Characterizing the Representativity Error of Cloud Profiling Observations for Data Assimilation

Active observations from profiling instruments such as cloud radar or lidar have proved invaluable in improving our understanding of clouds and their interaction with the atmosphere. However, while they undoubtedly contain a wealth of information about the atmospheric state, the assimilation of such observations into NWP models has so far had mixed success. One reason is the mismatch of scales between the relatively coarse model resolution and the narrow beam-width of the instruments. To obtain an optimal analysis, this representativity error due to this mismatch in scales must be included within the observation error covariance matrix. In this paper, we demonstrate how a relatively straightforward approach that uses the local variance of the measurement combined with a global estimate of correlation provides a useful estimate of the representativity error. We also show how the method can be used to estimate the correlation in representativity error between observations in both the horizontal and vertical, potentially removing the need to thin the observations, or inflate their observation error. The method is evaluated using 2-D and 3-D fields of simulated and observed radar reflectivity before an example application to profiling observations is shown using Cloudsat data.