Optimal Nonlinear Estimation for Cloud Particle Measurements

Abstract

Particle concentration is generally derived from measurements by cumulating particle counts on a given sampling period and dividing this particle number by the corresponding sampled volume. Such a procedure is a poor estimation of the concentration when the number of counts per sample is too low. It is shown that counting particles in a cloud is a conditionally Poisson random process given its intensity, which is proportional to the local average concentration of particles. Because of turbulence and mixing processes, the particle concentration in clouds fluctuates and so does the intensity of the counting process, which is referred to as an inhomogeneous Poisson process. The series of counts during a cloud traverse is a unique realization of the process. The estimation of the expected number of particles is thus a Bayesian procedure that consists in the estimation of the intensity of an a priori random inhomogeneous Poisson process from a unique realization of the process. This implies, of course, an a priori model for the possible variations of this intensity. The general theory of optimal estimation for point processes addresses the above problem. It is briefly recalled here, and its application to particle measurements in the atmosphere is tested with simulated series of particle counts. Two examples of estimation from droplet measurements in clouds are also shown and compared to the current method. Nonlinear estimation removes the noise inherent to the counting process while preserving sharp discontinuities in the droplet concentration.