# Development of a GPS Forest Signal Absorption Coefficient Index
###### Abstract  
In this paper GPS (Global Positioning System)-based methods to measure L-band GPS Signal-to-Noise ratios (SNRs) through different forest canopy conditions are presented. Hemispherical sky-oriented photos (HSOPs) along with GPS receivers are used. Simultaneous GPS observations are collected with one receiver in the open and three inside a forest. Comparing the GPS SNRs observed in the forest to those observed in the open allows for a rapid determination of signal loss. This study includes data from 15 forests and includes two forests with inter-seasonal data. The Signal-to-Noise Ratio Atmospheric Model, Canopy Closure Predictive Model (CCPM), Signal-to-Noise Ratio Forest Index Model (SFIM), and Simplified Signal-to-Noise Ratio Forest Index Model (SSFIM) are presented, along with their corresponding adjusted \(R^{2}\) and Root Mean Square Error (RMSE). As predicted by the CCPM, signals are influenced greatly by the angle of the GPS from the horizon and canopy closure. The results support the use of the CCPM for individual forests but suggest that an initial calibration is needed for a location and time of year due to different absorption characteristics. The results of the SFIM and SSFIM provide an understanding of how different forests attenuate signals and insights into the factors that influence signal absorption.  
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waves in a particular forest stand. However, ecologists have long recognized that forest structure is far from uniform.  
In the literature, there are many different techniques used to model signal loss through forest structure. For the research presented here, the most relevant model is the Canopy Closure Predictive Model (CCPM) described in [14]. The CCPM model consists of capturing two primary components: one based on the atmospheric attenuation, and the second based on attenuation by the forest canopy based on Beer's Law. When considering Beer's Law, if we consider the forest as a uniform slab of vegetation, the absorption of a signal exhibits a linear dependence between the signal propagation path length through the media, an absorption coefficient, and the concentration of medium yielding:  
\[L=\alpha dc \tag{1}\]  
where \(L\) is attenuation, \(d\) is the path length, \(c\) is the concentration of the media, and \(\alpha\) is an absorption coefficient [1]. The CCPM was developed for a managed pine forest and the Beer's Law component consists of the product of the sine of the zenith angle and the canopy closure value. The CCPM makes the assumption that the concentration and absorption parameters of Beer's Law can be combined into just the canopy closure (CC) of the forest, where CC is the percent of pixels classified as canopy in a window of interest inside a hemispherical sky-oriented photo (HSOP).  
As such, there is a need to determine the concentration of the forest through the path of signal propagation [5]. Our hypothesis is that while zenith angle may be the dominant factor in attenuation, other independent parameters leading to variations in signal strength will be observable, and that the inclusion of HSOP-derived CC data at 1-degree zenith angles can precisely measure the degree to which GPS signals from individual SVs are affected by forest canopy.  
The goal of this study is to estimate the values of L1-band GPS signals in multiple diverse forests using observations from GPS and CC values derived from HSOPs. The objectives are to (1) develop an atmospheric attenuation model for GPS SNR values, (2) develop an overall canopy closure predictive model (CCPM) independent of study site, and (3) create an adjustment index for each study site that can be applied to the CCPM in order to allow for refinement of predictions based on forest absorption characteristics.