An algorithm for generating stochastic cloud fields from radar profile statistics

Abstract

An algorithm is described for generating stochastic three-dimensional (3D) cloud fields from time–height fields derived from vertically pointing radar. This model is designed to generate cloud fields that match the statistics of the input fields as closely as possible. The major assumptions of the algorithm are that the statistics of the fields are translationally invariant in the horizontal and independent of horizontal direction; however, the statistics do depend on height. The algorithm outputs 2D or 3D stochastic fields of liquid water content (LWC) and (optionally) effective radius. The algorithm is a generalization of the Fourier filtering methods often used for stochastic cloud models. The Fourier filtering procedure generates Gaussian stochastic fields from a “Gaussian” cross-correlation matrix, which is a function of a pair of heights and the horizontal distance (or “lag”). The Gaussian fields are nonlinearly transformed to give the correct LWC histogram for each height. The “Gaussian” cross-correlation matrix is specially chosen so that, after the nonlinear transformation, the cross-correlation matrix of the cloud mask fields approximately matches that derived from the input LWC fields. The cloud mask correlation function is chosen because the clear/cloud boundaries are thought to be important for 3D radiative transfer effects in cumulus. The stochastic cloud generation algorithm is tested with 3 months of boundary layer cumulus cloud data from an 8.6-mm wavelength radar on the island of Nauru. Winds from a 915-MHz wind profiler are used to convert the radar fields from time to horizontal distance. Tests are performed comparing the statistics of 744 radar-derived input fields to the statistics of 100 2D and 3D stochastic output fields. The single-point statistics as a function of height agree nearly perfectly. The input and stochastic cloud mask cross-correlation matrices agree fairly well. The cloud fractions agree to within 0.005 (the total cloud fraction is 18%). The cumulative distributions of optical depth, cloud thickness, cloud width, and intercloud gap length agree reasonably well. In the future, this stochastic cloud field generation algorithm will be used to study domain-averaged 3D radiative transfer effects in cumulus clouds.