# UAV Multispectral Imagery Can Complement Satellite Data for Monitoring Forest Health
## 2 Methods
### Statistical Analysis  
Due to the revisit time of the RapidEye satellites and significant cloud cover in the study area, there were several instances where satellite imagery was not available for days where UAV and ground data had been acquired. As a result, the experimental dataset can be considered as a multivariate time series dataset that contains missing values for each observer on certain dates. Analysis of datasets with these characteristics is well studied with considerable research generated from diverse fields such as econometrics [66] and hydrology [67]. Numerous approaches have been developed to estimate the missing time series values to provide a complete dataset for subsequent analysis. All of these methods rely on developing statistical models between variables in the time series data and an ability to model the longitudinal component of the dataset through time. Methods to estimate missing values include multivariate imputation via chained equations [68], regression-based methods [69], and non-parametric, ensemble methods such as Random Forests [70]. Following an examination of several available methods, imputation based on the Random Forest algorithm via the MissForest R package [71] was selected for use in this study. A complete time series data set was produced with an observation of ground, UAV, and satellite imagery at every acquisition date. This enabled the time series datasets to be plotted through time and a direct exploration of the relationships between all three datasets to be made. The relationship between UAV and satellite derived spectral indices was explored using regression models. The purpose of the models was to understand the relationship between the two different sensor platforms and to develop predictive models that can be useful for extrapolating information on tree stress derived from the UAV data to larger areas. Ordinary least squares (OLS) was used to produce an initial model. Initial model diagnostic plots were carefully checked for evidence of non-compliance with the assumptions of linear regression analysis and a Durbin-Watson test was used to check for autocorrelation in the model residuals. No evidence of non-compliance was found and so model fitting proceeded using OLS. Univariate models were developed with UAV spectral index as the response and satellite spectral index as the predictor variable. Models up to and including the fifth order polynomial were fitted and the best model for each spectral index was selected based on the Akaike information criterion (AIC) outputted from the R statistical software (version 3.4.2) [72]. Random Forest (RF) regression models [70] were used to examine the capacity of spectral indices extracted from both platforms to detect stress symptoms (canopy discolouration) measured in the field. RF regression utilises ensemble decision tree classifiers, based on bootstrap aggregated sampling (bagging), to construct many individual decision trees, from which a final class assignment is determined [70]. RF has previously been used to successfully model several plantation forest variables using remotely sensed data [6; 7; 73; 74]. The RF algorithm constructs decision trees using a bootstrap sample from the available training data, with the remaining data assigned as out-of-bag (OOB) samples. At each node, a random subset of predictor variables is tested to partition the observation data into increasingly homogeneous subsets. The node-splitting variable selected from the variable subset is that which resulted in the greatest increase in data purity (variance or Gini) before and after the tree node split [75]. The OOB sample data are used to compute accuracies and error rates averaged over all predictions, and estimate variable importance [75; 76]. RF provides methods to estimate the importance of each predictor variable in the model. The mean decrease in accuracy (MDA) importance measure is calculated as the normalised difference between OOB accuracy of the original observations to randomly permuted variables [75; 76; 77].