## Simultaneous determination of aerosol optical thickness and exponent of Junge power law from satellite measurements of two near-infrared bands over the ocean

Optics Express, Vol. 15, Issue 8, pp. 5227-5236 (2007)

http://dx.doi.org/10.1364/OE.15.005227

Acrobat PDF (845 KB)

### Abstract

An iterative algorithm is presented in this study for simultaneous determination of both the aerosol optical thickness and the exponent of the Junge power law from the total reflectance data of two satellite-based, near-infrared bands over the ocean. The atmospheric aerosol model is assumed as the Junge power-law size distribution in retrieval of the data. Numerical simulations show that relative errors in retrieval of the aerosol optical thickness and the exponent of the Junge power law are less than 5% when the actual atmospheric aerosol follows the Junge power-law size distribution. For other aerosol size distributions, relative errors of the aerosol optical thickness are less than approximately 10%. The proposed method is applied to a case study of the data of two near-infrared channels of the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) over the East China Sea area. The results show that reasonable spatial distribution of the exponent of the Junge law and the aerosol optical thickness may be obtained on a pixel-by-pixel basis through use of the proposed retrieval algorithm.

© 2007 Optical Society of America

## 1. Introduction

*λ*in the visible and near-infrared regions contains coupling information of both radiance and reflectance between the atmosphere and the ground. If only satellite-derived data are relied on, it is difficult to simultaneously retrieve the two unknown parameters: the atmospheric parameter and the ground optical parameter. It is known that only accumulation and coarse model particles may be detected by using the method of optical remote sensing. With the assumption of spherical aerosol particles, the unknown aerosol optical parameters are size distribution, complex refractive index, and optical thickness. It is necessary for retrieval of aerosol concentration or atmospheric correction of satellite data to assume an aerosol model [1–3

1. C. R. N. Rao, E. P. McClain, and L. L. Stowe, “Remote sensing of aerosols over the
oceans using AVHRR data theory, practice, and
applications,” Int. J. Remote Sens. **10**, 743–749
(1989). [CrossRef]

4. D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, “Remote sensing of aerosol properties
over oceans using the MODIS/EOS spectral
radiances,” J. Geophys. Res. **102**, 16971–16988
(1997). [CrossRef]

5. F. S. Zhao and T. Nakajima, “Simultaneous determination of
water-leaving reflectance and aerosol optical thickness from coastal zone
color scanner measurements,” Appl. Opt. **36**, 6949–6956
(1997). [CrossRef]

*et al*. [6

6. F. Zhao, Y. Li, C. Dong, and N. Lu, “An algorithm for determination of
aerosol optical thickness from AVHRR imagery over
oceans,” Meteorol. Atmos. Phys. **80**, 73–88
(2002). [CrossRef]

5. F. S. Zhao and T. Nakajima, “Simultaneous determination of
water-leaving reflectance and aerosol optical thickness from coastal zone
color scanner measurements,” Appl. Opt. **36**, 6949–6956
(1997). [CrossRef]

*et al*. [6

6. F. Zhao, Y. Li, C. Dong, and N. Lu, “An algorithm for determination of
aerosol optical thickness from AVHRR imagery over
oceans,” Meteorol. Atmos. Phys. **80**, 73–88
(2002). [CrossRef]

8. R. M. Chomko and R. Gordon, “Atmospheric correction of ocean
color imagery: use of the Junge power-law aerosol size distribution with
variable refractive index to handle aerosol
absorption,” Appl. Opt. **37**, 5560–5572
(1998). [CrossRef]

9. P. E. Gill and W. Murray, “Quasi-Newton methods for
unconstrained optimization,” J. Inst.
Math. Appl. **9**, 91–108
(1972). [CrossRef]

*C*) can be retrieved with good accuracy; however, the aerosol optical thickness is retrieved with large errors. They thought that the discrepancy is due to significant differences in the scattering phase functions for bimodal, lognormal, and power-law distributions. The exponent of the Junge power law was determined by comparing the measured values of two near-infrared channels without the wavelength factor in their expressions, which is a possible error source for the retrieval of aerosol optical thickness. Even if the wavelength factor is included, relying on an analytical formula only, our numerical experiments may show that the relative errors in the estimation of size parameter

*ν*are in the 20-40% range and the maximum relative error of the aerosol optical thickness is close to 50%. To improve the accuracy of retrieval, a new iterative algorithm is presented in this study for retrieval of size parameter

*ν*and the aerosol optical thickness. Simulations show that the retrieval accuracy of size parameter

*ν*and the aerosol optical thickness is improved satisfactorily by using the iterative algorithm.

## 2. Retrieval scheme and simulated performance

### 2.1 The equation derived and the numerical simulations

*λ*in the single-scattering case can be written as [2

2. H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance
and aerosol optical thickness over the oceans with SeaWiFS: a preliminary
algorithm,” Appl. Opt. **33**, 443–452
(1994). [CrossRef] [PubMed]

10. M. Wang and H. R. Gordon, “Retrieval of the columnar aerosol
phase function and single-scattering albedo from sky radiance over the
ocean: simulations,” Appl. Opt. **32**, 4598–4609
(1993). [CrossRef] [PubMed]

*ρ*(

_{m}*θ*,

_{0}*ϕ*,

_{0}*θ*,

*ϕ*) is the reflectance by atmospheric molecules (Rayleigh scattering), parameters

*ω*,

_{a}*τ*, and

_{a}*P*(

_{a}*θ*,

_{0}*ϕ*,

_{0}*θ*,

*ϕ*) are the aerosol single-scattering albedo, aerosol optical thickness, and scattering phase function, respectively. Angles

*θ*and

_{0}*ϕ*are the solar zenith and azimuth angles, respectively. Likewise,

_{0}*θ*and

*ϕ*are the viewing zenith and azimuth angles.

*μm*is described in the Angstrom formula [11

11. A. Angström, “Techniques of determining the
turbidity of the atmosphere,” Tellus **13**, 214–223
(1961). [CrossRef]

*α*is the Angstrom coefficient and

*β*is the turbidity factor. Combining Eqs. (1) and (2), the following expression can be obtained:

*α*describes the relative spectral course of the extinction coefficient

*σ*in

_{e}*β*’ is the aerosol extinction coefficient at wavelength 1

*μ*. The formula is valid if the particle size distribution obeys the Junge power-law model. From Eq. (4), the ratio of the single scattering albedo in the two near-infrared bands is given by

_{m}*σ*is the scattering coefficient. The phase function is expressed as

_{s}*φ*is the scattering angle and

*β*(

_{s}*φ*) is the scattering function. The ratio of the phase function values in two near-infrared bands is given by

12. K. Bullrich, “Scattered radiation in the
atmosphere and the natural aerosol,” Adv.
Geophys. **10**, 99–260
(1964). [CrossRef]

*x*is the size parameter and

*i*is the intensity distribution function.

*η*(

*φ*) is insensitive to wavelength if the scattering angle is more than 4° [12

12. K. Bullrich, “Scattered radiation in the
atmosphere and the natural aerosol,” Adv.
Geophys. **10**, 99–260
(1964). [CrossRef]

*ν*and the Angstrom coefficient

*α*is

*et al*. [13

13. P. Y. Deschamps, M. Herman, and D. Tanre, “Modeling of the atmospheric effects
and its application to the remote sensing of ocean
color,” Appl. Opt. **22**, 3751–3758
(1983). [CrossRef] [PubMed]

*λ*

^{-α},

*i*.

*e*.,

13. P. Y. Deschamps, M. Herman, and D. Tanre, “Modeling of the atmospheric effects
and its application to the remote sensing of ocean
color,” Appl. Opt. **22**, 3751–3758
(1983). [CrossRef] [PubMed]

*ρ*(

_{p}*θ*,

_{0}*ϕ*,

_{0}*θ*,

*ϕ*) for 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 of

*ν*with

*τ*(550)=0.3 at a band of 550

_{a}*nm*, and the complex refractive index

*m*=1.45+0.0035

*i*. The size range of the particle radius in the calculations is taken as 0.04-10

*μm*. The two near-infrared bands are 0.765 and 0.865

*μm*with a bandwidth of 40

*nm*. Note that the simulated data were given for sensor viewing angles of 15°, 30°, 45°, 60°, and azimuth of 200°, with solar zenith of 30° and azimuth of 180°.

*ν*are calculated in terms of Eq. (11). The relative errors of

*ν*are listed in Table 1. The

*τ*(550) are calculated iteratively according to the iterative Eq. (16) in the next paragraphs by inputting the

_{a}*ν*to the 6S code [14] for radiative transfer calculation while ignoring the absorption of atmospheric molecules for the ocean’s surface of clear waters. The relative errors in retrievals of aerosol optical thicknesses

*τ*(550) are listed in Table 2.

_{a}*ν*are within 20–40% and the maximum relative error of

*τ*(550) is close to 50%. It is found that computational errors cannot be tolerated in computing the size distribution parameters of

_{a}*ν*and

*τ*(550). To see the influence of multiple scattering, we have also carried out simulations with

_{a}*τ*(550)=0.1 and 0.05, which are clear atmospheres over the ocean. Unfortunately, the relative errors of

_{a}*ν*are still within 20-35% in the case of small aerosol optical thickness, which indicates that multiscattering is not an important factor for the above errors. Simulations suggest that such large errors may not result only from the ignorance of multiple scattering according to Eq. (11). So, it is understood that large errors of

*τ*(550) can be ascribed to the inaccurate

_{a}*ν*.

### 2.2 The new iterative algorithm and the numerical simulations

*ν*and

*τ*(550), based on the process derived in the above equation, an expression is created:

_{a}*c*are calculated from the 6S mode in the two near-infrared bands. We denote the left side of Eq. (14) as

*Y*. Combining Eqs. (2) and (10), Eq. (14) then becomes

*α*cf is the input value for the 6S mode at the

^{n}*n*th iteration. Using the α calculated from Eq. (15), new

*τ*(550) can be obtained with a near-infrared wavelength by using the iterative calculation [15]

_{a}*τ*(550) is the input aerosol optical thickness for the 6S mode. This procedure is followed according to Eq. (16) until the convergence criterion of

^{n}_{a}*α*and new

*τ*(550) are selected as the next input values for the 6S mode, and the two procedures according to Eqs. (15) and (16) are repeated, until the convergence criterion of

_{a}*oα*and the

*τ*(550) in the last step are determined as the actual required values.

_{a}*ν*and

*τ*(550) are listed in Tables 3 and 4, respectively. It can be seen from Tables 3 and 4 that the relative errors of the retrieved

_{a}*ν*and

*τ*(550) are less than 5%, which indicates that excellent retrievals of both

_{a}*ν*and

*τ*(550) can be obtained for the Junge power-law model in the iterative algorithm.

_{a}### 2.3 Applications to other aerosol size distributions

*in-situ*observations have shown that lognormal distributions are more appropriate to describe realistic aerosol size distribution [16

16. E. M. Patterson and D. A. Gillette, “Commonalities in measured size
distributions for aerosol having a soil-derived
component,” J. Geophys. Res. **82**, 2074–2082
(1997). [CrossRef]

17. Y. Kim, H. Sievering, and J. F. Boatmann, “Airborne measurement of atmospheric
aerosol particles in the lower troposphere over the central United
States,” J. Geophys. Res. **93**, 12631–12644
(1988). [CrossRef]

*i*:

*r*

_{modN,i}is the mode radius,

*σ*measures the width of distribution, and

_{i}*N*is the total particle number density of the component

_{i}*i*in particles per cubic centimeter. The microphysical characteristics of the four components for the standard 6S aerosol types [18

18. E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, “Second simulation of the satellite
signal in the solar spectrum: an overview,”
IEEE Trans. Geosci. Remote Sens. **35**, 675–686
(1997). [CrossRef]

*i*at the two near-infrared bands (0.765 and 0.865

*μm*).

*ν*and

*τ*(550) can be obtained by using the proposed iterative algorithm with the microphysical characteristics in Table 5 and the volume percentages of the two basic components with maritime in Table 6, which are tabulated in Table 7. The true

_{a}*τ*(550) is 0.3. The sun-viewing geometries are uniform in the above tables. For the four cases of sun-viewing geometry, the difference of size distribution of parameter

_{a}*ν*is little. These values of

*ν*can be evaluated as equivalent exponents of the Junge power law for lognormal distributions. It can be found in Table 7 that the retrieved values of

*τ*(550) are in relative error by <5%.

_{a}*ν*is around 4.7 and the relative error of the

*τ*(550) is around 7%, which is shown in Table 8.

_{a}*i*for the maritime, continental, and urban aerosol models, respectively. The difference among the values of retrieved size distribution parameter

*ν*is small with various sun-viewing geometries for the same aerosol model. The relative errors in retrieved values of

*τ*(550) should be <10%. It can be summarized that it is responsible to approximate the actual atmospheric aerosol as the Junge power-law size distribution in the course of retrieval of aerosol concentrations in this iterative algorithm.

_{a}## 3. Example of application to SeaWiFS data

*ν*and

*τ*(550) were retrieved from SeaWiFS measurements on January 1, 2001, over the Taiwan Strait region with an aerosol complex refractive index of 1.45+0.0035

_{a}*i*[4

4. D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, “Remote sensing of aerosol properties
over oceans using the MODIS/EOS spectral
radiances,” J. Geophys. Res. **102**, 16971–16988
(1997). [CrossRef]

*ν*and

*τ*(550) are shown in Figs. 1 and 2. The black color represents clouds or land, or Case 2 waters in Figs. 1 and 2, which is distinguished from Case 1 waters in terms of the criterion of α > 4 or α≤ 0 during the iterative retrieval process. It can be seen from Fig. 1 that the values of

_{a}*ν*can be divided into three groups: 3.0-3.7 near the cloud region; 4.5-5.0 on the coast region, which is close to the one in the continental or urban aerosol models discussed above; and 3.7-4.5 on most open oceans in the Taiwan Strait. In the red areas in Fig. 1, the values of

*ν*between 5.25 and 6.0 are likely to be the influence of the uncertain aerosol model. Although the retrieved equivalent Junge index in the red areas is a little bit large in those cases, the corresponding optical depth that is retrieved is still reasonable (see Fig. 2). It can be seen from Fig. 2 that most of

*τ*(550) values vary within the range of 0.20 to 0.28. Though

_{a}*ν*is also in the 4.5-5.0 range on the east side of Taiwan, the

*τ*(550) is less than 0.15, which indicates clean air in that region. On the east side of Taiwan and most regions in the center of the Taiwan Strait, the aerosols possibly might obey the Junge power-law size distribution.

_{a}## 4. Conclusion

*ν*and

*τ*(550) is less than 5% if the actual atmospheric aerosol follows the Junge power-law size distribution. If actual atmospheric aerosol is the lognormal distribution, the equivalent exponent of the Junge power law can be obtained by the iterative method, and the relative error of retrieved

_{a}*τ*(550) is approximately <10%. The method has been also applied to SeaWiFS local data. It has been demonstrated that the values of retrieved

_{a}*ν*and

*τ*(550) are reasonable, and that

_{a}*ν*has a large spatial variation over a local-area image. It can be concluded that the assumption of uniform aerosol size distribution parameters over an entire image or a segmented image undoubtedly will lead to retrieval errors of aerosol concentrations.

## References and links

1. | C. R. N. Rao, E. P. McClain, and L. L. Stowe, “Remote sensing of aerosols over the
oceans using AVHRR data theory, practice, and
applications,” Int. J. Remote Sens. |

2. | H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance
and aerosol optical thickness over the oceans with SeaWiFS: a preliminary
algorithm,” Appl. Opt. |

3. | D. A. Siegal, M. Wang, S. Maritorena, and W. Robinson, “Atmospheric correction of satellite
ocean color imagery: the black pixel assumption,”
Appl. Opt. |

4. | D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, “Remote sensing of aerosol properties
over oceans using the MODIS/EOS spectral
radiances,” J. Geophys. Res. |

5. | F. S. Zhao and T. Nakajima, “Simultaneous determination of
water-leaving reflectance and aerosol optical thickness from coastal zone
color scanner measurements,” Appl. Opt. |

6. | F. Zhao, Y. Li, C. Dong, and N. Lu, “An algorithm for determination of
aerosol optical thickness from AVHRR imagery over
oceans,” Meteorol. Atmos. Phys. |

7. | S. S. Rao, |

8. | R. M. Chomko and R. Gordon, “Atmospheric correction of ocean
color imagery: use of the Junge power-law aerosol size distribution with
variable refractive index to handle aerosol
absorption,” Appl. Opt. |

9. | P. E. Gill and W. Murray, “Quasi-Newton methods for
unconstrained optimization,” J. Inst.
Math. Appl. |

10. | M. Wang and H. R. Gordon, “Retrieval of the columnar aerosol
phase function and single-scattering albedo from sky radiance over the
ocean: simulations,” Appl. Opt. |

11. | A. Angström, “Techniques of determining the
turbidity of the atmosphere,” Tellus |

12. | K. Bullrich, “Scattered radiation in the
atmosphere and the natural aerosol,” Adv.
Geophys. |

13. | P. Y. Deschamps, M. Herman, and D. Tanre, “Modeling of the atmospheric effects
and its application to the remote sensing of ocean
color,” Appl. Opt. |

14. | E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, |

15. | Q. Xu, H. W., and F. Zhao, “Retrieval of reflectance along
coastal zone with SeaWiFS,” J. Remote
Sens. (in Chinese) |

16. | E. M. Patterson and D. A. Gillette, “Commonalities in measured size
distributions for aerosol having a soil-derived
component,” J. Geophys. Res. |

17. | Y. Kim, H. Sievering, and J. F. Boatmann, “Airborne measurement of atmospheric
aerosol particles in the lower troposphere over the central United
States,” J. Geophys. Res. |

18. | E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, “Second simulation of the satellite
signal in the solar spectrum: an overview,”
IEEE Trans. Geosci. Remote Sens. |

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(010.1110) Atmospheric and oceanic optics : Aerosols

(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

(280.1100) Remote sensing and sensors : Aerosol detection

**ToC Category:**

Atmospheric and ocean optics

**History**

Original Manuscript: September 22, 2006

Revised Manuscript: January 16, 2007

Manuscript Accepted: March 8, 2007

Published: April 13, 2007

**Virtual Issues**

Vol. 2, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Qingshan Xu, Heli Wei, Ruizhong Rao, and Huanling Hu, "Simultaneous determination of aerosol optical thickness and exponent of Junge power law from satellite measurements of two near-infrared bands over the ocean," Opt. Express **15**, 5227-5236 (2007)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-8-5227

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### References

- C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989). [CrossRef]
- H. R. Gordon and M. Wang, "Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm," Appl. Opt. 33, 443-452 (1994). [CrossRef] [PubMed]
- D. A. Siegal, M. Wang, S. Maritorena, and W. Robinson, "Atmospheric correction of satellite ocean color imagery: the black pixel assumption," Appl. Opt. 39, 3582-3591 (2000). [CrossRef]
- D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997). [CrossRef]
- F. S. Zhao and T. Nakajima, "Simultaneous determination of water-leaving reflectance and aerosol optical thickness from coastal zone color scanner measurements," Appl. Opt. 36, 6949-6956 (1997). [CrossRef]
- F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002). [CrossRef]
- S. S. Rao, Optimization Theory and Applications (Wiley Eastern, Ltd., New Delhi, 1978).
- R. M. Chomko and R. Gordon, "Atmospheric correction of ocean color imagery: use of the Junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption," Appl. Opt. 37, 5560-5572 (1998). [CrossRef]
- P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972). [CrossRef]
- M. Wang and H. R. Gordon, "Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations," Appl. Opt. 32, 4598-4609 (1993). [CrossRef] [PubMed]
- A. Angström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961). [CrossRef]
- K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-260 (1964). [CrossRef]
- P. Y. Deschamps, M. Herman, and D. Tanre, "Modeling of the atmospheric effects and its application to the remote sensing of ocean color," Appl. Opt. 22, 3751-3758 (1983). [CrossRef] [PubMed]
- E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, The Second Simulation of the Satellite Signal in the Solar Spectrum (6S) User Guide (Laboratoire d'Optique Atmosphérique, France, 1997).
- Q. Xu, H. W., and F. Zhao, "Retrieval of reflectance along coastal zone with SeaWiFS," J. Remote Sens.(in Chinese) 6, 352-356 (2002).
- E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997). [CrossRef]
- Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988). [CrossRef]
- E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997). [CrossRef]

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