Ray Trace Modeling to Determine Optimal Forest Canopy Gap Size for Reduced Solar Irradiance During Snowmelt: Field Verification and Continental Scale Application

Abstract:

Forest hydrology has long debated the influence of forest gap size on the shortwave radiation regime and subsequent snowmelt rates. To address this question, a new ray trace solar transmittance model is presented to evaluate the sensitivity of gap influence on shortwave irradiance patterns to latitude, gap size, and time of year in fragmented forest environments. The ray trace model takes into account solar position, gap and forest geometry, and position within or near the gap, and was tested against measurements of shortwave radiation from 20 pyranometers in and around a gap in a mixed conifer forest and compared to simpler canopy transmittance models that ignored shading or that scaled transmittance according to leaf area index. The ray trace model reduced the large errors obtained by simple canopy transmittance models; at the 20 pyranometer locations, average biases in excess of ~ ±90 W m^-2 were reduced to better than 4 W m^-2. These results suggest that an accurate description of the spatial variability of solar irradiance in and around a forest gap requires explicit calculation of how gaps modify the canopy transmittance. To examine model sensitivity to key parameters, gap size, latitude, and day of year were varied under clear-sky conditions. The calculated spatial distribution patterns of cumulative daily solar irradiance inform how forest gap sizes might be optimized to minimize (shortwave) snowmelt energy. As gap size was changed for a given latitude and date, the (spatial) coefficient of variation (CV) of cumulative daily irradiance exhibited a distinct maximum that is a function of gap geometry and solar angle; smaller (larger) gaps with more diffuse (direct beam) radiation exhibited reduced spatial variability of irradiance. The results indicate that optimum forest gap sizes to reduce solar radiation while maximizing gap area depend on date and latitude; using mean snowmelt onset dates for a range of latitudes (31°N – 71°N) spanning North American conifer forests, the optimal gap radius relative to forest height H is 0.5H at and below 51°N and 0.8H at and above 61°N. The optimal forest gap size is found to be sensitive to the choice of snowmelt onset date; an earlier snowmelt onset by one-month would increase optimal forest gap radii to 0.7 – 1 H.