Use of Cloud Radar Doppler Spectra to Evaluate Stratocumulus Drizzle Size Distributions in Large-Eddy Simulations with Size-Resolved Microphysics

A case study of persistent stratocumulus over the Azores is simulated using two independent large-eddy simulation (LES) models with bin microphysics, and forward-simulated cloud radar Doppler moments and spectra are compared with observations. Neither model is able to reproduce the monotonic increase of downward mean Doppler velocity with increasing reflectivity that is observed under a variety of conditions, but for differing reasons. To a varying degree, both models also exhibit a tendency to produce too many of the largest droplets, leading to excessive skewness in Doppler velocity distributions, especially below cloud base. Excessive skewness appears to be associated with an insufficiently sharp reduction in droplet number concentration at diameters larger than ~200 μm, where a pronounced shoulder is found for in situ observations and a sharp reduction in reflectivity size distribution is associated with relatively narrow observed Doppler spectra. Effectively using LES with bin microphysics to study drizzle formation and evolution in cloud Doppler radar data evidently requires reducing numerical diffusivity in the treatment of the stochastic collection equation; if that is accomplished sufficiently to reproduce typical spectra, progress toward understanding drizzle processes is likely

Between Strassen and Chung normalizations for Lévy's area process

Let fL(t) : t 0g be L'evy's area process, let fl : R+ 7! R, and let fZ t : t 3g be the stochastic process defined by Z t (s) = L(ts)=(2t log log t); 0 s 1. Conditions on fl are given such that the set of all limit points of ffl(t)Z t : t 3g as t !1 is a.s. equal to the set of all continuous functions defined on [0; 1] which vanish at 0. AMS 1991 subject classifications: Primary 60F05; Secondary 60H05. Key words and phrases: Brownian motion; law of the iterated logarithm; L'evy's area process. 1 Introduction Let B = fB(t) : t 0g be an m-dimensional Brownian motion, let fl : R+ 7! R, let C m 0 denote the set of all R m -valued continuous functions defined on [0; 1] which vanish at 0, endowed with the uniform topology, and let OE(t) = ( 1 for 0 ! t ! 3; log log t for t 3: Let us consider the following conditions: (A) fl(t) !1 as t !1; (Bffi 0 ) there exist M ? 0 and 0 ! ffi ! ffi 0 2 such that fl(t) M OE ffi (t) for t sufficiently large. Baldi and Roynette (1992a) pro..