Determination of the Optical Thickness and Effective Particle Radius of Clouds from Reflected Solar Radiation Measurements. Part I: Theory

A method is presented for determining the optical thickness and effective particle radius of stratiform cloud layers from reflected solar radiation measurements. A detailed study is presented which shows that the cloud optical thickness (τc) and effective particle radius (re) of water clouds can be determined solely from reflection function measurements at 0.75 and 2.16 μm, provided τc ≳ 4 and re ≳ 6 μm. For optically thin clouds the retrieval becomes ambiguous, resulting in two possible solutions for the effective radius and optical thickness. Adding a third channel near 1.65 μm does not improve the situation noticeably, whereas the addition of a channel near 3.70 μm reduces the ambiguity in deriving the effective radius. The effective radius determined by the above procedure corresponds to the droplet radius at some optical depth within the cloud layer. For clouds having τc ≳ 8, the effective radius determined using the 0.75 and 2.16 μm channels can be regarded as 85%–95% of the radius at cloud top, which corresponds in turn to an optical depth 20%–40% of the total optical thickness of the cloud layer.