Earth-Science Reviews 64 (2004) 189–241 www.elsevier.com/locate/earscirev Optical properties of terrestrial clouds A. Kokhanovsky* Institute of Environmental Physics, University of Bremen, Otto Hahn Allee 1, D-28334 Bremen, Germany Institute of Physics, 70 Skarina Avenue, Minsk 220072, Belarus Received 18 January 2002; accepted 16 April 2003 Abstract The aim of this review is to consider optical characteristics of terrestrial clouds. Both single and multiple light-scattering properties of water clouds are studied. The numerous results discussed can be used for solutions to both inverse and direct problems of cloud optics. An introduction to main microphysical characteristics of water and ice clouds, including the effective size, the liquid water content and path, the concentration of particles, is given. The refractive index of water and ice, which is of importance for optical waves propagation in clouds, is also considered. We consider extinction and absorption coefficients, phase functions, and asymmetry parameters of water and ice clouds and their relationships with the size, shape, and concentration of water droplets and ice crystals. Simple analytical results for absorption, reflection, and transmission characteristics of cloudy media are given. They are valid for optically thick clouds with optical thickness larger than 5. We have reviewed studies of polarization of solar light reflected from clouds. Image transfer problems have been considered as well. Modern methods of passive remote sensing of water and ice clouds are discussed. The review is finished by the discussion of optical properties of inhomogeneous clouds, which is a main topic of modern cloud optics research. D 2003 Elsevier B.V. All rights reserved. Keywords: Radiative transfer; Light scattering and propagation; Water and ice clouds 1. Introduction serve as a blanket to protect the Earth’s surface against cooling at night. This is due to the fact that the Water, ice, and mixed clouds are major regulators of maximum of the terrestrial emission is in the far infra- solar fluxes in the terrestrial atmosphere (Kondratyev red, where water droplets are highly absorbing. and Binenko, 1984; Liou, 1992, 2002). They reflect a Clouds, mists, and fogs are very common. They large portion of incoming visible radiation back to reduce the visibility of objects in the atmosphere and outer space. The light energy absorbed by water drop- limit capabilities of atmospheric vision, remote sens- lets and ice crystals leads to heating of atmospheric ing, and detection systems (Zege et al., 1991). Thus, it layers. Another important role of cloudy media is to is of a great importance to understand the peculiarities of light interaction with cloudy media, which can be considered as a huge ‘‘colloid’’, composed of liquid * Institute of Environmental Physics, University of Bremen, and solid water particles, dispersed in the air. It should P.O. Box 330440. Otto Hahn Allee 1, D-28334 Bremen, Germany. Tel.: +49-421-218-4475; fax: +49-421-218-4555. be pointed out that water droplets and air around them E-mail address: [email protected] can be contaminated by various fine particles (e.g., (A. Kokhanovsky). soot and dust particles). These aerosol particles influ- 0012-8252/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0012-8252(03)00042-4 190 A. Kokhanovsky / Earth-Science Reviews 64 (2004) 189–241 ence both light-scattering and absorption properties of 2. Microphysical characteristics cloudy media, making the studies of light propagation in cloudy media even more difficult (Menon et al., 2.1. Water clouds 2002). The very existence of clouds is due to fine- aerosol particles, the so-called cloud nuclei (Twomey, 2.1.1. Particle-size distributions 1977), with typical radii between 5 and 200 nm Water clouds consist of small liquid droplets that (Mason, 1975). generally have the spherical shape although particles Studies of optical and microphysical properties of of other shapes can exist due to different external cloudy media have a long and fruitful history. The influences. For instance, the deformation of large results of these investigations have been summarized in particles due to the gravitation force is of importance numerous books and papers (Kondratyev and Binenko, for raining clouds with particles having radii 1 mm 1984; Zege et al., 1991; Liou, 1992, 2002; Kokhanov- and larger (Macke and Grossklaus, 1998). The aver- sky, 2001a). The main properties of cloudy media are age radius of droplets in nonraining water clouds is well understood now, but unsolved problems remain. usually around 10 Am and the approximation of The most important of these include the accounting for spherical particles works quite well. Natural clouds the three-dimensional shape of clouds (Evans, 1998; with droplets of uniform size throughout never occur Mackeetal.,1999;Schreier,2001;Schreierand due to the variability of physical properties of air both Macke, 2001), and their inhomogenity in horizontal in space and time domains (Twomey, 1977). Thus, and vertical directions (Cahalan et al., 1994, 2001; one can consider a radius of a droplet, a, as a random Platnick, 2000, 2001). The influence of aerosols inside value, which is characterized by the distribution cloudy media, which can be one of explanations of the function f(a). This function is normalized by the anomalous absorption paradox (Danielson et al., 1969; following condition: Rozenberg et al., 1978; Stephens and Tsay, 1990), also Z l should be clarified. f ðaÞda ¼ 1: ð2:1Þ Another current issue is the characterization of 0 optical properties of ice clouds, which have extremely complex microstructure (Liou, 1992, 2002; Liou and The integral Takano, 1994; Macke et al., 1996; Yang and Liou, Z 1998; Kokhanovsky and Macke, 1999; Yang et al., a2 FðaÞ¼ f ðaÞda ð2:2Þ 2000, 2001) and appear almost with the same fre- a1 quency as water clouds. One rarely finds two identical crystals in ice clouds because preferential shapes vary gives the fraction of particles with radii between a1 with temperature and pressure (Mason, 1975), which and a2 in a unit volume of a cloud. The distribution vary across cloudy media (Yang et al., 2001).It function f(a) can be represented as a histogram, should be stressed that optical properties of a single graphically or in a tabular form (Ayvazian, 1991). particle and, as a result, optical properties of a cloud However, it is the most common to use an analytical as a whole are highly influenced by particles’ shapes form of this function, involving only two or three (Mishchenko et al., 1995, 1996, 1999, 2000). parameters (Deirmendjian, 1969). Of course, this is a A complete review across all fields of cloud optics, great simplification of real situations occurring in which is in a state of a rapid transition, would be natural clouds, but most optical characteristics of a difficult within a single book, not to mention in a single cloud as a whole practically do not depend on the fine article. Thus, I will concentrate mostly on analytical structures of particle-size distributions (PSD) f(a) results, which can be used for cloud optical properties (Hansen and Travis, 1974). McGraw et al. (1998) studies. The formulae presented can be applied for found that the local optical properties of polydisper- rapid estimations of light fluxes in cloudy atmosphere sions can be modelled with high accuracy by just the and will assist understanding the information content of first six moments of the particle-size distribution, and transmitted and reflection functions of cloudy media in the use of certain combinations of moments can respect to microphysical characteristics of clouds. reduce the number of parameters even further. A. Kokhanovsky / Earth-Science Reviews 64 (2004) 189–241 191 In most cases, the function f(a) can be represented Cðl þ 4Þ hWi¼ w0; ð2:13Þ by the gamma distribution (Deirmendjian, 1969): l3Cðl þ 1Þ l Àl a f ðaÞ¼Na e a0 ; ð2:3Þ where where 3 4pa0 2 v0 ¼ ; s0 ¼ 4pa ; w0 ¼ qv0 ð2:14Þ llþ1 3 0 N ¼ lþ1 ð2:4Þ Cðl þ 1Þa0 are corresponding parameters for monodispersed par- ticles with radii a . One can obtain in the case of the is the normalization constant and C(l +1) is the 0 most often employed cloud model with a0 =4Am and Gamma function. It follows that the first derivative l = 6 (Cloud C.1 model of Deirmendjian, 1969): f V(a0) = 0 and the second derivative f U(a0) < 0 (see Eq. (2.3)). Thus, the function (Eq. (2.3)) has the maximum 7 14 7 hVi¼ v0; hRi¼ s0; hWi¼ w0; ð2:15Þ at a = a0. Note that Eq. (2.4) follows from Eq. (2.1) 3 9 3 and the definition of the Gamma function: c À 16 3 c À 12 2 Z l where v0 2.7 Â 10 m , s0 2 Â 10 m , c À 10 CðlÞ¼ xlÀ1eÀxdx: ð2:5Þ w0 2.7 Â 10 g. Although parameters (Eq. 0 (2.14)) are small, the very large numbers of cloud One can see that the parameter l characterizes the droplets (typically, 100 particles in cm3)create width of the particle-size distribution f(a), being important factors for atmospheric processes (see next smaller for wider distributions. Moments section). Z l Eq. (2.3) allows to characterize the cloud droplet n n ha i¼ a f ðaÞda ð2:6Þ distribution only by two parameters: a0 and l. 0 However, it should be remembered that neither is of the distribution (Eq. (2.3)) are calculated from the constant and can vary inside the body of a cloud. following simple analytical equation Thus, their values depend on the averaging scale, with large averaging scales producing more broad a n Cðl þ n þ 1Þ hani¼ 0 : ð2:7Þ particle-size distributions with smaller values of l.