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• 目的： TOA reflectance 转为 surface refletance。 主要包含两步： 1）大气校正； 2）BRDF校正

• 进度： 目前仅仅整理了常用的方法，其中，大气校正主要使用6s模型。具体操作待更新

1. 相关文献

1.1 参考[1] [2]

• The Bidirectional Reflectance Distribution Function (BRDF) was estimated as:

• Kvol: the surface anisotropy of reflected radiation was characterized by the Ross-Thick volumetric kernel,
• Kgeo: The Li-Sparse geometric kernel
• θs is the solar zenith angle (SZA)
• θv is the view zenith angle (VZA)
• ϕr is the relative azimuth angle.

We estimated fiso, fvol, and fgeo through minimizing a least squares cost function between the TOA reflectance factor calculated from GOES-16 and GOES-17 ABI radiances and the TOA reflectance factor estimated by the radiative transfer model of Qin et al. (2001)

The BRDF coefficients were estimated using observations collected at a SZA less than 70° for each day when there were at least 10 observations available during the day for the red and NIR ABI bands. For each day, the VZA from GOES-16 and GOES-17 along with diurnally varying SZA at 5-min intervals was used to fit the BRDF model.

We used discrete values of aerosol optical depth at 550 nm (AOD) as explained in He et al. (2019) with different aerosol types (biomass burning, continental, maritime, urban, and stratospheric) to estimate atmospheric parameters from 6S.

The AOD and aerosol type combination that resulted in the smallest least squares cost function between observed and estimated TOA reflectance was used as the values for AOD and aerosol type for the day.

To approximate surface reflectance at nadir viewing, we calculated the geometric and volumetric kernels at each SZA value during the day with a fixed VZA of 0°.

Then, we used the BRDF kernel coefficients (fiso, fvol, fgeo) to estimate the surface reflectance at nadir throughout the day.

1.2 参考[3]

2.2.1 Atmospheric Correction for TOC Reflectance

• We used the 6S-based look-up-table (LUT) to correct for atmospheric effects because it can be applied to various satellites. The 6S RTM calculates the satellite bandwidth; the bandwidth is divided into 2.5-nm intervals over the shortwave area. This RTM has a high accuracy but requires a significant amount of computing time for TOC reflectance estimations of large areas (Zhao et al. 2001). To compensate for this, several studies have used the LUT method (Liang et al. 2001; Nunes et al. 2008). Here, we used the 6S-based LUT referred to by the GOES-16 / Advanced Baseline Imager algorithm for surface albedo (Liang et al. 2010); the contents are shown in Table 2.

• If the LUT method is applied directly to atmospheric correction, discontinuities occur in the results. This is due to the discontinuity in the atmospheric correction coefficients that coincide with LUT intervals and is most prominent in SZA and VZA data in particular. Thus, in this study, we interpolated the SZA and VZA at 0.05° intervals.

2.2.2 BRDF for Normalized Reflectance

• We used the semi-empirical BRDF model on Ross-Thick/Li-Sparse-Reciprocal kernels for estimating normalized reflectance (Roujean et al. 1992). Polar orbiting satellites observe the reflectance under various VZA conditions during the BRDF modeling synthesis period. In contrast, geostationary satellites such as the Himawari-8 observe the surface reflectance at fixed VZA conditions for each pixel.

• Therefore, in this study, the normalization method of reflectance was performed considering the characteristics of geostationary satellites. This method was proposed by Yeom and Kim (2013) as a modification of the VZA given by Duchemin et al. (2002).

• In this approach, the VZA is fixed to the VZA of the pixel, and the SZA and relative azimuth angle (RAA) are modulated by the average of the synthesis period to calculate normalized reflectance. This can be represented as follows:

• where θs is the SZA, θv is the VZA and ϕ is the RAA.
• where ρnorm is the normalized reflectance,
• ρmodel(θs = mean, θv = θv, ϕ = mean) is the adjusted reflectance at the VZA of the pixel and the mean SZA during the composite period,
• ρmeasured is the TOC reflectance measured by the satellite, and -
• ρmodel(θs, θv, ϕ) is the calculated TOC reflectance using kernels with yielded empirical coefficients.
• The applied VZA is fixed to the VZA of the pixel, and the SZA and RAA are modulated by the average of the synthesis period to calculate the normalized surface reflectance. In this study, the synthesis period was set to 5 days. We used the mean value of the normalized reflectance calculated over 5 days to estimate the NDVI.

1.3 参考[4]

2.3.1. Atmospheric correction

6s model

2.3.2. BRDF normalization

1.4 参考[5]

2.1.2. GK-2A BRDF products

The GK-2A algorithm for BRDF parameters consists of two major steps including atmospheric correction and BRDF inversion

1. 大气校正：6s

2. BRDF校正

1.5 参考[6]

1.6 参考[7]

参考文献[2] 中的公式，计算得到的的是RTOA，要将RTOA转为地面反射率Rrc参考上面的公式

2. py6s大气校正具体案例

• 链接1 : link

• 链接2 :link

3. Reference

[0] Li X, Ryu Y, Xiao J, et al. New-generation geostationary satellite reveals widespread midday depression in dryland photosynthesis during 2020 western US heatwave[J]. Science Advances, 2023, 9(31): eadi0775.

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[2] He T, Zhang Y, Liang S, et al. Developing land surface directional reflectance and albedo products from geostationary GOES-R and Himawari data: Theoretical basis, operational implementation, and validation[J]. Remote Sensing, 2019, 11(22): 2655.

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[8] Hu C, Chen Z, Clayton T D, et al. Assessment of estuarine water-quality indicators using MODIS medium-resolution bands: Initial results from Tampa Bay, FL[J]. Remote Sensing of Environment, 2004, 93(3): 423-441.