Coupling sky images with radiative transfer models: a new method to estimate cloud optical depth

Abstract. A method for retrieving cloud optical depth (τ_c) using a UCSD developed ground-based sky imager (USI) is presented. The radiance red–blue ratio (RRBR) method is motivated from the analysis of simulated images of various τ_c produced by a radiative transfer model (RTM). From these images the basic parameters affecting the radiance and red–blue ratio (RBR) of a pixel are identified as the solar zenith angle (θ₀), τ_c, solar pixel angle/scattering angle (ϑ_s), and pixel zenith angle/view angle (ϑ_z). The effects of these parameters are described and the functions for radiance, I_λτ_c, θ₀, ϑ_s, ϑ_z, and RBRτ_c, θ₀, ϑ_s, ϑ_z are retrieved from the RTM results. RBR, which is commonly used for cloud detection in sky images, provides non-unique solutions for τ_c, where RBR increases with τ_c up to about τ_c = 1 (depending on other parameters) and then decreases. Therefore, the RRBR algorithm uses the measured I_λ^measϑ_s, ϑ_z, in addition to RBR^measϑ_s, ϑ_z, to obtain a unique solution for τ_c. The RRBR method is applied to images of liquid water clouds taken by a USI at the Oklahoma Atmospheric Radiation Measurement (ARM) program site over the course of 220 days and compared against measurements from a microwave radiometer (MWR) and output from the Min et al. (2003) method for overcast skies. τ_c values ranged from 0 to 80 with values over 80, being capped and registered as 80. A τ_c RMSE of 2.5 between the Min et al. (2003) method and the USI are observed. The MWR and USI  have an RMSE of 2.2, which is well within the uncertainty of the MWR. The procedure developed here provides a foundation to test and develop other cloud detection algorithms.