Remote Sensing of Environment 96 (2005) 212 – 227 www.elsevier.com/locate/rse Field work and statistical analyses for enhanced interpretation of satellite fire data Manoel F. Cardosoa,c,*, George C. Hurtta,b, Berrien Moore IIIa, Carlos A. Nobrec, Heather Baina a Institute for the Study of Earth, Oceans and Space, University of New Hampshire, Durham, NH 03824, USA b Department of Natural Resources, University of New Hampshire, Durham, NH 03824, USA c CPTEC/INPE Instituto Nacional de Pesquisas, Espaciais, Cachoeira Paulista, SP 12630-000, Brazil Received 23 April 2004; received in revised form 24 February 2005; accepted 26 February 2005 Abstract Because their broad spatial and temporal coverage, satellites provide the main source of fire data for Amazonia. A key to the application of these tools for environmental studies is the appropriate interpretation of the data they provide. To enhance the interpretation of satellite fire data for this region, we collected ground-based data on fires in 2001 and 2002 using a simple and passive method, and statistically related these data to corresponding estimates from AVHRR and MODIS fire products using error matrices. Multiple methods of analyses from simple to complex produced qualitatively similar results. Total accuracies for both fire products were very high (> 99%) and dominated by accurate (> 99%) non-fire detection. Kappa statistics and fire-detection accuracies were substantially lower, with omission errors higher than commission errors. Results calculated using several different sets of spatial-matching parameters of analysis showed that Kappa was 1 – 10.6% for AVHRR, and 0 – 1.4% for MODIS. User’s accuracy for fires was 0 – 40% for AVHRR and 3 – 100% for MODIS. Producer’s accuracy for fires was 0 – 8% for AVHRR and 0 – 1% for MODIS. Statistical evaluations of potential explanatory factors showed that fire size and sampling time were dominant factors for low accuracies. Results from this study indicate that current satellite fire products are providing a limited sample of the fire activity in the region, and that ground-based analyses can substantially contribute to the interpretation of these products. D 2005 Elsevier Inc. All rights reserved. Keywords: Amazonia; Large-scale biosphere – atmosphere experiment in Amazonia; LBA; Fire; Satellite; Accuracy 1. Introduction Fires can change on the time scale of hours, land – surface characteristics that can take centuries to develop. They affect ecosystem structure (Cochrane, 2003; Geist & Lambin, 2001), biogeochemical cycling (Crutzen & Andreae, 1990; Hughes et al., 2000), and the composition, chemistry, and energy balance of the atmosphere. Fires release greenhouse gases, reactive chemicals, and particles (Brasseur et al., 1999; Crutzen & Andreae, 1990; Crutzen & * Corresponding author. Institute for the Study of Earth, Oceans and Space, University of New Hampshire, Durham, NH 03824 USA. E-mail address: manoel.cardoso@unh.edu (M.F. Cardoso). 0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2005.02.008 Lelieveld, 2001), and can change the albedo and other important properties of the landscape (Beringer et al., 2003; Govaerts et al., 2002). For example, contemporary global carbon emissions from fires have been estimated to be 3.53 Pg year
1 (van der Werf et al., 2004). Fires also account for ¨ 8 Tg N year
1 to the atmosphere, an amount that represents approximately 25% of the annual anthropogenic emissions of nitrogen oxides which in turn cause significant increases in tropospheric ozone concentrations (Crutzen & Lelieveld, 2001). Aerosols from fires can cause the concentration of cloud condensation nuclei (CCN) in the atmosphere to be an order of magnitude higher, affecting both clouds microphysics and rainfall (Andreae et al., 2002; Kaufman & Fraser, 1997; Ramanathan et al., 2001; Rosenfeld, 2000). By altering the land surface properties, fire M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 activity can also cause significant regional-scale decreases in transpiration and energy balance (Beringer et al., 2003; Govaerts et al., 2002). Fires are an important topic in the international Large Scale Biosphere –Atmosphere Experiment in Amazonia, LBA (Keller et al., 2001; Souza et al., 2003: The LBA Science Planning Group, 1996). Nutrient losses during fires in Amazonia have been shown to reduce long-term agricultural productivity (Sá et al., 2002). Air quality in areas with burning activity can be as poor as in urban areas (WHO, 1999). Fires that escape from managed lands are considered a major threat to forests (Cochrane, 2003; Nepstad et al., 1999b). In addition, substantially increased burning activity is projected for Amazonia in response to future scenarios of land-use if the current relationships between fire activity and explanatory factors continue to hold (Cardoso et al., 2003). In Amazonia, fire information comes from ground-based and remote-sensing data. These sources of information have different properties and availability. Ground-based data typically provide direct measurements of the consequences of fires and provide quantities such as carbon consumed and nutrient losses. For example, Carvalho et al. (1998) and Fearnside et al. (2001) estimated the effects of fire on aboveground carbon stocks in forests near Manaus. Cochrane and Schulze (1999) evaluated the effects of fires on the structure and species composition in forests in eastern Amazonia. The impacts of fires on nutrient concentrations have been studied in primary forests by Guild et al. (1998) and Kauffman et al. (1995), in cattle pastures by Guild et al. (1998) and Kauffman et al. (1998), and in regenerating forests by Hughes et al. (2000). Based on interviews with farmers, relations between land use and fires were assessed by Guild et al. (1998) in Rondônia, and by Nepstad et al. (1999a) in this and other locations experiencing deforestation. While there are other examples of ground-based studies in the region, information of this kind is generally available only for limited regions and periods of time. Satellite-based data, on the other hand, primarily provide estimates of fire activity and generally have the most complete spatial and temporal coverage. For Amazonia, important examples of satellite-based sources of active fire data include the Brazilian Institute for Space Research (INPE) fire monitoring system based on NOAA polarorbiting satellites (CPTEC, 2003; Setzer & Malingreau, 1996), the UW-Madison CIMSS Biomass Burning Monitoring Program based on geostationary GOES satellites (Prins et al., 1998a; UW-CIMSS, 2003), and the NASA fire products using data from TERRA and AQUA platforms (Justice et al., 2002; NASA, 2003) These sources provide regional coverage at a spatial resolution of 1 –4 km at subdaily/daily frequency. To make use of satellite-based active fire products, it is clearly important to properly interpret the data they provide. Most of the data are provided as fire pixels, which are satellite picture elements wherein active burning is detected. 213 Fire pixels indicate fire activity, but they are not a direct measure of individual fire occurrence, area burned, or carbon emitted. For example, viewing and illumination angle effects can cause a single fire event to be detected in more than one satellite pixel (Setzer & Malingreau, 1996; Setzer et al., 1994). In addition, some fires are small and may not generate enough energy to be detected (Eva & Lambin, 1998; Li et al., 2001). Fires can occur at times other than satellite detection times (Eva & Lambin, 1998; Ichoku et al., 2003). Clouds and plant canopies can hide fires from remote detection (Boles & Verbyla, 2000; Setzer & Malingreau, 1996). Solar reflection, or glare, can lead to false positives (Giglio et al., 1999; Kasischke et al., 2003). Because of these and other complicating factors, methods to interpret these data are needed. Three major methods have been applied to assess satellite fire data in Amazonia. One method uses independent estimates from high-resolution products to assess the accuracy of coarser resolution products (Justice et al., 2002). Using this technique, data from the Moderate Resolution Imaging Spectroradiometer (MODIS) for January 2003 over Roraima were compared to higher resolution fire data provided by the Advanced Space-borne Thermal Emission and Reflection Radiometer (ASTER) (Morisette et al., 2003). The same technique has been used in other regions. In Southern Africa, for example, the probability of detection by MODIS has been shown to be a strong function of the detection by ASTER (Morisette et al., 2002), and the number of fire pixels detected by MODIS and ASTER have been shown to be positively correlated (Justice et al., 2002). A second method is the verification of fire pixels from airplanes, helicopters, or by passive ground observations. For example, as part of the Fire Monitoring Program at the Brazilian Environmental Protection Agency (PROARCO/ IBAMA), several observations were made from helicopters over the state of Acre in 2001. Estimates from these observations suggest that 35% of 2001 fires in Acre were detected with NOAA-12, and 63% were detected with GOES-8 (Selhorst & Brown, 2003). In other parts of Brazil, ¨ 98% of fires detected using the Advanced Very High Resolution Radiometer (AVHRR) at INPE have been confirmed by fire fighters, and omission errors have been estimated to be ¨ 26% (Setzer et al., 1992). Observations in other regions of Amazonia in 2001 by IBAMA also indicated that omission were larger than commission errors in MODIS fire data (Schroeder, 2003). The third method is the use of prescribed (controlled) burns. In this method, fire products are evaluated based on their ability to identify intentional fires set in synchronization with satellite detection. For example, in order to assess the GOES-8 ABBA fire product, three prescribed burns were set during the Smoke Clouds and Radiation-Brazil (SCAR-B) experiment, in September 1995 in Rondonia (Prins et al., 1998b). One fire could not be detected due to cloud cover. The remaining two fires were detected and had their size and temperature estimated. Controlled burns set 214 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 for emission studies during the field experiments BASE-A (Kaufman et al., 1992) and BASE-B (Ward et al., 1992) were also used to assess NOAA/AVHRR fire data. One fire, set on September 1989 in Mato Grosso was detected from satellites NOAA-10 and NOAA-11. The other controlled fire, set on September of 1990 in Pará, was detected from NOAA-9 and NOAA-11 (Setzer et al., 1994). All of these methods have advantages and disadvantages that should be considered. For example, the first method (product intercomparisons) allows for direct comparisons between products that are aligned in space and time, but depends on accurate fire detection from the reference (higher resolution) remote-sensing data. The second method (verification of fire pixels) allows for a large sample size, but is resource intensive to provide for the set of observations needed. The third method (prescribed burns) offers the opportunity for very detailed measurements, but it is limited in sample size and it is not passive. In this paper, we describe an additional method to enhance the interpretation of active fire data from satellites (Cardoso et al., 2002). The method consists of the collection of a relatively large set of passive ground-based data on both fire and non-fire occurrence, which are then statistically related to data from corresponding satellite fire products. Statistical analyses are based on error matrices following Congalton and Green (1999), and yield information on both fire and non-fire detection accuracies. Using this method in two regions in Brazil, in 2001 and 2002, we find that the total accuracies for AVHRR- and MODIS-based active fire products were very high (> 99%). These high total accuracies were primarily due to the correct detection of regions that were not burning. The accuracies for the detection of fires were considerably lower. Omission errors were higher than commission errors. The satellite products differed in their accuracy values. The omission errors for fire were lower for AVHRR than for MODIS, and commission errors were lower for MODIS than for AVHRR. 2. Ground-based data We identified two regions in Brazil to collect groundbased data on fire activity (Fig. 1). The first is located in the vicinity of Marabá, in the state of Pará. This region is primarily forest covered, and is experiencing rapid deforestation for the formation of pastures and for wood and charcoal production. The second region is located between Cuiabá and Alta Floresta, in the state of Mato Grosso. This region can be characterized as a transition zone between savannas and forests, with a more diverse set of land-uses and a significant area of croplands (e.g. soy). Both regions are located in or near the Arc of Deforestation (INPE, 2000) and experience high fire activity. These regions were selected for study because of their high fire occurrence, different environments, and ease of access by roads. Specific locations were chosen based on satellite fire pixels Fig. 1. Regions where ground-based fire data were collected: the vicinity of Marabá, in the state of Pará, visited from November 3 to 5, 2001 (region A); between Cuiabá and Alta Floresta, in the state of Mato Grosso, visited from July 12 to 15, 2002 (region B). Light black lines represent political boundaries. Dark black lines represent tracks driven. maps from previous years, and consulting with local researchers. Pará was visited from November 3 to 5, 2001, and Mato Grosso was visited from July 12 to 15, 2002. These dates were during the dry season for these regions when fires typically occur (Crutzen & Andreae, 1990). In each location, data on fire and non-fire occurrence were collected by visual inspection from roads primarily during daylight hours. All areas where we did not observe fires were considered as non-fires. Fire position and time were determined by direct measurement with a handheld Global Positioning System receiver (GARMIN GPS V), or estimated visually from measured positions. Data collected include fire position, time, size, and land-cover. Fire size was estimated in three categories: small (< 0.25 ha), medium (0.25 – 1 ha), and large (> 1 ha). Size combined the area actively burning and the area recently burned. In some cases, fire size could not be estimated because lack of visibility of the affected area. Land cover included several traditional categories including: savanna and grassland, woody savanna, forest, pasture, croplands, and two additional categories for charcoal production and sawmills, and for fires that could be specifically classified (‘‘other’’). Field equipment included a car, road maps, a portable GPS receiver, pens and paper. In total two people participated in Pará and three in Mato Grosso. The ground-based dataset is accessible from the LBA Data and Information System (LBA-DIS). In some locations, we drove out and back using the same road to enable the estimation of the rate of change in the fire state of the land surface with respect to time. On these repeated tracks, observations of fires could be classified as: fires that were observed only on the way out, fires that were observed only on the way back, and fires that were observed in both directions. Observations of points that were not burning (non-fires) were classified in a similar way: non- 215 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 fires that were observed only on the way out, non-fires that were observed only on the way back, and non-fires that were observed in both directions. (a) Fig. 2 provides a classification of observed fires by observation frequency, fire size, proximity to roads, and land cover. A total of 162 fire events were observed. Of Observation frequency Mato Grosso Observation frequency Pará Observation frequency ´ and Mato Grosso Para 2% Observed once 11% 20% Observed twice 80% 89 % 98% (b) Fire size Pará Fire size Mato Grosso Fire size Para ´ and Mato Grosso 5% 12% 23% 14% 29% Small 20% Medium 14% Large 45% Unknown (c) 35% 30% 51% Proximity to roads Pará Proximity to roads Mato Grosso 22% Proximity to roads Para´ and Mato Grosso 47% Close Far 41% 53% 59% 47% 53% (d) Land cover Pará 7% 37% Land cover Mato Grosso Land cover Para´ and Mato Grosso 10% 4% 5% 30% 33% 15% 22% 7% savanna or grassland woody savanna forest pasture 38% cropland 14% 14% 11% 11% 2% 20% 14% 6% charc. prod or sawmills other Fig. 2. Characteristics of fires observed on the ground in Pará, Mato Grosso and both regions combined. Rows contain: (a) observation frequency, (b) fire size, (c) proximity to roads, and (d) land cover. ‘‘Observed once’’ refer to fires that were observed only on the way out or only on the way back. ‘‘Observed twice’’ refer to fires that were observed both ways on repeated tracks. Fire size was estimated as small (< 0.25 ha), medium (0.25 – 1 ha), large (>1 ha), and unknown. Proximity to roads was classified as close (<1 km) and far (1 km). Land-cover types are described in the text. 216 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 daily frequency of small fires ranged from 4% to 29% in Pará, and from 29% to 67% in Mato Grosso. The frequency of medium fires ranged from 17% to 50% in Mato Grosso. The frequency of large fires ranged from 29% to 71% in Pará, and from 10% to 36% in Mato Grosso. these, 144 fires were observed once and 9 were observed twice. Forty-seven fires (29%) were classified as small, 35 (22%) were medium, 57 (35%) were large, and 23 (14%) did not have their size estimated. Eighty-six fires (53%) were estimated to be at distances equal to or greater than 1 km from roads, the remaining were estimated to be closer than 1 km. Forty-four fires (27%) were observed in forests, woody savannas and savannas or grasslands. Sixty-four fires (40%) occurred in pastures, croplands, and around charcoal productions or sawmills, and 54 (33%) were not specifically classified. The same number of fire events was observed in both regions, 81 in Pará and 81 in Mato Grosso, but the characteristics of these fires differed (Fig. 2). In Pará, most of fires were large and burning far from roads. In Mato Grosso, most of fires were small and a larger percentage was close to the roads. The number of fires that did not have size estimated was smaller in Mato Grosso. In Pará, fires were not observed in croplands, savannas or grasslands. In this region ¨ 50% of the fires were in pastures and in charcoal productions or sawmills, and ¨ 10% were in wood savannas and forests. In Mato Grosso, few fires occurred in pastures (2%). In this region, 43% of the fires were in savannas or grasslands, woody savannas, and forests, and 25% were in croplands and around charcoal productions or sawmills. The number of fires observed through time varied in both regions (Fig. 3). In Pará, the daily number ranged from 14 to 46. In Mato Grosso, the daily number ranged from 10 to 28. The daily fraction of fires observed close to roads in Pará ranged from 29% to 48%, and in Mato Grosso ranged from 50% to 56%. The daily patterns of fire size varied more than the daily patterns of proximity to roads. For example, the (a) We used two sources of satellite data that covered our regions of study. One source of information was the INPE/ AVHRR active fire product (CPTEC, 2003), which has been one of the main sources of information for ecological and atmospheric studies related to fire activity in Amazonia (EMBRAPA, 2003). In this product, active burnings are identified based on data from one AVHRR thermal channel centered at a wavelength close to 4 Am (Setzer & Malingreau, 1996). Fire pixels are selected by identifying thermal energy above a threshold. In a second step, anomalous fire pixels are filtered out if there are indications that they were caused by solar reflection on water or clouds (Setzer & Malingreau, 1996). The spatial resolution of the product is approximately 1 km at nadir. For the periods analyzed in this study, AVHRR fire information were produced from NOAA-12 afternoon overpasses, covering the analyses regions around 20 GMT (17:00 local standard time in Pará, and 16:00 local standard time in Mato Grosso) daily. Data were provided by the Brazilian Center for Weather Forecasts and Climate Studies (CPTEC). Hereafter we refer to this product simply as AVHRR. The second source of satellite-based fire information is one of the MODIS fire products (Justice et al., 2002; NASA, Fire size - Mato Grosso Fire size - Pará 50 50 Small 40 Medium 30 Large 20 Unknown 10 Number of fires Number of fires 3. Satellite data 0 Small 40 Medium 30 Large 20 Unknown 10 0 11/03/2001 11/04/2001 11/05/2001 07/12/2002 Date (b) 07/14/2002 07/15/2002 Date Proximity to roads - Mato Grosso Proximity to roads - Pará 50 40 Close 30 Far 20 10 Number of fires 50 Number of fires 07/13/2002 40 Close 30 Far 20 10 0 0 11/03/2001 11/04/2001 Date 11/05/2001 07/12/2002 07/13/2002 07/14/2002 07/15/2002 Date Fig. 3. Daily characteristics of fires observed on the ground in Pará and Mato Grosso. Rows contain: (a) fire size and (b) proximity to roads. 217 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 Pará. The same number of fire pixels was detected in both regions (56 in Pará and 56 in Mato Grosso). The daily number of fire pixels detected in the study regions varied considerably. In Pará, the number of fires detected ranged from 0 to 42 per day. In Mato Grosso, the number of fires detected ranged from 0 to 27 per day. All fire products detected some fires on just one day. 2003). These data provide a main source of information on fire activity for the NASA Earth Observing System (Lindsey & Salomonson, 2002). In particular, we analyzed information from the MOD14 active fire product version 3 (Justice et al., 2002). In this product, active burning is identified based on data from two MODIS thermal channels centered at wavelengths close to 4 and 11 Am. Fire pixels are identified based on both abnormally high thermal emission at shorter wavelengths, and on thermal emission that is significantly higher than the fire-free background. After detection, potential fire pixels may be filtered out if there are indications that they were caused by reflective surfaces or sun glint (Justice et al., 2002). The spatial resolution is similar to AVHRR, and approximately to 1 km at the nadir. For the periods analyzed in this study, available fire information were from the MODIS sensor onboard the TERRA platform, which overpasses the analyses regions around 2 GMT (23:00 local standard time in Pará, and 22:00 local standard time in Mato Grosso) and 14 GMT (11:00 local time in Pará, and 10:00 local time in Mato Grosso) daily. The data sampled in the morning are referred here as MODIS AM, and the data sampled in the afternoon are referred as MODIS PM. Data were obtained from NASA Earth Observing System Data Gateway. We analyzed satellite fire data that were up to 30 km from roads driven. Fig. 4 provides a summary of the characteristics of the fire pixels detected. In total, AVHRR detected the largest number of fires (88, 79%), followed by MODIS AM (15, 13%), and MODIS PM (9, 8%). No fire pixels were detected by MODIS PM in the study region of (a) Fire pixel Pará 4. Relations between ground- and satellite-based fire data In order to relate ground- and satellite-based fire information, these datasets must be aligned in space and time. This alignment is not straightforward because these data sources have different spatial and temporal characteristics. For example, satellite information is produced on a relatively coarse grid, while ground observations can be positioned on a relatively fine grid because they can be measured by a portable GPS. In addition, satellites observe the land surface at a relatively small number of specific times per day, while ground observations can occur at a variety of times and frequencies. The development of quantitative methods for aligning these datasets is a key challenge for interpreting and validating satellite products generally. To spatially relate ground- and satellite-based information, we first overlaid corresponding datasets in a Geographical Information System (GIS). We then defined a study area within each region according to the track (road Fire pixel Mato Grosso 2% Fire pixel Para and Mato ´ Grosso 8% 16% AVHRR 13% MODIS AM MODIS PM 59% 25% 79% 98% (b) Fire pixel - Mato Grosso Fire pixel - Pará 50 40 AVHRR 30 MODIS AM MODIS PM 20 10 Number of fires Number of fires 50 40 AVHRR 30 MODIS AM MODIS PM 20 10 0 0 11/03/2001 11/04/2001 Date 11/05/2001 07/12/2002 07/13/2002 07/14/2002 07/15/2002 Date Fig. 4. Characteristics of fire data detected by satellite in the study regions of Pará, Mato Grosso, and in both study regions combined. Rows contain: (a) total and (b) daily number of fire pixels detected using AVHRR, MODIS AM, and MODIS PM. 218 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 V Rg Track Rs Satellite data Fig. 5. Hypothetical study area. V is the observer’s field of view, R g and R s are radii that define circles representing uncertainty in the location of ground and satellite fire data, respectively. The study area is primarily defined by the track and V. Observations that intersect the perimeter defined by V are added to the study area. driven) and three spatial parameters (Fig. 5). The observer’s field of view perpendicular to the road (V) combined with the track defined the main characteristics of the study area within the region. Two additional spatial parameters R g and R s are radii that defined circles representing uncertainty in the location of ground and satellite fire data, respectively. Ground- and satellite-based fire data are said to ‘‘match’’ when their circles intersect, and are considered ‘‘nonmatches’’ otherwise. To relate ground-based non-fire data to the information from satellites, non-burning observations were located at the spatial resolution of the fire product being analyzed. Areas that were observed to not be burning from both ground and satellite observations were said to ‘‘match’’ at the resolution of the satellite product. In this study, we set R s equal to the fire product’s nominal spatial resolution. Parameters V and R g were not as straightforward to determine. The observer’s field of view can change according to many features on the landscape, such as topography. R g is difficult to determine for fires far from road. To evaluate the importance of parameters V and R g, we performed analyses where these parameters were set to fixed values (Analyses 1 and 2) and analyses where these parameters varied (Analysis 3: Sensitivity to Spatial Parameters). Because acquisition times for ground- and satellite-based fire data may not coincide, temporal relations between these datasets should be also taken into account. At one extreme, fire data could be interpreted to represent all fire activity in the region for the day. At the other extreme, fires could be assumed to be short-lived instantaneous events. In this case, fire data would represent only the fire activity at the specific detection/observation times. The reality is that fires burn for finite periods of time and typically less than one day. To account for the time differences between ground observations and satellite detections, we developed and applied time correction statistics. In all, we performed three analyses using progressively more sophisticated assumptions. The first analysis (Analysis 1) is the simplest and most transparent; it uses reasonable a priori estimates of parameter values and makes the simplistic assumption that all fire observations are valid for the entire day on which they are observed. The second analysis (Analysis 2) builds on Analysis 1 by including a statistical approach to account for the finite (< 1 day) duration of fires and the differences between ground- and satellite-based sampling times. The third analysis (Analysis 3) builds on Analysis 1 and 2 by evaluating the sensitivity of the results to different spatial-matching parameter values while accounting for the temporal considerations in Analysis 2. As discussed below, the results from these analyses are qualitatively similar. 5. Analysis 1: day-long fire length To start the analysis of these data, we began with a simple set of assumptions. We first assumed that all observations represented the fire activity within the day they were collected. Thus within a specific day, any observations that were matching in space were considered to be matching in time as well. To determine spatial matching we choose best guess values for V and R g. Because the regions we visited are mostly flat and the smoke from fires is visible from long distances, V was set to 5 km which is a conservative estimate of our typical field of view. R g was set to 1 km, which is greater than the uncertainty from the handheld GPS and not unreasonable large. Using these parameters values, corresponding groundand satellite-based fire data were compared and evaluated for matches and non-matches. Statistics were calculated using error matrices as defined in Congalton (1991) and Congalton and Green (1999), and similar to the ones used by Morisette and Khorram (2000). We used a binary classification representing fire and nonfire states (Fig. 6). The elements of the matrix quantify matches and non-matches between the reference and classified data. Element a is the number of matches for Ground data Satellite Data Ground data F NF F a b NF c d Fig. 6. Error matrix (Congalton, 1991; Congalton & Green, 1999). The categories are fire (F) and non-fire (NF). The columns are reference ground data, and the rows are classified satellite data. The elements represent sample units, where a is the number of fire matches, b is the number of satellite-detected fires that were not observed on the ground, c is the number of ground-observed fires that were detected by satellite, and d is non-fire matches. 219 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 fire. Element b is the number of detected fires that were not observed on the ground, c is the number of observed fires that were not detected and d is the number of matches for non-fires. Note that from these definitions a + b is equal to the number of all satellite fire detections, and a + c is equal to the number of all ground fire observations inside the analysis area. Using these elements, the following fire accuracies can be defined: uf ¼ a aþb ð1Þ a : aþc ð2Þ and pf ¼ In these equations, u f is the user’s accuracy for fire and p f is the producer’s accuracy for fire. u f can be interpreted as the fraction of all satellite fire observations that were verified on the ground, which is a measure of commission error for fires. p f can be interpreted as the fraction of all ground fire observations that was verified in the satellite fire data, which is a measure of omission error for fires. Analogous to the accuracies defined for fires above, user’s and producer’s accuracies for non-fire can be defined by: un ¼ d dþc ð3Þ d : dþb ð4Þ and pn ¼ In these equations, u n is the user’s accuracy for non-fire and p n is the producer’s accuracy for non-fire. u n can be interpreted as the fraction of all satellite non-fire observations that was verified on the ground. p n can be interpreted as the fraction of all ground non-fire observations that was verified in the satellite fire data. In addition to the specific accuracies above, we calculated the total and Kappa accuracies (Congalton, 1991). The total accuracy can be defined as the fraction between all fire and non-fire agreements and the total number of number of fire and non-fire observed on the ground and remotely, expressed as: T¼ aþd : aþbþcþd ð5Þ As described in Congalton (1991), Kappa is an additional summary measure of agreement that differs from total accuracy by incorporating off-diagonal elements of the error matrix as a product of the row and column marginal totals. This coefficient is always less than or equal to 1, and is a measure of the difference between the observed agreement and the agreement expected if the dataset being evaluated was built randomly. Results from our analysis are reported in terms of accuracies, which are inversely related to errors. The user’s accuracy is a measure of commission error, and the producer’s accuracy is a measure of omission error (Congalton, 1991). For example, u f equal to 0.6 shows that 60% of the satellite-detected fires were observed on the ground. This implies a commission error for fires that is equal to 0.4, or that 40% of fires detected by the product being analyzed were considered false positives. p f equal to 0.6 shows that 60% the ground-observed fires were detected by the fire product. This implies an omission error for fires that is equal to 0.4, or that 40% of the fires occurring on the ground were not detected by the fire product being analyzed. Table 1 displays the results from Analysis 1. Note that for all fire products, the number of matches for fires is small. Both AVHRR and MODIS PM had one match for fires; no fires were reported by MODIS AM. The number of cases where the products overestimated the number of fires was smaller than the number of cases where the products underestimated the number of fires. The number of detected fires that were not observed on the ground was smaller for MODIS PM than AVHRR. The number of observed fires that were not detected by satellite was similar for AVHRR and MODIS PM. The number of matches for non-fires was large for all fire products. In all cases, total accuracies were very high and exceeded 99% and Kappa was always low and less than 1.5%. This extremely high total accuracy was the result of the fact that the both ground observations and satellite products agreed that the vast majority of the land surface was not burning. Low Kappa accuracies resulted from the fact that the class with the largest agreement (non-fires) is also the dominant feature of the land surface. Fire accuracies were relatively low for all satellite products. Producer’s accuracy for fires was 0.7% for AVHRR and MODIS PM, and 0% for MODIS AM. User’s accuracy for fires was 7.7% for AVHRR and 33% for MODIS PM. We could not compute the user’s accuracy for fires for MODIS AM, because no fires were reported by that product with this set of parameter values (a + b = 0). Note that for both AVHRR and MODIS PM, the producer’s accuracy for fires was lower than user’s accuracy for fires. Table 1 Error matrices elements and fire and non-fire accuracies from Analysis 1 a b c d pf uf pn un T Kappa AVHRR MODIS AM MODIS PM 1 12 137 31823 0.7% 7.7% 99.9% 99.6% 99.5% 1.3% 0 0 138 31878 0.0% – 100.0% 99.6% 99.6% 0.0% 1 2 137 31874 0.7% 33.3% 99.9% 99.6% 99.6% 1.4% Results are based on a fixed set of parameters V = 5 km and R g = 1 km, and do not account for timing between ground observation and satellite detection. 220 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 6. Analysis 2: temporal correction In this analysis we relax the assumption that all fire observations are valid for the entire day on which they are obtained and address the issue of time differences between ground observations and satellite detections. These differences are important because fires observed by one method could potentially burn out before observation by the other, or new fires could potentially be initiated during the interval between the observations by the two methods. These events could potentially lead to spurious matches or non-matches. To address these issues, we used the data we collected from repeated ground tracks to parameterize statistical functions that describe the probability of the land surface changing states as a function of time. We then used these probability functions to modify the accuracy statistics to account for time differences. Fig. 7a presents data from repeated ground tracks on the fate of fires as a function of time between observations. Values of 1 indicate fires were identified on both ways on the track. Values of 0 indicate fires that were not observed on the repeated track. Fig. 7b presents analogous data on the fate of non-fire events (i.e. fire ignition after the first observation). In the Appendix we describe the use of these data in the derivation of estimate of the probability that the land surface changes fire state as a function of time between observations (e.g. fires burning out, and fire ignitions). These probabilities are represented by the solid curves in Fig. 7 and are expressed by the following equations: Pf ðt Þ ¼ e
kf t ð6Þ and ð7Þ Pn ðt Þ ¼ e
kn t : In these equations, P f(t) is the cumulative probability that a fire remains burning as a function of time, P n(t) is the cumulative probability that an area of land that is not burning remains not burning as a function of time t, and k f and k n are empirically determined constants. Using the method described in the Appendix, we estimated that k f = 0.471 h
1, and k n = 6.65  10
4 h
1. The value of k f implies that fires had an expected average burn length of 1.47 h. The value of k n suggests that fires had a low probability of initiating between observations, a result that is consistent with the fact that they are rare compared to non-burning conditions. Using these probability functions, we followed a method analogous to the one used in the derivation of Eqs. (1) and (2), and recalculated the fire accuracies correcting for time. Each element of the error matrix (e.g. a, b, c, d) was adjusted by the (a) State 1 1 = same state 0 = different state Pf (t) 0 0 0.1 0.2 0.3 0.4 0.5 Time (day) (b) 1 State Pn (t) 1 = same state 0 = different state 0 0 0.1 0.2 0.3 0.4 0.5 Time (day) Fig. 7. (a) Changes in fire activity as a function of time. Circles represent repeated observations plotted as a function of time between observations. A value of one represents fire/fire. A value of zero represents fire/non-fire. The solid black curve is the probability of a fire to remain burning as a function of time Eq. (6). (b) Changes in non-fire activity as a function of time. Circles represent repeated observations plotted as a function of time between observations. A value of one represents non-fire/non-fire. A value of zero represents non-fire/fire. The solid black curve is the probability of a non-fire to remain not burning as a function of time Eq. (7). The derivations of the probability curves are explained in the Appendix. 221 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 probability that the first observation was unchanged during the time interval between it and the observation by the second method. The user’s and producer’s accuracies for fire become a X Pf ðDti Þ uf ¼ i a X N X Pf ðDti Þ þ  Pn Dtj þ j i bX
N  ð8Þ Pf ðDtk Þ k and a X Pf ¼ a X i M X Pf ðDti Þ þ Pf ðDti Þ Pn ðDtm Þ þ c
M X m i q ð9Þ  Pf Dtq  In these equations, Dt is the absolute difference between the ground observation time (t g) and the satellite detection time (t s). i is an index for fires that match. Note that there are a such cases. j and k are indices for satellite-detected fires that were not observed on the ground. j is for cases in which t g > t s of which there are N such cases. k is for cases in which t g < t s of which there are b
N such cases. m and q are indices for fires observed on the ground that were not detected by satellite. m is for cases in which t g > t s; there are M such cases. q is for cases in which t g < t s; there are c
M such cases. The non-fire accuracies were recalculated accounting for time as follows: d X Pn ðDtr Þ un ¼ r d X M X Pn ðDtr Þ þ r m q d X Pn ¼ Pn ðDtm Þ þ c
M X d X Pn ðDtr Þ þ r N X r ð10Þ   Pf Dtq Pn ðDtr Þ   Pn Dtj þ j bX
N ð11Þ : Pf ðDtk Þ k In these equations, r is an index for non-fires that match of which there are d cases. The total accuracy was re-calculated correcting for time by: d a X X Pn ðDtr Þ Pf ðDti Þ þ T¼ a X i Pf ðDti Þ þ N X j   Pf Dtj þ i bX
N k r Pf ðDtk Þ þ M X m Pn ðDtm Þ þ c
M X q   Pf Dtq þ r X ð12Þ Pn ðDtr Þ d Note that the assumption that ground and satellite observations do not change within the day they were collected is equivalent to setting all Dt s equal to zero in the above equations. In this case, the probability functions presented above have values equal to one, by definition, and Eqs. (8) – (12) reduce to Eqs. (1) – (5). Table 2 Error matrices elements and fire and non-fire accuracies from Analysis 2 a b c d pf uf pn un T Kappa AVHRR MODIS AM MODIS PM 0.4 11.3 63.0 31823.0 0.6% 3.4% 99.9% 99.8% 99.8% 1.0% 0.0 0.0 138.0 31878.0 0.0% – 100.0% 99.6% 99.6% 0.0% 0.1 0.3 136.7 31874.0 0.1% 25.0% 99.9% 99.6% 99.6% 0.1% Results are based on a fixed set of parameters V = 5 km and R g = 1 km, and account for timing between ground observation and satellite detection. 222 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 Table 2 presents results calculated using the above equations. These results are qualitatively similar to the results in Analysis 1. User’s accuracies were higher than producer’s accuracy for fire, and total accuracies were very high and dominated by the large number of non-fire agreements. User’s accuracy for fire was higher for MODIS PM, and producer’s accuracies for fire were low for both AVHRR and MODIS PM. Accuracies for MODIS AM did not change when accounting for time. Quantitatively, correcting for time reduced elements a, b, and c in the error matrices for both AVHRR and MODIS PM, and led to reduced Kappa and fire accuracies compared to Analysis 1. Kappa was 1.0% for AVHRR and 0.1% for MODIS PM. User’s accuracy for fires was 3.4% for AVHRR and 25% for MODIS PM. Producer’s accuracy for fires was 0.6% for AVHRR and 0.1% for MODIS PM. The non-fire and total accuracies were largely unaffected. 7. Analysis 3: sensitivity to spatial parameters In this analysis we considered both the time differences between ground observations and satellite detections, and the sensitivity of the results to different values of the spatialmatching parameters V and R g. It is important to evaluate the effects of these parameters because their values are not straightforward to determine in all situations, and incorrect values could lead to false matches or non-matches that could affect accuracies. For example, inaccurate values of the uncertainty in position of ground observations (R g) could lead to either spurious matches to satellite pixels far away, or spurious omissions of correctly detected fires. Inappropriate values of V could lead to errors in accuracy estimates if the resulting study area included land not actually observed from the ground. Small values of V could be too restrictive and cause accurate detection to not be considered. (a) To assess the importance of these parameters, we repeated the calculations described in Analysis 2 using multiple combinations of values for parameters V and R g. In total, we evaluated 35 combinations of parameter values. Values of V were set to 1, 5, 10, 15, 20, 25 and 30 km. Values of R g were set to 1, 2, 3, 4 and 5 km. Each combination of these parameter values resulted in a new study area within the domain and new set of circles of position for ground observations (Fig. 5). These in turn led to new values in the corresponding error matrices. The accuracies calculated from these error matrices are presented in contour plots in Fig. 8. Fig. 8 illustrates that the values of spatial-matching parameters V and R g were important for determining fire accuracies. The influence of these parameters was different for different products and different accuracy statistics. The user’s accuracy for fires for AVHRR ranged from approximately 0% to 40% and depended strongly on both V and R g. (b) User's accuracy for fires - AVHRR 5 30%-40% 3 2 Rg (km) Rg (km) 4 10%-20% 0%-10% 6%-8% 4%-6% 20%-30% 4 Producer's accuracy for fires - AVHRR 5 2%-4% 0%-2% 3 2 1 1 1 5 10 15 20 25 30 1 (c) 5 10 15 20 25 30 V (km) V (km) User's accuracy for fires - MODIS PM 5 75%-100% 50%-75% Rg (km) 4 25%-50% 0%-25% 3 2 1 1 5 10 15 20 25 30 V (km) Fig. 8. Contour plots (interpolated) of fire accuracies from Analysis 3. (a) User’s and (b) producer’s accuracy for fires for AVHRR data. (c) User’s accuracy for fires from MODIS PM data. Producer’s accuracy for fires for MODIS PM, and both producer’s and user’s fire accuracies for MODIS AM were consistently low (<1%) for all combinations of V and R g. Non-fire and total accuracies for all products were consistently high (>99%), and Kappa accuracies for MODIS AM and MODIS PM were low (<1%) in all cases and are not shown here. For AVHRR, Kappa ranged from 1% to 10.6% reflecting the combinations between user’s and producer’s accuracies for fires with highest values for R g between 4 and 5 km and V between 1 and 5 km. M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 This accuracy increased for larger values of R g and decreased for larger values of V. The highest values of accuracy corresponded to values of R g between 4 and 5 km and values of V between 1 and 5 km. For AVHRR, the producer’s accuracy for fires was generally lower than the user’s accuracy and ranged from 0 –8%. The accuracy increased with increasing values of R g, but was relatively insensitive to values of V. The highest values corresponded to values of R g greater than 4 km. Unlike AVHRR, the user’s accuracy for fires for MODIS PM did not depend on R g, but like AVHRR, decreased with increasing values of V. User’s accuracy for fires for MODIS PM ranged from 25 –100% for V between 1 and 5 km and from 0– 25% for higher values of V. These accuracies are generally higher than AVHRR, but depended strongly on a small number of matches. For all products, the non-fire accuracies and total accuracies were very high (> 99%) and relatively insensitive to spatial-matching parameters. MODIS AM had no matches under all of these parameter combinations, leading to fire accuracies that were either 0% or undefined, and Kappa accuracies equal to 0%. MODIS PM had producer’s accuracy for fires and Kappa accuracies < 1% for all parameter values. Kappa accuracies for AVHRR ranged from 1% to 10.6% and depended on both V and R g, reflecting the combinations between user’s and producer’s accuracies for fires. AVHRR Kappa coefficient was highest for R g between 4 and 5 km and V between 1 and 5 km; it was equal to 6.6% for R g between 4 and 5 km and V between 25 and 30 km, and equal to 1.3% for R g between 1 and 2 km and V between 1 and 5 km. 8. Discussion This work was motivated by two main considerations. The first is the fact that fires are major disturbances in Amazonia that affect both the land surface and the atmosphere (Andreae et al., 2002; Cochrane, 2003; Nepstad et al., 1999b). The second is the fact that satellites provide the most comprehensive source of information on fire activity for the region (Dwyer et al., 2000; Li et al., 2001). Together these two considerations suggest that it is important to correctly interpret the data from satellite-based active fire products. To add to the existing methods of analyses, we developed and applied a new method to collect passive ground observations on fire and non-fire activity, and to statistically relate them to satellite-based fire data. Results from these analyses showed that total accuracies were very high (> 99%) and dominated by correct non-fire detection. In the majority of cases, fire accuracies were lower than total accuracies, and omission errors were larger than commission errors. AVHRR had lower omission errors, and MODIS had lower commission errors. In all, we performed more than 35 sets of calculations considering different assumptions. While the quantitative estimates of the accuracies differed in the different analyses, these qualitative conclusions applied in the majority of the 223 cases. Quantifying and characterizing the accuracies of these products is important because it can form the basis for accurately interpreting existing products, for developing statistical corrections for current data, and for developing new and improved products in the future (Eva & Lambin, 1998). Our results can be compared to results from other independent studies. Fire accuracies have previously been reported for MODIS, AVHRR and other products using a variety of techniques. For example in Brazil, airborne and ground-based observations in Acre, indicated that 10– 50% of fires were detected by NOAA-12 and GOES-8 in 2001 (Selhorst and Brown, 2003). GOES-8 detected two out of three controlled burns in Amazonia in 1995 (Prins et al., 1998b). Based on ground and airborne observations by IBAMA in 2001, omission errors were found to be larger than commission errors for MODIS (Schroeder, 2003). In Canada, evaluations based on burned area and corresponding AVHRR thermal data estimated that the fire detection algorithm used for MODIS had fire commission error <1% and fire omission error of 81% in 1995 (Ichoku et al., 2003). Validations using burned area indicated that omission was lower than fire commission errors in NOAA-14 fire data for boreal forests (Li et al., 2000). AVHRR-based burned area estimates for Alaska presented very high (> 99%) total, user’s and producer’s accuracies for non-burned background areas, whereas burned areas had considerably lower accuracies (Remmel & Perera, 2002). When comparing our results to these other studies, one important difference is that our fire accuracies are generally lower. To understand why the fire accuracies reported here are relatively low, one has to consider the differences between our study and previous studies. The first point to consider is that we have used a broader definition of accuracy than is used in most other studies. Our definition of accuracy is from the user’s perspective and includes all factors that can affect fire detection and lead to differences between ground- and satellite-based data. These factors include such phenomena as fires that are too small to be detected remotely, fires that occur at times different than the satellites detection, cloud coverage, and others. Previous studies have used more restrictive definitions. Prescribed burns, for example, have been typically prepared to be large and hot enough to trigger detection and to burn during satellites detection times. Assessments by airborne verification of fire pixels have been pre-conditioned on the existence of thermal anomalies that are large enough to trigger fire classification. Comparisons between satellite fire products have been limited to detectable fires and to the overpass times of the satellites. With our broader definition of accuracy it is reasonable to expect lower values because it includes more factors. One might question whether our methods contributed to the low accuracies. Our database does not represent a random sample of the Amazon region. Although random sampling has desirable statistical properties (Congalton, 1988; Congalton, 1991; Stehman & Czaplewski, 1998), it would have 224 M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 lead to very limited sample sizes in the time frame of a typical field campaign (days) because fires are rare. Our field work was specifically designed to collect a large and efficient sample of fires observed on the ground. Data were collected during the dry season in areas located on or near the Arc of Deforestation where most of fires in Amazonia occur. Roads provided a simple and efficient method to cover large areas and increase the likelihood of observing active fires and enabled the inclusion of multiple land cover and land use types. The presence of roads, while implicated in fire activity, is not known to impede fire detection per se. Our method does depend on spatial-matching parameters that are not exactly known in all cases. Too strict of an implementation could conceivably lead to excessively low accuracies. We do not believe this to be the case. For example, one could be generous and ignore the requirement for spatial and temporal matching entirely, and require simply that any fire pixels that occur inside the study regions be considered to match ground observations. In this case, producer’s fire accuracies elevate to only 6% for MODIS PM, 10% for MODIS AM and 62% for AVHRR. The user’s fire accuracies trivially elevate to 100% simply because there were less fire pixels than fires observed on the ground for all sensors. Moreover, to the extent these accuracies are elevated by relaxing the spatial and temporal matching criteria, the increases are more likely to be caused by artificial agreement than true matching. Simply requiring that the observations were on the same day reduces AVHRR producer’s accuracy from 62% to 42%, and user’s accuracy from 100% to 68%. Finally, concentrating the analyses near the roads where our position estimates are the best (V = 1 km) does not substantially increase the accuracies as one might expect if position errors are to blame. The accuracies we calculated also accounted for the impact of different sampling time between ground observations and satellite detections. The results demonstrated that accounting for differences between observation and detection times lowered fire accuracies for both instruments. To understand this result, it is important to begin by noting that any method that aims to correct for time differences between observations has to account for the possibility that the surface changes states between observation times. For example, fires can potentially burn out or be initiated during the interval. If the probabilities of these events were equal, their effects would offset and cancel in the calculation of the accuracies. However, if they were not equal, correcting for time could affect the accuracy calculations. Our data indicated that these probabilities are not equal. Fires have a burn length that is typically on the order of hours, which implies that observations of fires are valid for only relatively short periods of time. Areas that were not burning, on the other hand, were likely to remain in this state for relatively long periods because fires are rare overall. With this asymmetry, fire accuracies should generally be reduced when accounting for sampling time differences because the weight on matches commonly decrease in time more rapidly than the weight on non-matches. We next evaluated the effects of several non-methodological factors that could have caused low accuracies. In particular we estimated the impact of fire size, fire type, and cloud coverage on the accuracies of the products. One limitation to perform these analyses is the small sample size we have managed to obtain. While 162 observed fire events is a large number in some contexts, it is a small number when one tries to partition multiple effects. With this caveat in mind, we searched for trends in the relations between accuracies and complicating factors for fire detection. Fire size is important to evaluate as a limiting factor for fire detection because satellite thermal sensors may not identify small (low energy) fires (Boles & Verbyla, 2000; Kasischke et al., 2003; Setzer & Malingreau, 1996), and because it is not generally well understood how many small fires there are. We estimated the probability of obtaining our results under the null hypothesis that fire size was not a factor. We aggregated the ground data to two binomial classes, small and non-small, and applied the binomial theorem. The data from the field aggregated in this way totaled 28% small and 72% non-small fires. Under the null hypothesis that size was not a factor, this gave an estimate of the binomial parameter p, the probability of detecting a small fire, of 0.28. The binomial parameter n, the number of trials, was set equal to the number of matches. For AVHRR, the maximum number of matches was 10 (Analysis 3), none of which were small. Given these parameters, the probability of detecting 0 small fires in a sample of 10 is less than 5%, implying that we should reject the null hypothesis and consider fire size as a significant factor. A direct estimate of the expected omission error due to fire size could be calculated if one knew the size thresholds of the fire products and the area actively burning at the overpass times. The fire front size threshold for AVHRR has been estimated to be 50 m (Setzer & Malingreau, 1996). For MODIS, an estimate of the minimum detectable fire size is 100 m2 (NASA, 2004). Because our method for data collection was not constrained to overpass times, our data do not provide direct estimates of the actively burning area at the time of satellite overpass in most cases. However, if one assumes that our estimates of fire size are representative of the area actively burning at the overpass times, then the small fires we observed are not likely to have been detected, and the expected omission error is 28% (the proportion of the small fires in the ground data) for both fire products. While the expected omission error may be somewhat larger if the actively burning area were consistently smaller than our size estimates, we conclude that fire size is an important factor but is unlikely to account for all observed omission error. The next factor we analyzed was land cover. Land cover is important to evaluate as a potentially complicating factor because different land covers have different properties that can affect fire frequency and detection, such as fuels, albedo, and land-use activities (Eva & Lambin, 1998; Li et M.F. Cardoso et al. / Remote Sensing of Environment 96 (2005) 212 – 227 al., 2003). To evaluate land cover, we compared two frequency distributions of land cover types on which fires occurred: one for all ground observations (Fig. 2) and the second for fire matches. For the two important categories of fires on pastures and woody savannas, the values of these distributions were nearly equal, implying no bias. For the remaining categories there was some evidence of bias, however. Eighteen percent of the fires observed on the ground were in the three categories of savannas or grasslands, forests, and croplands, but none of the matches were in these categories. In addition, one third of the fires observed on the ground were classified as ‘‘other’’; for matches, this fraction was higher and was 55%. These categories where there were biases tend to be either small or very heterogeneous and will require further studies to interpret. Cloud coverage is another potentially important factor. Clouds can physically mask the passive detection of thermal anomalies by satellites leading to omission errors (Boles & Verbyla, 2000; Ichoku et al., 2003). They can also create glare, which can appear as artificial thermal anomalies and lead to false positives (Li et al., 2000). To evaluate the impact of clouds on our results, we tested the null hypothesis that cloud coverage and fire occurrence were not related. For AVHRR, we used state-level daily cloud-cover data from CPTEC. For MODIS PM, we used scene-level cloud information from the MODIS product. Considering values from both sensors with parameter values that led to the maximum number of matches, the coefficient of correlation between cloud cover and producer’s accuracy was equal to 0.47 with 12 degrees of freedom. Between cloud cover and user’s accuracy the correlation coefficient was equal to 0.31 with 3 degrees of freedom. Statistically testing these correlation coefficients at a 5% level of significance (Khazanie, 1996), we cannot reject the null hypothesis. Thus, despite of the expectation of a significant cloud effect, we did not find one in this study presumably because of our small sample size or the coarse-resolution cloud data used. Assessment studies such as this one can be used to improve the interpretation of satellite data and potentially inform the development of new algorithms and sensors. For example, our results show that limited remote sensing sampling frequency and small fire size contributed to low accuracies of fire detection. Future products should be developed to sample at greater frequency and lower energy thresholds to detect a greater fraction of the fires on the landscape. The challenge for increasing frequency could potentially be met by geostationary platforms or more rapidly orbiting sensors. The challenge for reducing the energy threshold could potentially be met by higher spatial resolution. The many efforts that are under way to meet these challenges by NASA and other agencies should be continued and even expanded. The key to this study has been the relatively large set of ground-based data without which such assessments could not be performed. To build on the results from this study, a larger investment in ground-based data on 225 fires and the statistical analyses that relate them to satellite observations is needed. If this investment were made it would lead to more accurate fire products, that in turn would enable significant advances in a diverse set of environmental sciences, and in atmospheric studies in particular. Acknowledgments We gratefully acknowledge the generous support of the National Aeronautics and Space Administration, the LBAECO program, the UNH/NASA Joint Center for Earth Sciences, and the UNH Graduate School. We also thank the comments, suggestions, and technical knowledge given by: Yoram Kaufman, Charles Ichoku, Vincent Salomonson, Alberto Setzer, Pedro Lagden, Raffi Simanoglu, Michael Keller, Ane Alencar, Michael Routhier, Nicolau Priante, Russ Congalton, and George Vourlitis. Appendix A. Derivation of the equations for the temporal correction Observing fires on a specific location at the land surface can be seen as a binomial experiment in which the outcome is either one of the two possibilities: burning or not burning. On repeated tracks, each point on the land surface has two observations separated by a period of time t. These pairs of observations can be categorized into two types: same state, and different state. We define the probability of observing the land surface in the same state after a period of time t as P(t), and the probability of observing the land surface in a different state after a period of time t is 1
P(t). Assuming that the change in state is a binomial random variable, we searched for probability functions P(t) that maximized the following log-likelihood (l) function (Edwards, 1992): X l¼ ð lnPðti Þ þ lnðl
Pðti ÞÞÞ ðA1Þ i where i is a index for each pair of observations for each location. Because the probability of fires changing state is potentially different than the probability of non-fires changing state, there are actually two binomial experiments: one for transitions fire/fire and fire/non-fire, the other for non-fire/non-fire and non-fire/fire. Let P f(t) apply to the first case, and P n(t) apply to the second. We used the data illustrated in Fig. 7 to parameterize simple forms of these functions. Our approach consisted of a large number of iterations (> 10,000) of the Metropolis simulated annealing algorithm (Metropolis et al., 1953; Press et al., 1992) for each case. The one-parameter exponential functional form (Eqs. (6) and (7)) yielded the best results (highest likelihood); the results are plotted in Fig. 7. More flexible 2parametrer models (e.g. Gaussian) were attempted, but did not yield improved results. 226 M.F. 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