Development of an ice crystal scattering database for the global change observation
mission/second generation global imager satellite mission: investigating the refractive index grid
system and potential retrieval error

Husi Letu; Takashi Y. Nakajima; Takashi N. Matsui

doi:10.1364/AO.51.006172

1. Introduction

Ice clouds regularly cover about 30%–40% of the Earth’s surface, and have been identified as a key observation target in the study of the atmospheric radiation budget and cloud-climate feedback mechanism [1–6]. Climate model simulations and satellite remote sensing retrieval techniques are effective for clarifying the radiative and optical properties of ice clouds in climate systems. Aircraft-based instruments, such as the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) and the International Cirrus Experiment (ICE) have demonstrated that ice clouds are mostly composed of nonspherical ice crystals. These differ from warm water cloud droplets, which are composed of spherical particles. Lorenz–Mie theory [7] exactly describes the single-scattering property of spherical particles in warm water clouds. Nakajima et al. [8] retrieved optical and microphysical properties, such as optical depth, effective particle size, and the liquid water path of warm water clouds, from the Very High Resolution Radiometer (AVHRR) sensor on board the National Oceanic and Atmospheric Association (NOAA) satellite, using the single-scattering property of spherical particles and the R-STAR radiative transfer solver [9]. Unlike spherical particles, however, determining the single-scattering property of nonspherical ice crystals requires several complex numerical light scattering solvers.

There are many studies concerning the single-scattering properties of nonspherical ice crystals [10–21]. Macke et al. [10] calculated the scattering phase function of ice crystals using the geometrical-optics approximation (GOA) method. Takano and Liou [11] applied the GOA method to compute the scattering, absorption, and polarization properties of large ice crystals with various irregular structures. Yang [12] and Ishimoto [13] improved the geometrical-optics method (IGOM) for the solution of light scattering by nonspherical particles in large ice crystals. Furthermore, Yang et al. [14] developed the finite-difference time-domain (FDTD) method for obtaining solutions of light scattering by nonspherical particles in small, hexagonal ice crystals. Mano [15] calculated the light scattering properties for small hexagonal ice crystals using the boundary element method. Nakajima et al. [16] developed the LIght Scattering solver Applicable to particles of arbitrary Shape (LISAS)—Surface Integral Equations Method of Müller-type (SIEMM) to calculate the light scattering properties of hexagonal ice crystals with a size parameter of up to about 25.

Clarifying the optical and microphysical properties of ice clouds from satellite remote sensing data requires the development of a scattering and absorption property database for nonspherical ice crystals by means of the above-mentioned light scattering solvers. Yang et al. [22] published a scattering and absorption property database for 0.2 to 5 μm wavelength using the FDTD and IGOM methods. Six ice crystal shapes are included in the database: plates, solid and hollow columns, planar bullet rosettes, spatial bullet rosettes, and aggregates. Furthermore, Yang et al. [23] made another database from a composite method that is based on a combination of the FDTD technique, the T-matrix [24], IGOM, and Lorenz–Mie theory in the near- through far-infrared spectral region (3–100 μm). In the database developed by Yang et al. [22,23] (Ping Yang DB), wavelengths are divided into 56 bands between 0.2 to 5 μm, and 49 bands between 3 to 100 μm. Despite there having been numerous previous studies related to the scattering database, fundamental scattering and absorption properties of ice particles and radiative transfer computations are still needed for more accurate estimations [25]. For example, the refractive index of ice is averaged for each band by using solar spectral irradiance data from LOWTRAN7 [24]. The wavelength domain covers almost all the visible to infrared satellite sensor channels so that it might be applied to general satellite sensors and, for example, broadband radiative flux calculations. However, this complex refractive index grid system for calculating wavelengths is somewhat coarse for application of the database to specific satellite projects that require high accuracy retrievals. It is worth pointing out that these databases have not been designed or optimized for application to satellite remote sensing or broadband radiative flux calculations with specific and limited narrow bandwidths. Satellite sensors commonly have different channel specifications, such as center wavelength and bandwidth; thus, when developing an ice particle scattering database for a specific satellite sensor, the database design should be unique, based on the sensor channel specifications. This is the motivation behind this paper.

There are two approaches to optimizing a light scattering database: optimizing the complex refractive index grid system and optimizing the wavelength bin for a specific sensor channel. In the former method, a suitable grid system is determined by investigating the radiance error of radiative transfer calculations caused by differing fineness of step size of the complex refractive index. In the latter method, the database is optimized by selecting different wavelength bins in the sensor channels based on specific limited center wavelengths and bandwidths. This study focuses on the former case.

There are two principles for designing the ice crystal scattering database: maintain the accuracy of the retrieval error of the effective particle radius for the Global Change Observation Mission (GCOM-C)/Second Generation Global Imager (SGLI) satellite mission and reduce the computation time by meeting principle 1 when developing the ice crystal scattering database using the LISAS/GOA [26], LISAS/SIEMM, and IGOM methods. This study investigates the significance of optimizing the refractive index grid system in GCOM-C/SGLI satellite sensor channels based on the above principles. To determine a suitable grid system of complex refractive indices, we calculate the difference of radiance at different refractive index grid systems in the 1.6 μm SGLI channel used for estimating both cloud droplet and snow grain size. We used the R-STAR radiative transfer solver for the calculations.

The remainder of this paper is organized as follows. In Section 2, we introduce the SGLI sensor specifications. In Section 3, we define the shape, size parameter, aspect ratio, and the radii of the corresponding equivalent volume spheres for a nonspherical ice crystal. Then, we introduce the method for optimizing the grid system of refractive index in the 1.6 μm SGLI channel. In Section 4, we discuss the difference of radiance calculated from the light scattering database with different grid system of refractive index using the R-STAR radiative transfer solver. We present our conclusions in Section 5.

2. GCOM-C/SGLI Sensor

The GCOM-C mission measures essential geophysical parameters on the Earth’s surface and in the atmosphere to facilitate understanding of the global radiation budget. The GCOM-C satellite is scheduled to launch in around 2014 by the Japan Aerospace Exploration Agency (JAXA) [27]. The SGLI sensor on board the GCOM-C satellite is a passive optical radiometer for observing global ocean, land, atmosphere, and cryosphere in order to monitor climate change. The SGLI sensor is a successor of the Global Imager (GLI) aboard the ADEOS-II satellite, and is an optical sensor capable of multichannel observation at wavelengths from near-UV (0.38 μm channel) to thermal infrared. The SGLI consists of two radiometer instruments, the Visible and Near-Infrared Radiometer (VNR) and the Infrared Scanner (IRS). SGLI-VNR is capable of observing polarized and nonpolarized radiance. The VNR employs a wide-swath (1150 km) push-bloom scan with a line CCD detector. The IRS employs a conventional cross-track mirror scan system (1400 km swath) with a cooled infrared detector [28].

Table 1 shows the SGLI channel specifications. There are 19 channels in SGLI, including two polarized VNR channels. The instantaneous fields of view of the SGLI are 0.25, 0.5, and 1.0 km, and VNIR channels other than VN9 are 0.25 km [29].

Table 1. Specification of the SGLI

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3. Material and Methods

A. Definition of the Ice Crystal Particles and the Light Scattering Solvers

Ice crystal shape is affected by a number of factors, including temperature, pressure, and humidity [30]. Hexagonal columns and plates are known to be important habits of ice cloud crystals, as confirmed by in situ measurements of ice clouds and 22° halo effects [31]. In this study, basic column and plate ice crystal shapes were selected for calculating the single-scattering property. The size parameter, aspect ratio, and radii of corresponding equivalent spheres for a nonspherical ice crystal were respectively defined as follows:

α = \frac{2 π r_{eqv}}{λ},

a_{r} = \frac{2 a}{L},

r_{eqv} = \frac{3 v}{4 A},

where

α

is the size parameter,

λ

is the wavelength,

r_{eqv}

is the radii of the corresponding equivalent volume spheres for a nonspherical ice crystal, and

a_{r}

is the aspect ratio of the hexagonal column.

L

and

a

are illustrated in Fig. 1.

v

is the ice crystal volume, and

A

is the project area.

Fig. 1. Definition of the hexagonal column and plate.

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Figure 1 also shows the definition of the hexagonal column and plate. When the radius of the corresponding equivalent volume spheres for a hexagonal column is a constant value, the wavelength of the incident microwave increases and the size parameter will become smaller.

To develop the ice crystal scattering database, a combination of the LISAS/SIEMM, IGOM, and LISAS/GOA light scattering solvers is employed to calculate the optical properties of the hexagonal shapes (Table 2). Different scattering solvers have different applicable regions in terms of the size parameter [32]. The LISAS/SIEMM solver is applied to determine the single-scattering properties for size parameters less than 25. The IGOM solver is applied to determine the single-scattering properties for size parameters from 25 to 200. The remaining cases were calculated using the LISAS/GOA solver.

Table 2. Size Parameter Resolutions Selected for Calculating Light Scattering Properties

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B. Optimizing the Grid System of Refractive Index

Optimizing ice crystal shape and size parameters as well as refractive index grid systems in satellite sensor channels is important for retrieving satellite-observed nonspherical ice cloud parameters, such as optical thickness and effective particle size. Toward this end, Xie et al. [33] and Liu et al. [34] optimized the ice crystal shape and size parameter. However, there had been no research on optimizing grid systems of the complex refractive index in the channels of specific satellite sensors.

In this study, the grid system of the refractive index is determined by step size of the real and imaginary parts. Determination of a grid system with different step sizes of complex refractive index is related to the accuracy of retrieving ice cloud parameters, such as optical thickness and effective particle radius, the calculation time for developing the nonspherical light scattering database, and the total size of the database. The GCOM-C/SGLI requires retrieving ice cloud parameters with high accuracy, and thus must calculate the exact satellite observation radiance in SGLI channels by using a radiative transfer solver. Because the ice cloud’s radiance is a function of the ice refractive index, the retrieved ice cloud parameters vary with the refractive index grid system in the sensor channels. Thus, to develop a suitable light scattering database of nonspherical ice crystals for a specific satellite project, we need to optimize the grid system of the complex refractive index in the satellite sensor channels. Here, twelve step-size patterns for the real and imaginary parts in the SW3 channel of SGLI are selected for optimizing the refractive index grid system (Table 3).

Table 3. Step Sizes of the Real and Imaginary Parts of Complex Refractive Index in the SGLI-SW3 Channel^a

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Visible and near-infrared satellite channels, such as 0.6, 0.8, 1.6, and 2.2 μm, are used to retrieve cloud microphysical properties [8,35,36]. Many Earth observation satellite sensors, such as the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor aboard the Terra and Aqua satellites, the NOAA/AVHRR satellite sensor, the Cloud and Aerosol Imager sensor aboard the Greenhouse Gases Observing Satellite (GOSAT), the Multi-Spectral Imager (MSI) sensor aboard the Earth Clouds, Aerosols, and Radiation Explorer (EarthCARE) (scheduled to launch around 2014), and the GCOM-C/SGLI satellite sensor described in this study use the 1.6 μm channel, which is important for simultaneous retrieval of cloud effective particle radius. In this study we focus on the 1.6 μm (SW3) channel of the SGLI because it has a relatively wide bandwidth (0.2 μm). Figure 2 shows the grid system for the 1.6 μm channel (SW3), that transmissivity of the response function is greater than 1%. In the Ping Yang DB, there are only three calculation points for the refractive index in the 1.48–1.78 μm wavelength range at which transmissivity of the response function is greater than 1%. However, complex refractive indices have significant variation in the SW3 channel domain (Fig. 2). To design a suitable ice crystal scattering database for GCOM-C/SGLI, the refractive index grid system in the SW3 channel was investigated. Refractive index data for ice was taken from Warren and Brandt [37].

Fig. 2. Grid system of the real and imaginary parts of refractive index in the SW3 channel where transmissivity of the response function is greater than 1% (step size of the real part ( $Δ m_{r}$ ) is 0.001, step size of the imaginary part ( $\ln (Δ m_{i})$ ) is 1.28).

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The LISAS/GOA solver is effective for calculating the single-scattering properties of ice crystals when the size parameter is sufficiently large. Xie et al. [31] retrieved the effective particle size of ice clouds using several ice cloud models consisting of homogeneous and inhomogeneous hexagonal ice crystals from MODIS and Multi-Angle Imaging Spectro-Radiometer (MISR) data. Results indicated that the mode of the histogram for effective particle size is about 70 μm. In this case, when the wavelength is 1.6 μm the size parameter is 137. From this result, we considered that LISAS/GOA solver is sufficient for the feasibility research such as optimization of the light scattering database. Exact solutions such as FDTD and LISAS/SIEMM require much more computing time than LISAS/GOA in this case. The effective particle size ( $D_{e}$ ) used in Xie et al. [31] is calculated as follows:

D_{e} = \frac{2 \int_{0}^{\infty} r^{3} n (r) d r}{\int_{0}^{\infty} r^{2} n (r) d r},

n (r) = \frac{N}{σ \sqrt{2 π}} exp [- \frac{{(Lnr - {Lnr}_{0})}^{2}}{2 σ^{2}}],

where

n (r)

is the number size distribution as a function of the particle radius

r

,

r_{0}

is the mode radius, and

σ

is the log standard deviation of the size distribution.

Table 3 shows the step size of the real and imaginary parts of complex refractive index in the SGLI-SW3 channel, which is used for optimizing the light scattering database. Two types of step size are selected for optimizing the real and imaginary parts in the SW3 channel. In type 1, real part step sizes are set as a constant value (0.001), then the step size of imaginary parts vary from 0.04 to 1.28. In type 2, step sizes of the real part change from 0.001 to 0.032, with imaginary part step sizes set as a constant value (0.04). Cloud optical thickness 8 was used for calculating type 1 and type 2 in this study as the noise-to-signal ratio of the GCOMC/SGLI standard cloud product was designed based on cloud optical thickness 8. Hereafter, we denote this optical thickness as COT 8.

The method for determining the suitable grid system of the complex refractive indices in the SW3 channel was as follows:

(1) One of twelve step-size patterns for the real and imaginary parts of the refractive index in the SW3 channel is selected.
(2) A light scattering database is created based on the different step sizes of the real and imaginary parts of refractive index by using the LISAS/GOA technique.
(3) “Exact” radiance is calculated from the light scattering database with the smallest step size (0.001, 0.04) of the real and imaginary parts by using the R-STAR radiative transfer solver (see Table 3).
(4) The difference in radiance is calculated between the exact radiance and the radiances with other step sizes of the refractive index.

4. Results and Discussions

For optimizing the ice crystal light scattering database for the SGLI sensor, the difference of radiance with different step sizes of the real and imaginary parts of the refractive index in the SW3 channel was investigated. Difference of radiance is calculated from the difference between “Exact” radiance and the radiance at different step sizes of the real and imaginary parts of refractive index. “Exact” radiance is obtained based on the smallest step size (see Table 3).

Figure 3 shows the difference of radiance at different step sizes of the real and imaginary part of the complex refractive index with COT 8. First of all, there is not a significant difference between the radiance with different step sizes of the imaginary part [Fig. 3(a)]. Therefore, difference of radiance is large when the step size of the real part is coarse, and the difference is small when the step size is fine [Fig. 3(b)]. The difference of radiance is close to 0 when step size of the real part is smallest.

Fig. 3. (a) Difference of radiance at different step sizes of the imaginary part ( $I (Δ m_{i})$ : radiance with variance in step size of the imaginary part; $I_{true}$ : exact radiance at finest step size of 0.04). (b) Difference of radiance at different step sizes of the real part of ice refractive index in the SGLI-SW3 channel calculated by R-STAR ( $I (Δ m_{r})$ : radiance with variance step size of the real part; $I_{true}$ : exact radiance at the finest step size of 0.001; noise: 1.75%, SGLI sensor noise in SW3 channel; aspect ratio of hexagonal: $2 a / L = 1$ , $solar zenith angle = 30 °$ , $satellite zenith angle = 0 °$ , $relative azimuthal angle = 0 °$ , atmospheric model: US-standard, $optical thickness = 8$ ).

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Now we discuss these radiance errors in terms of retrieval errors in the satellite mission. Primary uncertainties and bias components [Eq. (6)] included in the retrieved cloud effective particle radius are satellite sensor noise, and fineness of the refractive index grid system. Sensor noise is proportional to the observed radiation, so when reflected solar radiation by clouds increases, sensor noise will also become stronger. Uncertainties of the direct model were not previously estimated, but it is clear that uncertainties of the refractive index grid system can be estimated in this study:

E_{re} = | \frac{Δ r_{e}}{Δ L} | (| Δ L_{sensor} | + | Δ L_{m} |),

where

E_{re}

is the retrieval error of the cloud effective particle radius.

Δ r_{e}

is the derivation of the effective particle radius,

Δ L

is the derivation of the calculation radiance with different step size of the ice crystal refractive index,

Δ r_{e} / Δ L

is the sensitivity of the effective particle radius against radiance,

Δ L_{sensor}

is the derivation of the sensor observing radiance,

Δ L_{m}

is the derivation of the radiance with different refractive index grid system.

From Fig. 3 we can see that radiance error by step size of the real and imaginary parts is basically smaller than the noise-to-signal ratio of 1.75% ( $SNR = 57$ ). Because the GCOM-C satellite mission requires retrieving cloud microphysical properties such as cloud optical thickness and effective particle radius with high quality, it is necessary to reduce the retrieval error of the cloud effective particle radius caused by SGLI sensor noise and the refractive index grid system. In this regard, difference of radiance at different step sizes of the real part [Fig. 3(b)] is worthy of discussion.

Figure 4 shows the cloud retrieval error of the effective particle radius with different step size of the real part of ice refractive index in the SGLI-SW3 channel with COT8. Retrieval error becomes larger with increasing effective particle radius. Retrieval error is small when step size of the refractive index is fine, and it is large when step size is coarse. Furthermore, total error—which includes both sensor noise and error caused by different step size of the refractive index—is generally smaller than 2 μm when step size of the real part is 0.004. Thus, in order to ensure the total retrieval error less than 2 μm, it is required that step size of the real part of the refractive index is not larger than 0.04.

Fig. 4. Cloud retrieval error of the effective particle radius with different step sizes of the real part of ice refractive index in SGLI-SW3 channel (aspect ratio of hexagonal: $2 a / L = 1$ , $solar zenith angle = 30 °$ , $satellite zenith angle = 0 °$ , $relative azimuthal angle = 0 °$ , atmospheric model: US-standard, $optical thickness = 8$ ).

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5. Conclusions

In this study, we investigated a grid system of the complex refractive index in the GCOM-C/SGLI SW3 channel for developing an ice crystal scattering database. The shape of ice crystals was assumed to be a hexagonal column. The LISAS/GOA solver was used to optimize the light scattering database in terms of refractive index.

For optimizing the grid system of refractive index in the SGLI-SW3 channel, the difference between the exact radiance and the radiance at different step sizes of the real and imaginary parts of refractive index was calculated when optical thickness of the ice cloud was 8 using the R-STAR radiative transfer solver. Radiance error caused by different grid systems of refractive index is smaller than the noise-to-signal ratio of 1.75% for SGLI-SW3. The step size of the imaginary part was not significant. However, the step size of the real part was found to be significant in the difference of radiance. Difference of radiance is large when the step size of the real part is coarse, and the difference is small when the step size is fine.

Furthermore, retrieval error of the effective particle radius caused by the sensor noise and error caused by the refractive index grid system were investigated. Results indicated that, when the step size of the real part is 0.04 with COT8, total error of the effective particle radius is generally smaller than 2 μm. Hence, optimization of the refractive index in the SGLI channel is a significant step toward developing a suitable light scattering database for nonspherical ice crystals.

This study was supported by the GCOM-C/SGLI and the EarthCARE project of the Japan Aerospace Exploration Agency (JAXA), and the Greenhouse Gases Observing Satellite (GOSAT) project of the National Institute of Environmental Study, Tsukuba, Japan. This study was also partly supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan through a grant in aid for scientific research (B) (22340133).

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Channel	$λ_{c}$ (μm)	$Δ λ$ (nm)	SNR	$L_{std}$ $(VN, P, SW : W / m^{2} / sr / μm T : Kelvin)$	IFOV (m)
VN1	0.380	10	250	60	250
VN2	0.412	10	400	75	250
VN3	0.443	10	300	64	250
VN4	0.490	10	400	53	250
VN5	0.530	20	250	41	250
VN6	0.565	20	400	33	250
VN7	0.673	20	400	23	250
VN8	0.673	20	250	25	250
VN9	0.763	12	1200	40	1000
VN10	0.868	20	400	8	250
VN11	0.868	20	200	30	250
P1	0.673	20	250	25	1000
P2	0.868	20	250	30	1000
SW1	1.050	20	500	57	1000
SW2	1.380	20	150	8	1000
SW3	1.630	200	57	3	250
SW4	2.210	50	211	1.9	1000
T1	10.8	740	0.2	300	500
T2	12.0	740	0.2	300	500

Solvers	Adopted Size Parameter	Calculation Method	Reference
LISAS/SIEMM	1–25	Maxwell equation	Nakajima T. Y. [16]
IGOM	25–200	$Ray-tracing + Electromagnetic theory$	Ishimoto et al. [13]
LISAS/GOA	More than 200	Ray-tracing technique	Nakajima T. Y. [26]

Type I (Number of database)	0	1	2	3	4	5
Step size of real part ( $Δ m_{r}$ )	0.001	0.001	0.001	0.001	0.001	0.001
Step size of imaginary part ( $Δ \ln (m_{i})$ )	0.04	0.08	0.16	0.32	0.64	1.28
Type II (Number of database)	0	1	2	3	4	5
Step size of real part ( $Δ m_{r}$ )	0.001	0.002	0.004	0.008	0.016	0.032
Step size of imaginary part ( $Δ \ln (m_{i})$ )	0.04	0.04	0.04	0.04	0.04	0.04

Channel	$λ_{c}$ (μm)	$Δ λ$ (nm)	SNR	$L_{std}$ $(VN, P, SW : W / m^{2} / sr / μm T : Kelvin)$	IFOV (m)
VN1	0.380	10	250	60	250
VN2	0.412	10	400	75	250
VN3	0.443	10	300	64	250
VN4	0.490	10	400	53	250
VN5	0.530	20	250	41	250
VN6	0.565	20	400	33	250
VN7	0.673	20	400	23	250
VN8	0.673	20	250	25	250
VN9	0.763	12	1200	40	1000
VN10	0.868	20	400	8	250
VN11	0.868	20	200	30	250
P1	0.673	20	250	25	1000
P2	0.868	20	250	30	1000
SW1	1.050	20	500	57	1000
SW2	1.380	20	150	8	1000
SW3	1.630	200	57	3	250
SW4	2.210	50	211	1.9	1000
T1	10.8	740	0.2	300	500
T2	12.0	740	0.2	300	500

Solvers	Adopted Size Parameter	Calculation Method	Reference
LISAS/SIEMM	1–25	Maxwell equation	Nakajima T. Y. [16]
IGOM	25–200	$Ray-tracing + Electromagnetic theory$	Ishimoto et al. [13]
LISAS/GOA	More than 200	Ray-tracing technique	Nakajima T. Y. [26]

Development of an ice crystal scattering database for the global change observation mission/second generation global imager satellite mission: investigating the refractive index grid system and potential retrieval error

Abstract

1. Introduction

2. GCOM-C/SGLI Sensor

3. Material and Methods

A. Definition of the Ice Crystal Particles and the Light Scattering Solvers

B. Optimizing the Grid System of Refractive Index

4. Results and Discussions

5. Conclusions

References

Cited By

Figures (4)

Tables (3)

Equations (6)

Applied Optics