Relationships among cloud occurrence frequency, overlap, and effective thickness derived from CALIPSO and CloudSat merged cloud vertical profiles

A cloud frequency of occurrence matrix is generated using merged cloud vertical profiles derived from the satellite‐borne Cloud‐Aerosol Lidar with Orthogonal Polarization (CALIOP) and cloud profiling radar. The matrix contains vertical profiles of cloud occurrence frequency as a function of the uppermost cloud top. It is shown that the cloud fraction and uppermost cloud top vertical profiles can be related by a cloud overlap matrix when the correlation length of cloud occurrence, which is interpreted as an effective cloud thickness, is introduced. The underlying assumption in establishing the above relation is that cloud overlap approaches random overlap with increasing distance separating cloud layers and that the probability of deviating from random overlap decreases exponentially with distance. One month of Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) and CloudSat data (July 2006) support these assumptions, although the correlation length sometimes increases with separation distance when the cloud top height is large. The data also show that the correlation length depends on cloud top hight and the maximum occurs when the cloud top height is 8 to 10 km. The cloud correlation length is equivalent to the decorrelation distance introduced by Hogan and Illingworth (2000) when cloud fractions of both layers in a two‐cloud layer system are the same. The simple relationships derived in this study can be used to estimate the top‐of‐atmosphere irradiance difference caused by cloud fraction, uppermost cloud top, and cloud thickness vertical profile differences.