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Modeling of light depolarization by cubic and hexagonal particles in noctilucent clouds
Atmospheric Research 79 (2006) 175 – 181 www.elsevier.com/locate/atmos
Modeling of light depolarization by cubic and hexagonal particles in noctilucent clouds Alexander A. Kokhanovsky * Institute of Environmental Physics, Bremen University, Otto Hahn Allee 1, D-28213 Bremen, Germany Received 3 February 2005; accepted 12 June 2005
Abstract Noctilucent clouds (NLCs) play an important indicative role in the physics of the summer polar mesopause. They consist of tiny ice crystals with characteristic dimensions generally smaller than 200 nm. However, the predominant shape of particles is not known. Therefore, biases in the size of crystals obtained from ground and space by light scattering and polarimetric techniques in the assumption of spherical scatterers can be considerable. This is due to the influence of shape effects on the scattering characteristics of particles. We test the assumption of the hexagonal and cubical particles as candidates for the predominant shapes of particles in NLCs using Maxwell electromagnetic theory to calculate the linear depolarization ratio (LDR). We compare results of recent measurements of LDRs with our calculations. Generally, theory and experiments agree very well at the NLC peak. The shape of crystals close to the cloud top cannot be explained by the model of compact particles. Relatively high light depolarization ratios detected from the upper part of the NLC are in agreement with models of elongated needle-like particles or particles having dimensions much larger than those usually attributed to NLC events. D 2005 Elsevier B.V. All rights reserved. Keywords: Light depolarization; Noctilucent clouds; Cubic and hexagonal particles
* Tel.: +49 421218 2915; fax: +49 421218 4555. E-mail address: [email protected]. 0169-8095/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2005.06.002
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1. Introduction The lowest temperatures in the terrestrial atmosphere are reached at the height range 80–90 km in areas surrounding the poles. For instance, they are close to 150 K in summer at these heights. Smaller values (e.g., 130 K and even below this limit) have also been reported (Gadsden and Schroeder, 1989; Schmidlin, 1991; Lu¨bken and Mu¨llemann, 2003). Such low values of temperature allow the formation of water molecular clusters and even macroscopic ice particles. These particles have typical characteristic sizes (e.g., radii of volume-equivalent spheres) generally smaller than 200 nm (Thomas and McKay, 1985; Kokhanovsky, 2005a,b) and are of a nonspherical shape (Baumgarten et al., 2002). The presence of particles produces the enhanced light scattering in correspondent atmospheric layers (Gadsden and Schroeder, 1989). This enhanced light scattering in the mesosphere has been observed from ground, satellite and rocket-borne measurements as so-called noctilucent clouds (NLCs). It is believed that Leslie (1885) was first to report on the phenomenon in the scientific magazine. Although similar observations were presented by Backhouse (1885) and Jesse (1885) about at the same time. NLCs are very tenuous objects (typically, the optical thickness is 10 4 or even below this value). This means that the extinction coefficient r ext for 1-km-thick cloud is around 10 4 km 1. McHugh et al. (2003) report values of r ext = 10 7–10 4 in the spectral range 2.45–6.26 Am as derived from the Halogen Occultation Experiment (HALOE). Note that NLC extinction coefficients derived from HALOE eight channels in the spectral range 2.45–10 Am show remarkable agreement with model spectra based on ice particle extinction with effective radii between 69 an 128 nm (Hervig et al., 2001). So we are sure that particles in NLCs are composed of ice. Because of comparatively large values of k selected for the HALOE, shape effects on the extinction spectra derived can be neglected (Bohren, 1983). NLCs can be seen from the ground by forward scattering of solar light only during twilight, when the observer and the atmosphere below clouds are in darkness while the clouds themselves remain sunlit. This condition occurs for solar depression angles 6–168 (Avaste et al., 1980; Taylor et al., 2002). von Zahn and Berger (2003) argue that in midsummer a persistent cloud of icy particles covers the summer pole down to about 608 latitude at mesopause heights. Particles are too small, however, to cause visible NLCs. Crystals formed at temperatures below 120 K will be amorphous; cubic ice forms between 120 K and 150 K; hexagonal ice is the main structure above 150 K (Hobbs, 1974; Mayer and Hallbrucker, 1987). The range of temperatures T = 125–160 K is typical for summer polar mesosphere (Lu¨bken and Mu¨llemann, 2003). This means that both cubic and hexagonal ice crystals may exist in NLCs and be predominant forms there (Murray et al., 2005). We check this hypothesis using the comparison of calculated and measured lidar depolarization ratios for randomly oriented hexagonal ice cylinders and cubes. Until recently light scattering characteristics of cubic and hexagonal particles could not be treated in the framework of the Maxwell electromagnetic theory due to the complexity associated with boundary conditions for such shapes. Therefore, such models as circular cylinders and ellipsoidal particles have been used to model the shape of particles in NLCs (Mishchenko, 1991; Baumgarten et al., 2002). Needless to say that such shapes are very remote from the shape of ice crystals in NLCs.
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Recent advances in the electromagnetic scattering theory (Draine, 1988; Rother et al., 2001; Wriedt, 2002) allowed to study more complex shapes including cylinders with noncircular cross-sections. Among different approaches proposed we use here the technique based on the discrete dipole approximation (DDA) (Draine, 1988). This technique does allow to obtain accurate results for particles of arbitrary shapes having sizes smaller than the light wavelength, which is the typical case for NLCs. The main idea of the DDA is the substitution of a particle by an array of dipoles and the use of the wellknown exact solution (Purcell and Pennypacker, 1973) for the problem of light interaction with an array of finite number of dipoles. The crucial point is the choice of the number of dipoles N to be used in calculations (Draine and Flatau, 1994). Clearly, the larger number of dipoles, the more accurate results are. Calculations presented in this paper are based on the presentation of a particle by approximately 400 000 dipoles. This allows to obtain accurate results for characteristics considered. In particular, we were able to reproduce Mie scattering results for a sphere with accuracy better than 1% for this choice of N. The refractive index of ice crystals was assumed to be equal 1.31 (Warren, 1984). All calculations were performed at the laser wavelength 532 nm at which lidar measurements of NLCs properties are usually conducted (Baumgarten et al., 2002).
2. The linear depolarization ratio The results of numerical calculations of the linear depolarization ratio (LDR) d = I 8 / I || for randomly oriented cubes and hexagonal cylinders as the function of the radius of the volume-equivalent spherical particle in the exact backward direction obtained in the framework of DDA are given in Fig. 1. Only the scattering of light in the single scattering regime for particles of the same shape and size in random orientation is studied in this work. Possible effects of polydispersity are ignored. The details of DDA technique are given by Draine (1988) and Kokhanovsky (2005b). Note that subscripts 8 and || refer to different registration schemes. In the first case the scattered light intensity component (I 8) which is cross-polarized in respect to the emitting laser beam is measured. The opposite is true for the component I ||. Clearly, there is no depolarization for spherical particles and d = 0.0 (van de Hulst, 1981; Kokhanovsky, 2003). The depolarization of light by nonspherical particles (even in the Rayleigh regime and at a random orientation (Bohren, 1983)) differs from zero. This is confirmed by results presented in Fig. 1. We see that the value of the linear depolarization is very small for cubes having sizes smaller than 170 nm (d V 1.6%). Similar results follow for hexagonal cylinders with the aspect ratio f assumed in calculations shown in Fig. 1. We found that the values of LDR grow with f. This allows to explain experimental results shown in Fig. 1 using models of still smaller particles (e.g., 40 nm for the aspect ratio 4 as found by us using DDA calculations). However, mechanisms of the asymmetric crystal growth at the NLCs typical heights were not identified so far. Note that dashed lines in Fig. 1 represent maximal values of d measured in three separate experiments (Baumgarten et al., 2002) at the altitude of the NLC peak. These measurements make it plausible to assume that shapes of crystals at the NLC peak are dominated by cubic or
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2.4
0
0
69 N16 E 2.2 cubes hexagonal cylinders
2.0
linear depolarization, %
1.8 July 20th, 1999
1.6 1.4 1.2
August 14th, 2000
1.0
0.8 August 3rd, 2000 0.6 0.4 0.2 0.0 0
50
100
150
200
250
radius, nm Fig. 1. The dependence of the linear depolarization ratio on the size of randomly oriented ice cubes and hexagonal cylinders at the wavelength 532 nm. The size is defined as the radius of a volume-equivalent sphere. The length of the cylinder is assumed to be equal to the length of the side of its hexagonal cross-section. The dashed lines show the maximal values of the linear depolarization ratio detected by Baumgarten et al. (2002) at the ALOMAR observation site (69 8N, 16 8E) on August 3rd and 14th, 2000 and on July 20th, 1999.
hexagonal scatterers of a comparatively large size. These shapes are also correspondent to underlying ice structures (Hobbs, 1974; Murray et al., 2005) possible for typical summer mesospheric temperatures above poles. The interpretation of LDR measurements as shown in Fig. 1 using smaller sizes of particles is possible assuming long hexagonal cylinders. Fig. 1 confirms that the selection of a particular shape is not an easy procedure even using data obtained with advanced lidar systems. For the correct determination of the predominant shape, in situ imaging techniques are of importance. But this is difficult to achieve at such a height (c85 km) even using up-to-date measurement techniques and capabilities. We would like to underline that lidar experiments performed by Baumgarten et al. (2002) identified the variability of LDR with height. This indicates that the size or shape of particles may change with the height in NLCs. In particular, they found values of d = 3.4 F 2.0% at the top of the noctilucent cloud. Therefore, taking into account typical sizes of crystals, cubes are not dominated shapes at NLCs tops (see Fig. 1). We left with the hexagonal crystal model then. Also the model of compact hexagonal crystals with the diameter of cross-section close to that of its length cannot be selected to represent data near the cloud top. Then we have: d V 1.6% at a V 200 nm (see Fig. 1). Instead the model of more depolarizing long hexagonal cylinders should be used. Our DDA showed that the hexagonal plates are weak depolarizers as compared with long hexagonal cylinders.
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Baumgarten et al. (2002) report the average value of d = 1.7F1.0% for the NLC observed on August 3rd, 2000 at 69 8N, 16 8E. The values of d equal to 0.7–1.6 are consistent with the model of randomly oriented ice cubes and compact hexagonal crystals having values of a = 150–250 nm or even slightly larger. However, it is often found that the sizes of particles in NLCs are at least three times smaller (Von Cossart et al., 1999). To have values of LDR in the range 0.7–1.6 for the size range 40–60nm, one needs to assume that hexagonal prisms are presented in NLCs as long columnar crystals (at least with ratios of the side size of the hexagonal cross-section to the length of the cylinder equal to 0.25 as we find using DDA calculations for such particles). Values of d above 1.6% can be explained only if the model of needle-like (partially or completely oriented) ice particles is invoked (see, e.g., Baumgarten et al., 2002). However, the mechanisms of the possible particle orientation (Bohren, 1983) and the preferential particle growth in a fixed direction (Svanberg et al., 1998) have been not identified so far. We conclude that the shape of crystals near cloud tops remains unclear. This should be clarified in the future.
3. Discussion and conclusions It comes as a great surprise that apparently NLCs have not been discovered till 1885 (Gadsden and Schroeder, 1989). Therefore, one may conclude that NLCs properties have been changed in industrial era in such an extent that they become visible (e.g., due to larger sizes of particles). Roble and Dickinson (1989) argue that the global warming in the lower atmosphere is accompanied by the global cooling in the upper atmosphere. Lower temperatures at mesosphere can contribute to easier condensation of water vapor into small crystals. If the assumption of the global mesospheric cooling is indeed true, then NLCs give early warning to us in respect to global climate changes (e.g., see Klostermeyer, 2002; Shettle et al., 2002). This means that NLCs deserve much more attention. In particular, global measurements of the ice crystal sizes and concentrations in NLCs should be performed on a regular basis. This is possible using limb UV-observations from satellite platforms (Carbary et al., 2002; von Savigny et al., 2004). Then the contribution to the observed signal from the ground surface and lower atmosphere is greatly reduced. This allows to detect trends in these microphysical parameters as an early warning of an anthropogenic climate change in the antropocene era, which is an important issue of modern science. In particular, Crutzen and Steffen (2003) claim that we already live on the planet which is operating in a no-analogue state. Note that the problem of the size/concentration of particles in NLCs cannot be properly addressed if the shape of crystals remains an unknown parameter. 120-year research of NLCs did not bring answer to this important question. I hope that this communication in the year of the 120th anniversary of the NLCs discovery (Leslie, 1885) will attract more research in the area of noctilucent clouds optical and microphysical properties. In particular, I show that the model of randomly oriented compact ice hexagonal particles (and also cubes) can explain the measured linear depolarization ratios at the peak of NLC. For this, however, one must assume that the sizes of particles are quite large. Relatively high linear depolarization ratios close to the cloud
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top can be explained also using the model of small needle-like oriented particles (Baumgarten et al., 2002). But the reason for the orientation or the preferential growth of tiny ice crystals in noctilucent clouds is not identified so far. In particular, mechanisms of the aerodynamical/electric/magnetic alignment do not work for tiny ice crystals in mesosphere (Bohren, 1983). Also it could be well the case that the extraterrestrial particles contribute to the values of d observed, which complicates the problem even further. More measurements (especially those involved polarization (Witt, 1960; Gadsden et al., 1979) are needed to solve the problem of the crystal shapes in NLCs. Without the solution of this problem, the size of particles in NLCs derived from ground-based and satellite remote sensing techniques remains highly uncertain. For instance, unrealistically small/ large sizes derived may lead us to a contradiction with independent measurements of water vapor content in mesosphere (Ko¨rner and Sonnemann, 2001). Results as shown in Fig. 1 are valid for monodispersed particles. In particular, the value of d at backscattering direction was calculated as the ratio (1 f) / (1 + f), where f is the normalized phase matrix element P 44/P 11 given in the output of the DDA code (Draine and Flatau, 1994). The account for the polydispersity of particles may change the magnitude of peaks shown in Fig. 1. We did not make attempts to perform such calculations due to computer time constrains. Indeed, calculations as shown in Fig. 1 are extremely time consuming. However, we believe that the resonance behavior is less pronounced for randomly oriented monodispersed nonspherical particles as compared to spherical scatterers. Water can present in NLCs in the form of cubic and hexagonal ice (Murray et al., 2005). This means that the models of particles based on cubic and hexagonal shapes must be advanced in optics of noctilucent clouds (Kokhanovsky, 2005a,b).
Acknowledgements The author thanks B.T. Draine for the DDA code and J. Miao for the help to clear important questions related to its performance. I also express my gratitude to J.P. Burrows, K.H. Fricke, C. von Savingny, and G. Witt for important discussions on the subject of NLCs. This work was partially funded by the BMBF via GSF/PT-UKF(07UFE 12/8) and DFG Project BU 688/8-1.
References Avaste, O.A., et al., 1980. Advances in Noctilucent cloud research in the space era. PAGEOPH 118, 528 – 580. Backhouse, T.W., 1885. The luminous cirrus cloud of June and July. Meteorol. Mag. 20, 133. Baumgarten,, et al., 2002. Investigation of the shape of noctilucent cloud particles by polarization lidar technique. Geophys. Res. Lett. 29, 13, doi:10.1029/2001GL013877. Bohren, C.F., 1983. On the size, shape, and orientation of noctilucent cloud particles. Tellus 35B, 65 – 72. Carbary, J.F., et al., 2002. Particle characteristics from the spectra of polar mesospheric clouds. J. Geophys. Res. 107 (D23), 4686, doi:10.1029/2001JD001154. Crutzen, P., Steffen, W., 2003. How long we have been in the anthropocene era? Clim. Change 61, 251 – 257. Draine, B.T., 1988. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848 – 872.
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Draine, B.T., Flatau, P.J., 1994. Discrete-dipole approximation for scattering calculations. J. Opt. Soc. Am. 11 (4), 1491 – 1499. Gadsden, M., Schroeder, W., 1989. Noctilucent Clouds. Springer-Verlag, Berlin. Gadsden, M., et al., 1979. Detection of circularly polarized light from noctilucent clouds. Nature 278, 628 – 629. Hervig, M., et al., 2001. First confirmation that water ice is the primary components of polar mesospheric clouds. Geophys. Res. Lett. 28 (6), 971 – 974. Hobbs, P.V., 1974. Ice Physics. Clarendon, Oxford. Jesse, O., 1885. Auffalende Abenderscheinungen am Himmel. Meteorol. Z. 2, 311 – 312. Kokhanovsky, A.A., 2003. Polarization Optics of Random Media. Springer-Praxis, Berlin. Kokhanovsky, A.A., 2005a. Phase matrix of crystals in noctilucent clouds. SPIE Proc. 5829, 44 – 52. Kokhanovsky, 2005b. Microphysical and optical properties of noctilucent clouds, Earth-Sci. Rev. 71, 127–146. Klostermeyer, J., 2002. Noctilucent clouds getting brighter. J. Geophys. Res. 107 (D14), doi:10.1029/ 2001JD001345. Ko¨rner, U., Sonnemann, G.R., 2001. Global three-dimensional modeling of the water vapor concentration of the mesosphere–mesopause region and implications with respect to the noctilucent cloud region. J. Geophys. Res. 106 (D9), 9639 – 9651. Leslie, R.C., 1885. Sky glows. Nature 32, 245. Lu¨bken, F.-J., Mu¨llemann, A., 2003. First in situ temperature measurements in the summer mesosphere at very high latitudes (78 8N). J. Geophys. Res. 108 (D8), 8448, doi:10.1029/2002JD002414. Mayer, E., Hallbrucker, A., 1987. Cubic ice from liquid water. Nature 325, 601 – 602. McHugh, M., et al., 2003. Improved mesospheric temperature, water vapor and polar mesospheric cloud extinctions from HALOE. Geophys. Res. Lett. 30 (8), 1440, doi:10.1029/2002GL016859. Mishchenko, M.I., 1991. Light scattering by nonspherical ice grains: an application to noctilucent cloud particles. Moon, Earth, and Planets 57, 203 – 211. Murray, B.J., Knopf, D.A., Bertram, A.K., 2005. The formation of cubic ice under conditions relevant to Earth’s atmosphere. Nature 434, 202 – 205. Purcell, E.M., Pennypacker, C.R., 1973. Scattering and absorption of light by nonspherical dielectric grains. Astron. J. 186, 705 – 714. Roble, R.G., Dickinson, R.E., 1989. How will changes in carbon dioxide and methane modify the mean structure of the mesosphere and thermosphere. Geophys. Res. Lett. 16, 1441 – 1444. Rother, T., et al., 2001. Light scattering on hexagonal ice columns. J. Opt. Soc. Am. 18, 2512 – 2517. Schmidlin, F.J., 1991. The inflatable sphere: a technique for the accurate measurement of middle atmosphere temperatures. J. Geophys. Res. 96, 22673 – 22682. Shettle, E.P., et al., 2002. Three-satellite comparison of polar mesospheric clouds: evidence for long-term change. J. Geophys. Res. 107 (D12), doi:10.1029/2001JD000668. Svanberg, M., et al., 1998. Collision dynamics of large water clusters. J. Chem. Phys. 108 (14), 5888 – 5897. Taylor, M.J., et al., 2002. Mesospheric cloud observations at unusually low latitudes. J. Atmos. Sol.-Terr. Phys. 64, 991 – 999. Thomas, G.E., McKay, C.P., 1985. On the mean particle size and water content of polar mesospheric clouds. Planet. Space Sci. 33 (10), 1209 – 1224. van de Hulst, H.C., 1981. Light Scattering by Small Particles. Dover, NY. Von Cossart, G., Fiedler, J., von Zahn, U., 1999. Size distributions of NLC particles as determined from 3-colour observations of NLC by ground-based lidar. Geophys. Res. Lett. 26, 1513 – 1516. von Savigny, C., et al., 2004. NLC detection and particle size determination: first results from SCIAMACHY on ENVISAT. Adv. Space Res. 34, 851 – 856. von Zahn, U., Berger, U., 2003. Persistent ice cloud in the midsummer upper mesosphere at high latitudes: threedimensional modeling and cloud interactions with ambient water vapor. J. Geophys. Res. 108 (D8), 8451, doi:10.1029/2002JD002409. Warren, S.G., 1984. Optical constants of ice from the ultraviolet to the microwave. Appl. Opt. 23, 1206 – 1225. Witt, G., 1960. Polarization of light from Noctilucent Clouds. J. Geophys. Res. 65, 925 – 933. Wriedt, T., 2002. Using the T-matrix light scattering computations by non-axisymmetric particles: superellipsoids and realistic shapes. Part. Part. Charact. 19, 256 – 268.
Modeling of light depolarization by cubic and hexagonal particles in noctilucent clouds Alexander A. Kokhanovsky * Institute of Environmental Physics, Bremen University, Otto Hahn Allee 1, D-28213 Bremen, Germany Received 3 February 2005; accepted 12 June 2005
Abstract Noctilucent clouds (NLCs) play an important indicative role in the physics of the summer polar mesopause. They consist of tiny ice crystals with characteristic dimensions generally smaller than 200 nm. However, the predominant shape of particles is not known. Therefore, biases in the size of crystals obtained from ground and space by light scattering and polarimetric techniques in the assumption of spherical scatterers can be considerable. This is due to the influence of shape effects on the scattering characteristics of particles. We test the assumption of the hexagonal and cubical particles as candidates for the predominant shapes of particles in NLCs using Maxwell electromagnetic theory to calculate the linear depolarization ratio (LDR). We compare results of recent measurements of LDRs with our calculations. Generally, theory and experiments agree very well at the NLC peak. The shape of crystals close to the cloud top cannot be explained by the model of compact particles. Relatively high light depolarization ratios detected from the upper part of the NLC are in agreement with models of elongated needle-like particles or particles having dimensions much larger than those usually attributed to NLC events. D 2005 Elsevier B.V. All rights reserved. Keywords: Light depolarization; Noctilucent clouds; Cubic and hexagonal particles
* Tel.: +49 421218 2915; fax: +49 421218 4555. E-mail address: [email protected]. 0169-8095/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2005.06.002
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1. Introduction The lowest temperatures in the terrestrial atmosphere are reached at the height range 80–90 km in areas surrounding the poles. For instance, they are close to 150 K in summer at these heights. Smaller values (e.g., 130 K and even below this limit) have also been reported (Gadsden and Schroeder, 1989; Schmidlin, 1991; Lu¨bken and Mu¨llemann, 2003). Such low values of temperature allow the formation of water molecular clusters and even macroscopic ice particles. These particles have typical characteristic sizes (e.g., radii of volume-equivalent spheres) generally smaller than 200 nm (Thomas and McKay, 1985; Kokhanovsky, 2005a,b) and are of a nonspherical shape (Baumgarten et al., 2002). The presence of particles produces the enhanced light scattering in correspondent atmospheric layers (Gadsden and Schroeder, 1989). This enhanced light scattering in the mesosphere has been observed from ground, satellite and rocket-borne measurements as so-called noctilucent clouds (NLCs). It is believed that Leslie (1885) was first to report on the phenomenon in the scientific magazine. Although similar observations were presented by Backhouse (1885) and Jesse (1885) about at the same time. NLCs are very tenuous objects (typically, the optical thickness is 10 4 or even below this value). This means that the extinction coefficient r ext for 1-km-thick cloud is around 10 4 km 1. McHugh et al. (2003) report values of r ext = 10 7–10 4 in the spectral range 2.45–6.26 Am as derived from the Halogen Occultation Experiment (HALOE). Note that NLC extinction coefficients derived from HALOE eight channels in the spectral range 2.45–10 Am show remarkable agreement with model spectra based on ice particle extinction with effective radii between 69 an 128 nm (Hervig et al., 2001). So we are sure that particles in NLCs are composed of ice. Because of comparatively large values of k selected for the HALOE, shape effects on the extinction spectra derived can be neglected (Bohren, 1983). NLCs can be seen from the ground by forward scattering of solar light only during twilight, when the observer and the atmosphere below clouds are in darkness while the clouds themselves remain sunlit. This condition occurs for solar depression angles 6–168 (Avaste et al., 1980; Taylor et al., 2002). von Zahn and Berger (2003) argue that in midsummer a persistent cloud of icy particles covers the summer pole down to about 608 latitude at mesopause heights. Particles are too small, however, to cause visible NLCs. Crystals formed at temperatures below 120 K will be amorphous; cubic ice forms between 120 K and 150 K; hexagonal ice is the main structure above 150 K (Hobbs, 1974; Mayer and Hallbrucker, 1987). The range of temperatures T = 125–160 K is typical for summer polar mesosphere (Lu¨bken and Mu¨llemann, 2003). This means that both cubic and hexagonal ice crystals may exist in NLCs and be predominant forms there (Murray et al., 2005). We check this hypothesis using the comparison of calculated and measured lidar depolarization ratios for randomly oriented hexagonal ice cylinders and cubes. Until recently light scattering characteristics of cubic and hexagonal particles could not be treated in the framework of the Maxwell electromagnetic theory due to the complexity associated with boundary conditions for such shapes. Therefore, such models as circular cylinders and ellipsoidal particles have been used to model the shape of particles in NLCs (Mishchenko, 1991; Baumgarten et al., 2002). Needless to say that such shapes are very remote from the shape of ice crystals in NLCs.
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Recent advances in the electromagnetic scattering theory (Draine, 1988; Rother et al., 2001; Wriedt, 2002) allowed to study more complex shapes including cylinders with noncircular cross-sections. Among different approaches proposed we use here the technique based on the discrete dipole approximation (DDA) (Draine, 1988). This technique does allow to obtain accurate results for particles of arbitrary shapes having sizes smaller than the light wavelength, which is the typical case for NLCs. The main idea of the DDA is the substitution of a particle by an array of dipoles and the use of the wellknown exact solution (Purcell and Pennypacker, 1973) for the problem of light interaction with an array of finite number of dipoles. The crucial point is the choice of the number of dipoles N to be used in calculations (Draine and Flatau, 1994). Clearly, the larger number of dipoles, the more accurate results are. Calculations presented in this paper are based on the presentation of a particle by approximately 400 000 dipoles. This allows to obtain accurate results for characteristics considered. In particular, we were able to reproduce Mie scattering results for a sphere with accuracy better than 1% for this choice of N. The refractive index of ice crystals was assumed to be equal 1.31 (Warren, 1984). All calculations were performed at the laser wavelength 532 nm at which lidar measurements of NLCs properties are usually conducted (Baumgarten et al., 2002).
2. The linear depolarization ratio The results of numerical calculations of the linear depolarization ratio (LDR) d = I 8 / I || for randomly oriented cubes and hexagonal cylinders as the function of the radius of the volume-equivalent spherical particle in the exact backward direction obtained in the framework of DDA are given in Fig. 1. Only the scattering of light in the single scattering regime for particles of the same shape and size in random orientation is studied in this work. Possible effects of polydispersity are ignored. The details of DDA technique are given by Draine (1988) and Kokhanovsky (2005b). Note that subscripts 8 and || refer to different registration schemes. In the first case the scattered light intensity component (I 8) which is cross-polarized in respect to the emitting laser beam is measured. The opposite is true for the component I ||. Clearly, there is no depolarization for spherical particles and d = 0.0 (van de Hulst, 1981; Kokhanovsky, 2003). The depolarization of light by nonspherical particles (even in the Rayleigh regime and at a random orientation (Bohren, 1983)) differs from zero. This is confirmed by results presented in Fig. 1. We see that the value of the linear depolarization is very small for cubes having sizes smaller than 170 nm (d V 1.6%). Similar results follow for hexagonal cylinders with the aspect ratio f assumed in calculations shown in Fig. 1. We found that the values of LDR grow with f. This allows to explain experimental results shown in Fig. 1 using models of still smaller particles (e.g., 40 nm for the aspect ratio 4 as found by us using DDA calculations). However, mechanisms of the asymmetric crystal growth at the NLCs typical heights were not identified so far. Note that dashed lines in Fig. 1 represent maximal values of d measured in three separate experiments (Baumgarten et al., 2002) at the altitude of the NLC peak. These measurements make it plausible to assume that shapes of crystals at the NLC peak are dominated by cubic or
178
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2.4
0
0
69 N16 E 2.2 cubes hexagonal cylinders
2.0
linear depolarization, %
1.8 July 20th, 1999
1.6 1.4 1.2
August 14th, 2000
1.0
0.8 August 3rd, 2000 0.6 0.4 0.2 0.0 0
50
100
150
200
250
radius, nm Fig. 1. The dependence of the linear depolarization ratio on the size of randomly oriented ice cubes and hexagonal cylinders at the wavelength 532 nm. The size is defined as the radius of a volume-equivalent sphere. The length of the cylinder is assumed to be equal to the length of the side of its hexagonal cross-section. The dashed lines show the maximal values of the linear depolarization ratio detected by Baumgarten et al. (2002) at the ALOMAR observation site (69 8N, 16 8E) on August 3rd and 14th, 2000 and on July 20th, 1999.
hexagonal scatterers of a comparatively large size. These shapes are also correspondent to underlying ice structures (Hobbs, 1974; Murray et al., 2005) possible for typical summer mesospheric temperatures above poles. The interpretation of LDR measurements as shown in Fig. 1 using smaller sizes of particles is possible assuming long hexagonal cylinders. Fig. 1 confirms that the selection of a particular shape is not an easy procedure even using data obtained with advanced lidar systems. For the correct determination of the predominant shape, in situ imaging techniques are of importance. But this is difficult to achieve at such a height (c85 km) even using up-to-date measurement techniques and capabilities. We would like to underline that lidar experiments performed by Baumgarten et al. (2002) identified the variability of LDR with height. This indicates that the size or shape of particles may change with the height in NLCs. In particular, they found values of d = 3.4 F 2.0% at the top of the noctilucent cloud. Therefore, taking into account typical sizes of crystals, cubes are not dominated shapes at NLCs tops (see Fig. 1). We left with the hexagonal crystal model then. Also the model of compact hexagonal crystals with the diameter of cross-section close to that of its length cannot be selected to represent data near the cloud top. Then we have: d V 1.6% at a V 200 nm (see Fig. 1). Instead the model of more depolarizing long hexagonal cylinders should be used. Our DDA showed that the hexagonal plates are weak depolarizers as compared with long hexagonal cylinders.
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Baumgarten et al. (2002) report the average value of d = 1.7F1.0% for the NLC observed on August 3rd, 2000 at 69 8N, 16 8E. The values of d equal to 0.7–1.6 are consistent with the model of randomly oriented ice cubes and compact hexagonal crystals having values of a = 150–250 nm or even slightly larger. However, it is often found that the sizes of particles in NLCs are at least three times smaller (Von Cossart et al., 1999). To have values of LDR in the range 0.7–1.6 for the size range 40–60nm, one needs to assume that hexagonal prisms are presented in NLCs as long columnar crystals (at least with ratios of the side size of the hexagonal cross-section to the length of the cylinder equal to 0.25 as we find using DDA calculations for such particles). Values of d above 1.6% can be explained only if the model of needle-like (partially or completely oriented) ice particles is invoked (see, e.g., Baumgarten et al., 2002). However, the mechanisms of the possible particle orientation (Bohren, 1983) and the preferential particle growth in a fixed direction (Svanberg et al., 1998) have been not identified so far. We conclude that the shape of crystals near cloud tops remains unclear. This should be clarified in the future.
3. Discussion and conclusions It comes as a great surprise that apparently NLCs have not been discovered till 1885 (Gadsden and Schroeder, 1989). Therefore, one may conclude that NLCs properties have been changed in industrial era in such an extent that they become visible (e.g., due to larger sizes of particles). Roble and Dickinson (1989) argue that the global warming in the lower atmosphere is accompanied by the global cooling in the upper atmosphere. Lower temperatures at mesosphere can contribute to easier condensation of water vapor into small crystals. If the assumption of the global mesospheric cooling is indeed true, then NLCs give early warning to us in respect to global climate changes (e.g., see Klostermeyer, 2002; Shettle et al., 2002). This means that NLCs deserve much more attention. In particular, global measurements of the ice crystal sizes and concentrations in NLCs should be performed on a regular basis. This is possible using limb UV-observations from satellite platforms (Carbary et al., 2002; von Savigny et al., 2004). Then the contribution to the observed signal from the ground surface and lower atmosphere is greatly reduced. This allows to detect trends in these microphysical parameters as an early warning of an anthropogenic climate change in the antropocene era, which is an important issue of modern science. In particular, Crutzen and Steffen (2003) claim that we already live on the planet which is operating in a no-analogue state. Note that the problem of the size/concentration of particles in NLCs cannot be properly addressed if the shape of crystals remains an unknown parameter. 120-year research of NLCs did not bring answer to this important question. I hope that this communication in the year of the 120th anniversary of the NLCs discovery (Leslie, 1885) will attract more research in the area of noctilucent clouds optical and microphysical properties. In particular, I show that the model of randomly oriented compact ice hexagonal particles (and also cubes) can explain the measured linear depolarization ratios at the peak of NLC. For this, however, one must assume that the sizes of particles are quite large. Relatively high linear depolarization ratios close to the cloud
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top can be explained also using the model of small needle-like oriented particles (Baumgarten et al., 2002). But the reason for the orientation or the preferential growth of tiny ice crystals in noctilucent clouds is not identified so far. In particular, mechanisms of the aerodynamical/electric/magnetic alignment do not work for tiny ice crystals in mesosphere (Bohren, 1983). Also it could be well the case that the extraterrestrial particles contribute to the values of d observed, which complicates the problem even further. More measurements (especially those involved polarization (Witt, 1960; Gadsden et al., 1979) are needed to solve the problem of the crystal shapes in NLCs. Without the solution of this problem, the size of particles in NLCs derived from ground-based and satellite remote sensing techniques remains highly uncertain. For instance, unrealistically small/ large sizes derived may lead us to a contradiction with independent measurements of water vapor content in mesosphere (Ko¨rner and Sonnemann, 2001). Results as shown in Fig. 1 are valid for monodispersed particles. In particular, the value of d at backscattering direction was calculated as the ratio (1 f) / (1 + f), where f is the normalized phase matrix element P 44/P 11 given in the output of the DDA code (Draine and Flatau, 1994). The account for the polydispersity of particles may change the magnitude of peaks shown in Fig. 1. We did not make attempts to perform such calculations due to computer time constrains. Indeed, calculations as shown in Fig. 1 are extremely time consuming. However, we believe that the resonance behavior is less pronounced for randomly oriented monodispersed nonspherical particles as compared to spherical scatterers. Water can present in NLCs in the form of cubic and hexagonal ice (Murray et al., 2005). This means that the models of particles based on cubic and hexagonal shapes must be advanced in optics of noctilucent clouds (Kokhanovsky, 2005a,b).
Acknowledgements The author thanks B.T. Draine for the DDA code and J. Miao for the help to clear important questions related to its performance. I also express my gratitude to J.P. Burrows, K.H. Fricke, C. von Savingny, and G. Witt for important discussions on the subject of NLCs. This work was partially funded by the BMBF via GSF/PT-UKF(07UFE 12/8) and DFG Project BU 688/8-1.
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