# Spatial Distribution of Forest Fire Emissions: A Case Study in Three Mexican Exoregions
## 3 Results
### Variables to Estimate Emissions
#### 3.1.2 Burning Efficiency  
For the Random Forest Regression (RFR) model, the OOB estimate yielded a correlation of 0.73 between the observed and predicted values, an absolute error of 0.079, and an RMSE (Root Mean Square Error) of 0.009. The model explained 49% of the variance in the data. The variables with a higher importance in the RFR model were (Figure 4): the vegetation type, land cover, biomass, VCF (Vegetation Continuous Field) tree cover, and 100 h fuel moisture; of these variables, the fuel moisture was the most dynamic variable (daily) and had a coarser spatial resolution. The least important variables were the VCF short vegetation cover, VCF bare ground cover and EVI; this last variable is dynamic, because it changes throughout the year.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Biomass** & **Biomass NPP** & **Biomass NPP** & **Biomass NPP** & **Biomass NPP** \\  & **Alianza map** & **2011** & **2012** & **2013** & **2014** \\ \hline Biomass Alianza map & 1.0000 & 0.8174 & 0.8320 & 0.8180 & 0.8176 \\ Biomass NPP 2011 & 0.8174 & 1.0000 & 0.9956 & 0.9950 & 0.9608 \\ Biomass NPP 2012 & 0.8320 & 0.9956 & 1.0000 & 0.9949 & 0.9641 \\ Biomass NPP 2013 & 0.8180 & 0.9950 & 0.9949 & 1.0000 & 0.9639 \\ Biomass NPP 2014 & 0.8176 & 0.9608 & 0.9641 & 0.9639 & 1.0000 \\ \hline \end{tabular}  
* The correlation was calculated using ENVI (Environment for Visualizing Images) software. NPP: Net Primary Productivity.  
\end{table}
Table 1: Biomass map and biomass from the NPP correlation 1.  
Figure 3: Annual updated biomass. A: 2011; B: 2012; C: 2013; D: 2014.  
The variables had three different spatial-temporal characteristics: (a) Permanent or referential, such as the field data on the vegetation type, complemented with the map of the land use and vegetation, and the biomass data from a map [26]. (b) The annual variation, such as the land cover (2005), tree cover percentage, no tree cover percentage, and without vegetation cover percentage coming from VCF. (c) The intra-annual variation, which is associated with the relative differences in EVI of 16-day composites; the difference was calculated from one composite before and one after the fire (defined by the burned area date), and the 100 h fuel moisture for a specific date. These characteristics may be an influence on the burning efficiency behavior.  
We used prediction intervals calculated by Quantile Regression Forest [49], as an evaluation element. The prediction intervals were the widest for tropical forests (maximum \(\pm\)0.2), and the narrowest for temperate forests (minimum \(\pm\)0.04). Temperate forests had the highest values of burning efficiency and a higher correlation than tropical forests. Table 2 lists the burning efficiency estimated by RFR model applied to burned areas of March, 2006, in contrast to the data presented by CONAFOR [50]. These estimates range from 0.37 in dry tropical forests to 0.61 in oak forests. The higher values correspond to oak vegetation, followed by tropical vegetation. The lowest estimates correspond to pine vegetation. There were not large variations between the estimates of the same vegetation type; in all cases the differences between the maximum and minimum values were smaller than 0.19. The values estimated by the RFR model were consistently lower than those of CONAFOR. The estimates most similar to those from CONAFOR were registered in tropical forests, and those that were most different were in dry tropical forests.