Sampling errors and bias in satellite-derived fractional cloud cover estimates from exponential and deterministic cloud fields as a consequence of instrument pixel size and number

The proposed European Space Agency's cloud profiling radar Millimetre Active Cloud Structure Imaging Mission is a nadir-pointing radar with a 1-km footprint; it will need to integrate the received signal power for a reasonable amount of time (1.4-14 s) along track to detect a cloud. As a result, the radar will provide a set of long (10-100 km) narrow pixels that are registered either as cloudy or as clear, depending on how much cloud there is in each. These are thus likely to give a biased estimate of fractional cloud cover over a region because the radar will be unable to detect small clouds or gaps. For a nadir-pointing radar the clouds and gaps essentially form a ID sequence that can be modeled by a general single-server queue. This model allows analytical expressions to be found for the bias and sampling error in specific cases. Such expressions are presented for the two extremes of the Erlang queuing model, that is, for an exponential and a deterministic queue. These are then compared to results derived from satellite images of clouds.