A method for inferring cloud optical depth is introduced and assessed using simulated surface radiometric measurements produced by a Monte Carlo algorithm acting on fields of broken, single-layer, boundary layer clouds derived from Landsat imagery. The method utilizes a 1D radiative transfer model and time series of zenith radiances and irradiances measured at two wavelengths, 1 and 2 , from a single site with surface albedos ␣ 1 Ͻ ␣ 2. Assuming that clouds transport radiation in accordance with 1D theory and have spectrally invariant optical properties, inferred optical depths Ј are obtained through cloud-base reflectances that are approximated by differencing spectral radiances and estimating upwelling fluxes at cloud base. When initialized with suitable values of ␣ 1, ␣ 2, and cloud-base altitude h, this method performs well at all solar zenith angles. Relative mean bias errors for Ј are typically less than 5% for these cases. Relative variances for Ј for given values of inherent are almost independent of inherent and are Ͻ50%. Errors due to neglect of net horizontal transport in clouds yield slight, but systematic, overestimates for Շ 5 and underestimates for larger . Frequency distributions and power spectra for retrieved and inherent are often in excellent agreement. Estimates of depend weakly on errors in h, especially when h is overestimated. Also, they are almost insensitive to errors in surface albedo when ␣ 1 is underestimated and ␣ 2 overestimated. Reversing the sign of these errors leads to overestimation of , particularly large . In contrast, the conventional method of using only surface irradiance yields almost entirely invalid results when clouds are broken.
Though results are shown only for surfaces resembling green vegetation (i.e., ␣ 1 K ␣ 2), the performance of this method depends little on the values of ␣ 1, and ␣ 2. Thus, if radiometric data have sufficient signal-tonoise ratios and suitable wavelengths can be found, this method should yield reliable estimates of for broken clouds above many surface types.
