Polarization of Thermal Microwave Atmospheric ... - AMS Journals

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JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 60

Polarization of Thermal Microwave Atmospheric Radiation Due to Scattering by Ice Particles in Clouds A. V. TROITSKY

AND

A. M. OSHARIN

Institute of Radiophysics, Nizhny Novgorod, Russia

A. V. KOROLEV Sky Tech Research, Inc., Richmond Hill, Ontario, Canada

J. W. STRAPP Cloud Physics Research Division, Meteorological Service of Canada, Downsview, Ontario, Canada (Manuscript received 21 May 2002, in final form 23 January 2003) ABSTRACT The polarization difference DT b between the vertical and horizontal components of thermal radiation emitted by clouds was studied using 37- and 85-GHz radiometers. The measurements were conducted during the Alliance Icing Research Project in Ottawa, Canada, during the winter of 1999/2000. Polarization differences (DT b ) greater than 0.1 K were observed in approximately 30% of the cloudy periods. Characteristic values of the polarization difference at 85 GHz were about 2 K with a maximum value of about 4.5 K. Polarization difference at 37 GHz usually did not exceed 2.5 K and was typically 2–6 times less than that at 85 GHz. Both positive and negative polarization differences were observed. It is suggested that the microwave polarization results from scattering of atmospheric thermal radiation by cloud ice particles. The observations were interpreted with a model of radiative transfer in mixed-phase clouds. The characteristic polarization difference observed during groundbased measurements was found to agree with predictions of the radiative transfer model for typical values of cloud liquid and ice water content.

1. Introduction Thermal microwave atmospheric radiation has been studied since the 1950s. For decades the thermal microwave radiation was assumed to be unpolarized for both the clear and cloudy atmosphere (e.g., Basharinov et al. 1974; Stepanenko et al. 1987; Jansen 1993). This assumption was applied to the interpretation of measurements of natural microwave thermal atmospheric emission and radiation from space sources passing through the atmosphere. Kutuza (1977) observed the polarization of downwelling thermal microwave radiation at a wavelength l 5 2.25 cm in the presence of liquid precipitation. Detailed studies conducted by Kutuza et al. (1998) and Zagorin and Kutuza (1998) suggested that the observed polarization is caused by the nonsphericity and preferential Corresponding author address: Alexei Korolev, Sky Tech Research, Inc., 28 Don Head Village Blvd., Richmond Hill, ON L4C 7M6, Canada. E-mail: [email protected]

q 2003 American Meteorological Society

orientation of raindrops. Experimental observations of the upwelling microwave radiation from precipitating clouds have also been collected from spaceborne platforms (e.g., Spencer et al. 1989; Heymsfield and Fulton 1994; Petty and Turk 1996; Petty 2001). Polarization of the microwave radiation by nonspherical particles has also been discussed in a number of theoretical studies (e.g., Czekala 1998; Evans and Vivekanandan 1990; Evans and Stephens 1995a; Turk and Vivekanandan 1995). A detailed review can be found in Mishchenko et al. (2000). The phenomenon of polarization of the nonprecipitating cloudy atmosphere was first observed in ground-based observations at l 5 3.2 mm by Troitsky and Osharin (1999, 2000). It was found that the polarization effect is rather common in winter clouds. The average difference between the vertical and horizontal polarization brightness temperatures was found to be approximately 3 K at 94 GHz for a zenith viewing angle 708. It was suggested that the observed polarization could be explained by the scattering of

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atmospheric radiation on preferentially oriented ice particles. The study of the polarized characteristics of the cloudy atmosphere is important for several reasons. The microwave radiation of the nonprecipitating atmosphere consists of two components: emitted and scattered. The emitted thermal microwave radiation is unpolarized, whereas the scattered may have a polarized component. Conventional measurements using unpolarized radiometers do not allow separation of emitted and scattered radiation. The polarized measurements provide an assessment of the scattered component in the form of the polarization difference, or the second Stokes parameter. Thus, the polarized measurements may be useful for testing models of microwave radiative transfer in the cloudy atmosphere. Another important application is related to the measurement of the mixed-phase composition of clouds. The intensity of thermal microwave radiation, or the first Stokes parameter, provides information about the liquid water path of clouds. The difference between the vertical and horizontal polarizations, or the second Stokes parameter, provides information on the ice water path, shape and size of the cloud particles. This is an important step toward remote sensing of mixed-phase clouds. This study presents the results of measurements of polarization of thermal microwave radiation at 37 and 85 GHZ, conducted during the Alliance Icing Research Study (AIRS) project in Ottawa, Canada, during the winter of 1999/2000 (Isaac et al. 2001). The observations are interpreted using a model of radiative transfer in mixed-phase clouds. 2. Scattering of thermal microwave radiation by mixed-phase clouds The emitted thermal microwave radiation of the cloudy atmosphere is defined here as the radiation of atmospheric gases and cloud droplets, having a thermal origin. Molecular oxygen and water vapor are the primary gaseous absorbers and emitters in the microwave range of the spectrum. The intensity of the microwave radiation emitted by ice particles is relatively small. However, these particles may effectively scatter the radiation emitted by the atmospheric gases and liquid droplets. Polarization of thermal microwave radiation due to scattering can be caused by both spherical and preferentially oriented nonspherical particles (Troitsky and Osharin 2000), having a wide variety of shapes (Korolev et al. 2000). Small ice particles with a Reynolds number Re , 10 have a random spatial orientation. However, as they grow, they tend to orient themselves such that their largest projection is perpendicular to the vector of their falling velocity (e.g., Pruppacher and Klett 1997). The polarization of electromagnetic radiation, propagating in a direction (u, f) can be described by the

four Stokes parameters, forming a vector I 5 (I, Q, U, V)T , where ‘‘T’’ refers to the matrix transpose. The first Stokes parameter I is equal to the total intensity (the sum of the vertically and horizontally polarized components: I 5 Iv 1 Ih ); Q represents the difference of Iv and Ih ; U is the same as Q in a reference frame, rotated 458 from the propagation direction relative to the original (laboratory) frame of reference; and V describes the difference of the right and left circularly polarized components of the radiation intensity. For microwave radiation the polarization of the electromagnetic radiation, propagating in direction (u, f), is frequently described by the four ‘‘modified’’ Stokes parameters (Ishimaru 1978; Tsang et al. 1985), forming a vector I 5 (Iv , Ih , U, V)T . Since the Rayleigh–Jean’s approximation is valid here, the intensity of radiation I a having a polarization a can be expressed through the brightness temperature T b,a as I a 5 k B T b,a /l 2 ,

(1)

where the subscript a denotes v (vertical) or h (horizontal) components of radiation, k B is Boltzmann’s constant, and l is the wavelength of the radiation. For the radiative transfer model described below, the following assumptions have been made. A cloud was considered as a plane-parallel layer embedded in the atmosphere. The vertical profiles of temperature and water vapor were specified as per McClatchey et al. (1972) for a midlatitude winter. The microwave absorption by oxygen and water vapor was calculated on the basis of the atmospheric model of Liebe (1989). The cloud was assumed to be uniformly filled with ice particles (scattering component) and liquid droplets (absorbing component). The earth’s surface was considered to be a blackbody having temperature T s . Following Tsang et al. (1985) the vector radiative transfer equation for the modified Stokes parameters I 5 (Iv , Ih , U, V)T in a plane-parallel layer with randomly distributed and oriented nonspherical particles, can be written as cosu

dI(u, f, z) dz

5 2k ext (u, f )I(u, f, z)

E E 2p

1

df9

0

p

du9 sinu9P(u, f; u9, f9)I(u9, f9, z)

0

1 J(u, f, z).

(2)

Here, 0 # u # p, 0 # f # 2p are the zenith and azimuth angles of the unit vector, respectively, specifying the direction of the radiation propagation; 0 , z , ` is the vertical coordinate (z 5 0 at the ground level); kext (u, f) is the total extinction matrix due to cloud particles and atmospheric gases; P(u, f; u9, f9) is the single scattering phase matrix denoting scattering from direction (u9, f9) to (u, f); J(u, f, z) is the source

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FIG. 1. The dependence of the thermal radiation polarization difference DT b as a function of zenith angle u for a mixed-phase cloud having differing IWC values but constant LWC 5 0.1 g m 23 , and an average ice particle size ^D & 5 500 mm. Ice particles were assumed to be spheres [(a) 85 GHz and (b) 37 GHz] and oblate spheroids [(c) 85 GHz and (d) 37 GHz].

term of the thermal radiation emitted by cloud particles and weakly absorbing gases; T(z) is the vertical profile of the thermodynamic temperature of the atmosphere; and k(z) 5 kO 2(z) 1 kH 2O(z) is the total absorption coefficient due to oxygen and water vapor. The boundary condition at the cloud top (z 5 z 2 ) can be written as

5

k Ia (p 2 u, z2 ) 5 B2 secu l

E

Ia (u, z1 ) 5

z2

[ E

z

z2

]6

k(z9) dz9 , (3a)

U(p 2 u, z2 ) 5 0,

(3b)

V(p 2 u, z2 ) 5 0,

(3c)

and at the cloud base (z 5 z1 ) as

k(z) dz

0

dzT(z)k(z)

0

3 exp 2secu

z

dzT(z)k(z)

]

z1

z1

1 secu

`

3 exp 2secu

5 [ E E [ E

kB T exp 2secu l2 S

z1

]6

k(z9) dz9 , (4a)

U(u, z1 ) 5 0,

(4b)

V(u, z1 ) 5 0.

(4c)

Note that Eq. (3) describes the angular distribution of the atmospheric downwelling radiation, whereas Eq. (4) describes the combined upwelling radiation from the earth’s surface and the subcloud air layer impacting the cloud base from below. The elements of the extinction and phase matrices

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polarization a( a, b 5 v, h). The extinction matrix due to ice particles kext,i ( u, f) can be expressed as elements of a forward scattering amplitude matrix (Tsang and Ding 1991):

can be expressed in terms of a 2 3 2 complex amplitude matrix f ab (u , f ; u9, f9), describing the scattering of the electromagnetic wave from the direction (u 9, f9) and polarization b to direction (u , f) and

Im^ f vv & 0 k ext,i (u, f ) 5 l  2 Im^ f hv & 2 Re^ f hv & 2

0 2 Im^ f hh & 2 Im^ f vh & 22 Re^ f vh &

 

Here, the angular brackets identify the quantities as statistical averages over size and orientation distributions of cloud particles. It is assumed that the diameter of cloud droplets is less than 100 mm. Under this assumption, water drops are treated as Rayleigh spheres, and the extinction matrix due to liquid droplets kext,w (u, f), through the absorption coefficient kabs,w can be expressed as follows:

^| f vv| 2 & ^| f hv| 2 & P(u, f; u9, f9) 5  2 Re^ f vv f hv *& *& 2 Im^ f vv f hv

kabs,w 5

 

(6)

Re^ f vv f vh *& Re^ f hv f hh *& Re^ f vv f hh * 1 f vh f hv *& Im^ f vv f hh * 1 f vh f hv *&

kB k (u , f )T(z). l 2 abs b b

E E E E 2p

 2Im^ f vv f vh *& 2Im^ f hv f hh *& . 2Im^ f vv f hh * 2 f vh f hv *& Re^ f vv f hh * 2 f vh f hv *& 

 

(8)

kabs,3 (u b , f b ), kabs,4 (u b , f b )|T .

(10)

Here,

du9 sinu9[P11 (u9, f9; u, f ) 1 P21 (u9, f9; u, f )],

(11)

du9 sinu9[P12 (u9, f9; u, f ) 1 P22 (u9, f9; u, f )],

(12)

p

df9

0

5

E E E E 2p

kabs,3 (u, f ) 5 22 kext,13 (u, f ) 1 kext,23 (u, f ) 2

5

(7)

0

2p

0

2

p

df9

0

kabs,2 (u, f ) 5 kext,22 (u, f ) 2

1

6p LWC « 21 Im w . lr «w 1 2

k abs (u b , f b ) 5 |kabs,1 (u b , f b ), kabs,2 (u b , f b ),

(9)

As shown by Tsang (1991), the radiation in the di-

kabs,1 (u, f ) 5 kext,1 (u, f ) 2

(5)

rection (u, f) is determined by the absorption in the backward direction (u b , f b ) 5 (p 2 u, p 1 f) and the vector of absorption

The term in Eq. (2) describing the source of emitted thermal radiation for the case of the Rayleigh–Jeans approximation is J(u, f, z) 5

 

Here, r is the liquid water bulk density, « w is the complex dielectric permittivity of water (Liebe 1989), and LWC is liquid water content of the cloud. The phase matrix is given by bilinear combinations of the complex amplitudes f ab 5 f ab (u, f; u9, f9):

^| f vh| 2 & ^| f hh| 2 & 2 Re^ f vh f hh *& 2 Im^ f vh f hh *&



2Re^ f vh &  Re^ f hv & . Re^ f vv 2 f hh & Im^ f vv 1 f hh & 

The absorption coefficient kabs,w is independent of the droplet size distribution and can be expressed as per Basharinov and Kutuza (1968),

k ext,w (u, f ) 5 k abs,w

5 diag(kabs,w , kabs,w , kabs,w , kabs,w ).

Im^ f vh & Im^ f hv & Im^ f vv 1 f hh & Re^ f hh 2 f vv &

kabs,4 (u, f ) 5 2 kext,14 (u, f ) 1 kext,24 (u, f ) 2

0

du9 sinu9[P13 (u9, f9; u, f ) 1 P23 (u9, f9; u, f )] , (13)

0

2p

p

df9

0

6

p

df9

6

du9 sinu9[P14 (u9, f9; u, f ) 1 P24 (u9, f9; u, f )] .

0

(14)

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FIG. 2. The dependence of the thermal radiation polarization difference DT b as a function of zenith angle u for a mixed-phase cloud having differing LWC but constant IWC 5 0.2 g m 23 , and an average ice particle size ^D & 5 500 mm. Ice particles were assumed to be spheres [(a) 85 GHz and (b) 37 GHz] and oblate spheroids [(c) 85 GHz and (d) 37 GHz].

Consider two types of ice particle shapes: spheres and plates. For simplicity, approximate the shape of the plates by oblate spheroids having their axes of symmetry oriented vertically. These assumptions eliminate the azimuth dependence in Eq. (2), so that only the first two modified Stokes parameters remain nonzero; that is, cosu

dIa (u, z) dz

5 2kext,a (u)Ia (u, z)

OE

p

1 1

b5v,h

du9 sinu9[a(u), b(u9)]Ib (u9, z)

0

kB k (u)T. l 2 abs,a

(15)

Here, [a(u), b(u9)] 5 # 20p df9 P ab (u, f; u9, f9), Pvv 5

P11 , Psh 5 P12 , Phv 5 P 21 , Phh 5 P 22 , kext,a (u) 5 2l Im^ f aa &, kabs,a (u) 5 kext,a (u) 2 S b5v,h # p0 du9 sinu9[b(u9), a(u)], and T is the average temperature of the cloud layer. The system of radiative transfer equations given in (15) was solved numerically using the discrete ordinate eigenanalysis method (Tsang et al. 1985), which takes into account all orders of scattering contribution. In the case of ice spheres and ice spheroids, the interaction characteristics for the vector radiative transfer equation were calculated using Mie theory (Bohren and Huffman 1983) and by the T-matrix method (Mishchenko et al. 2000), respectively. Note that this model imposes no restrictions on the size parameter x 5 pD/ l of ice crystals. After the two Stokes parameters were determined, the measured brightness temperature components at the ground level (z 5 0) were computed as follows:

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FIG. 3. The dependence of the thermal radiation polarization difference DT b as a function of average ice particles size ^D &, for a mixedphase cloud having differing LWC but constant IWC 5 0.2 g m 23 . The zenith angle was set at u 5 668C. Ice particles are the same as in Figs. 1 and 2.

Tb,a 5

[

l2 I exp 2secu kB a 1 secu

E

E

]

z1

k(z) dz

0

[

z1

dzk(z)T(z) exp 2secu

0

E

]

z

k(z9) dz9 ,

0

(16) where I a is the intensity of the downwelling radiation at the cloud base. The brightness temperature difference DT b 5 T b,v 2 T b,h at the ground is DTb 5

[

l2 (I 2 Ih ) exp 2secu kB v

E 0

z1

]

k(z) dz ,

(17)

where Iv , Ih are the intensities of the downwelling radiation at cloud base. As stated above, the Rayleigh– Jeans approximation was used here to convert Iv and Ih intensities into corresponding brightness temperatures

T bv and T b,h . For the 85-GHz T b,v , T b,h , and equivalent blackbody brightness temperatures for both, polarizations may be biased by about 2 K. However, this bias does not affect the polarization difference DT b 5 T b,v 2 T b,h (Evans and Stephens 1995b). 3. Modeling of the polarization of thermal microwave radiation in clouds A plane-parallel cloud was assumed to have a thickness Dz 5 2 km, a cloud base of z1 5 1 km, and a cloud top of z 2 5 3 km. The average thermodynamic temperature of the cloud was chosen to be 2108C (McClatchey et al. 1972). The liquid and ice water contents (LWC and IWC, respectively) were assumed constant in the vertical and horizontal, and were varied from 0 to 0.5 g m 23 for LWC, and from 0 to 0.3 g m 23 for IWC. The size distribution of ice particles was approx-

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FIG. 4. Time history of (a) LWP, (b) DT b (37), and (c) DT b (85) measured during AIRS on 26 Dec 1999 in Ottawa.

imated by an exponential function (Pruppacher and Klett 1997): n(D) 5 A exp(2D/^D&),

(18)

where D is the diameter (sphere) or the length of the longest axis (spheroid), n(D) is the number of particles in the size interval (D, D 1 dD), ^D& is the average size of the ice particles. Platelike ice crystals were approximated by oblate spheroids with a dimensional relationship given by d 5 2.02D 0.449 (Auer and Veal 1970), where D and d (in microns) are the maximum and minimum axes of the spheroid, respectively. We restricted our consideration to ice crystals having two types of habits: spheres and plates. These habits represent two extreme cases of the aspect ratio of cloud ice particles, giving the largest range of polarization differences. The complex dielectric permittivity of ice at T 5 2108C were chosen as « i (37) 5 3.15 1 0.00278i and « i (85)

5 3.15 1 0.00637i for frequencies of 37 and 85 GHz, respectively (Hufford 1991). Figure 1 shows angular dependencies of the thermal radiation polarization difference DT b 5 T b,v 2 T b,h in a mixed-phase cloud for different IWC values at 37 and 85 GHz. The calculations were conducted for an LWC 5 0.1 g m 23 , and for ice particles having ^D& 5 500 mm, and Dmax 5 2 mm. Note that DT b changes sign for plates at u . 808. The absolute value of the polarization difference | DT b | increases approximately linearly with increasing IWP for all zenith angles. The absolute value of the polarization difference | DT b | reaches a maximum in the range of angles of 708 , umax (85) , 808 for 85 GHz and 808 , umax (37) , 858 for 37 GHz, with little difference between spheres and plates (Fig. 1). The total optical thickness of the atmosphere [t (u) 5 t 0 / cosu ] for these values of umax is close to unity. Since the vertical extinction t 0 at 85 GHz is greater than that

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TROITSKY ET AL.

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at 37 GHz, umax (85) , umax (37). The condition cosumax ø t 0 is always true for the plane-parallel approximation. The reduction of DT b to zero at zenith viewing angles close to 908 is caused by the ‘‘blackening’’ of the atmosphere at these angles due to the increase of the total extinction. Figure 2 shows DT b versus zenith angle as a function of LWC, for a constant IWC 5 0.2 g m 23 and ^D& 5 500 mm. Figure 2 indicates that, in accordance with the suggested model, an increase of LWC results in an increase of absorption and a shifting of the maximum of DT b toward smaller zenith angles umax . This is true for both spheres (Figs. 2a,b) and plates (Figs. 2c,d). In the case of plates, the absolute value of the polarization difference decreases significantly for all angles and frequencies. For LWC . 0.4 g m 23 the values of | DT b | at 37 GHz may even exceed those at 85 GHz for platelike ice particles. For spherical ice the effect of LWC on DT b is more complex than for plates. An increase in LWC (total absorption t w , 2) leads to an increase of

the polarization difference DT b for angles u , umax . An increase in LWC (t w . 2) leads to a decrease in DT b . Figure 3 shows DT b versus ^D&, for a constant IWC 5 0.2 g m 23 and LWC 5 0.1 g m 23 . Zenith viewing angle was set at u 5 668, which is close to umax (85). The behavior of DT b versus ^D& is significantly different for spheres and plates. For plates the absolute value of polarization difference | DT b | monotonically increases with the average particle size. For spheres, the 85-GHz | DT b | maximizes at a value of ^D& corresponding to the first maximum in the dependence of scattering cross section of a single sphere on diameter D. 4. Instrumentation The thermal microwave radiation was measured with dual-polarized 37- and 85-GHz radiometers. Both radiometers were installed inside a special thermal-stabilized trailer to avoid the effect of temperature changes on the measurements. The observations were conducted

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FIG. 6. Time history of (a) LWP, (b) DT b (37), and (c) DT b (85) measured during AIRS on 16 Jan 2000 in Ottawa.

at a zenith angle of 658 through a radiotransparent window, with both radiometers pointed in the same direction in order to receive radiation from approximately the same cloud volume. Both radiometers had horn antennas with a half-power beamwidth of 38. The sensitivities for each polarization channel of the 37- and 85-GHz radiometers were 0.1 and 0.3 K, respectively, for an integration time of 1 s. The total transmission coefficients of the polarized channels of the radiometers were equalized with an accuracy better than 0.3%. Calibration was performed using two sources of unpolarized radiation: the clear sky and a blackbody. During calibration the blackbody was located at the far field of the antenna and oriented perpendicular to the electric axis of the horn. The blackbody temperature was maintained at the ambient air temperature. The brightness temperature of the clear sky was calculated using radiosonde data, or using the method of optimal extrapolation of the near-ground temperature, humidity,

and pressure values (Gandin and Kagan 1976). The level of zero polarization difference was taken to be that of the clear atmospheric radiation or that of the blackbody. Though the clear-sky brightness temperature changes with time, this does not influence the calibration of the polarization difference, since the clear-sky radiation is unpolarized in the microwave, and polarization difference at any time is equal to zero. The antenna temperature T a,a at the radiometer input is related to the measured brightness temperature T b,a of the cloudy atmosphere as follows: Ta,a 5 ha (1 2 ba )Tb,a 1 ha ba Tbg,a 1 ha (1 2 ba )T0 ,

(19)

where b a is the scattering coefficient of the antenna, denoting the fraction of power in the sidelobes, h a is the antenna efficiency, and Tbg,a is the background brightness temperature at the corresponding polarization

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TROITSKY ET AL.

averaged over the sidelobes of the antenna, and T 0 is the ambient thermodynamic temperature. Since the amplitude of the measured output signal U a is linearly related to the antenna temperature at the radiometer input, that is, T a,a 5 A a U a 1 B a , it can be shown that Ta,bb,a 2 Ta,atm,a T 2 Tb,atm,a 5 b,bb,a Ta,atm,a 2 Ta,a Tb,atm,a 2 Tb,a 5

Ubb,a 2 Uatm,a . Uatm,a 2 Ua

(20)

Here, T a,bb,a is the antenna temperature of a blackbody in the far-field zone of antenna, T a,atm,a is the antenna temperature of the clear sky, and T a,a is the antenna temperature of the cloudy atmosphere at vertical and horizontal polarizations. From Eq. (20) it follows Tb,a 5 Tb,atm,a 2

Tb,bb,a 2 Tb,atm,a (U 2 Ua ). U b,bb,a 2 Uatm,a atm,a

(21)

Here, (T b,bb,a 2 T b,atm,a )/Ubb,a 2 Uatm,a 5 K a is the transmission coefficient of the radiometer polarization channel. Substituting Kv 5 Kh 5 K into Eq. (21) yields an expression for the measured polarization difference DTb 5 Tb,v 2 Tb,h 5 K [(Uv 2 Uh ) 2 (Uatm,v 2 Uatm,h )].

(22)

The estimated accuracy of brightness temperature measurements for both polarizations was about 2 K at 85 GHz and 2.5 K at 37 GHz. The estimated accuracy of polarization difference measurements was 0.4 K at 85 GHz and 0.2 K at 37 GHz. These values were determined from the fluctuation sensitivity of the radiometers. Systematic errors due to calibration procedure were eliminated using the above differential measurement scheme [Eq. (22)]. The signals were integrated over 10-s intervals during postprocessing. The liquid water path of clouds was derived from the measurements of the atmospheric absorption t w (37) at 37 GHz for the zenith viewing angle u 5 658 as LWP 5

t w (37) cosu 2 (t O2 1 t H2O ) , c (37; T )

(23)

where c (37; T) 5 kabs,w /LWC is the specific absorption coefficient due to cloud water. The absorption tO 2 1 tH 2O due to oxygen and water vapor and cloud temperature T were set according to average climatic data, taking into account the ground-based temperature, pressure, and humidity. The estimated accuracy of the single channel method for deriving cloud LWP is 15%–20%. 5. Experimental studies of polarization of thermal radiation for a cloudy atmosphere Measurements of the polarization of thermal microwave radiation of the cloudy atmosphere were con-

1617

ducted during the AIRS project, from 2 December 1999 to 17 February 2000. The radiometers were located at the Ottawa International Airport. The total time of observations was 1736 h. Cloudy conditions were observed for 640 h, or 37% of the total observation time. The ambient temperature during the observations varied from 2248 to 1 138C. Polarization of the atmospheric radiation in cloudy conditions was observed for 188 h, or ;30% of the time with cloudy conditions. The cases with melting layers were excluded based on the monitoring of the surface temperature and the data from radio soundings. Figures 4, 5, and 6 show examples of the time history of LWP derived from 37-GHz radiometer measurements, and the observed 37- and 85-GHz vertical–horizontal polarization differences [DT b (37) and DT b (85)]. Both positive and negative values of the polarization difference DT b were observed. The phenomenon of polarization difference sign change is demonstrated in Figs. 5 and 6. Negative values of DT b occur more frequently than positive values. During the AIRS project, positive and negative values of DT b were observed approximately 15% and 85% of the time, respectively, when nonzero polarization differences occurred. According to the theoretical analysis in section 3 the sign of DT b depends mainly on the ice particle shape. The polarization difference for oblate ice particles oriented horizontally has a predominantly negative sign at a zenith angle 658. Polarization differences due to spherical and quasi-spherical ice particles are positive. Therefore, during the AIRS time periods in which polarization differences were observed, the results suggest that 85% of the time contained ice particles with preferred orientation, and 15% contained particles with spherical and quasi-spherical shape. The duration of periods with polarization difference varied from minutes to an hour. Assuming that the average wind speed was about 20 km h 21 , the inferred spatial scale of the polarized regions would be from hundreds of meters to kilometers. This scale can be interpreted as the scale of zones of ice particles having the same scattering properties. The polarization differences did not correlate with the liquid water path. This can be seen in Figs. 4–6. The coefficient of correlation between LWP and DT b usually varied between 20.3 and 10.3. For those cases with LWP , 0.4 kg m 22 , the polarization differences DT b (37) and DT b (85) were often well correlated. Figures 4 and 6 show examples of such correlation. In Fig. 4 the correlation coefficient between DT b (37) and DT b (85), reaches 0.95 for the time interval of 1000–1800 UTC, while in Fig. 6 the correlation coefficient is about 0.91 for the period 0300–1800 UTC. The average value of DT b (85) in the absence of precipitation is approximately 2 K, with a maximum observed value of approximately 4.5 K. The values DT b (37) usually do not exceed 2.5 K and, and typically are 2–6 times less than the simultaneously measured

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DT b (85) (Figs. 4 and 6). The values and ratios of DT b (37) and DT b (85) are in a good agreement with theoretical estimates for the case of low absorption clouds. In clouds with high liquid water path (LWP . 0.4 kg m 22 ), DT b (37) was usually greater than DT b (85) (e.g., Fig. 5, 0700 UTC). In these cases the absorption t at 85 GHz due to the water fraction is greater than 1, while the corresponding absorption at 37 GHz is only about 0.3, resulting in stronger decrease in DT b (85) than for DT b (37). Interesting cases were observed for clouds with LWP , 0.4g m 22 when DT b (37) . DT b (85). Examples are shown in Fig. 7 (0445–0500 UTC) and Fig. 8 (1730– 1900 UTC). In these two cases even the time derivatives of DT b (37) and DT b (85) have an opposite sign. These observations may suggest that the clouds were composed of predominantly very large ice particles with D . 2 mm. The presence of large ice particles would reduce DT b (85) down to zero or even changes its sign, whereas DT b (37) would stay high. For spherical ice this

conjecture is supported by calculations (see Fig. 3). The effect of large snow particles on DT b (37) and DT b (85) may be illustrated by the cases of 15 December 1999 (Fig. 7) and 7 January 2000 (Fig. 8), when the size of aggregates at ground level reached 10 mm. It should be noted that situations with | DT b (37) | . | DT b (85) | were usually observed in snowfalls. In heavy snowfalls DT b (85) was usually close to zero (Troitsky and Osharin 2000); however, DT b (37) was about several kelvins. 6. Conclusions The following conclusions were reached as a result of this study. 1) During the AIRS project, polarization of microwave radiation at 37 and 85 GHz was observed for 188 h, corresponding to approximately 30% of the total cloudy period. The results suggest that during these periods of polarization, horizontally oriented cloud

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FIG. 8. Time history of (a) LWP, (b) DT b (37), and (c) DT b (85) measured during AIRS on 7 Jan 2000 in Ottawa.

particles, having oblate and prolate shape, occurred approximately 85% of the time, and spherical and quasi-spherical particles occurred approximately 15% of the time. 2) Characteristic values of the polarization difference at 85 GHz at a zenith angle of 668 are about 2 K, with a maximum value of 4.5 K. Corresponding polarization differences at 37 GHz usually do not exceed 2.5 K, and are usually 2–6 times less than that at 85 GHz. The polarization difference DT b 5 Tb,v 2 Tb,h was found to be both positive and negative. 3) The phenomenon of polarization of the thermal microwave radiation of a cloudy atmosphere results from the multiple scattering of atmospheric radiation on ice crystals in the clouds. Polarization characteristics predicted by the radiative transfer equation for a mixed-phase cloud are in agreement with groundbased observations at 37 and 85 GHz. 4) The magnitude of the polarization difference depends on the ice water path (IWP), while the intensity

of the microwave radiation is determined by the liquid water path (LWP). This suggests that for some cases information on the cloud-phase composition, and the ice and water paths can be determined separately from simultaneous measurements of the polarization difference and intensity. 5) The sign of the polarization differences and spectral relations between the polarization differences at 85 and 37 GHz are related to cloud microstructure (ice crystal shapes and characteristic size of the crystals), suggesting the possibility of retrieval of cloud microphysical parameters from remote radiometric multifrequency measurements. Acknowledgments. The National Search and Rescue Secretariat of Canada provided funding for the AIRS project. The authors are grateful to M. I. Mishchenko for his computer code, calculating the amplitude and phase matrices of the particles, having an axially sym-

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metric shape. Arkadi Troitsky and Alexander Osharin have been supported by RFBR (Grant 00-02-16037) and the Ministry of Education of Russia (Grant E00-3.531). Alexei Korolev has performed this work under the Contract KM175-012030/001/TOR to the Meteorological Service of Canada. The Panel of Energy Research and Development and the National Search and Rescue Secretariat provided funding for this work. REFERENCES Auer, A. H., Jr., and D. L. Veal, 1970: The dimension of ice crystals in natural clouds. J. Atmos. Sci., 27, 919–926. Basharinov, A. E., and B. G. Kutuza, 1968: Investigations of radioemission and absorption of the cloudy atmosphere in millimeter and centimeter wavelength range. Proc. GGO, 222, 100– 110. ——, A. S. Gurvich, and S. T. Egorov, 1974: Radioemission of Earth as Planet. Nauka, 188 pp. Bohren, C. F., and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. Wiley, 530 pp. Czekala, H., 1998: Effects of ice particle shape and orientation on polarized microwave radiation for off-nadir problems. Geophys. Res. Lett., 25, 1669–1672. Evans, K. F., and J. Vivekanandan, 1990: Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles. IEEE Trans. Geosci. Remote Sens., 28, 423– 437. ——, and G. L. Stephens, 1995a: Microwave radiative transfer through clouds composed of realistically shaped ice crystals. Part I: Single scattering properties. J. Atmos. Sci., 52, 2041–2057. ——, and ——, 1995b: Microwave radiative transfer through clouds composed of realistically shaped ice crystals. Part II: Remote sensing of ice clouds. J. Atmos. Sci., 52, 2058–2072. Gandin, L. S., and R. L. Kagan, 1976: Statistical Method of Interpretation of Meteorological Data. Gidrometeoizdat, 359 pp. Heymsfeld, G. M., and G. M. Fulton, 1994: Passive microwave and infrared structure of mesoscale convective systems. Meteor. Atmos. Phys., 54, 123–140. Hufford, G., 1991: A model for the complex permittivity of ice at frequencies below 1 THz. Int. J. Millimeter Waves, 12, 677– 682. Isaac, G. A., S. G. Cober, J. W. Strapp, A. V. Korolev, A. Tremblay, and D. L. Marcotte, 2001: Recent Canadian research on aircraft in-flight icing. Can. Aeronaut. Space J., 47, 213–221. Ishimaru, A., 1978: Wave Propagation and Scattering in Random Media. Academic Press, 572 pp. Jansen, M. A., Ed.,1993: Atmospheric Remote Sensing by Microwave Radiometry. Wiley, 572 pp. Korolev, A., G. Isaac, and J. Hallett, 2000: Ice particle habits in stratiform clouds. Quart. J. Roy. Meteor. Soc., 126, 2873–2902.

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