2.1.

Study Area and Retrieval of Hemispherical-Directional Reflectance Factors

The area selected for this study lies in the southern part of Hebei Province, as shown in Fig. 2. The area is relatively flat and in a rural region, away from the urban areas. The land is planted mainly in wheat and corn. The selected images were obtained by the HJ-1A and HJ-1B CCDs during the period from July 2, 2009 to July 12, 2009. The time period coincided with the growing stage for corn and was kept short to ensure that the changes in the vegetation cover were small.

Fig. 2

Location of the study area.

The next step consisted of screening the cloudy images of the study area. The images would be rejected whenever they appeared cloudy by visual inspection or when the presence of clouds made it impossible to determine the exact location of the study area.

In total, four images were selected with a variety of scan angles, including forward and backward view angles ($-47$ to $+47\mathrm{deg}$). The collected images are level-2 products from the China Center for Resource Satellites. The solar/view zenith and azimuth angles of the images were then computed based on the metadata.

The calibration coefficients of the CCD’s four spectral bands are supplied together with the level-2 data to convert the digital number to radiance. Atmospheric corrections were then applied to the radiance images by using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) module in the ENVI 4.7 software. The atmospheric correction for all images was based on a mid-latitude summer atmospheric model and rural aerosol model. The input values of the scene and sensor information, such as sensor altitude and flight date and time, were provided by the metadata. The default values were given to other unknown inputs like visibility (40 km), aerosol scale height (2 km), and carbon dioxide mixing ratio (390 ppm), as defined in the FLAASH. The FLAASH module was then executed to compute ground surface reflectance factors under the guidelines given in the FLAASH User’s Guide.¹⁷

After the computations of solar/view angles and reflectance factors of all 4 days’ data, the common regions in them were retrieved by using the layer stacking tool in the ENVI software. Because of the large FOV and high temporal resolution of HJ-1A and HJ-1B CCDs, a large common area was retrieved after the image compositing.

2.2.

Kernel-Driven Model and its Inversion

The final step was to apply the semiempirical kernel-driven BRDF model to invert the multiple-temporal atmospherically corrected directional reflectance factors to normalize them to user-defined sun–target–sensor geometry. In this paper, we used the linear kernel-driven model proposed by Wanner et al.,¹⁸ which has been validated^19,20 and applied for MODIS land surface BRDF/albedo product.¹⁶ In this model, the BRDF is expanded into a linear sum of terms (the so-called kernels), characterizing different scattering modes. This can be generally described using the following expression:

To invert the kernel-driven model with $m$ observations of HDRF (noted as $y_{\mathrm{obs}}(1),y_{\mathrm{obs}}(2),\dots ,y_{\mathrm{obs}}(m)$), we used the following equation:

Finally, the solution of the kernel parameters can be written as

With more than three uncorrelated multiangular observations, Eq. (3) can provide estimates of the three parameters. Using Eq. (1) in forward mode and the inverted parameters, the reflectance factor under the standard sun–target–sensor can be estimated.

3.1.

Validation of the Linear Semiempirical BRDF Model

The semiempirical model approach will be useful only if the models can be shown to be adequate, which demands that it be tested first. Surface HDRFs obtained in situ is essential if we want to evaluate the models in isolation from the other confounding influences (e.g., the effects of the atmosphere) and in a relatively controlled manner. The data were acquired in 2004 at the China National Experimental Station for Precision Agriculture in Xiaotangshan County, which is located in Changping District, Beijing, China. The experimental site consisted mainly of winter wheat. An Analytical Spectral Devices FieldSpec Pro spectrometer (Analytical Spectral Devices, Boulder, Colorado) mounted on a goniometric instrument was used to measure the wheat canopy multiangular radiation. Multiangular measurements were carried out with viewing zenith angles from $-60\mathrm{deg}$ (forward direction) to $+60\mathrm{deg}$ (backward direction) at 10-deg intervals in the principal plane (PP, where the sun, the target, and the sensor are aligned in the same plane). Zhao et al.²² gave detailed information about this experiment.

In this study, HDRFs in two characteristic spectral bands of vegetation were used to invert the kernel-driven model: red (666 nm) and NIR (850 nm), with the solar zenith and azimuth angles being 36.3 and 177 deg, respectively. To test the performance of the model and its inversion, we reconstructed the HDRFs by using Eq. (2) and the inverted parameters. Figure 3 shows the comparisons of observed and modeled (or reconstructed) HDRF profiles in PP. The root-mean-square error (RMSE) between observed and modeled HDRFs is 0.006 for the red band and 0.01 for the NIR band. For the measured HDRFs in the red band in Fig. 3(a), a local maximum value appears around the antisolar direction, called the hotspot effect. Modeled (or reconstructed) profiles of HDRFs adequately replicate this phenomenon. Overall, the model fits are considered very satisfactory, bearing in mind the likely sources of error in the measured reflectance factors and the approximations made in the model derivation.

Fig. 3

Observed versus modeled HDRF distributions in PP for the red (a) and NIR (b) bands.

3.2.

Directional Effects of HJ-1A’s and HJ-1B’s CCD Data

As stated before, our study area lies in a flat and rural region, with relatively monotonous land cover types. After screening the cloud contaminated images between July 2, 2009 and July 12, 2009, we chose the image data from the following 4 days: July 2, July 3, July 9, and July 12. The preprocessed data for the blue band (band 1 in each sensor, 0.43 to 0.52 μm) are shown in Fig. 4. The values of these HDRFs are in the range [0.0309, 0.2122].

Fig. 4

Images in the blue band of CCD for (a) $7/2$, (b) $7/3$, (c) $7/9$, and (d) $7/12$, 2009.

Next, Eq. (4) was used to invert the BRDF data sets. Equation (2) was used to normalize these BRDF values to the nadir view geometry with the solar zenith angle and the relative difference between solar and view azimuth angles being 20 and 0 deg, respectively. The normalized HDRFs and inverted model parameters are shown in Fig. 5. The normalized HDRFs [Fig. 5(a)] are still in the range [0.0309, 0.2122], ruling out the apparent failure of the BRDF model inversion. The distribution of isotropic model parameters [$f_{\mathrm{iso}}$, Fig. 5(b)] shows a similar pattern with the normalized HDRFs [Fig. 5(a)], consistent with the physical meaning that it represents the reflectance factor observed at nadir with the sun at zenith. However, due to the approximate nature of the kernels, determining what information is contained within the parameters $f_{\mathrm{vol}}$ and $f_{\mathrm{geo}}$ is not straightforward. The problem lies in the fact that the volumetric and geometric kernels are not necessarily orthogonal because volumetric and geometric effects are not mutually exclusive.²³

Fig. 5

Normalized results and model parameters for HDRFs in Fig. 4, using the kernel-driven BRDF model: (a) normalized reflectance factor, (b) isotropic model parameters, $f_{\mathrm{iso}}$, (c) geometric model parameters, $f_{\mathrm{geo}}$, and (d) volumetric model parameters, $f_{\mathrm{vol}}$.

To further analyze the anisotropy observed by the HJ-1A and HJ-1B CCDs and to evaluate the performance of the kernel-driven model inversion, three land cover types were selected: corn in the elongation stage (type 1), fallow farmland after the harvest of the winter wheat (type 2), and a village of farmers (type 3). The cover types were determined according to the false color composite map [R4G3B2, Fig. 6(a)] and historical land-use maps. The average values of $5\times 5\text{pixels}$’ HDRFs in the blue band were used here to analyze their distribution with the view zenith angles. These values were then used to invert the kernel-driven BRDF model [Eq. (2)] so as to reconstruct the profiles under the same sun–target–sensor geometry.

Fig. 6

Observed versus modeled HDRF distributions in the blue band for three different land cover types: (a) false color composite of part of the study area, black rectangle shows three land cover types. Observed versus modeled HDRF distributions for type 1 (b), type 2 (c), and type 3 (d).

All three types of targets show distinct anisotropic reflectance distributions with the view zenith angles, and the HDRFs in the backward directions generally are larger than those in the forward directions. For type 3 [Fig. 6(d)], which has evident 3-D structures of buildings, a clear hotspot phenomenon appears around the backscattering direction. Therefore, the directional effects in the HJ-1A and HJ-1B CCD data cannot be ignored. Similar non-Lambertian features exist in the other three bands.

By inverting the kernel-driven BRDF model and reconstructing the profiles for these three types [Figs. 6(b)–6(d)], we plotted the observed and modeled HDRFs together to evaluate the inversion. The reconstructed HDRFs generally follow the patterns of the observed ones, although with some bias, especially for type 1 [Fig. 6(b)]. The RMSEs for types 1, 2, and 3 are 0.0136, 0.008, and 0.007, respectively.