Measuring solar reflectance of variegated flat roofing materials using quasi-Monte Carlo method

• Solar reflectance of variegated roofs are measured using a quasi-Monte Carlo approach.
• The convergence rate is significantly improved.
• Sensitivity of the convergence depends on the range of spot solar reflectance.
• An equation to estimate the required number of random spots is proposed.

The Cool Roof Rating Council recommends applying the Monte Carlo (MC) method to ASTM standard C1549 to estimate the mean solar reflectance (R) of a variegated roofing sample. For samples with high degree of variation in the solar reflectance, the MC approach is slow in convergence. Applying proper set point of low-discrepancy sequences on the variegated roof sample can increase the convergence rate for about 40%.We measure solar reflectance of a variegated roofing sample (gridded to 1″ × 1″ cells) with C1549 and calculate R by averaging the measured solar reflectance. Then, we estimate R using MC and quasi-Monte Carlo (QMC) technique as a function of the number of random spots on the measured sample.To further investigate the performance of QMC, we analyze the sensitivity of the standard error of the mean reflectance of selected sample spots for a variety of simulated samples, where the range and distribution of the solar reflectance is varied. Based on the simulated and experimental results, we recommend using QMC for measuring the solar reflectance of variegated surfaces and propose an equation to estimate the required number of random spots as a function of the mix and the range of solar reflectance of samples.