Determination of the Scaled Optical Thickness of Clouds from Reflected Solar Radiation Measurements

A method is presented for determining the scaled optical thickness of clouds from reflected solar radiation measurements. The procedure compares measurements of the reflection function with asymptotic expressions for the reflection function of optically thick layers. Analytic formulas are derived which explicitly show the dependence of the reflection and transmission functions of nonabsorbing atmospheres, on cloud optical thickness (τc), ground albedo (Ag) and asymmetry factor (g). For nonconservative atmospheres, the dependence of the reflection function on single scattering albedo (ω0) and asymmetry factor are contained implicitly in the asymptotic functions and constants. These asymptotic expressions for both conservative and nonconservative atmosphere are shown to be valid when the scaled optical thickness (1−g)τc≥??1.45, corresponding to clouds of optical thickness τc≥??9. By utilizing the asymptotic expression for the reflection function of an optically thick, conservatively scattering atmosphere. a simple expression is obtained relating the measured reflection function to scaled optical thickness. This expression shows that the ground albedo produces a constant bias in the derived optical thickness, regardless of the value of the measured reflection function. High-resolution images of the reflection function of clouds have been obtained with a multichannel scanning radiometer operated from a high-altitude aircraft. An image of the reflection function of clouds obtained from a stratiform cloud system in central Oklahoma is analyzed using two different phase functions. Results show that details of the single scattering phase function have an impact on the derived optical thickness, although the dominant influence is the cloud asymmetry factor which appears explicitly in the analysis.