## 2 Materials and Methods
### Methods
#### 2.7.2. Canopy Structure and Area Solar Radiation Metrics
The determination of the extinction coefficient requires direct measurement of \(LAI\) over consecutive seasons, as there is significant atmospheric and canopy structural variability in the determination of its value [37]. A meta-study of canopy light extinction showed significant intra-annual negative correlations between extinction coefficient (K) and seasonal changes in \(LAI\) in natural ecosystems [38]. In another study, a K value of 0.48 and \(LAI\) of 6.2 are thresholds at which 95% of incident solar radiation is intercepted by the forest canopy in a stand of _Pseudotsuga menziesii_[33], a dominant upper strata canopy species in the Klamath Mixed Conifer forest-type. Figure 5: Classified optical \(LAI\) map centered on the study area landscape in 2 m resolution (Source: DigitalGlobe). The _LAI_ variable defines the number of equivalent layers of leaves relative to a unit of ground area, but the fraction of _PAR_ that is absorbed (_fPAR_) measures the proportion of available radiation in the photosynthetically active wavelengths that are absorbed by a canopy [39]. The basis for calculating _fPAR_ using an exponential function is based on [PERSON]'s law:  
\[fPAR=P\infty[1-\exp(-LAI)] \tag{5}\]  
where _P_\(\infty\) is the asymptotically limiting value of _PAR_ absorption for an infinitely thick canopy and was set to 0.94, with the assumption made that the canopy leaves are randomly distributed [24]. This assumption was made in the _LAI_ calculation for this study as well. Both parameters are used for evaluating surface photosynthesis, evapotranspiration and primary productivity for the analysis of ecosystem functions such as terrestrial energy, carbon, water cycle processes and the biogeochemistry of vegetation [39]. In addition to _LAI_ derived from satellite imagery, insolation and canopy metrics were derived from LiDAR surface and point-cloud data to measure localized strata variables effecting solar radiation in the understory. 1. Canopy Height (CHM) in meters was determined from the LiDAR digital surface model (DSM) and the first returns data at 1 m resolution. It was utilized to derive area incident solar radiation adjusted for topography as well as to provide data required for sample plot selection by using the average values at 30 m resolution matched to the gridded canopy metrics raster [40; 41; 42]. 2. Area Solar Radiation (_ASR_) in \(\mathrm{WH/m^{2}}\) was derived using the sum of 12 monthly values (2015 calendar year) for the analysis extent and resampled to 30 m resolution. _ASR_ was modeled in ArcGIS using the sum of the LiDAR bare earth surface product (DEM) and the canopy height model (CHM) product as the topographic parameter, including topographic elevation data for the entire watershed used as the horizon parameters for the _ASR_ model equations [43; 44]. Radiation parameters included diffuse model type (radiation flux varied with zenith angle in a non-uniform overcast sky condition), diffuse proportion (proportion of global normal radiation flux that is diffuse by month), and atmospheric transmissivity (fraction of radiation that passes through the atmosphere by month). Input parameters were derived from meteorological data acquired from a field station within close proximity to the analysis extent in 2015. _ASR_ is a term used to describe irradiation, or the sum of downward area irradiance per unit area over a stated time interval expressed in \(\mathrm{WH/m^{2}}\). Irradiance is the instantaneous density of solar radiation on a unit area expressed in \(\mathrm{W/m^{2}}\). It comprises a global radiation value (_Global_\({}_{tot}\)), or the sum of direct (_Dir_\({}_{tot}\)) and diffuse (_Dir_\({}_{tot}\)) radiation of all sun map and sky map sectors as shown in the solar model equation [43; 44]: \[ASR=Global_{tot}=Dir_{tot}+Dif_{tot}\] (6) _Dir_\({}_{tot}\) for a given location is the sum of the direct insolation (_Dir_\({}_{\theta,\alpha}\)) from all sun map sectors.