Land Surface Albedo Retrieval in the Visible Band in Hefei, China, Based on BRDF Archetypes Using FY-2G Satellite Data

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Abstract

Land surface albedo inversion based on satellite data requires multiple consecutive (generally greater than or equal to 7) observations. Due to weather reasons such as cloud occlusion, it is difficult to obtain sufficient observation data, which leads to low inversion accuracy and even unsuccessful inversion. The anisotropic flat index (AFX) index was used to classify the 5-year multiangle observation data set of reflectance and eight bidirectional reflectance distribution function (BRDF) archetypes were obtained in Hefei, Anhui, China. The eight obtained BRDF archetypes in the Hefei area were applied to FY-2G satellite data for land surface albedo retrieval, and the retrieved land surface albedo was compared with MODIS land surface albedo products. The results show that the land surface albedo can be retrieved well using FY-2G data by BRDF archetypes.

1. Introduction

The reflection of the surface to the sun is anisotropic due to the surface structure, material composition, and incident conditions, which is usually described by the BRDF [1,2]. According to Nicodemus’s definition in the 1970s, BRDF is specifically expressed as the ratio of the spectral radiance increment in the reflected light direction caused by the incident light increment to the spectral irradiance increment in the differential solid angle of the incident light direction [3]. Land surface albedo is defined as the ratio of the reflected solar ratio to the incoming solar radiation [4,5], which can be obtained by the integration of BRDF [6]. Land surface albedo is an important parameter in the study of surface energy balance, global flux changes, medium and long-term weather forecasting, land cover, and even the specific surface structure [7,8,9]. It is of great significance to accurately estimate the land surface albedo [10].

At present, the more commonly used land surface albedo inversion method is to fit the multiangle observation data through the kernel-driven BRDF model, which is realized by the extrapolation and integration of the BRDF model [11,12,13]. The kernel-driven model is a kind of semiempirical model. This model uses a linear combination of different scattering kernels to simulate the bidirectional reflection characteristics of the surface. Each kernel has a certain physical meaning and represents a main type of surface scattering [14,15]. The inversion of land surface albedo using the kernel-driven model has certain requirements for the amount of observation data and the distribution of observation angles [16,17,18]. For example, the amount of observation data is required to be greater than or equal to seven points, and the range of observation angles is as large as possible. In addition, the limitations of satellite sensor sampling capability and the influence of weather limit the inversion accuracy [19]. Although the Fengyun geostationary meteorological satellite observes the Earth once every hour [20], which meets the requirements for the quantity of surface albedo observation data, the observation angle of the geostationary meteorological satellite for a specific area is relatively fixed, and the distribution range changes little, thus limiting the application of inversion of land surface albedo using a kernel-driven model.

Assuming that the same type of region has similar BRDF shapes, Strugnell and Lucht [18] proposed fitting the a priori shape to the BRDF shape that is optimal for the observation data to improve the inversion accuracy. Jiao et al. [21,22] proposed using the anisotropic flat index (AFX) and multiangle observation datasets to build a BRDF archetype database and used the BRDF archetype as a priori knowledge to extract albedo. Zhang et al. [19,23] showed that when the view zenith angle is less than 40°, the relative accuracy of this method is improved by 5%∼10% compared with the MODIS full-inversion algorithm. In addition, the introduction of BRDF archetypes can improve the overall classification accuracy by approximately 5% [24,25]. Yang et al. [26] used the AFX and the albedo-to-nadir reflectance ratio (AN ratio) as prior knowledge and combined MODIS BRDF for high temporal-spatial resolution Landsat-8 albedo inversion. Zhao et al. [27] combined both the AFX and the perpendicular anisotropic flat index (PAFX) to build a 3-by-3 matrix of BRDF archetypes for albedo inversion. In summary, the AFX-based BRDF archetype inversion method provides a good way to solve the albedo inversion problem mentioned above.

The main purpose of this study is to introduce a new inversion method to solve the problem of fixed observation angles when retrieving land surface albedo from Fengyun-2G (FY-2G) geostationary satellites to realize the rapid retrieval of daily land surface albedo in Hefei, Anhui, China. This study serves to model the environmental radiation field in Hefei, Anhui, and provide effective surface input parameter support. Second, aiming at the surface reflection characteristics of the Hefei area, the BRDF archetype of this area is extracted instead of applying the global-scale BRDF archetype, which makes the prior knowledge of BRDF more targeted. Finally, this research contributes to improving the utilization rate of Fengyun geostationary satellite data.

2. Methodology

2.1. Theoretical Basis

2.1.1. BRDF Model

The BRDF is a function of the observation and illumination angle and can describe the reflection distribution of the surface. The semiempirical kernel-driven model is usually obtained by linearly weighting the scattering kernel with a certain physical meaning [28]. The RossThick-LiSparseR kernel-driven BRDF model (the so-called RTLSR model) was selected in this research [29] in which surface reflection consists of three parts: isotropic scattering, volume scattering, and geometric optical scattering. The mathematical description of its model is as follows:

$$R({\theta }_{\nu },{\theta }_s,\phi ,\lambda )=f_{iso}\left(\lambda \right)+f_{vol}\left(\lambda \right)k_{vol}({\theta }_{\nu },{\theta }_s,\phi )+f_{geo}\left(\lambda \right)k_{geo}({\theta }_{\nu },{\theta }_s,\phi )$$

(1)

where $k_{vol}({\theta }_{\nu },{\theta }_s,\phi )$ and $k_{geo}({\theta }_{\nu },{\theta }_s,\phi )$ represent the volume scattering kernel and the geometric optics scattering kernel, respectively, and the isotropic scattering kernel is defined as 1. $f_{iso}\left(\lambda \right)$, $f_{vol}\left(\lambda \right)$ and $f_{geo}\left(\lambda \right)$ correspond to the kernel coefficients of each kernel. ${\theta }_{\nu }$ is the observation zenith angle, ${\theta }_s$ is sun zenith angle, and $\phi$ is the relative azimuth angle. $\lambda$ is the wavelength. The RossThick kernel is selected to describe the volume scattering, and the LiSparseR kernel is selected to describe the geometric optical scattering. Figure 1 shows the 3D shapes for the RossThick volume scattering kernel (Figure 1a,b) and LiSparseR geometric optics scattering kernel (Figure 1c,d) at two given solar zenith angles (15° and 45°). The X–Y plane in the figure is the polar coordinate drawing plane, the polar diameter of the polar coordinates represents the observed zenith angle, and the polar angle of the polar coordinates represents the relative azimuth angle. The blue–green–red colors indicate the low-to-high transition of kernel values and distinctly reflect the dome–bowl variability of kernel shapes at different illumination geometries. The RossThick kernel shows a typical “bowl-shaped” curve, and the reflectance increases with increasing observation zenith angle. The LiSparseR kernel curve is similar to the dome-shaped curve in the backscattering direction, especially in the hotspot direction, with prominent peak reflectance. The actual surface BRDF curve is the linear weighting of these two shapes.

2.1.2. Land Surface Albedo Definition

The directional hemispherical albedo ${\alpha }_{BSA}$ (also known as black-sky albedo, BSA) and the double hemispherical albedo ${\alpha }_{WSA}$ (also known as white-sky albedo, WSA) can be obtained by integrating the bidirectional reflectivity on the angle [30]:

$${\alpha }_{BSA}({\theta }_s,\lambda )=\sum _k[f_k\left(\lambda \right)\times h_k\left({\theta }_s\right)]$$

(2)

$${\alpha }_{WSA}\left(\lambda \right)=2{\int }_0^{\pi /2}{\alpha }_{BSA}({\theta }_s,\lambda )cos{\theta }_{s}sin{\theta }_{s}d{\theta }_s=\sum _k{f}_k\left(\lambda \right)·H_k$$

(3)

$$h_k\left({\theta }_s\right)=\frac{1}{\pi }{\int }_0^{2\pi }{\int }_0^{\pi /2}{k}_k({\theta }_{\nu },{\theta }_s,\phi )cos{\theta }_{\nu }sin{\theta }_{\nu }d{\theta }_{\nu }d{\phi }_{\nu }$$

(4)

$$H_k=2{\int }_0^{\pi /2}{h}_k\left({\theta }_s\right)cos{\theta }_{s}sin{\theta }_{s}d{\theta }_s$$

(5)

where $f_k\left(\lambda \right)$ is the kernel coefficient of the BRDF model, $k_k\left(\lambda \right)$ is the kernel of the BRDF model, and $h_k\left({\theta }_s\right)$ is the integral of the zenith angle and azimuth angle checked by the BRDF model. $H_k$ is the integral of each kernel of the BRDF over all angles. The subscript k here means isotropic scattering, volume scattering, and geometric optical scattering. The actual surface albedo is the weighted sum of the black-sky albedo and the white-sky albedo according to the sky diffuse light scattering factor S:

$$\alpha =(1-S)\times {\alpha }_{BSA}+S\times {\alpha }_{WSA}.$$

(6)

S is defined as the ratio of incident sky radiance due to the scattering of solar radiation in the atmosphere to total incident radiation [31]. In this study, the S at noon of the day is calculated according to the day in a year and latitude information. The empirical formula are expressed as:

$${\theta }_{sun}=2\pi (doy-1)/365$$

(7)

$$\begin{array}{cc}\hfill la{t}_{sun}& =(0.006894-0.399512cos\left({\theta }_{sun}\right)+0.072075sin\left({\theta }_{sun}\right)\hfill \\ & -0.006799cos\left(2{\theta }_{sun}\right)+0.000896sin\left(2{\theta }_{sun}\right)\hfill \\ & -0.002689cos\left(3{\theta }_{sun}\right)+0.001516sin\left(3{\theta }_{sun}\right))\times 180/\pi \hfill \end{array}$$

(8)

$${\varphi }_{sun}=arcsin(sin(lat/180\times \pi )sin(la{t}_{sun}/180\times \pi )+cos(lat/180\times \pi )cos(la{t}_{sun}/180\times \pi ))$$

(9)

$${\theta }_{bs}=\pi /2-{\varphi }_{sun}$$

(10)

$$S=0.122+0.85\times e^{-4.8cos\left({\theta }_{bs}\right)}$$

(11)

where ${\theta }_{sun}$ is the noon sun angle, $doy$ represents the order of each day in the year, $la{t}_{sun}$ represents the noon sun latitude, ${\varphi }_{sun}$ represents the local noon sun elevation angle, ${\theta }_{bs}$ represents the local noon sun zenith angle, and $lat$ represents the latitude data of the observation point.

2.1.3. Anisotropic Flat Index (AFX)

The AFX has an expression derived from the kernel-driven BRDF model and is especially appropriate for the description of the MODIS anisotropic reflectance [19]. For the convenience of calculation, the AFX equation was simplified by Jiao et al. [24,25]:

$$AFX\left(\lambda \right)=\frac{{\alpha }_{WSA}\left(\lambda \right)}{f_{iso}\left(\lambda \right)}=1+\frac{f_{vol}\left(\lambda \right)}{f_{iso}\left(\lambda \right)}\times 0.189184-\frac{f_{geo}\left(\lambda \right)}{f_{iso}\left(\lambda \right)}\times 1.377622$$

(12)

It can be considered that the AFX index is the normalization of the volume scattering coefficient and the geometric optical scattering coefficient to the isotropic scattering coefficient. When the volume scattering effect is dominant, $AFX$ > 1; when the geometric optical scattering effect is dominant, $AFX$ < 1; and when the two scattering effects are close, $AFX\approx 1$, the surface is approximately Lambertian.

The analysis of the distribution shape of the BRDF archetype with angles and several typical BRDF shapes of vegetation surfaces are drawn in Figure 2, and the observation data come from the measurement data of the University of Maryland in the United States. The figure shows the curves of the BRDF of vegetation surfaces with an observation angle with a solar zenith of 45° on the principle plane (PP) and cross-principal plane (CPP). Figure 2a,b show the BRDF changes in the visible red band (0.58∼0.68 $\mathsf{\mu }$m), and (Figure 2c,d) are the BRDF curves of the same surfaces in the near-infrared band (0.73∼1.1 $\mathsf{\mu }$m). When the scattering characteristics of the surface are dominated by volume scattering, AFX is greater than 1, and the BRDF is bowl-shaped. When the shape of the BRDF tends to be flat, AFX tends to be 1, and the volume scattering and geometric optics scattering effects are close. The reflectivity is also affected by the wave band, because the vegetation surface is affected by chlorophyll, and the visible and near-infrared bands are quite different. To facilitate the research, the isotropic factor $f_{iso}$ is normalized to 0.5, $f_i=f_i/f_{iso}$, to eliminate the influence of the spectrum. The normalized BRDF shape and AFX value will not change.

AFX is used as a characteristic parameter of BRDF, which is used to classify the shape of BRDF. The iterative self-organizing data analysis techniques algorithm (ISODATA) is used to classify AFX and to establish different types of BRDF archetype libraries, and the mean values of each class are used as BRDF archetype parameters. When the multiangle data space is insufficiently sampled, it provides prior knowledge for albedo inversion.

2.2. BRDF Archetype Inversion Algorithm

The core idea of surface albedo inversion using the BRDF archetype is to construct a BRDF archetype database based on a large amount of multiangle reflectance observation data and establish a linear relationship between the BRDF archetype and real BRDF to reduce the amount of input data and provide stable inversion results. The specific steps include calculating the fitting error between the reflectivity corresponding to each BRDF archetype and the real surface reflectivity under the same geometric conditions and selecting the BRDF archetype corresponding to the minimum error as the optimal BRDF archetype.

Here, it is assumed that there is a set of multiangle reflectivity observation data $\rho :\left\{{\rho }_1,{\rho }_2,\cdots ,{\rho }_n\right\}$, which corresponds to the $BRDF$ of the real surface. It is assumed that the corresponding BRDF archetype is known as $BRD{F}^{\prime }$, and the reflectivity data corresponding to the observation position of the data $\rho$ are ${\rho }^{\prime }:\left\{{\rho }_1^{\prime },{\rho }_2^{\prime },\cdots ,{\rho }_n^{\prime }\right\}$. Taking the adjustment coefficients A and B, the difference between $\rho$ and $A·{\rho }^{\prime }+B$ is minimized by translating the BRDF archetype.

By calculating the minimum regression fitting error between the real surface reflectance and the BRDF archetype fitting reflectance, the calibration adjustment coefficients A and B are obtained. Since the conventional least squares fitting method is greatly affected by abnormal observations, to ensure the inversion accuracy and improve the inversion stability, the Huber loss fitting method is introduced. This method combines the advantages of root mean square error (MSE) and mean absolute error (MAE) fitting and reduces the sensitivity to outliers. By minimizing the loss function, the optimal fitting coefficient can be obtained. The core formula is

$$\underset{w,\sigma }{min}\sum _{i=1}^n[\sigma +H_i\left(\frac{X_i\omega -y_i}{\sigma }\right)\sigma ]+{\alpha \left|\right|\omega \left|\right|}_2^2$$

(13)

$$H_i=\left\{\begin{array}{cc}\frac{1}{2}{[{\rho }_i-f\left({\rho }_i^{\prime }\right)]}^2,\hfill & \hfill |{\rho }_i-f\left({\rho }_i^{\prime }\right)|\le \delta \\ \delta |{\rho }_i-f\left({\rho }_i^{\prime }\right)|-\frac{1}{2}{\delta }^2,\hfill & \hfill |{\rho }_i-f\left({\rho }_i^{\prime }\right)|>\delta \end{array}\right.$$

(14)

The parameter X is the training vector, which is the simulated land surface bidirectional reflectance obtained by the BRDF archetype under the same geometric conditions as the actual observation, in the form of an n-dimensional one-element array; y is the target vector, which is the land surface bidirectional reflectance of the land surface observed by the satellite, in the form of a one-dimensional n-element array. $\omega$ is the coefficient vector, $\alpha$ is the complexity parameter, and ${\sigma }^2$ is defined as the variance estimate of the noise. $f\left({\rho }_i^{\prime }\right)$ is a linear function of ${\rho }_i^{\prime }$. For the detailed algorithm solution of Huber regression in the above formula, see the book [32]. To obtain the optimal archetype coefficients and improve the regression fitting accuracy, define the fitting parameter epsilon as $({\rho }_i-f\left({\rho }_i^{\prime }\right))/\delta$ and set the epsilon range to [1.0,1.1,1.2,1.35,1.5,1.75,2.0,2.5,3.0]. Since the Huber loss fitting regression involves many parameters, to make the reading clear, the definitions of the parameters are listed in

Table 1. Description of Huber loss fitting regression parameters.

Variable	Definition
X	Training vector (n-dimensional one-element), $X=[\left[{\rho }_1^{\prime }\right],\left[{\rho }_2^{\prime }\right],\dots ,\left[{\rho }_n^{\prime }\right]]$
y	Target vector (one-dimensional n-elements), $y=[{\rho }_1,{\rho }_2,\dots ,{\rho }_n]$
H	Huber loss function
$\delta$	Epsilon
${\sigma }^2$	Variance estimate of the noise
$\omega$	Coefficient vector
$\alpha$	complexity parameter
n	Number of data
i	Serial number

in detail. The sum of the regression loss of each BRDF archetype in different epsilon parameters is compared, and the adjustment coefficients A and B corresponding to the smallest loss are taken as the final BRDF archetype coefficients. The relationship between $BRDF$ and $BRD{F}^{\prime }$ can be expressed as

$$BRDF=A\times BRD{F}^{\prime }+B$$

(15)

The actual surface black-sky albedo ${\alpha }_{BSA}$ and white-sky albedo ${\alpha }_{WSA}$ can be expressed as

$${\alpha }_{BSA}=A\times {\alpha }_{BSA}^{\prime }+B=A\times \sum _k{f}_k^{\prime }\left(\lambda \right)h_k\left({\theta }_s\right)+B$$

(16)

$${\alpha }_{WSA}=A\times {\alpha }_{WSA}^{\prime }+B=A\times \sum _k{f}_k^{\prime }\left(\lambda \right)H_k+B$$

(17)

where ${\alpha }_{BSA}^{\prime }$ and ${\alpha }_{WSA}^{\prime }$ are the black-sky and white-sky albedos obtained using the optimal BRDF archetype, respectively. $f_k^{\prime }\left(\lambda \right)$ is the BRDF archetype kernel parameter. $h_k\left({\theta }_s\right)$ and $H_k$ are the BRDF kernel integral functions; see Formulas (4) and (5). The subscript k represents isotropic scattering, volume scattering, and geometric optical scattering.

2.3. Overview of the Albedo Inversion Process

The aim of this research is mainly to realize the daily inversion of land surface albedo in the Hefei area, so the geostationary satellite FY-2G observation data, which observe the earth once every hour, are selected as the inversion data. Since the observation angle of the Hefei area by geostationary satellites is relatively fixed, to obtain a more representative BRDF archetype, the multiangle observation data of MODIS for many years were selected to construct the BRDF archetype database. Figure 3 shows the basic flow chart of land surface albedo retrieval in the Hefei area in this study.

Before the actual land surface albedo inversion, the BRDF archetype database in the Hefei area was constructed. First, data preprocessing (effective data extraction, data matching, etc.) is performed on MODIS multiangle data over the past 5 years, and the BRDF model parameter dataset is obtained by using the BRDF model. Then, the corresponding AFX index is calculated, the data are classified according to AFX, and the classification error is calculated, to obtain the optimal classification number. Then, the average BRDF model parameters are calculated within the class, and the BRDF archetype database is constructed. In the land surface albedo inversion, the FY-2G satellite data are first preprocessed (cloud mask, interest area clipping, etc.). Then, based on the one-day observation data of FY-2G and the BRDF archetype database, the adjustment coefficient and the optimal BRDF archetype are obtained through Huber loss fitting. Finally, the real land surface albedo is obtained by the semiempirical kernel-driven BRDF model.

3. Study Data and Processing

3.1. Study Data

Hefei is located in the central part of Anhui Province, China. It is the capital of Anhui Province, with a center latitude and longitude of 31°52′ N, 117°17′ E and a total area of 11,445 km². The climate belongs to the subtropical monsoon humid climate, and the landforms are dominated by hills. The geographical location and vegetation cover types are shown in Figure 4. The vegetation coverage data come from the MODIS land cover product (https://www.bu.edu/lcsc/data-documentation/, (accessed on 19 August 2023)), and the coverage type is classified according to the International Geosphere-Biosphere Program (IGBP) classification scheme [33]. As a plain-based region, Hefei’s main surface type is cropland. This research mainly focuses on surface reflection characteristics and surface albedo inversion in Hefei, Anhui, China.

The FY-2G satellite scans the Earth once every hour and every half an hour during the flood period. The SVISSR detector carried by FY-2G has only one visible light channel, and its spectral range is from 0.550 to 0.750 microns. This study selects the multiangle observation data of the FY-2G geostationary meteorological satellite on the 24th, 107th, 228th, and 302nd days of 2019 to carry out inversion research on the surface albedo in Hefei. The data come from the FENGYUN satellite data service network (http://satellite.nsmc.org.cn, (accessed on 19 August 2023)).

Considering that the variation range of observation angles of geostationary satellites to a region is small, while the range of observation angles of polar-orbiting satellites is large, the MODIS reflectance product MOD09GA/MYD09GA in the red band was atmospherically corrected for the past five years from 2015 to 2019 and was selected in this research. The multi-angle observation data in the MODIS red band were used to construct typical BRDF archetypes in the Hefei area. At the same time, MODIS surface albedo product data MCD43A3 were selected to verify the inversion results. MODIS data were obtained from the EARTHDATA SEARCH website (https://search.earthdata.nasa.gov, (accessed on 19 August 2023)).

3.2. Data Processing

The spectral response curves of the FY-2G visible channel and MODIS red channel are shown in Figure 5. The solid line in the figure represents the FY-2G visible channel (0.550∼0.750 $\mathsf{\mu }$m), and the dashed line represents the red band (0.620∼0.670 $\mathsf{\mu }$m) of MODIS. For the difference between spectral channels, the reflectance spectral data of 156 surface types in the U.S. Geological Survey (USGS) spectral database (https://crustal.usgs.gov, (accessed on 19 August 2023)) were selected to convolve with the MODIS red band and FY-2G visible band spectral response functions to obtain the corresponding channel reflectance. The two reflectance data points are linearly fitted to obtain the corresponding linear conversion expression. Figure 6 shows the fitting curves and fitting errors of the two reflectivities. The spectral correction formula between the two bands is

$${\rho }_{FY-2G_{visible}}=0.8920·{\rho }_{MODI{S}_{red}}+0.0175$$

(18)

The spatial resolution of the FY-2G visible light band is 1.25 km, and the spatial resolution of the MODIS red band is 0.25 km. Since the spatial resolution of the visible light band of FY-2G is inconsistent with the spatial resolution of the corresponding band of MODIS, it is necessary to resample the observation data of MODIS to make it consistent with the spatial resolution of the observation data of FY-2G.

Before land surface albedo inversion, satellite multiangle observation data need to be geometrically corrected to be projected onto a designated projection plane, and then the image is clipped according to the vector data in the Hefei area to obtain the observation data in the Hefei area. Finally, cloud removal processing is required, deducting the cloudy pixels to obtain completely clear sky pixels.

4. BRDF Archetype Construction

The MODIS multiangle reflectivity observation data carried on Aqua/Terra in the past five years were used to construct the BRFD archetype database in the Hefei area. The MODIS reflectance observation data after atmospheric correction and cloud mask are substituted into the semiempirical kernel-driven BRDF model mentioned above to obtain the corresponding model parameters. According to the physical meaning of the model, invalid data with model parameters greater than 1 and less than 0 are eliminated, and the BRDF model parameters of the Hefei area are obtained. According to Formula (12), AFX can also be obtained.

To determine the optimal number of BRDF archetypes in the Hefei area, the data are divided into 2∼10 categories according to the AFX value through the iterative self-organizing data analysis techniques algorithm (ISODATA), and the corresponding fit root mean square error (fit-RMSE) is calculated. Figure 7 shows the corresponding fit-RMSE when the number of BRDF archetypes is set to 2 10. The solar zenith angle is set to 45°, and the observation zenith angle is selected as 5 angles ($0^{°},{15}^{°},{30}^{°},{45}^{°},{60}^{°}$). The fit-RMSE at each angle reaches a minimum value when the number of archetypes is eight, and when the observed zenith angle is $0^{°}$, the minimum fit-RMSE is 0.294. The fit-RMSE is greatly affected by the observed zenith angle. When the observed zenith angle exceeds 45°, the fitting error is as high as 0.06. In summary, the number of prototypes in the BRDF archetype database is finally selected as 8.

Next, the fitting errors of 8 BRDF archetypes are discussed. Figure 8 shows the fit-RMSE of each archetype when the number of BRDF archetypes is 8. The left y-axis in the figure corresponds to the fit-RMSE, and the right y-axis corresponds to the average AFX value. The gray solid line in the figure is the change curve of AFX. In general, the fit-RMSE increases with increasing zenith angle. The fit-RMSE of the class 8 BRDF archetype is at least 0.0221 when the zenith angle is $0^{°}$, while the fit-RMSE of class 1 is at most 0.0817 when the zenith angle is ${45}^{°}$. The figure shows that when the AFX is small (approximately 0.7000), the BRDF archetype fit-RMSE is the largest.

According to the previous analysis, eight BRDF archetypes can be selected to summarize the bidirectional reflection distribution pattern of the surface in Hefei for MODIS multiangle observation data. Through the ISODATA clustering analysis algorithm, the eight BRDF archetypes in the Hefei area from five years of MODIS red band multiangle observation data were established.

Table 2. AFX value and model parameter of each BRDF archetype.

Class	${\mathit{AFX}}_{\mathit{mean}}$	${\mathit{AFX}}_{\mathit{max}}$	${\mathit{AFX}}_{\mathit{min}}$	${\mathit{f}}_{\mathit{iso}}$	${\mathit{f}}_{\mathit{vol}}$	${\mathit{f}}_{\mathit{g}\mathit{e}\mathit{o}}$
1	0.7261	0.8780	0.00006	0.1320	0.0775	0.0380
2	0.9799	1.0771	0.8780	0.1196	0.1295	0.0196
3	1.1276	1.1810	1.0771	0.1130	0.1816	0.0145
4	1.2075	1.2352	1.1810	0.1091	0.2103	0.0124
5	1.2584	1.2827	1.2352	0.1068	0.2286	0.0114
6	1.3230	1.3680	1.2827	0.1044	0.2540	0.0104
7	1.4509	1.5610	1.3680	0.1012	0.3116	0.0097
8	1.7203	2.0000	1.5610	0.0979	0.4413	0.0095

shows the mean and range of AFX and the model parameter values corresponding to each BRDF archetype. Figure 9 shows the shape of the BRDF archetypes with the view zenith angle when the solar zenith angle is ${45}^{°}$, in which Figure 9a shows the changing trend of the principle plane (PP), and Figure 9b shows the changing trend of the cross-principle plane. The BRDF in Figure 9 is the result of normalizing the isotropic scattering coefficient when assuming $f_{iso}=0.5$. As the AFX value increases, the shape of the BRDF changes from dome-shaped to bowl-shaped, and the $f_{vol}$ coefficient increases, while the $f_{geo}$ coefficient gradually decreases. This means that with increasing AFX, the geometrical optics effect is gradually weakened, and the volume scattering effect is gradually enhanced.

To study the distribution characteristics of BRDF in Hefei, a dominant analysis of BRDF archetypes was carried out, and the percentage of the total number of AFX occupied by each BRDF archetype class in the Hefei area was counted. In Figure 10, the dominant archetypes in the red band are class 1 and class 2, and the proportion of the two is 53.5872%, of which class 1 accounts for 25.1024%, and class 2 accounts for 28.4848%. These are followed by class 3 with 13.9363%, class 7 with 8.8175%, class 6 with 6.7951%, class 4 with 6.1926%, class 8 with 5.9409%, and finally class 5 with 4.7304%.

Based on MODIS multiangle observation data, eight typical BRDF archetype databases in Hefei, Anhui, China were successfully constructed, which provided sufficient prior knowledge for the next step of using geostationary satellite observation data to invert the land surface albedo in Hefei.

5. Albedo Inversion and Analysis

5.1. Application of FY-2G Albedo Retrieval

The FY-2G observation data of 4 days in 2019 were selected for albedo retrieval in Hefei, which were the 24th day, the 107th day, the 228th day, and the 302nd day. On these days, there was less cloud cover over Hefei throughout the day. Figure 11 shows the average angle distribution of each image in these 4 days. The coordinates in the figure are polar coordinate systems, the circumference represents the relative azimuth angle, and the radius is the zenith angle. The “inverted triangle” symbol represents the observation zenith angle, and the “dot” symbol represents the solar zenith angle. It can be seen from the diagram that the observation zenith angle range of FY-2G in Hefei is relatively fixed, generally approximately 40°, and the solar zenith angle and relative azimuth angle change over a large range, which meets the requirement of the BRDF model parameter fitting.

The top of atmospheric (TOA) reflectivity received by the satellite needs to be atmospherically corrected to obtain the true surface reflectance. FY-2G does not have aerosol products, and the MODIS MOD04_L2 aerosol product for the corresponding times was chosen as the aerosol input parameter for the atmospheric correction. The average aerosol optical thicknesses in Hefei corresponding to these four different times at 550 nm are 0.4100, 0.3372, 0.2967, and 0.9498. With the known aerosol optical parameters, the real surface reflectance can be obtained by using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiation transmission model [34] to remove atmospheric interference. Since FY-2G observes the Earth once an hour, multiple sets of multiangle reflectance data can be obtained for multiple observations in the same area within a day so that the real surface albedo of the day can be retrieved according to the BRDF model. The S is calculated according to the local latitude and the observation time. The S value will not change much in one day in Hefei, and the noon mean values of these four days are 0.1638, 0.1318, 0.1308, and 0.1506.

Figure 12 shows the albedo retrieved using FY-2G satellite data based on the BRDF archetypes. The four images in Figure 12 from left to right are the 24th, 107th, 228th, and 302nd days of 2019, and the time is at noon of the day. The image sequence in the subsequent images is arranged in this time sequence and is not described one by one. The ranges of albedo in the figure are 0.0175∼0.1431, 0.0269∼0.1295, 0.0350∼0.1409, and 0.0031∼0.1820. The average surface albedos per day are 0.0779, 0.0822, 0.0692, and 0.0832. The adjustment coefficients A and B are shown in Figure 13. The average values of A are 1.3346, 1.2199, 0.9898, and 1.2216, and the average values of B are −0.0662, −0.0387, −0.0327, and −0.0415 corresponding to the four different periods in Hefei. The loss value in the Huber loss regression fitting is used to evaluate the fitting error. The smaller the loss value is, the better the fitting result. The fitting losses to each pixel under the optimal BRDF archetype are shown in Figure 14. When the loss value is large, the fitting result is inaccurate, so the abnormal points with a loss greater than 0.01 are removed during inversion. The average fitting losses in Hefei are 0.0005, 0.0015, 0.0010, and 0.0023. Using the obtained eight BRDF archetypes, the daily fast inversion of the land surface albedo in Hefei, Anhui was realized, and the inversion fitting error met the requirements.

Figure 15 shows the proportion of each class in the eight BRDF archetypes during the albedo inversion of the Hefei area. Among them, class 1 accounted for more than 90%. This result is slightly different from the statistical result based on MODIS reflectance data, and the proportion of class 2 in the FY-2G albedo inversion is extremely small. It is speculated that the reason for this phenomenon may be due to the difference in performance of the two sensors, the difference in spatial resolution, and the difference in homogenization of the surface during observation.

5.2. Results Analysis and Verification

Due to the lack of field measurement data, the MODIS albedo product MCD43A3 (Albedo 16-Day L3 Global 500 m) was used to evaluate the results of albedo retrieval in this study. It presents the inversion results of the white-sky albedo and the black-sky albedo [35]. Figure 16 shows the albedo product obtained by weighting the sky diffusely scattered light scale factor S according to the black-sky and white-sky albedo in MCD43A3. In addition, the data have undergone spatial scale change and spectral correction; see Section 3.2 for the data processing method. The distribution ranges of the surface albedo of the Hefei area on these four days are 0.0412∼0.1863, 0.0302∼0.1978, 0.0169∼0.1693, and 0.0420∼0.2071. Figure 17 shows the comparison error between the FY-2G albedo inversion results and the MODIS albedo product. The missing blank pixels in the figure are because the MODIS albedo product has no effective value in the pixel. The average errors of each scene image are −0.0257, −0.0073, 0.0133, and −0.0294. The root mean square errors (RMSEs) are 0.0375, 0.0235, 0.0275, and 0.0436. At the same time, the pixels with high-quality assurance (QA) in MODIS albedo products were selected for comparison. The MODIS albedo products had 190, 1, 270, and 109 high-QA pixels in Hefei during the four days. Figure 18 shows the comparison scatter plot between the FY-2G albedo inversion results and the high-QA MODIS albedo products. The average root mean square errors are 0.0329, 0.0043, 0.0192, and 0.0406, and the absolute errors are −0.0240, −0.0043, 0.0138, and −0.0260. The inversion results are in good agreement with the high-QA MODIS albedo products. The inversion results on the 24th, 107th, and 302nd days are generally smaller than those of MODIS, and the inversion results on the 228th day are generally higher than those of MODIS.

At the same time, the albedo inversion results of Huber loss regression fitting and least squares regression fitting are compared. Figure 19 is a scatter diagram of the albedo inversion results obtained by using these two fitting methods. In the figure, the abscissa is the albedo fitted by the least square method, and the ordinate is the albedo obtained by the Huber loss method. It can be seen from the comparison results that the surface albedo results obtained by the two regression analysis methods are relatively consistent. The Pearson’s coefficient of the two results is 0.96829, and the R-square is 0.93736. Considering the relatively small sample size, although the comparison results show that there is little difference between the two methods, the amount of fitting regression data is sufficient on the premise that it is based on geostationary satellite data, but the Huber loss regression method has certain advantages in theory. The land surface albedo inversion results obtained in this study have higher accuracy and better method stability.

5.3. Comparison of AFX with Vegetation Index

The MODIS vegetation index product was chosen to discuss the relationship between the AFX and vegetation index (see Figure 20). The left picture in Figure 20 is a comparison between the normalized difference vegetation index (NDVI) and AFX, and the right picture is a comparison between the enhanced vegetation index (EVI) and AFX. Principal component analysis (PCA) was used to analyze the two sets of data, and the first two principal components are shown as straight lines in Figure 20. In the figure, the first principal component is represented by a nearly horizontal red line, and the second principal component is represented by a nearly vertical black line. The first principal component of NDVI and AFX accounts for 71.8362%, which is almost parallel to the NDVI axis, and the second principal component accounts for 28.1638%, which is almost parallel to the AFX axis. The first principal component of the EVI and AFX accounts for 80.4505%, which is almost parallel to the EVI axis, and the second principal component accounts for 19.5495%, which is almost parallel to the AFX axis. The analysis shows that NDVI explains more overall changes, while AFX reveals significant changes. AFX and NDVI/EVI are approximately orthogonal. For FY-2G visible light channel data, AFX contains other information related to vegetation structure. The results of this study show that the land surface albedo retrieved by the FY-2G visible channel can reveal changes in the surface vegetation structure.

6. Discussion

Taking eight BRDF archetypes as prior knowledge, daily land surface albedo inversion research in the Hefei area was realized by using FY-2G geostationary satellite data. In this study, the BRDF archetype solved the problem of the small distribution range of observation angles from geostationary meteorological satellites, and the high-frequency Earth observations from geostationary satellites solved the problem of the high demand for inversion data. The daily inversion of albedo provides support for the study of the daily variation in the surface albedo and the modeling of the daily radiation environment field in Hefei. Compared with the least squares fitting method, the Huber loss fitting method proposed in this study has stronger robustness performance and higher adaptability to abnormal observation data.

However, there are still several problems in this study: 1. The constructed BRDF archetype has relatively large limitations, and it is only for the Hefei area. 2. There is no further analysis of the applicability of the kernel-driven BRDF model when the geostationary satellite has a large observation angle. 3. The amount of data was small, and only four days of data were inverted. In response to these problems, several schemes have been conceived. 1. The considered surface reflection characteristics are related to the surface type, so several typical surfaces (such as deserts, water bodies, sparse vegetation, forest vegetation, etc.) are selected to construct their typical BRDF archetype databases to realize the wider application. 2. Based on the kernel-driven BRDF model, a hotspot-corrected RossThick-LiSparseReciprocal model is introduced. 3. More geostationary satellite observation data need to be obtained for long-term land surface albedo retrieval. The next work plan will also be carried out around these three points.

7. Conclusions

In this study, based on the multiangle observation data of the reflectance of MODIS in the past 5 years, the surface reflection characteristics of the Hefei area were divided into eight categories according to the AFX index, and the corresponding BRDF archetype was constructed. The distribution characteristics of AFX and BRDF archetypes in the visible band in the Hefei area are analyzed. Albedo inversion based on FY-2G satellite data is realized based on eight BRDF archetypes as prior knowledge. A comparative analysis of the albedo inversion results based on FY-2G observation data shows that the inversion accuracy of the BRDF archetypes obtained by using the 5-year observation data from MODIS is better, and this method is feasible. With the help of the principal component analysis method, the relationship between AFX and the vegetation index of the FY-2G visible channel was discussed, and the orthogonal relationship between the two was revealed.

The research in this paper is mainly based on satellite observation data and lacks the support of field measurement data. Therefore, the next work plan is to conduct a large number of BRDF measurement experiments in Hefei, China to further optimize the BRDF archetype database and verify the accuracy of the method.