# Development of a GPS Forest Signal Absorption Coefficient Index
## 2 Materials and Methods
### Hemispherical Sky-Oriented Photos and Image Processing  
A single HSOP image was taken at each GPS receiver setup location in each forest with the camera directed straight up, and the top of the photo oriented north. The resulting photos are circular, with zenith in the center of the image and the horizon on the outer edge. An example is shown in Figure 2. The camera and lens combination used to collect these images consisted of an IPIX fisheye lens mounted on a Coolpix P6000 Nikon camera (Nikon Ltd., Tokyo, Japan).  
Figure 3 shows the frequency distribution of the number of GPS SV observations recorded during the spring data collect at West Point, NY.  
Figure 2: A hemispherical sky-oriented photo taken during the spring data collection at West Point, New York, with the global positioning system (GPS) satellite vehicle positions (red circles) plotted inside the image.  
Image processing of the collected HSOP images was conducted using ArcGIS software (Environmental Systems Research Institute (ESRI), CA, USA). ArcGIS allows for the establishment of spatial reference, the delineation of each photo into one-degree rings associated with each angle from the horizon, and the ability to convert each image into a binary, black and white, image, where the sky is white and forest structure black. Tools within ArcGIS allow for the isolation of the blue channel of each HSOP for the creation of the binary image. This is beneficial because the blue channel is better suited to distinguish clouds and sun glare [16; 17; 18; 19; 20; 21] than the red and green channels. When creating the binary image, the Natural Breaks function was used to determine appropriate threshold values. Additionally, each histogram and binary image was visually inspected for accuracy. During this process, each Red, Green and Blue (RGB)histogram and corresponding open-sky threshold values were examined to ensure there were no abnormalities. The resulting binary images were then compared to the original images to ensure proper classification. Figures 4 and 5 are the resulting binary HSOPs from the Intensive Management Practice Assessment Center (IMPAC), a managed forest in Gainesville, Florida, during needle minimum and needle maximum. The three plots in each of these forests were unique in that the species and spacing of the trees were the same. The difference between the plots resulted in different fertilization processes resulting in different DBH and tree heights between the plots.  
During image processing, the percentage of pixels classified as canopy at specific angles from the horizon inside each specific forest was calculated. These CC values serve as the concentration of forest media at specific angles inside the forest. Instrumental to our modeling process is the calculation of CC fractions for each angle from zenith. This was conducted using the zonal statistics tool within ArcGIS for each 1\({}^{\circ}\) ring, as shown in Figure 6. Using the zonal statistics tool, the corresponding CC value for each SV location was extracted for use in statistical modeling.  
Figure 3: The frequency distribution of GPS observations at different angles from the horizon during the data collection in the spring at West Point, New York.  
Figure 4: The resulting binary Hemispherical Sky-Oriented Photos (HSOPs) taken at the Intensive Management Practice Assessment Center managed forest taken during the needle minimum period with the GPS satellite vehicle positions (red circles) plotted inside the image.  
Figure 5: The resulting binary images taken at the Intensive Management Practice Assessment Center managed forest taken during the needle maximum period with the GPS satellite vehicle positions (red circles) plotted inside the image.  
Figure 6: The \(1^{\circ}\)-ringed hemispherical sky-oriented photo with a gray scale range of values associated with the canopy closure values. Dark colored rings indicate a high level of canopy closure and white rings indicate less forest media.