Uncertainty in stratiform cloud optical thickness inferred from pyranometer measurements at the sea surface

The relative 'plane-parallel' error in a mean cloud optical thickness retrieved from ground-based pyranometer measurements is estimated. The plane-parallel error is defined as the bias introduced by the assumption in the radiative transfer model used in cloud optical thickness retrievals that the atmosphere, including clouds, is horizontally homogeneous on the scale of an individual retrieval. The error is estimated for the optical thickness averaged over the whole domain, which simulates the mean cloud optical thickness obtained from a time series of irradiance measurements. The study is based on 3D Monte Carlo radiative transfer simulations for non-absorbing, all-liquid, layer clouds. Liquid water path distributions in the clouds are simulated by a bounded cascade fractal model. The sensitivity of the error is studied with respect to the following factors: averaging time of irradiance used in an individual retrieval, mean cloud optical thickness, cloud variability, cloud base height and solar zenith angle. In the simulations presented in this paper, the relative bias in the dornain averaged cloud optical thickness retrieved from pyranometer measurements varies from +1% for optically thin clouds to nearly -20%. The highest absolute value of the relative bias is expected for thick and variable clouds with high bases (e.g. 1 km) and retrievals based on long-term mean irradiances (averaging time of the order of several tens of minutes or hours). The bias can be diminished by using short-term irradiance averages, e.g. of one minute, and by limiting retrievals to low-level clouds.