Statistical properties of the normalized ice particle size distribution

Abstract

[1] Testud et al. (2001) have recently developed a formalism, known as the ''normalized particle size distribution (PSD)'', which consists in scaling the diameter and concentration axes in such a way that the normalized PSDs are independent of water content and mean volume-weighted diameter. In this paper we investigate the statistical properties of the normalized PSD for the particular case of ice clouds, which are known to play a crucial role in the Earth's radiation balance. To do so, an extensive database of airborne in situ microphysical measurements has been constructed. A remarkable stability in shape of the normalized PSD is obtained. The impact of using a single analytical shape to represent all PSDs in the database is estimated through an error analysis on the instrumental (radar reflectivity and attenuation) and cloud (ice water content, effective radius, terminal fall velocity of ice crystals, visible extinction) properties. This resulted in a roughly unbiased estimate of the instrumental and cloud parameters, with small standard deviations ranging from 5 to 12%. This error is found to be roughly independent of the temperature range. This stability in shape and its single analytical approximation implies that two parameters are now sufficient to describe any normalized PSD in ice clouds: the intercept parameter N* 0 and the mean volume-weighted diameter D m . Statistical relationships (parameterizations) between N* 0 and D m have then been evaluated in order to reduce again the number of unknowns. It has been shown that a parameterization of N* 0 and D m by temperature could not be envisaged to retrieve the cloud parameters. Nevertheless, D m -T and mean maximum dimension diameter -T parameterizations have been derived and compared to the parameterization of Kristjánsson et al. (2000) currently used to characterize particle size in climate models. The new parameterization generally produces larger particle sizes at any temperature than the Kristjánsson et al. (2000) parameterization. These new parameterizations are believed to better represent particle size at global scale, owing to a better representativity of the in situ microphysical database used to derive it. We then evaluated the potential of a direct N* 0 -D m relationship. While the model parameterized by temperature produces strong errors on the cloud parameters, the N* 0 -D m model parameterized by radar reflectivity produces accurate cloud parameters (less than 3% bias and 16% standard deviation). This result implies that the cloud parameters can be estimated from the estimate of only one parameter of the normalized PSD (N* 0 or D m ) and a radar reflectivity measurement.

The effective density of small ice particles obtained from in situ aircraft observations of mid‐latitude cirrus

“…The largest λD bin has low statistics (implied by the wide bin width). Delanoë et al (2005) used an extensive set of airborne measurements to show the statistical properties of normalized PSDs and were able to relate the two modes. This has the advantage of having fewer degrees of freedom to fit.…”

Evaluation of ice cloud representation in the ECMWF and UK Met Office models using CloudSat and CALIPSO data

“…After convergence, the state vector and look-up tables are used to calculate IWC and effective radius. The forward model assumes a microphysical model describing the shape of the particle size distribution (Delanoë et al, 2005) and the relationships between particle mass, cross-sectional area and size. The ice particle mass is assumed to follow the Brown and Francis (1995) mass-size relationship derived from aircraft data.…”

Ice crystal number concentration estimates from lidar-radar satellite remote sensing. Part 1: Method and evaluation

“…DARDAR retrieves profiles of ice cloud properties by combining measurements from the CloudSat Cloud Profiling Radar (CPR) and the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP). Although DARDAR does not operationally provide N i , and has not been tested for this purpose, its retrieval framework that aims at constraining parameters of a PSD 15 parameterization (Delanoë et al, 2005, hereinafter D05) makes it an suitable candidate to estimate this quantity. Nevertheless, a careful evaluation remains necessary to determine if the D05 parameterization is theoretically capable of predicting N i and if lidar-radar measurements can provide sufficient information to properly constrain it.…”