Algorithm Theoretical Basis Document of CAPCOM for
GCOM/SLGIPI: Takashi Y. Nakajima (Tokai University TRIC)
Associate Scientist: Husi Letu (Tokai University TRIC)

2011/09/20

Table of Contents

1.

Adaptation to the retrieval algorithm (CAPCOM) ........................................................................ 22.

Logic Flow ......................................................................................................................................... 33.

Physical and Mathematical aspects of the CAPCOM .................................................................... 5

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Formulations of the radiative components ....................................................................................... 7Reference:.................................................................................................................................................... 9「紙へリサイクル可」

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Adaptation to the retrieval algorithm (CAPCOM)CAPCOM is acronyms of Comprehensive Analysis Program for Cloud OpticalMeasurement. The CAPCOM uses LUT (Look up Table)-Iteration Method (LIM) to retrieve
the target geophysical parameters from satellite-derived radiance data. In the CAPCOM, a
non-absorption band (Band 14), an absorption band (Band 16,17), and a thermal band (Band 18)
are used to derive cloud optical thickness (CLOP), cloud effective particle radius (CLER), andcloud top temperature (CLTT) (Fig. 1). Adding to these radiance data, some ancillary input data,such as the vertical profile of the temperature, pressure, water vapor, ground albedo are also
used to calculate related geophysical parameters; cloud top height (CLHT) and cloud top
pressure (CLTP) are retrieved by comparing cloud top temperature and temperature profile fromancillary data; liquid water path (CLWP) is calculated by cloud optical thickness and effective
particle radius.

Fig. 1: Look up table for simulation of reflected solar radiances in SGLI channels(1.05μm vs 1.6μm and 1.05µm vs 2.1μm)「紙へリサイクル可」

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2.

Logic FlowFour LUTs are prepared for this purpose, i. e., LUT of cloud-reflected radiance in bands 14and 16, transmissivities and reflectivity in bands 14 and 17, band 18 transmissivity. Table 1summarizes the grid system of the LUTs and Fig. 2 illustrates the flow of the analysis. We used
Newton-Raphson method to iterate a main loop in the program. Some related parameters, suchas; cloud liquid water path and cloud top height are also calculated in the CAPCOM withtemperature slicing data from objective analysis such as JMA GANAL dataset. We found thatthe iteration does not converge in some cases of optically thin clouds when the removed
radiation significantly dominates over the signal. In this case we cancel the analysis.

Table 1. The grid system of the look up tables; θ , θ0 , φ are the satellite
and solar zenith angle, and relative azimuth angle. τ c and re arecloud optical thickness and effective particle radius.

Quantities

Grid point valuesθ (degrees)0, 5, 10, 20, 30, 35, 50, 45, 50, 55, 60

θ0 (degrees)0, 5, 10, 20, 30, 35, 50, 45, 50, 55, 60, 65, 70

φ (degrees)

0 to 180 (divided by every 10 degrees)τ c (Water cloud)1., 5., 8., 12., 17., 23., 31., 41., 54., 70

τ c (Ice cloud)0.1,0.5,1.,2.,4.,8.,16.,32.,48.,64.

re (Water cloud)4., 7., 9., 11., 14., 17., 22., 30., 38., 46., 54., 62.

re (Ice cloud)5.,10.,20.,40.,60.,80.,100.,110.,120.,130.,140.,150.
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Fig. 2 Flow chart of the CAPCOM「紙へリサイクル可」

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3.

Physical and Mathematical aspects of the CAPCOM
The solar reflectance method utilizes non-absorbing visible (Vis) and water-absorbing

short-wave infrared (SWIR) wavelengths, such as 1.6, 2.2 and 3.7 µm, for the simultaneous
retrieval of the cloud optical thickness at the 0.5µm wavelength and the effective particle radius.
In this paper, we mainly discuss the solar reflectance method making use of SGLI Band 14(1.05 µm), 16 (1.6 µm) and/or 17(2.2 mm), and 8 (10.8 µm). The effective particle radius of theclouds ( re ) is defined by∫ r n(r)dr ,r ≡∫ r n(r)dr∞ 3

e0∞ 2(1)

0where n(r) is the number size distribution as a function of the particle radius r. We used alog-normal size distribution in the calculations, (ln r − ln r )2 c0,n (r) = exp−22σr(2)where c is a constant, r0 is the mode radius, which is related to the effective particle radius as

re = r0e 2.5σ , and σ is the log-standard deviation of the size distribution. Here, σ = 0.35 was
2assumed for marine stratocumulus clouds in our analyses. For the satellite signal simulation, weused an accurate and efficient radiative transfer scheme (Nakajima and Tanaka 1986, 1988)
extended to include the thermal radiative transfer (Stamnes et al. 1988). We assumed a Lambertsurface for the underlying surface. This assumption will not introduce a significant error in the「紙へリサイクル可」

5analyses if we use an equivalent flux albedo for cloudy atmospheres (Nakajima et al. 1991)
We retrieved τ c at the 0.5-µm wavelength and re from SGLI Band 14 and 16(and/or 17)
on the basis of the fact that Band 14 and 16 (17) primarily depend on the cloud optical thickness
and the effective particle radius, respectively. Although the concept of the retrieval is simple,
some difficulties occur when determining the cloud properties from the measured SGLI spectral
radiance. It is necessary to remove the unexpected radiation components (e.g. solar radiationreflected by the ground) from the observed radiance.

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Formulations of the radiative components
According to the radiative transfer theory for parallel plane layers with an underlying

Lambert surface, we remove the unexpected radiation components, such as the solar radiationreflected by the ground surface and the thermal radiation emitted from the cloud layer and theground surface, from the satellite-received radiance, Lobs, in order to decouple the radiation
component reflected by the cloud layer, L, as follows:L(Z c ,Dc , τ c ,re ;µ, µ0 , φ )(3)= Lobs (Z c ,Dc , τ c ,re ;µ, µ0 , φ )AgµFτ (Z c ,Dc , τ c ,re ;µ0 ) 0 0−τ (Z c ,Dc , τ c ,re ;µ)1− r (Z c ,Dc , τ c ,re )Agπ

where F0 is the extraterrestrial solar flux, and τ c and τ u are the optical thicknesses of thecloud layer, and the atmosphere above the cloud layer, respectively. µ 0 and µ are the cosinesof the solar and satellite zenith angles, respectively, φ is the azimuthal angle of the satellite
relative to the sun. Zc and Dc are the top height and the geometrical thickness of the cloud,respectively.
The transmissivity t , the plane albedo r , and the spherical albedo r are given byt(t c ,re ; µ 0 )=2π∫ ∫ T (t ,r ;µ ,µ ,φ )µdµdφ + e t µπ
1

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010− /ce07(4)0r(τ c ,re ; µ )=2π∫ ∫ R(τ ,r ;µ ',µ ,φ )µ ' dµ ' dφπ
101c0r (τ c ,re ) = 2∫ r (τ ,r ;µ)µdµ ,10(5)ece(6)

where T (τ c ,re ; µ ,µ 0 ,φ ) and R(τ c ,re ; µ ',µ ,φ ) are bi-directional transmission and reflection
functions respectively. The second term in Eq. (3) is ground-reflected radiation components
Multiple reflections between the ground surface and the upper layer are taken into considerationin Eqs. (3). However, this effect is sufficiently small to regard r (τ c ,re ) Ag as almost zero,
especially for optically thin clouds and ground surfaces with low reflectance. On the contrary,with optically thick clouds and large ground albedo, this effect is relatively large at visible
wavelengths since the large cloud spherical albedo reflects radiation from the ground surface,
while the relatively large transmissivity allows this radiation component to be transmitted intospace. These formulations are exact when we consider monochromatic radiance. We further
introduce a process of averaging of the variables in the formulations with respect to thewavelength. For example, t is averaged with a sub-channel response function of SGLI as n M×tϕξ
()∑ n ∑ n,k n,k  / ∑ϕ n , v =1
 k =1n =1
Nt=(5)

where ϕ n is the response function of the n-th subchannel wavelength for each SGLI Band,ξ n,k is the weight of the k-th k-distribution, and tn,k is the transmissivity for the k-th
k-distribution at the n-th wavelength. This averaging process, which was applied to Eqs. (3)introduces a non-negligible error into the case of thin cloud layers in which the spectral「紙へリサイクル可」

8variation of tn,k becomes large.

However, in most cases in which this process is applied, theerror remains small, and it is possible to estimate the undesirable radiation components in Eqs.
(3) by using spectrally averaged variables for each channel.

Reference:[1]. Nakajima, T. Y., and T. Nakajima, 1995: Wide-area determination of cloud microphysicalproperties from NOAA AVHRR measurements for FIRE and ASTEX regions. Journal of theAtmospheric Sciences, 52, 4043-4059.
[2]. Kawamoto, K., T. Nakajima, and T. Y. Nakajima, 2001: A global determination of cloud
microphysics with AVHRR remote sensing. Journal of Climate, 14, 2054-2068.
[3]. Stamnes, K., Tsay, S. -C., Wiscombe, W. J., & Jayaweera, K. (1988). Numerically stablealgorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting
layered media. Applied Op- tics, 27(12), 2502–2509.
[4]. Nakajima, T. et al. Determination of the optical thickness and effective particle radius ofclouds from reflected solar radiation measurements. Part II. Marine stratocumulus observations.
J. Atmos. Sci. 48, 728–750, 1991.

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