Accurate Retrieval of Asymmetry Parameter for Large and Complex Ice Crystals From In‐Situ Polar Nephelometer Measurements

Abstract

The retrieval of the asymmetry parameter from nephelometer measurements can be challenging due to the inability to detect the whole angular range. Here, we present a new method for retrieving the asymmetry parameter of ice crystals with relatively large size parameters (>50) from polar nephelometer measurements. We propose to fit the angular scattering measurement with a series of Legendre polynomials and the best fitted coefficients give the asymmetry parameter. The accuracy of the retrieval is analyzed by accessing the smoothness of the phase function, which is closely linked to the complexity of ice particle. It is found that the uncertainty of retrieval could be smaller than 0.01, provided the measured intensity profile is smooth enough. As an application, we report an case study on Arctic cirrus, which shows a mean value for the asymmetry parameter of 0.72. Plain Language SummaryThe asymmetry parameter of ice crystals is a parameter that can largely determine cirrus cloud's interaction with solar radiation energy, and therefore its magnitude is important for climate and weather prediction models. In-situ measurements using nephelometers is a direct way to measure partial angular scattering functions, and the accuracy of these measurements is of upmost importance. In this paper, we report a novel method for retrieving the asymmetry parameter from polar nephelometer measurements. Depending on the smoothness of the measured angular scattering function, the accuracy of the retrieval could be very high. We report a case study over the Arctic region, showing a low asymmetry parameter around 0.72.

Toward Better Constrained Scattering Models for Natural Ice Crystals in the Visible Region

“…In the development of an algorithm for retrieving the asymmetry parameter from the measurements of a polar nephelometer, Xu et al. (2022) introduced a so‐called C p parameter that describes the smoothness and isotropic degree of the phase function. It is defined as: $$${C}_{p}={\left(\sum\limits _{l=0}^{\infty }\vert {\hat{c}}_{GO,l}\vert \right)}^{-1},$$$ where $${\hat{c}}_{GO,l}$$ is the expansion coefficients of phase function due to the reflection – refraction of light ray (without forward diffraction) by using a series of Legendre polynomials P l (cos(Θ)), that is, $$${P}_{GO}({\Theta })=\sum\limits _{l=0}^{\infty }(2l+1){\hat{c}}_{GO,l}{P}_{l}(\mathrm{cos}({\Theta })).$$$ …”

“…The algorithm for retrieving C p from polar nephelometer measurement is described in Xu et al. (2022). Note that the first coefficient $${\hat{c}}_{GO,0}$$ is set to be: $$${\hat{c}}_{GO,0}=1,$$$ such that the integral of the intensity is normalized properly.…”

“…The retrieval algorithm is described in detail in Xu et al. (2022). In summary, a Gaussian quadrature is applied to simultaneously compute the values of g and C p , the accuracy of integration increase as the C p value increases.…”

“…It was found that the C p parameter is closely connected to the distortion parameter δ proposed by Macke, Mueller, and Raschke (1996). The algorithm for retrieving C p from polar nephelometer measurement is described in Xu et al (2022). Note that the first coefficient 𝐴𝐴 𝐴 𝐴𝐴𝐺𝐺𝐺𝐺𝐺0 is set to be:…”

“…By the analysis of in‐situ measured angular scattering intensities of ice crystal ensembles using Legendre polynomials, Xu et al. (2022) found that the real ice crystals in an Arctic cirrus case study had a much higher complexity than the idealized models. Additionally, Tang et al.…”