## 2 Materials and Methods
### Tree Cover Probability  
A binomial logistic regression model was used to calculate the probability of a 5 m SPOT5 pixel containing tree cover. The explanatory variables tested were: a climatological variable; an indicator of brightness; an indicator of greenness; variation in brightness and greenness over time; and interactions between variables. The response variable was the presence or absence of tree cover. The model was trained using 25,930 image-interpreted points (Figure 3B), which were selected using a stratified  
Figure 3: The distribution of training and validation datasets used in the development of the New South Wales (NSW) maps. (**A**) The location of images across NSW and Queensland (QLD) used to train the SPOT5 FPC model using Landsat FPC data; (**B**) Sites used to train the probability model interpreted from high resolution (0.5–2.5 m) imagery; (**C**) Sites of field measured FPC, used to validate the SPOT5 FPC map; (**D**) The sample of airborne lidar taken from the available lidar data used to validate the binary tree cover map; (**E**) Pixels interpreted from high resolution (2.5 m) imagery used to validate the binary tree cover map, which were stratified by catchment. random sampling method. Stratification was based on thirteen major catchments exhibiting a variety of terrain and vegetation types, as well as the Landsat derived FPC. Each point was visually assessed against high resolution imagery (0.5-2.5 m pixels), and if it was located on a mixed pixel it was manually shifted to the nearest 3 by 3 pixel window (15 m by 15 m) that featured a complete cover of its stratified attribute. Any points that were obscured by cloud, cloud shadow or water in at least one image were removed. A combination of brightness and greenness indicators were selected as explanatory variables as they had previously been shown to relate to soil, grass and tree cover features [49]. Red reflectance was used as the indicator of brightness, and FPC was used as an indicator of greenness [49]. The multi-temporal variables were calculated from the four observations for each pixel, and were used to separate persistent tree cover from fluctuating ground cover. Using robust regression to exclude outliers, linear models were fitted to the red reflectance and FPC time series. The fitted value at the midpoint of each time series was used in the modelling. The red reflectance was transformed by adding 0.001 and taking the natural logarithm to remove the skewness and improve the normality of the distribution [36]. Overstorey vegetation tends to have low variation in red reflectance and FPC over time. As such, the variation in FPC and red reflectance, from the fitted line, expressed as the ratio of the fitted value at the midpoint was also used. The variation was calculated as the weighted mean residual of the points from the fitted line, where the weights were those returned from the robust regression. The other parameter considered for the probability model was vapour pressure deficit (VPD), which was previously used to model FPC [36]. VPD varies spatially and is related to vegetation foliage characteristics. In Australia, smaller needle-like foliage tends to be found in areas with high VPD, while larger broad-leaf foliage tends to be found in areas with low VPD. The overstorey vegetation in high VPD areas in the study area also tends to have lower FPC and brighter background reflectance than that in low VPD areas. To allow for these relationships we included interaction terms between the red reflectance and FPC, red reflectance and VPD, and FPC and VPD. The VPD data were obtained from a gridded dataset, interpolated from a network of weather stations [50]. A variety of models was assessed, using the kappa statistic to determine how well they classified the training data, where a pixel was classified as tree cover when its probability was at least 50%. The best model, which achieved a kappa statistic of 0.81, used the following explanatory variables: FPC, red reflectance, VPD, and variation in FPC.