The recent focus of parameterization of the radiative properties of clouds has been to include the microphysical properties of the cloud. A variety of parameterization have been developed for both the shortwave and the longwave. In parameterizing the longwave properties of clouds, it is useful to consider the two stream solution of the radiative transfer equation appropriate for a thermal source. These radiative transfer equations are considered

Ackerman, Steven A.

Smith, William L.

English

NASA Technical Reports Server

N90-28297
July 1989 Ackerman and Smith
IR Spectral Characteristics of Cirrus Clouds
Steven A. Ackerman and William L. Smith
Coopemh'_e ln._itute /or Mefeomlogioal Satdlite 5_u_et
Space Science and Enci_eria¢ Center, 1_5 West Dayton _.
Uni_erdty of Wi_co_dn-Madito_ MadiJon, WI. 55706
(July 1989)
The recent focus of parameterizations of the radiative properties of clouds has been to include
the microphysical properties of the cloud. A variety of parameterizations have been developed
for both the shortwave and the longwave. In parameterizing the longwave properties of clouds, it
is useful to consider the two stream solution of the radiative transfer equation appropriate for a
thermal source. While various solutions exist, here we consider the form
where
(rt) = F-(vb) + 1 - s - r s - t LB(rb)J
(1)
r = p(1 - e -r`') (2)
1 - p2e-r'It
t = e-""O - p_) (3)
1 -- p2e-r'#
(1 -- t -_- I')s: C4)
_(I-_o+ 2_o_)_
(6)
_,o9 (7)
P= 1- wo ÷ wo_ + K
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FIRE Meeting
where B is the Plank function/_ is the backscatter coefficient and p is the diffusivity factor (/2
1.66). For an isothermal cloud, B(_), equations (12)-(18) indicate the necessity to parameterize
two variables, p and KQezt. Physically, p is the reflectance for an infinitely thick cloud. The value
of p as a function of wavelength is shown in figure 1 for ice spheres. For wavelengths between 10
and 13/_m, p is a weak function of the particle size and p < 0.08. p can become large for small
particles for regions outside this window.
To parameterize KQezt we consider the ratio of KQezt to Q_b_. This ratio (Figure 2) displays a
similar dependency on wavelength and particle size as that depicted by p, with a strong dependency
on particle size outside the window region. For wavelengths between 10 and 13 pm, KQ_t _ Qabs.
In parameterizing the longwave properties of clouds in the 10-13 #m window region, it is therefore
useful to parameterize Qab,. An appropriate parameterization of Q_b, is that of the modified
anomalous diffraction theory. Figure 3 depicts the relations between wavelength and Q_bs for
two different droplet sizes. The stars represent Mie calculations while the circles denote the
approximation of equation (9). The open symbols are for a 30/_m particle while the solid symbols
represent the calculations for a 1/_m droplet. The approximation is excellent, even for droplets as
small as 1/_m.
The dependence of effective emittance on the particle size can be expressed to second order
using MADT as
e:l-exp(p_rffn(r){_m2r3_[l_(l_m-2)3/2)]dr+r4_2m2[l_(l_m_2)2)]}drdz)
where _: = 4rrni/A is the absorption coefficient of water/ice. The first term of the exponential
represents the dependency on the water content of the cloud, while the second term displays a
dependency on the fourth moment of the size distribution. As an estimate of the particle size at
which the emissivity becomes dependent on the droplet size we consider the radius at which
l,- : (9)
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July 1989 Ackerman and Smith
Figure 4 depicts thi3 radius, R, as a function of wavelength for water (solid lines) and ice
(dashed lines) spheres. A cloud with a monomodal distribution of particles of size R or greater
will display a sensitivity to droplet size. For example, if we have two water clouds, one with a
monomodal size distribution of 12/_m particle and the other with a 8/_m droplet distribution, the
cloud emissivity in the 8-11.5/_m band will be sensitive primarily to the LWP, while the 11.5 to 14
/_m band emissivity would also display a sensitivity to the size distribution. This is in agreement
measurements and calculations of fogs. In the the case of ice clouds, the 11- 13 pm band will
display a dependency on the size distribution for particles greater than 4pm.
In summary, high spectral resolution measurements in the 8-13 pm "window ') region are
appropriate for remotely sensing the microphysical properties of ice clouds as: windows in gaseous
absorption are available; this is the most sensitive region to particle size; the value of p is small
compared to other wavelengths; and KQe_t _ Qabs.
To demonstrate this dependency of particle size on IR observations, we consider the spectral
variation of the equivalent blackbody temperatures in the _window" region, four spectral band-
widths: 8 pm (8.3-8.4), 10/_m (10.07-10.173), 11 /_m (11.062-11.249) and 12 pm (11.93-12.063).
The equivalent blackbody temperature observations were made with the HIS (High resolution In-
terferometer Spectrometer) aboard the NASA ER2 during FIRE on 2 November, 1986. Figure 5
is a scatter diagram of the BTs-BTll versus BTll-BT12. Each symbol in figure the figure repre-
sents a range in the BTll as noted in the legend. The differences in the brightness temperatures
observed in these channels are very useful in detecting the presence of cirrus clouds. The cloud
free regions have negative differences in BTs-BTll due to absorption by water vapor. While cirrus
clouds have positive differences owning to the optical properties of ice. The cirrus BTs-BTI1 are
greater than the BTlI-BT12 as expected from figure 3.
The magnitude of the HIS measured BT differences is related to the cloud particle size dis-
tribution. This is demonstrated in figure 6 where the brightness differences are determined with
theoretical radiative transfer calculations using a doubling/adding model and assuming various
surface temperatures, cloud top temperatures, and different ice water content and geometric thick-
443
FIRE Meeting
nesses. The cloud is assumed to have a lapse rate of-6 °K km -1 and is homogeneous. The cloud
particles are assumed to be spheres with a gamma size distribution and effective radii as denoted
in the symbol legend. These calculations demonstrate that the ice cloud with the smaller rell
(stars) display the large BT differences observed by the HIS while the ice cloud with the larger
refl do not. The magnitude of the ABT is also related to the IWP (e.g. very thin clouds are
similar to the clear sky values.
The envelope of the calculations is depicted on figure 5 by the solid line. Differences be-
tween the theory and observations are seen at the larger BTs-BTtl values. This difference may
be attributed to particle shape, or to a non-homogeneous vertical/horizontal distribution of the
particles. The effect of particle shape is demonstrated by the dashed line which is the envelop for
a cirrus cloud consisting of small ice cylinders.
4. SUMMARY
• The HIS spectra show spectralvariationsinequivalentblackbody temperatures in the win-
dow region of greater than 5°C, for a given cirruscloud.
• The brightness temperature differencesbetween 8 and 11 #m and 11 and 12 #m are useful
parameters fordetecting the presence of cirrusclouds.
• Theoretical calculationsindicate that the magnitude of the spectral variation in bright-
ness temperature isrelatedto the particlesize.The smaller particlesare associatedwith larger
brightness temperature differences.
• The magnitude of the brightness temperature differencesare also related to the particle
shape. Calculationsassuming sphericalparticlesare in betteragreement with the majority of HIS
observationsthan similarcalculationsassuming cylindricalparticles.
444
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445



IR spectral characteristics of cirrus clouds

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