# Spatial Distribution of Forest Fire Emissions: A Case Study in Three Mexican Exoregions
## 2 Materials and Methods
### Variables for Estimating Emissions
#### 2.2.2 Burning Efficiency  
The burning efficiency corresponds to the fraction of the biomass or fuel consumed by the fire in a specific area; Mexican studies have used default values from general tables, or [19] have used information from the CONSUME model, which was designed specifically for the USA [19]. Here, we propose a Random Forest Regression (RFR) model, which has been extensively used in the last years for satellite classification, including forest fire studies [32]. This used the field data of fuel loads and their consumption, from 67 prescribed burnings in 2006 and 2007 (in 200 m\({}^{2}\) areas) in the following types of vegetation: oak, oak-pine, pine, pine-oak, cloud forest, shrubland, dry tropical forest, tropical forest, and tropical rainforest (data supplied by Dr. [PERSON], National Institute of Forestry, Agriculture and Livestock Research [INIFAP]).  
The burning efficiency was calculated with a Random Forest in the regression mode. The model was implemented in the R programming language. The variables used to create the model included fuel, weather conditions, and topography, all of which affect fire behavior. The following variables were considered: (a) the above-mentioned biomass carbon map, (b) a land use and vegetation map (1:250,000) produced by INEGI, (c) land cover maps for 2005 and 2010 produced with MODIS data at a 250 m spatial resolution [33], (d) Vegetation Continuous Field products (MOD44), downloaded from the MODIS web page, and (e) a time series of the Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) at a 250 m spatial resolution in a composite of 16 days. We used the difference between the vegetation indices before and after each fire. In this case, both vegetation indices were used in order to select the best option. The weather conditions were obtained through a 100 h fuel moisture model, which used MODIS and Tropical Rainfall Measuring Mission (TRMM) data [34] for the temperature and precipitation and which applied the Tetens-Murray equation [35]. The model uses the flow of moisture into the types of fuels from one day to another [34]. The topography was expressed through a digital elevation model in terms of three indicators: altitude, slope, and aspect.  
The final RFR model consisted of 1000 trees. The individual tree predictions were then aggregated using the mean statistic. The coordinates of 67 areas of prescribed burning were characterized with 37 variables obtained from the above-mentioned cartographic and satellite products, in accordance with the date of the burning. The RFR model was assessed by means of the out-of-bag (OOB) estimations of accuracy (e.g., the correlation between the observed and predicted values), and the importance of the explanatory variables for the RFR model. In each run of the algorithm, the indicators were changed or removed depending on the importance of their participation in the RFR model. The method is described with more detail in [36]. The resulting RFR model was tested on the burned areas identified in March 2006.