## 2 Materials and Methods
### Methods
#### 2.7.2. Canopy Structure and Area Solar Radiation Metrics
Direct insolation from the sun map sector (_Dir_\({}_{\theta,\alpha}\)) with a centroid at zenith angle (\(\theta\)) and azimuth angle (\(\alpha\)) is calculated using the following equation: \[Dir_{\theta,\alpha}=S_{Const}\times\beta^{m(\theta)}\times SunDur_{\theta, \alpha}\times SunGap_{\theta,\alpha}\times\cos(AngIn_{\theta,\alpha})\] (7) where: \(\bullet\)\(S_{Const}\) is the solar flux outside the atmosphere at the mean earth-sun distance, known as solar constant. The solar constant used in the analysis is 1367 \(\mathrm{W/m^{2}}\). This is consistent with the World Radiation Center (WRC) solar constant; \(\bullet\)\(\beta\) is the transmissivity of the atmosphere (averaged over all wavelengths) for the shortest path (in the direction of the zenith); \(\bullet\)\(m(\theta)\) is the relative optical path length, measured as a proportion relative to the zenith path length;\(SunDur_{\Theta,\alpha}\) is the time duration represented by the sky sector. For most sectors, it is equal to the day interval (for example, a month) multiplied by the hour interval (for example, a half hour). For partial sectors (near the horizon), the duration is calculated using spherical geometry;
* \(SunGap_{\Theta,\alpha}\) is the gap fraction for the sun map sector;
* \(AngIn_{\Theta,\alpha}\) the angle of incidence between the centroid of the sky sector and the axis normal to the surface [43, 44]. Total diffuse solar radiation for the location (\(Dif_{tot}\)) is calculated as the sum of the diffuse solar radiation (\(Dif\)) from all the sky map sectors. The diffuse radiation at its centroid (\(Dif\)) is calculated, integrated over the input time interval, and corrected by the gap fraction and angle of incidence using the following equation: \[Dif_{\Theta,\alpha}=R_{glb}\times P_{dif}\times Dur\times SkyGap_{\Theta, \alpha}\times Weight_{\Theta,\alpha}\times\cos(AngIn_{\Theta,\alpha})\] (8) where: \(\bullet\)\(R_{glb}\) is the global normal radiation; \(\bullet\)\(P_{dif}\) is the proportion of global normal radiation flux that is diffused; \(\bullet\)\(Dur\) is the time interval for analysis; \(\bullet\)\(SkyGap_{\Theta,\alpha}\) is the gap fraction (proportion of visible sky) for the sky sector; \(\bullet\)\(Weight_{\theta,\alpha}\) is the proportion of diffuse radiation originating in a given sky sector relative to all sectors; \(\bullet\)\(AngIn_{\Theta,\alpha}\) is the angle of incidence between the centroid of the sky sector and the intercepting surface [43, 44]. 3. Intensity of return (IR) is a measure of amplitude describing the peak power ratio of the laser return to the emitted laser, calculated as a function of surface reflectivity. Values are corrected for variability between flight lines and pre-processed at a 0.5 m pixel resolution before being processed using the BCAL vegetation intensity tools and output to a 30 m resolution for the vegetation excluding bare earth data [40, 41, 42]. Research indicates that the returns of high-intensity and the low intensity peak count of the intensity distribution were predictive of live and dead tree biomass, respectively [45]. 4. Total Vegetation Density is a derived percent ratio of vegetation to ground returns per m\({}^{2}\) or: \[NDVI=\frac{NIR-Red}{NIR+Red} \tag{2}\]0 (9) where \(n_{i}\) is the number of vegetation returns in the ith layer [41, 42]. 5. Canopy Relief Ratio is a derived mean height less the minimum height divided by the maximum height less the minimum height per m\({}^{2}\) or: \[NDVI=\frac{NIR-Red}{NIR+Red} \tag{2}\]1 (10) This ratio represents the relative shape of the canopy from altimetry observation which describes the degree to which canopy surfaces are in the upper (\(CRR>0.5\)) or in the lower (\(CRR<0.5\)) portions of the height range [41, 42, 46, 47]
6. Texture of Heights (\(TH\)) is the variance of height of points per pixel equal to the SD of height > ground threshold and height < crown threshold per m\({}^{2}\) or: \[NDVI=\frac{NIR-Red}{NIR+Red} \tag{2}\]2 (11) where \(n_{i}\) is the number of returns in the ith layer [41, 42].