Using Copulas to Model Complex Clouds
Oreopoulos, L., UMBC
Cloud Distributions/Characterizations
Cloud Modeling
Norris, PM, L Oreopoulos, AY Hou, WK Tao, and X Zeng. 2008. "Representation of 3D heterogeneous cloud fields using copulas: Theory for water clouds." Quarterly Journal of the Royal Meteorological Society (in press), doi: 10.1002/qj.321, currently available at
Contours containing (brown-80%, orange-60%, cyan-40%, and blue-20%) of the joint inter-layer S probability, such that the probability densities within each contour are larger than those outside. Thick contours are from the GCE thin contours are from our Gaussian copula. The separation of layers is 256 m (left panel) and 1652 m (right panel). The expected reduction in inter-layer correlation with increasing layer separation is observed (i.e., contours aligned more along the diagonal for 256 m).
Percent biases in domain standard deviation of water path (WP sdev), transmitted solar flux (TRN) and downwelling longwave radiation to the surface (DLR) of three cloud generators (GCOP=Gaussian Copula, MRO=Geleyn and Hollingsworth Maximum Random Overlap, RAIS=a total water version of the Räisänen et al. generator) relative to exact GCE values (ICA calculations for the radiative quantities). S-only marginal fits and 100 generator realizations were used with the bias spread shown as error bars.
The realistic prediction of cloud cover and cloud properties by global climate models (GCMs) is a well-known limiting factor in the accuracy of today's climate predictions. Cloud prediction by GCMs is made difficult by the fact that the scale of cloud variability is often much smaller than the grid resolutions that are computationally available to them. Climate modelers address this scale problem by seeking to estimate the variability of the unresolved cloud properties in terms of the resolved scale properties such as temperature, moisture, and atmospheric motion. For example, the cloudy fraction of each la
Our work aims at addressing all the above issues simultaneously by describing the joint horizontal and vertical variability in the unresolved properties of a GCM-sized grid column. To do this, we use generalized skewed distributions to fit the saturation ratio S (ratio of total moisture content to the saturation vapor content) and temperature (T) variability within each la
We believe that this new theory and its implementation as a cloud generator has significant potential in both GCM cloud modeling and in the assimilation of high resolution cloud data being provided by modern Earth observing satellites and ground-ba