other variables that describe buffers or
distances to populated areas could have better relationships with fire frequency, since a
large amount of fires are attributed to land use management.
For this study we wanted to analyze the temporal series of the GBS data (fire occurrence)
and NDVI, which were in weekly or bi-weekly products. However, due to the large
amount of data and with the purpose of making a more simple analysis, the analysis was
simplified in a monthly basis. It would be interesting to generate similar results in a
weekly or bi-weekly temporal scale, because predictions in a more accurate temporal
scale could be more interesting for researching or managing purposes. Moreover, it
would be interesting to generate these models for countries that are experiencing changes
in the fire regimes.
Predicting the occurrence of fires in Africa
37
Acknowledgements
A journey is easier when you travel together. Interdependence is certainly more valuable
than independence. This thesis is the result of my Master study in Wageningen
University, where I have been accompanied and supported by many people. It is a
pleasure to have now the opportunity to express my gratitude for all of them.
I would like express my sincere gratitude to my supervisors for all their guidance in this
thesis work. To Frank van Langevelde for all his immense assistance with the statistical
analysis, and the helpful comments during the whole process. To Aldo Bergsma for his
kindly help with all the technical issues using the software, and to Arnold Bregt for his
guidance and his interesting comments. I also thank Xiao Guan (Sam) for his help with
the software and technical issues, and to Sytze de Bruin for his help analyzing the
original idea.
I also would like to thank Thomas Groene for invite me to develop my thesis in this topic
and for his comments in my work, and to Cesar Carmona-Moreno, for sharing with us the
original idea, and who provided and explained the GBS data, starting point of this thesis.
I would like to give immense thanks to my friends, who support me during all this
process, especially Christopher, my favorite editor; Lina, Lidia and Paul for their help
and comments. Thanks to my collegues in GAIA, who made my days more enjoyable, to
my teachers in the Resource Ecology Group and the laboratory of Geo-Information
Science and Remote Sensing, for their endless help and to all my friends, and corridor
mates, who made my stay in Wageningen one of the most fruitful and enjoyable
experiences of my life.
Predicting the occurrence of fires in Africa
38
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Predicting the occurrence of fires in Africa
42
Appendix 1. Validation of the regression models between fire frequency and
environmental, climatic and anthropogenic variables.
Characteristics of the coefficients for the models adjusted and validation models of fire frequency
and some environmental, climatic and anthropogenic variables.
Models fitted*
Variables
Coefficient
Confidence limits
Validation models*
p-value
Coefficient
1.00
-0.3653
Confidence limits
p-value
Model 1
Intercept
-0.3648
Cecs
0.0361
0.0301
0.0422
1.00
0.0360
0.0300
0.0420
1.00
Goat
-0.0004
-0.0007
-0.0002
0.87
-0.0004
-0.0007
-0.0002
0.82
-0.0405
-0.0465
-0.0344
1.00
-0.0399
-0.0459
-0.0338
1.00
Herbaceous %
0.0003
0.0003
0.0004
1.00
0.0003
0.0003
0.0004
1.00
Temp*herbac
0.0013
0.0011
0.0014
1.00
0.0012
0.0011
0.0014
1.00
0.87
-1.7677
Herbaceous%
2
1.00
Model 2
Intercept
-1.7640
1.00
Herbaceous%
0.0170
0.0148
0.0192
1.00
0.0186
0.0165
0.0208
1.00
NDVI
0.9714
0.3311
1.6117
1.00
0.4069
-0.1895
1.0033
0.52
Precipitation
-0.0053
-0.0075
-0.0030
1.00
-0.0043
-0.0062
-0.0023
1.00
Temperature
0.0647
0.0476
0.0818
1.00
0.0682
0.0521
0.0843
1.00
1.00
-2.3074
Model 3
Intercept
-2.2894
1.00
Cecs
0.0346
0.0265
0.0427
1.00
0.0346
0.0265
0.0428
1.00
Herbaceous %
-0.0210
-0.0300
-0.0120
0.99
-0.0209
-0.0300
-0.0118
0.99
Ndvi
-4.4660
-8.9032
-0.0287
0.49
-4.4515
-8.9052
0.0021
0.49
Precipitation
0.0190
0.0024
0.0357
0.61
0.0191
0.0025
0.0358
0.61
Tree %
0.0261
0.0105
0.0417
0.87
0.0255
0.0098
0.0413
0.88
Humidity
0.0687
0.0436
0.0938
1.00
0.0696
0.0442
0.0949
1.00
Herbaceous2%
0.0003
0.0003
0.0004
1.00
0.0003
0.0003
0.0004
1.00
-6.0654
-9.8088
-2.3221
0.89
-6.0434
-9.8136
-2.2731
0.88
-0.0002
-0.0004
-0.0001
0.87
-0.0002
-0.0004
-0.0001
0.82
Humid
-0.0007
-0.0010
-0.0005
1.00
-0.0007
-0.0010
-0.0005
1.00
Ndvi*temp
0.4194
0.2886
0.5501
1.00
0.4180
0.2870
0.5490
1.00
Prec*temp
-0.0009
-0.0016
-0.0003
0.74
-0.0009
-0.0016
-0.0003
0.74
2
Ndvi
2
Tree
2
* All proportion of p-values are significant (99% confidence interval)
Note: The models are validated when the coefficients of the validation model are within the confidence limits of the
coefficients of the original model.
Predicting the occurrence of fires in Africa
43
Characteristics of the coefficients for the models adjusted and validation models of fire frequency
and some environmental, climatic and anthropogenic variables.
Variables
Models fitted*
Coefficient
Confidence limits
Validation models*
p-value
Coefficient
1.00
1.7479
Confidence limits
p-value
Model 4
Intercept
1.7319
1.00
Cecs
0.0367
0.0308
0.0426
1.00
0.0376
0.0316
0.0435
1.00
Ndvi
-8.4135
-10.8772
-5.9499
1.00
-8.4285
-10.8934
-5.9638
1.00
Population
-0.0019
-0.0027
-0.0011
0.98
-0.0019
-0.0028
-0.0011
0.99
Precipitation
0.0171
0.0047
0.0294
0.75
0.0174
0.0051
0.0297
0.78
Tree %
-0.0232
-0.0271
-0.0194
1.00
-0.0235
-0.0274
-0.0196
1.00
Humidity
-0.0079
-0.0118
-0.0041
1.00
-0.0080
-0.0119
-0.0041
0.99
Ndvi*temp
0.3987
0.3008
0.4966
1.00
0.3996
0.3016
0.4975
1.00
Ndvi*bare
-0.0663
-0.0841
-0.0486
1.00
-0.0675
-0.0855
-0.0495
1.00
Temp*bare
-0.0005
-0.0006
-0.0005
1.00
-0.0005
-0.0006
-0.0004
1.00
Prec*temp
-0.0008
-0.0014
-0.0003
0.89
-0.0009
-0.0014
-0.0003
0.89
* All proportion of p-values are significant (99% confidence interval)
Note: The models are validated when the coefficients of the validation model are within the confidence limits of the
coefficients of the original model.
Predicting the occurrence of fires in Africa
44
Appendix 2. Probability models for monthly fire occurrence in South Africa
a
0.015
b 0.8
probability of fire in January
0.014
probability of fire in January
Models of the probability of fire occurrence, fitted from the logistic regressions from January till
April. Left side shows models based in the most significant variable. Right figures show models
based in 2 variables. Lines show the different tendencies for different values of the second month.
0.013
0.012
0.011
0.01
0.009
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.008
0
0
100
200
300
400
500
NDVI April
0.0116
0.0114
0.0112
0.011
0.0108
0.0106
0.0104
0.0102
600
300
600
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
100
200
300
400
500
100
200
600
300
NDVI April
NDVI March
f
0.015
100
400
400
200
500
500
600
300
600
0.12
0.0145
probability of fire in March
probability of fire in March
200
500
500
0.8
NDVI April
0.014
0.0135
0.013
0.0125
0.012
0.0115
0.011
0.0105
0.1
0.08
0.06
0.04
0.02
0
0.01
0
0
100
200
300
400
500
100
200
600
NDVI April
NDVI March
h
0.02
0.018
probability of fire in April
probability of fire in April
100
400
400
0
0
g
300
NDVI April
d 0.9
0.012
0.0118
0.01
e
200
NDVI March
probability of fire in February
probability of fire in February
c
100
600
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
300
NDVI April
400
100
400
200
500
300
NDVI April
400
100
400
200
500
500
600
300
600
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0
0
100
200
300
400
500
NDVI April
Predicting the occurrence of fires in Africa
100
200
600
NDVI May
500
600
300
600
45
probability of fire in May
i
0.006
j
0.005
probability of fire in May
Models of the probability of fire occurrence, fitted from the logistic regressions from May till
August. Left side shows models based in the most significant variable. Right figures show models
based in 2 variables. Lines show the different tendencies for different values of the second month.
0.004
0.003
0.002
0.001
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0
0
100
200
300
400
500
100
600
NDVI October
100
400
NDVI June
l
0.0002
0.00018
probability of fire in June
probability of fire in June
k
200
300
400
NDVI October
0.00016
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
200
500
500
600
300
600
0.0018
0.0016
0.0014
0.0012
0.001
0.0008
0.0006
0.0004
0.0002
0.00002
0
0
0
0
100
200
300
400
500
100
200
300
400
NDVI December
600
NDVI December
NDVI October
m 0.00045
100
400
200
500
500
600
300
600
n 0.07
probability of fire in July
probability of fire in July
0.0004
0.00035
0.0003
0.00025
0.0002
0.00015
0.0001
0.00005
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0
0
100
200
300
400
500
NDVI December
200
300
400
NDVI December
NDVI January
100
400
200
500
500
600
300
600
p 0.07
1
0.9
probability of fire in August
probability of fire in August
o
100
600
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0
0
100
200
300
400
500
NDVI March
Predicting the occurrence of fires in Africa
600
100
200
300
NDVI March
NDVI October
100
400
400
200
500
500
600
300
600
46
Models of the probability of fire occurrence, fitted from the logistic regressions from September
till December. Left side shows models based in the most significant variable. Right figures show
models based in 2 variables. Lines show the different tendencies for different values of the second
month.
r0.6
0.12
probability of fire in September
probability of fire in September
q
0.1
0.08
0.06
0.04
0.02
0.5
0.4
0.3
0.2
0.1
0
0
0
0
100
200
300
400
500
100
NDVI May
NDVI September
t
0.12
0.1
0.08
0.06
0.04
0.02
300
NDVI May
100
400
400
200
500
500
600
300
600
0.5
0.45
probability of fire in October
probability of fire in October
s
200
600
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0
0
100
200
300
400
500
NDVI February
0.05
0.04
0.03
0.02
0.01
200
500
600
300
600
0.5
0.4
0.3
0.2
0.1
0
0
0
100
200
300
400
500
100
600
200
300
400
NDVI February
NDVI November
NDVI February
100
400
200
500
500
600
300
600
x0.25
0.03
probability of fire in December
probability of fire in December
100
400
500
v0.6
0.06
0
w
200
300
400
NDVI February
NDVI October
probability of fire in November
probability of fire in November
u
100
600
0.025
0.02
0.015
0.01
0.005
0.2
0.15
0.1
0.05
0
0
0
0
100
200
300
400
500
ndvi February
Predicting the occurrence of fires in Africa
100
600
NDVI December
200
300
400
NDVI February
100
400
200
500
500
600
300
600
47
Appendix 3. Logistic models for fire occurrence in South Africa, based on monthly
NDVI.
Fire occurrence in January
AIC
F1=-4.4625-0.0038n1+0.0042n2-0.014n3+0.0089n4+0.0066n5-0.0064n6-0.0012n7+0.0048n80.0048n9+0.0023n10-0.0018n11+0.0045n12
28539
F1=-4.5320230-0.0110392n3+0.0111984n4
29242
F1=-4.539+0.0004141n4
30709
Fire occurrence in February
F2=-4.692-0.0049n2-0.0119n3+0.01078n4+0.0062n12
26242
F2=-4.5561701-0.0115591n3+0.0114788n4
26947
F2=-4.564485+0.0002253n4
28407
Fire occurrence in March
F3=-4.61-0.003n1-0.0041n3+0.00366n4+0.0011n10+0.0033n12
30652
F3=-4.4559474-0.0042309n3+0.0044408n4
30811
F3=-4.5575930+0.0005225n4
31268
Fire occurrence in April
F4=-4.169-0.0037n1-0.0064n4+0.0076n5-0.00593n10+0.0066n12
27842
F4=-4.409616-0.005734n4+0.0057576n5
28619
F4=-3.9495159-0.0014n4
29250
Fire occurrence in May
F5=-5.8-0.001n3+0.0066n6-0.0107n10+0.0029n12
7314.4
F5=-5.7834785+0.0079090n6-0.0098488n10
7351.8
F5=-5.3327221-0.0025836n10
7583.2
Fire occurrence in June
F6=-9.591-0.01n1+0.0057n3+0.0055n9-0.0127n10+0.0111n12
516.03
F6=-9.349174-0.007517n10+0.006146n12
529.92
F6=-10.101030+0.002552n12
540.56
Fire occurrence July
F7=-9.237-0.0119n1+0.00229n3+0.001165n12
1054.5
F7=-9.139129-0.010712n1+0.012551n12
1055.2
F7=-9.2815983+0.0024699n12
1085.1
Fire occurrence in August
F8=-5.47+0.0039n3+0.0073n7-0.0051n8-0.011n10+0.0036n11
15791
F8=-5.4859845+0.0059066n3-0.0074136n10
16047
F8=-6.1960013+0.0025258n3
16681
*n is the value of the NDVI from January through December (1-12).
Predicting the occurrence of fires in Africa
48
Logistic models for fire occurrence in South Africa, based on monthly NDVI.
Fire occurrence in September
AIC
F9=-3.2038-0.0027n1+0.003n2+0.0038n3-0.0055n4+0.0057n5+0.0007n6+0.0019n7+0.0013n80.007n9-0.004n10+0.0013n11+0.0013n12
95977
F9=-3.22+0.00653n5-0.006875n9
98708
F9=-3.65+0.002463n5
102308
Fire occurrence in October
F10=-3.496-0.00048n1+0.0049n2+0.0026n3-0.0062n4+0.0061n50.001n6+0.0029n7+0.00097n8-0.0038n9-0.0078n10+0.00063n11+0.00096n12
95494
F10=-3.377+0.006464n2-0.007022n10
97594
F10=-4.104+0.003256n2
103178
Fire occurrence in November
F11=-4.362+0.00078n1+0.0052n2-0.002n3+0.0023n4+0.0031n5+0.0018n6+0.001n7+0.0014n80.0057n9-0.0013n10-0.0083n11+0.0017n12
57551
F11=-4.226+0.008464n2-0.008162n11
59653
F11=-4.849693+0.003382n2
64252
Fire occurrence in December
F12=-4.5713+0.00565n2+0.00255n5-0.00336n11-0.003999n12
40150
F12=-4.5312783+0.0063713n2-0.0055456n12
40461
F12=-4.833+0.002062n2
41690
*n is the value of the NDVI from January through December (1-12).
Predicting the occurrence of fires in Africa
49
Appendix 4. . Validation of the logistic models for the prediction of fire occurrence
in South Africa
Logistic models for every month based in NDVI, from January to December (NDVI1-NDVI12).
Characteristics of the coefficients of the models for South Africa and validation models for
Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
January
Model 1
Intercept
-4.4625
-17.0644
NDVI1
-0.0038
-0.0388
0.0633
0.0382
NDVI2
0.0042
-0.0291
0.0510
0.003
NDVI3
-0.0141
-0.0905
0.0326
-0.0259
NDVI4
0.0090
-0.0608
0.0360
0.0428*
NDVI5
0.0067
-0.0256
0.1625
-0.0018
NDVI6
-0.0064
-0.1106
0.0919
-0.0569
NDVI7
-0.0012
-0.1366
0.0723
-0.0029
NDVI8
0.0048
-0.1514
0.0717
-0.0328
NDVI9
-0.0047
-0.0581
0.2130
0.1097
NDVI10
0.0023
-0.1277
0.0584
0.0163
NDVI11
-0.0018
-0.0610
0.0893
-0.0523
NDVI12
0.0045
-0.1404
0.0342
-0.0111
Model 2
Intercept
-4.532
-13.3166
NDVI3
-0.011
-0.0183
0.0054
-0.0028
NDVI4
0.0112
-0.0059
0.0192
0.0137
Model 3
Intercept
-4.5389
NDVI4
0.0004
-13.9249
-0.0001
0.0120
0.0119
February
Model 1
Intercept
-4.692
-2.6570
NDVI2
-0.0050
-0.0490
-0.0015
-2.96E-14
NDVI3
-0.0120
-0.0422
0.0228
3.60E-17
NDVI4
0.0108
-0.0219
0.0373
2.18E-17
NDVI12
0.0063
-0.0048
0.0317
7.91E-20
Model 2
Intercept
-4.5562
NDVI3
-0.0116
-2.6570
-0.0249
0.0089
4.56E-19
NDVI4
0.0115
-0.0087
0.0219
8.69E-19
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
50
Logistic models for every month based in NDVI, from January to December (NDVI1-NDVI12).
Characteristics of the coefficients of the models for South Africa and validation models for
Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
February
Model 3
Intercept
-4.5645
NDVI4
0.0002
-2.6571
-0.0037
0.0055
1.22E-18
March
Model 1
Intercept
-4.61
NDVI1
-0.003
-0.0404
0.0101
-1.36E-17
-2.6570
NDVI3
-0.0041
-0.0141
0.0100
-1.36E-18
NDVI4
0.0037
-0.0213
0.0071
5.97E-17
NDVI10
0.0011
-0.0064
0.0260
3.70E-17
NDVI12
0.0033
-0.0209
0.0333
8.59E-18
Model 2
Intercept
-4.4559
-2.6571
NDVI3
-0.0042
-0.0096
0.0042
4.39E-17
NDVI4
0.0044
-0.0057
0.0091
2.74E-17
Model 3
Intercept
-4.5575
NDVI4
0.0005
-2.6571
-0.0091
0.0015
1.22E-18
April
Model 1
Intercept
-4.169
-3.282
NDVI1
-0.0037
-0.0173
0.0138
-0.0074
NDVI4
-0.0064
-0.0222
0.0034
-0.0141
NDVI5
0.0076
-0.0003
0.0344
-0.0139
NDVI10
-0.0059
-0.0224
0.0028
-0.0009
NDVI12
0.0066
-0.0132
0.0185
0.0320*
Model 2
Intercept
-4.4096
0.9252
NDVI4
-0.0057
-0.0238
-0.0035
-0.0088
NDVI5
0.0057
0.0014
0.0229
0.0003*
Model 3
Intercept
-3.9495
1.0051
NDVI4
-0.0014
-0.0105
0.0016
-0.0087
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
51
Logistic models for every month based in NDVI, from January to December (NDVI1-NDVI12).
Characteristics of the coefficients of the models for South Africa and validation models for
Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
May
Model 1
Intercept
-5.8002
NDVI3
-0.0011
-0.0217
0.0441
-2.88E-18
-2.657
NDVI6
0.0066
-0.0260
0.4542
-3.87E-17
NDVI10
-0.0107
-0.2972
-0.0038
6.63E-18
NDVI12
0.0029
-0.2587
-0.0006
-1.95E-17
Model 2
Intercept
-5.7835
NDVI6
0.0079
-0.0110
0.0212
-1.36E-18
-2.657
NDVI10
-0.0098
-0.0198
0.0133
-3.45E-19
May
Model 3
Intercept
-5.3327
NDVI10
-0.0026
-2.6570
-0.0263
0.0097
1.52E-18
June
Model 1
Intercept
-9.591
-2.6570
NDVI1
-0.01
-0.0161
0.0025
-3.03E-17
NDVI3
0.0057
0.0023
0.0136
-4.47E-17*
NDVI9
0.0055
0.0014
0.0154
5.69E-17*
NDVI10
-0.0127
-0.1254
0.0152
-5.56E-17
NDVI12
0.0111
0.0023
0.1423
2.13E-17*
Model 2
Intercept
-9.3492
-2.6570
NDVI10
-0.0075
-0.1265
0.0125
-5.40E-18
NDVI12
0.0061
-0.0123
0.0154
3.45E-19
-0.0128
0.185
-1.17E-18
Model 3
Intercept
-10.101
NDVI12
0.0025
-2.6570
July
Model 1
Intercept
-9.237
NDVI1
-0.0119
-0.1290
0.0125
7.55E-18
-2.6570
NDVI3
0.0023
-0.0054
0.0145
3.69E-17
NDVI12
0.0012
-0.0036
0.0253
2.58E-17
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
52
Logistic models for every month based in NDVI, from January to December. Characteristics of
the coefficients of the models for South Africa and validation models for Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
July
Model 2
Intercept
-9.1391
-2.6570
NDVI1
-0.0107
-0.0536
0.0247
-1.13E-17
NDVI12
0.0125
-0.0380
0.0397
4.86E-18
Model 3
Intercept
-9.2816
NDVI12
0.0025
-2.6570
-0.0561
0.0569
-1.17E-18
August
Model 1
Intercept
-5.47
-2.6570
NDVI3
0.0039
-0.0033
0.0134
-2.60E-18
NDVI7
0.0073
-0.0094
0.0288
-5.21E-17
NDVI8
-0.0051
-0.0250
0.0128
7.83E-17
NDVI10
-0.011
-0.0303
0.0055
6.91E-17
NDVI11
0.0036
-0.0112
0.0126
-8.30E-17
Model 2
Intercept
-5.4859
-2.6570
NDVI3
0.0059
-0.0007
0.0120
-1.40E-17
NDVI10
-0.0074
-0.0180
0.0030
-2.50E-17
-0.0059
0.0090
-1.09E-18
Model 3
Intercept
-6.196
NDVI3
0.0025
-2.6570
September
Model 1
Intercept
-3.2038
NDVI1
-0.0027
-0.0089
0.0088
-3.2885
0.0022
NDVI2
0.0030
-0.0031
0.0116
0.0052
NDVI3
0.0030
-0.0062
0.0095
-0.0031
NDVI4
-0.0055
-0.0127
0.0056
0.0024
NDVI5
0.0057
-0.0097
0.0132
-0.0043
NDVI6
0.0007
-0.0116
0.0162
-0.0071
NDVI7
0.0019
-0.0080
0.0235
0.0085
NDVI8
0.0013
-0.0150
0.0144
-0.0051
NDVI9
-0.0070
-0.0243
-0.0033
0.0045*
NDVI10
0.0040
-0.0070
0.0052
-0.0049
NDVI11
0.0013
-0.0101
0.0062
-0.0056
NDVI12
0.0013
-0.0075
0.0092
0.0078
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
53
Logistic models for every month based in NDVI, from January to December (NDVI1-NDVI12).
Characteristics of the coefficients of the models for South Africa and validation models for
Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
September
Model 2
Intercept
-3.22
-0.1727
NDVI5
0.0065
0.0041
0.0130
-0.0041*
NDVI9
-0.0069
-0.0162
-0.0036
0.0023*
Model 3
Intercept
-3.65
NDVI5
0.0025
-0.1518
-0.0010
0.0044
-0.0027*
October
Model 1
Intercept
-3.496
-1.464
NDVI1
-0.0005
-0.0091
0.0077
-0.0079
NDVI2
0.0049
-0.0022
0.0133
1.51E-05
NDVI3
0.0026
-0.0058
0.0114
-0.0053
NDVI4
-0.0062
-0.0178
0.0030
0.0141*
NDVI5
0.0061
-0.0051
0.0194
0.0030
NDVI6
0.0010
-0.0149
0.0126
0.0156*
NDVI7
0.0029
-0.0109
0.0179
0.0137
NDVI8
0.0009
-0.0137
0.0141
-0.0152*
NDVI9
-0.0038
-0.0162
0.0080
0.0127*
NDVI10
-0.0078
-0.0170
-0.0008
-0.0054
NDVI11
0.0006
-0.0055
0.0069
-0.0097*
NDVI12
0.0009
-0.0069
0.0088
0.0143*
Model 2
Intercept
-3.377
-0.1531
NDVI2
0.0065
-0.0039
0.0092
0.0016
NDVI10
-0.007
-0.0117
-0.0032
-0.0050
Model 3
Intercept
-4.104
0.7803
NDVI2
0.0032
-0.0060
0.0040
-0.0028
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
54
Logistic models for every month based in NDVI, from January to December (NDVI1-NDVI12).
Characteristics of the coefficients of the models for South Africa and validation models for
Swaziland.
Variables
Models fitted
Coefficient
Validation models
Confidence limits
Coefficient
November
Model 1
Intercept
-4.362
NDVI1
0.00078
-6.5783
NDVI2
0.0052
-0.0129
0.0144
0.0161*
NDVI3
-0.002
-0.0003
0.0283
-0.0195*
NDVI4
0.0023
-0.0309
0.0023
0.0156*
NDVI5
0.0031
-0.0052
0.0376
-0.0104*
NDVI6
0.0018
-0.0196
0.0304
0.0109
NDVI7
0.001
-0.0494
0.0122
-0.0047
-0.0210
0.0159
-0.0006
NDVI8
0.0014
0.0016
0.0612
-0.0115*
NDVI9
-0.0057
-0.0407
-0.0015
0.0144
NDVI10
-0.0013
-0.0249
0.0103
-0.0052
NDVI11
-0.0083
-0.0174
0.0036
-0.0016
NDVI12
0.0017
-0.0138
0.0153
0.0019
Model 2
Intercept
-4.226
NDVI2
0.0085
0.0036
0.0155
-7.1654
0.0087
NDVI11
-0.0082
-0.0172
-0.0014
-0.0038
-0.0035
0.0059
0.0065*
Model 3
Intercept
-4.8497
NDVI2
0.0034
-7.8488
December
Model 1
Intercept
-4.5713
NDVI2
0.0056
-0.0095
0.0147
-10.3736
0.0094
NDVI5
0.0025
-0.0137
0.0171
0.0037
NDVI11
-0.0037
-0.0169
0.0188
-0.0110
NDVI12
-0.0039
-0.0264
0.0113
0.0054
Model 2
Intercept
-4.5313
NDVI2
0.0064
-0.0050
0.0085
-7.9538
0.0082
NDVI12
-0.0055
-0.0156
0.0056
-0.0018
Model 3
Intercept
-4.833
-8.3039
NDVI2
0.0021
0.0004
0.0072
0.0071
All proportion of p-values are significant (99% confidence interval)
Predicting the occurrence of fires in Africa
55