A method for inferring cloud optical depth tau 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, lambda1 and lambda2 , from a single site with surface albedos, alpha_lambda1 < alpha_lambda2. Assuming that clouds transport radiation in accordance with 1D theory and have spectrally invariant optical properties, inferred optical depths tau' 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 alpha_lambda1, alpha_lambda2, and cloud-base altitude h, this method performs well at all solar zenith angles. Relative mean bias errors for tau' are typically less than 5% for these cases. Relative variances for tau' for given values of inherent tau are almost independent of inherent tau and are < 50%. Errors due to neglect of net horizontal transport in clouds yield slight, but systematic, overestimates for tau < 5 and underestimates for larger tau. Frequency distributions and power spectra for retrieved and inherent tau are often in excellent agreement. Estimates of tau depend weakly on errors in h, especially when h is overestimated. Also, they are almost insensitive to errors in surface albedo when alpha_lambda1 is underestimated and alpha_lambda2 overestimated. Reversing the sign of these errors leads to overestimation of tau, particularly large tau. In contrast, the conventional method of using only surface irradiance yields almost entirely invalid results when clouds are broken.