# Forecasting the Impacts of Prescribed Fires
## 2 Methodology
### Burn Activity Forecasting
#### 2.1.1 Burn Days  
The response variable is data labeled with two classes-burn day or no-burn day-coded as a binary variable. When the total burn area in a county on a particular day was greater than 30 ha, it was considered to be a burn day in that county and it was assigned a value of 1; otherwise it was a no-burn day and was given a value of 0. The 30-ha limit was determined from the distribution of daily total burn areas by county and is approximately equal to the mean minus one standard deviation. A set of 21 variables from the fire danger rating data were selected as predictor variables. A detailed description of these variables can be found in Appendix A. Missing values, most commonly for wind speed, were replaced by the average of the available values in the dataset for that variable. Data for the years 2010-2014 were used to train the model. Later, the model was evaluated using the data for January-April 2015. The Classification and Regression Tree (CART) is a classification method that constructs a decision tree model using historical training samples which can then be used to classify new, unseen data. For the details of the algorithm, please see Appendix B. The CART classifier is a binary decision tree, which is constructed by splitting the learning data into two branches, recursively. An example of a decision tree generated by CART and a graphical representation of the decision boundary are shown in Figures 13 and 14, respectively. CART selects the best predictors on its own, prioritizes them and discards the least important ones. CART is non-parametric, i.e., it does not make any assumptions about the statistical distribution of variables, unlike linear regression which has two parameters--slope and intercept. CART can handle outliers that affect other models such as linear regression. The decision tree classifier model was implemented in python programming language using the Scikit-learn library ([PERSON], 2012). Scikit-learn uses an optimized version of the CART algorithm. Information gain between two nodes is selected as splitting criteria for growing the tree. This is calculated using information entropy between the nodes as shown in Figure 15. The predictor variable which gives the highest information gain is placed at the root node and this procedure continues recursively to grow the tree. If we let the decision tree grow until all of the samples are classified, then it may overfit the training data. An overfitted decision tree tends to address noise instead of the underlying relationship. Hence, we needed to specify and limit the depth to which the tree could grow. This is called _\"pruning\"_ the tree. The optimal depth was determined by measuring the model's performance on the evaluation dataset. Performance evaluation will be described in Section 2.4 below. The decision tree model was trained with a range of depths, and the shallowest tree with the best forecasting performance was selected. Because of pruning, some of the 21 variables included in training may have been excluded from the decision tree model. Two types of models were trained: a statewide model and county-specific models. In the statewide model, one decision tree model was trained to forecast PB activity for the entire state. To train the model, burn permit data of the counties in which the 18 fire weather stations reside were used. A single training dataset was created by concatenating the fire weather data from the 18 stations and the corresponding burn permit data. A single decision tree was then trained with this dataset. The depth of the tree was optimized by the pruning methodology discussed above. Once the decision tree model was trained, every county in Georgia (159 counties in total) was assigned a station near to it. Forecast fire danger data from each assigned station was used to forecast PB activity for the corresponding county. In the county-specific models, every county had its own optimal decision tree for forecasting PB activity.