Analytic characterization of random errors in spectral dual-polarized cloud radar observations

Alexander Myagkov,Davide Ori

doi:10.5194/amt-15-1333-2022

Alexander Myagkov, Davide Ori

Open Access

https://doi.org/10.5194/amt-15-1333-2022

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Abstract

Abstract. This study presents the first-ever complete characterization of random errors in dual-polarimetric spectral observations of meteorological targets by cloud radars. The characterization is given by means of mathematical equations for joint probability density functions (PDFs) and error covariance matrices. The derived equations are checked for consistency using real radar measurements. One of the main conclusions of the study is that the convenient representation of spectral polarimetric measurements including differential reflectivity ZDR, correlation coefficient ρHV, and differential phase ΦDP is not suited for the proper characterization of the error covariance matrix. This is because the aforementioned quantities are complex, non-linear functions of the radar raw data, and thus their error covariance matrix is commonly derived using simplified linear relations and by neglecting the correlation of errors. This study formulates the spectral polarimetric measurements in terms of a different set of quantities that allows for a proper analytic treatment of their error covariance matrix. The results given in this study allow for utilization of spectral polarimetric measurements for advanced meteorological applications, among which are variational retrieval techniques, data assimilation, and sensitivity analysis.

Highlights

Cloud radars are a major component of state-of-the-art, ground-based observation platforms (Illingworth et al, 2007; Kollias et al, 2020)
At values of ρHV close to 0, VARρ has unrealistically high values, which result from ρHV in the denominator of Eq (54)
The results reveal that the first-order Taylor approximation cannot adequately represent most of the nondiagonal components of the error covariance matrix

Summary

Introduction

Cloud radars are a major component of state-of-the-art, ground-based observation platforms (Illingworth et al, 2007; Kollias et al, 2020). Their unique capabilities make these instruments extremely valuable for cloud and precipitation research. Due to relatively low attenuation of microwave signals by liquid water, cloud radars profile clouds up to the top even in the presence of light to moderate rain. These capabilities promote cloud radars for investigation of different formation and development processes throughout the life cycle of clouds. Cloud radars help to characterize initial ice formation and development in mixed-phase clouds (Bühl et al, 2019a, b), improve characterization of pure liquid clouds (Rusli et al, 2017; Acquistapace et al, 2017), estimate rates of aggregation (Kneifel et al, 2015, 2016) and riming (Kalesse et al, 2016; Moisseev et al, 2017; Kneifel and Moisseev, 2020), and quantitatively analyze solid and liquid precipitation (Matrosov, 2005; Matrosov et al, 2006, 2008; Tridon and Battaglia, 2015; Tridon et al, 2017, 2019)

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Conclusion