1. Introduction

Cirrus clouds cover a significant part of the Earth’s surface and hence influence significantly the radiation balance and climate, primarily because of radiation extinction and reflection effects [1]. Especially strong influence on radiation transmission and scattering has predominant orientation of particles in the horizontal plane [2]. This orientation can be caused by aerodynamic forces of particles falling free in the atmosphere [3]. Lidar observations provide the most complete information on the properties of crystal particles [4–6]. The presence of crystal particles in these observations is primarily manifested through the depolarization of backscattered radiation. Situations with randomly oriented particles having the depolarization ratio δ = 0.3–0.6 depending on the particle shape are most frequently observed [7,8]. The particles whose long axes are predominantly oriented in the horizontal plane cause specular light reflection; they have δ close to zero and enhanced backscattering [9]. The CALIPSO experiments with a space-based polarization lidar [10] demonstrate a significant relative fraction of these particles at temperatures from –5 to –35°С.

This paper presents results of ground-based lidar observations of the polarization structure of cirrus cloudiness with high spatial and temporal resolution and reveals the spatial structure of formations in which particles with pronounced horizontal orientation are dominant.

2. Depolarization parameters

Generally, the experimentally measured backscattering phase matrices (BSPM) have nonzero nondiagonal elements $a_{12},a_{14},\text{ and }{a}_{34}$ [11]. With allowance for the well-known symmetry relations [12,13] for purely random (chaotic) orientation of crystal particles in the cloud, the BSPM assumes the simple diagonal form [14,15]

Let us assume that laser radiation is linearly polarized (the initial vector is $S_0^L={\left[1,1,0,0\right]}^T$). Then the 2nd (normalized by the intensity) Stokes parameter Q is expressed through the measured signal components as follows: $Q=(I_{\parallel }-I_{\perp })/\left(I_{\parallel }+I_{\perp }\right)=\left(a_{12}+a_{22}\right)/\left(1+a_{12}\right)$. The 4th Stokes parameter is measured analogously; in this case, the circularly polarized beam ($S_0^C={\left[1,0,0,-1\right]}^T$) was used, and the λ/4 plate in front of the receiver was rotated through an angle of 45°: $V=(I_{\parallel }-I_{\perp })/\left(I_{\parallel }+I_{\perp }\right)=\left(a_{14}-a_{44}\right)/\left(1-a_{14}\right)$. For the diagonal matrix, expressions are simplified: $Q=a_{22}=1-d$ and $V=-a_{44}=1-2d$. The assumption about the chaotic orientation of particles is very convenient for interpretation of experimental observations. Measurements [11] confirm that the zero value of $a_{14}$ is the most probable one ($a_{14}=0\pm 0.05$). At the same time, significant number of cases with pronounced predominant azimuth orientation of particles was observed: the average value of the element was $a_{12}=-0.22\pm 0.2$.

For chaotic particle orientation, the well-known relationship between the depolarization ratios for linearly and circularly polarized radiation ${\delta }^C=2{\delta }^L/\left(1-{\delta }^L\right)$ [14,17] is transformed into

3. Experimental results

The optical scheme of the polarization LOSA-S lidar channel was presented in [19]. An LS2137U laser (532 nm, 300 mJ) with pulse repetition frequency of 10 Hz was used. A lens 0.15 m in diameter with a focal distance of 0.75 m was used for a receiving antenna. A quarter-wavelength λ/4 quartz plate was inserted into the beam to change the polarization state of transmitted radiation from linear to circular one. The Wollaston prism was inserted into the scattered beam to form two beams with mutually orthogonal polarization states. A λ/4 plate was also placed in front of the prism. The fast axis of the λ/4 plates could be oriented at an angle of 0 or 45° to the reference plane. Two FÉU-84 photomultipliers simultaneously registered the parallel ($I_{\parallel }$) and orthogonal ($I_{\perp }$) signal components in the measuring channels. Rotating simultaneously the plates in front of the source and receiver, we could measure either the second (Q) or fourth (V) component of the Stokes vector of backscattered radiation. The error in calibration of the relative photodetector sensitivity did not exceed 4%. As a rule, echo-signals were accumulated during 3.2 s (32 laser pulses). Taking into account the ADC digitization frequency (25 MHz), we can consider that the spatial resolution of the data on the cloudiness structure was about 20 m.

Experimental data presented in this work were obtained since April, 2009 till May, 2010. A total of 30 records of sensing of high clouds not screened by underlying cloudiness were obtained. Figure 1 shows an example of lidar signals from cirrus cloudiness. From the data of balloon sensing at the station Novosibirsk (250 km to the south-west of the observation point), the temperature at an altitude of 8 km and 12:00 UCT was –34.5°С, and the tropopause height was 12.1 km (–59°С) [20]. Each signal was accumulated during 3.2 s (32 laser pulses). The component $I_{\parallel }$ corrected for the squared distance is shown at the upper figure in artificial colors, and the depolarization parameter d is shown at the lower figure. Grey color illustrates regions with the scattering ratio R < 4.

 

Fig. 1 Observations of crystal clouds at successively changed (from linear to circular) state of initial laser beam polarization. May 28, 2009, 16:35 – 17:19.

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The polarization state of the transmitter and receiver radiation was periodically changed by simultaneous rotation of both quarter-wavelength plates through an angle of 45° (circular) or 0° (linear). The corresponding polarization states are indicated at the top of the figure.

In calculations of d in the case of circular polarization, the parameter K ₄ was adjusted so that to minimize visible changes of the depolarization pattern at the interface between regions with different initial polarization states. In this case, we succeeded in obtaining this for $K_4=1.52$, which corresponds to the Stokes parameters Q = 0.1 and V = –0.37 at points with maximum depolarization. Cloud regions with the most pronounced specular backscattering are indicated by white ellipses. They are characterized by the maximum backscattering and low depolarization (d < 0.1). At the same time, regions with pronounced vertical flows (indicated by green ellipses), including the entire lower cloud boundary, had high depolarization close to d = 0.9.

The data shown in Fig. 1 represent a rather rare case in which the choice of one value K ₄ made it possible to achieve exact joining of the depolarization pattern at interfaces between regions for the entire cloud thickness. As a rule, different spatial formations inside of the cloud can call for the application of different K ₄ values. In our measurements, these values changed from 1.4 to 1.8. Undoubtedly, the K ₄ value was influenced by the azimuth orientation of particles causing the occurrence of the nondiagonal BSPM elements.

Figure 2 shows an analogous example of sensing with circularly polarized laser radiation. The tropopause height at 00:00, UCT was 10.5 km (–55°C). In this case, $K_4=1.6$ was chosen to calculate the d value. As in the majority of other cases of cirrus cloudiness sensing, specularly scattering objects are shaped as thin horizontal layers. Probably, ascending flows that make a steady-state levitation of crystal particles and their orientation in the horizontal plane possible prevail in these layers.

 

Fig. 2 Observations of crystal clouds using circularly polarized laser radiation. May 19, 2009, 10:25 – 11:12.

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Figure 3 shows the record of a specularly reflecting layer at an altitude of 6400 m. To the right of the figure, the vertical signal profile (crosses) and values of the a ₄₄ element (the blue curve) are shown for the brightest point of the layer indicated by the arrow at the upper left of the figure. The tropopause height was 11.1 km (–61.6°С), and T = –29°С at an altitude of 6200 m. The thickness of the layer with the pronounced horizontal orientation of particles (a ₄₄ < –0.6) was about 200 m, whereas the specularly reflective layer (distinguished from the $I_{\parallel }$ component) was much thinner. The field-of-view angle of the receiver for a 6-km range was about 50 μrad. Obviously, when the particle deviates at a greater angle, specular reflection disappears, but the a ₄₄ value changes weakly and still remains in the range (−1…-0.6) typical of the horizontally oriented particles.

 

Fig. 3 Observations of crystal clouds using circularly polarized laser radiation. April 24, 2009, 18:38 – 18:54.

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In some scattering events, signals from individual specularly reflective particles are clearly pronounced. An example of such record is shown in Fig. 1, where separate bright spots are clearly pronounced against the total background to the left of the layer at 6500 m. In records of single lidar pulses, specular particles are manifested through sharp peaks of the $I_{\parallel }$ component, but as a rule, are absolutely unnoticed for the $I_{\perp }$ component. In the case of the strongest reflections, the depolarization ratio was in the limits $\delta \approx 2-10\%$. In Fig. 4 (records of each lidar signal), individual particles are manifested against the background of layers with high depolarization at 6500 and 7000 m. It seems likely that particles in these layers were chaotically oriented, but some of them acquired horizontal orientation when they fall down. These free-falling particles were concentrated at a level of 6200 m, passed into the steady-state levitation state, and formed a layer with specular reflection below which no specular particles were present.

 

Fig. 4 Observations of individual specularly reflective particles with recording of each lidar signal. Circular polarization. The component $I_{\parallel }$ is shown at the left of the figure, and the depolarization parameter d ($K_4=1.6$) is shown in the centre. The record of single pulse number 103 is shown at the right of the figure. May 28, 2009, 16:30 – 16:41.

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4. Summary

Lidar observations of the cirrus cloud structure using linearly and circularly polarized radiation revealed the presence of thin (several tens of meters) specularly reflective horizontal layers with low depolarization degree and high backscattering coefficient. In the structures shaped as vertical stripes (free-falling particles or pronounced turbulent flows), radiation was strongly depolarized, which indicated that chaotic orientation of particles dominated in these cloud regions. It seems likely that the anomalous zones with pronounced horizontal orientation of crystal particles are caused by homogeneous ascending flows promoting the steady-state levitation of crystals and their orientation in the horizontal plane.

The double excess of the depolarization degree typical of the diagonal BSPM and sensing with circularly polarized laser beam in comparison with linearly polarized beam was not observed in our experiment in which values of the parameter $K_4$ were within the limits 1.4–1.8. This testified to the presence of pronounced azimuth orientation of particles for which the nondiagonal a ₁₂ element was nonzero.