Abstract

Computing time and retrieval error of the effective particle radius are important considerations when developing an ice crystal scattering database to be used in radiative transfer simulation and satellite remote sensing retrieval. Therefore, the light scattering database should be optimized based on the specifications of the satellite sensor. In this study, the grid system of the complex refractive index in the 1.6 μm (SW3) channel of the Global Change Observation Mission/Second Generation Global Imager satellite sensor is investigated for optimizing the ice crystal scattering database. This grid system is separated into twelve patterns according to the step size of the real and imaginary parts of the refractive index. Specifically, the LIght Scattering solver Applicable to particles of arbitrary Shape/Geometrical-Optics Approximation technique is used to simulate the scattering of light by randomly oriented large hexagonal ice crystals. The difference of radiance with different step size of the refractive index is calculated from the developed light scattering database using the radiative transfer (R-STAR) solver. The results indicated that the step size of the real part is a significant factor in difference of radiance.

© 2012 Optical Society of America

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 [16]. 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 [1021]. 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].

Tables Icon

Table 1. Specification of the SGLI

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=2πreqvλ,
ar=2aL,
reqv=3v4A,
where α is the size parameter, λ is the wavelength, reqv is the radii of the corresponding equivalent volume spheres for a nonspherical ice crystal, and ar 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.

Tables Icon

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

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).

Tables Icon

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

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 (Δmr) is 0.001, step size of the imaginary part (ln(Δmi)) 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 (De) used in Xie et al. [31] is calculated as follows:

De=20r3n(r)dr0r2n(r)dr,
n(r)=Nσ2πexp[(LnrLnr0)22σ2],
where n(r) is the number size distribution as a function of the particle radius r, r0 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(Δmi): radiance with variance in step size of the imaginary part; Itrue: 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(Δmr): radiance with variance step size of the real part; Itrue: exact radiance at the finest step size of 0.001; noise: 1.75%, SGLI sensor noise in SW3 channel; aspect ratio of hexagonal: 2a/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:

Ere=|ΔreΔL|(|ΔLsensor|+|ΔLm|),
where Ere is the retrieval error of the cloud effective particle radius. Δre is the derivation of the effective particle radius, ΔL is the derivation of the calculation radiance with different step size of the ice crystal refractive index, Δre/ΔL is the sensitivity of the effective particle radius against radiance, ΔLsensor is the derivation of the sensor observing radiance, ΔLm 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: 2a/L=1, solar zenithangle=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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References

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  1. D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
    [Crossref]
  2. K. N. Liou, “Influence of cirrus clouds on weather and climate processes: A global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
    [Crossref]
  3. G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
    [Crossref]
  4. J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
    [Crossref]
  5. J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
    [Crossref]
  6. P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
    [Crossref]
  7. G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
    [Crossref]
  8. T. Y. Nakajima and T. Nakajima, “Wide-area determination of cloud microphysical properties from NOAA AVHRR measurements for FIRE and ASTEX regions,” J. Atmos. Sci. 52, 4043–4059 (1995).
    [Crossref]
  9. T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
    [Crossref]
  10. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [Crossref]
  11. Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
    [Crossref]
  12. P. Yang and K. N. Liou, “Geometric-optics-integral equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [Crossref]
  13. H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
    [Crossref]
  14. P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. 13, 2072–2085 (1996).
    [Crossref]
  15. Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
    [Crossref]
  16. T. Y. Nakajima, T. Nakajima, K. Yoshimori, S. K. Mishra, and S. N. Tripathi, “Development of a light scattering solver applicable to particles of arbitrary shape on the basis of the surface integral equations method of Müller-type (SIEMM): Part I. Methodology, accuracy of calculation, and electromagnetic current on the particle urface,” Appl. Opt. 48, 3526–3536 (2009).
    [Crossref]
  17. Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
    [Crossref]
  18. Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
    [Crossref]
  19. Q. Fu, “A new parameterization of an asymmetry factor of cirrus clouds for climate models,” J. Atmos. Sci. 64, 4144–4154 (2007).
    [Crossref]
  20. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
    [Crossref]
  21. L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
    [Crossref]
  22. P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
    [Crossref]
  23. P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
    [Crossref]
  24. M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
    [Crossref]
  25. A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
    [Crossref]
  26. T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
    [Crossref]
  27. K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
    [Crossref]
  28. M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
    [Crossref]
  29. T. Y. Nakajima, T. Tsuchiya, H. Ishida, T. N. Matsui, and H. Shimoda, “Cloud detection performance of spaceborne visible-to-infrared multispectral imager,” Appl. Opt. 50, 2601–2616 (2011).
    [Crossref]
  30. T. Kobayashi, “The growth of snow crystals at low supersaturation,” Philadelphia Mag. 6, 1363–1370 (1961).
    [Crossref]
  31. Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
    [Crossref]
  32. Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
    [Crossref]
  33. Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
    [Crossref]
  34. X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
    [Crossref]
  35. T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
    [Crossref]
  36. T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
    [Crossref]
  37. S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
    [Crossref]

2012 (3)

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

2011 (3)

T. Y. Nakajima, T. Tsuchiya, H. Ishida, T. N. Matsui, and H. Shimoda, “Cloud detection performance of spaceborne visible-to-infrared multispectral imager,” Appl. Opt. 50, 2601–2616 (2011).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

2010 (3)

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
[Crossref]

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

2009 (4)

2008 (2)

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

2007 (2)

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Q. Fu, “A new parameterization of an asymmetry factor of cirrus clouds for climate models,” J. Atmos. Sci. 64, 4144–4154 (2007).
[Crossref]

2005 (1)

2000 (3)

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
[Crossref]

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

1998 (2)

Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[Crossref]

1997 (1)

T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
[Crossref]

1996 (3)

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[Crossref]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. 13, 2072–2085 (1996).
[Crossref]

P. Yang and K. N. Liou, “Geometric-optics-integral equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[Crossref]

1995 (2)

Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[Crossref]

T. Y. Nakajima and T. Nakajima, “Wide-area determination of cloud microphysical properties from NOAA AVHRR measurements for FIRE and ASTEX regions,” J. Atmos. Sci. 52, 4043–4059 (1995).
[Crossref]

1994 (1)

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

1993 (1)

1990 (1)

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

1986 (2)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: A global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[Crossref]

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[Crossref]

1972 (1)

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[Crossref]

1961 (1)

T. Kobayashi, “The growth of snow crystals at low supersaturation,” Philadelphia Mag. 6, 1363–1370 (1961).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Alexander, A. K.

T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
[Crossref]

Amano, T.

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

Bi, L.

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[Crossref]

Brandt, R. E.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Couvert, P.

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

Dim, J.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

Ding, S.

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

Doutriaux-Boucher, M.

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

Flatau, P. J.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

Fu, Q.

Q. Fu, “A new parameterization of an asymmetry factor of cirrus clouds for climate models,” J. Atmos. Sci. 64, 4144–4154 (2007).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
[Crossref]

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[Crossref]

Goloub, P.

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

Heidinger, A.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

Heymsfield, A.

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[Crossref]

Hiramatsu, M.

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Hu, Y.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

Hu, Y. X.

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

Huang, H.-L.

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

Iaquinta, J.

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

Ishida, H.

Ishimoto, H.

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Kahn, R.

Kattawar, G. W.

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[Crossref]

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

Kobayashi, T.

T. Kobayashi, “The growth of snow crystals at low supersaturation,” Philadelphia Mag. 6, 1363–1370 (1961).
[Crossref]

Laszlo, I.

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

Liou, K. N.

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

P. Yang and K. N. Liou, “Geometric-optics-integral equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[Crossref]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. 13, 2072–2085 (1996).
[Crossref]

Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[Crossref]

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: A global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[Crossref]

Liu, X.

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

Macke, A.

Mano, Y.

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
[Crossref]

Masuda, K.

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Matsui, T. N.

Meng, Z.

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

Menzel, W. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

Mie, G.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Minnis, P.

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

Mishchenko, M. I.

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[Crossref]

Mishra, S. K.

Mitchell, D.

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

Murakami, H.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

Nakajima, T.

T. Y. Nakajima, T. Nakajima, K. Yoshimori, S. K. Mishra, and S. N. Tripathi, “Development of a light scattering solver applicable to particles of arbitrary shape on the basis of the surface integral equations method of Müller-type (SIEMM): Part I. Methodology, accuracy of calculation, and electromagnetic current on the particle urface,” Appl. Opt. 48, 3526–3536 (2009).
[Crossref]

T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
[Crossref]

T. Y. Nakajima and T. Nakajima, “Wide-area determination of cloud microphysical properties from NOAA AVHRR measurements for FIRE and ASTEX regions,” J. Atmos. Sci. 52, 4043–4059 (1995).
[Crossref]

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[Crossref]

Nakajima, T. Y.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

T. Y. Nakajima, T. Tsuchiya, H. Ishida, T. N. Matsui, and H. Shimoda, “Cloud detection performance of spaceborne visible-to-infrared multispectral imager,” Appl. Opt. 50, 2601–2616 (2011).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
[Crossref]

T. Y. Nakajima, T. Nakajima, K. Yoshimori, S. K. Mishra, and S. N. Tripathi, “Development of a light scattering solver applicable to particles of arbitrary shape on the basis of the surface integral equations method of Müller-type (SIEMM): Part I. Methodology, accuracy of calculation, and electromagnetic current on the particle urface,” Appl. Opt. 48, 3526–3536 (2009).
[Crossref]

T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
[Crossref]

T. Y. Nakajima and T. Nakajima, “Wide-area determination of cloud microphysical properties from NOAA AVHRR measurements for FIRE and ASTEX regions,” J. Atmos. Sci. 52, 4043–4059 (1995).
[Crossref]

Nordell, B.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

Okamura, Y.

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Orikasa, N.

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Riedi, J.

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

Shimoda, H.

Shiratama, K.

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Stackhouse, P. W.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

Stephens, G. L.

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
[Crossref]

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

Strabala, K. I.

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

Sun, W. B.

Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
[Crossref]

Suzuki, K.

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
[Crossref]

Takamura, T.

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

Takano, Y.

Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[Crossref]

Tanaka, K.

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

Tanaka, M.

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[Crossref]

Travis, L. D.

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[Crossref]

Tripathi, S. N.

Tsay, S. C.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

Tsuchiya, T.

Uchiyama, A.

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Warren, S. G.

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Wei, H.

Winker, D.

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

Woolf, H. M.

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

Wu, D. L.

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

Wylie, D. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

Wyser, K.

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

Xie, Y.

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

Yang, P.

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[Crossref]

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
[Crossref]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. 13, 2072–2085 (1996).
[Crossref]

P. Yang and K. N. Liou, “Geometric-optics-integral equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[Crossref]

Yoshimori, K.

Zhang, Z.

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

Ann. Phys. (1)

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Appl. Opt. (7)

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[Crossref]

P. Yang and K. N. Liou, “Geometric-optics-integral equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[Crossref]

Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
[Crossref]

T. Y. Nakajima, T. Nakajima, K. Yoshimori, S. K. Mishra, and S. N. Tripathi, “Development of a light scattering solver applicable to particles of arbitrary shape on the basis of the surface integral equations method of Müller-type (SIEMM): Part I. Methodology, accuracy of calculation, and electromagnetic current on the particle urface,” Appl. Opt. 48, 3526–3536 (2009).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[Crossref]

P. Yang, H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[Crossref]

T. Y. Nakajima, T. Tsuchiya, H. Ishida, T. N. Matsui, and H. Shimoda, “Cloud detection performance of spaceborne visible-to-infrared multispectral imager,” Appl. Opt. 50, 2601–2616 (2011).
[Crossref]

Geophys. Res. Lett. (1)

J. Riedi, M. Doutriaux-Boucher, P. Goloub, and P. Couvert, “Global distribution of cloud top phase from POLDER/ADEOS I,” Geophys. Res. Lett. 27, 1707–1710 (2000).
[Crossref]

Int. J. Remote Sens. (1)

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, Y. X. Hu, and D. L. Wu, “Determination of ice cloud models using MODIS and MISR data,” Int. J. Remote Sens. 33, 4219–4253 (2012).
[Crossref]

J. Aerosol Sci. (1)

Z. Meng, P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, “Single-scattering properties of nonspherical mineral dust aerosols: A database for application to radiative transfer calculations,” J. Aerosol Sci. 41, 501–512 (2010).
[Crossref]

J. Appl. Meteorol. Clim. (1)

P. Yang, Z. Zhang, G. W. Kattawar, S. G. Warren, B. A. Baum, H.-L. Huang, Y. Hu, D. Winker, and J. Iaquinta, “Effect of cavities on the optical properties of bullet rosettes: Implications for active and passive remote sensing of ice cloud properties,” J. Appl. Meteorol. Clim. 47, 2311–2330 (2008).
[Crossref]

J. Atmos. Ocean. Technol. (1)

X. Liu, S. Ding, L. Bi, and P. Yang, “On the use of scattering kernels to calculate ice cloud bulk optical properties,” J. Atmos. Ocean. Technol. 29, 50–63 (2012).
[Crossref]

J. Atmos. Sci. (7)

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part I: Sensitivity analysis of the MODIS-derived cloud droplet size,” J. Atmos. Sci. 67, 1884–1896 (2010).
[Crossref]

T. Y. Nakajima, K. Suzuki, and G. L. Stephens, “Droplet growth in warm water clouds observed by the A-Train. Part II: A multi-sensor view,” J. Atmos. Sci. 67, 1897–1907 (2010).
[Crossref]

Q. Fu, “A new parameterization of an asymmetry factor of cirrus clouds for climate models,” J. Atmos. Sci. 64, 4144–4154 (2007).
[Crossref]

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[Crossref]

T. Y. Nakajima and T. Nakajima, “Wide-area determination of cloud microphysical properties from NOAA AVHRR measurements for FIRE and ASTEX regions,” J. Atmos. Sci. 52, 4043–4059 (1995).
[Crossref]

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, and P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1754 (1990).
[Crossref]

Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[Crossref]

J. Clim. (1)

D. P. Wylie, W. P. Menzel, H. M. Woolf, and K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[Crossref]

J. Climate (2)

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[Crossref]

Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 25, 2223–2237 (1998).
[Crossref]

J. Geophys. Res. (4)

J. Dim, H. Murakami, T. Y. Nakajima, B. Nordell, A. Heidinger, and T. Takamura, “The recent state of the climate: driving components of cloud type variability,” J. Geophys. Res. 116, D11117 (2011).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Y. Xie, P. Yang, G. W. Kattawar, P. Minnis, and Y. X. Hu, “Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size,” J. Geophys. Res. 114, D11203 (2009).
[Crossref]

P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. 13, 2072–2085 (1996).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (4)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[Crossref]

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[Crossref]

H. Ishimoto, K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, “Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds,” J. Quant. Spectrosc. Radiat. Transfer 113, 632–643 (2012).
[Crossref]

Mon. Weather Rev. (1)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: A global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[Crossref]

Philadelphia Mag. (1)

T. Kobayashi, “The growth of snow crystals at low supersaturation,” Philadelphia Mag. 6, 1363–1370 (1961).
[Crossref]

Proc. SPIE (3)

T. Y. Nakajima, T. Nakajima, and A. K. Alexander, “Radiance transfer through light scattering media with nonspherical large particles: direct and indirect problems,” Proc. SPIE 3220, 2–12 (1997).
[Crossref]

K. Tanaka, Y. Okamura, T. Amano, M. Hiramatsu, and K. Shiratama, “Development status of the second-generation global imager (SGLI) on GCOM-C,” Proc. SPIE 7474, 74740N (2009).
[Crossref]

M. Hiramatsu, K. Tanaka, Y. Okamura, T. Amano, and K. Shiratama, “Design challenge on forthcoming SGLI boarded on GCOM-C,” Proc. SPIE 6744, 67440L (2007).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

Definition of the hexagonal column and plate.

Fig. 2.
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 (Δmr) is 0.001, step size of the imaginary part (ln(Δmi)) is 1.28).

Fig. 3.
Fig. 3.

(a) Difference of radiance at different step sizes of the imaginary part (I(Δmi): radiance with variance in step size of the imaginary part; Itrue: 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(Δmr): radiance with variance step size of the real part; Itrue: exact radiance at the finest step size of 0.001; noise: 1.75%, SGLI sensor noise in SW3 channel; aspect ratio of hexagonal: 2a/L=1, solar zenith angle=30°, satellite zenith angle=0°, relative azimuthal angle=0°, atmospheric model: US-standard, optical thickness=8).

Fig. 4.
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: 2a/L=1, solar zenithangle=30°, satellite zenith angle=0°, relative azimuthal angle=0°, atmospheric model: US-standard, optical thickness=8).

Tables (3)

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Table 1. Specification of the SGLI

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

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

Equations (6)

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α=2πreqvλ,
ar=2aL,
reqv=3v4A,
De=20r3n(r)dr0r2n(r)dr,
n(r)=Nσ2πexp[(LnrLnr0)22σ2],
Ere=|ΔreΔL|(|ΔLsensor|+|ΔLm|),

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