Minimizing systematic errors in cloud fraction estimates from spaceborne cloud radars

In order to detect weakly reflecting clouds, radar pulse returns are often averaged over a considerable time to increase the probability of the sample volume being registered as cloudy. However, if the sample volume is registered as cloudy, it may not be completely cloud filled. Hence, equating the observed cloud fraction to the fraction of sample volumes that are registered as cloudy may underestimate or overestimate the actual cloud fraction. A published cloud detection criterion (γ_observed < Y _req) based on the observed radiometric resolution, Y_observed, of the final cloud product is used to demonstrate how thresholds for Y_req are derived to minimize the difference between the observed and true long-term cloud fractions. As an example, thresholds for observing difficult-to-detect thin (mean thickness of 200 m) liquid water clouds, the reflectivities of which are shown to follow a Weibull distribution, are derived with specific reference to both the EarthCARE and CloudSat radar designs. These show that the CloudSat design, with a proposed Y_req = 2, will tend to underestimate the cloud fraction of such clouds, and a value of Y_req = 4 may be more appropriate. However, at Y_req = 2 the CloudSat long-term observed cloud fraction is insensitive to the mean size, and hence the spatial distribution, of such clouds and so would be useful in detecting changes in cloud fraction. On the other hand, the proposed EarthCARE radar is more sensitive and has a longer sampling volume and so should give unbiased estimates of such clouds for a Y_req of 1.5. Its longer sampling volume, however, makes it more responsive to changes in mean cloud size, and so any changes in its long-term returned cloud fraction could result from such changes, as well as from changes in cloud fraction.