1. Introduction
Linking different models for various applications in remote sensing is an important method. Typical examples arise from linking leaf optical properties models with canopy bidirectional reflectance models to characterize the entire process of light absorption and scattering of the vegetation canopy. The benefit of this technique also makes it possible to retrieve both leaf biochemistry characteristics and canopy structures from satellite data [
1]. By linking the optical Properties Spectra (PROSPECT) broadleaf model and the homogeneous Scattering by Arbitrarily Inclined Leaves (SAIL) canopy reflectance (CR) model, the PROPECT+SAIL (named PROSAIL) model has been widely used to simulate canopy spectral and directional reflectance and to retrieve biophysical parameters [
1,
2,
3]. The practicability of this model has been substantially validated using large numbers of field measurements. Specifically, at the leaf level, various leaf observations from the LOPEX, CALMIT, ANGERS and HAWAII campaigns launched from 1993 to 2007 have been used for validation [
2], and at the canopy level, the model was comparable to many other 1-D and 3-D models in the famous controlled Radiation Transfer Model Intercomparison (RAMI) experiments from Phase 1 to Phase 3 [
4,
5,
6]. This model was also used in conjunction with a kernel-driven model to evaluate the emissivity estimation in cases with insufficient field data [
7], and to assess a novel Angular and Spectral Kernel-driven (ASK) model [
8]. Similarly, the PROSPECT model has also been linked with the A two-layer Canopy Reflectance Model (ACRM) [
9], the New Advanced Discrete (NADI) model [
10] and the 3-D Discrete Anisotropic Radiative Transfer (DART) model (URL:
http://teledetection.ipgp.jussieu.fr/prosail/) for various applications. More extensively, the other conifer leaf model named the LIBERTY model was linked with the 4-Scale CR model to generate the so-called 5-Scale model [
11,
12,
13] for the enhancement of simulation ability of these models.
To implement quantitative remote sensing inversion from reflection signatures of land surface, the intrinsic anisotropy reflection characteristics of land surface play a key role, which can be characterized by Bidirectional Reflectance Distribution Function (BRDF) successfully [
14]. As an essential source of BRDF data, available remotely sensed multiangle observations and BRDF products at the global scale (e.g., satellite multiangle data from the Moderate-resolution Imaging Spectroradiometer (MODIS) and Polarization and Directionality of the Earth’s Reflectances (POLDER)) contain important biophysical/structural information of the land surface, which is usually used as primary input parameters of physical BRDF models to drive inversion procedures [
15,
16,
17,
18,
19,
20]. Therefore, direct multiangle observations from satellite sensors are desperately needed to drive model inversion procedures for estimation of various biophysical/structural variables of the land surface. For example, the bi-directional reflectance product of MODIS (i.e., MOD09A1) has typically been used for LAI and albedo estimation through the ACRM [
21] as well as the SAIL CR model, which were reported to yield high-accuracy retrievals based on such direct satellite multiangle observations [
22,
23,
24].
However, in situations where satellite sensors cannot provide direct observations due to their insufficient BRDF sampling capacity (e.g., MODIS), or cloud contaminations or poor atmospheric conditions, a kernel-driven BRDF model provides an essential tool to derive the wanted BRFs in a given viewing and solar geometries by an interpolation or extrapolation method [
18]. Such modeled BRFs are then usually input into the inversion procedure of physical model. A typical example is the accurate retrieval of the clumping index (CI) of vegetation foliage through use of the BRFs in the directions of Hotspot and Darkspot that are used to calculate the Normalized Difference between the Hotspot and Darkspot (NDHD) index [
25,
26]. This NDHD index was, in return, utilized to map the global CI through a simulation inversion procedure built by the 4-Scale physical CR model [
26,
27]. Likewise, by simulating customized directional reflectance as the training dataset for a physical process in regard to directional escape probabilities, canopy height at three typical forest regions was accurately estimated [
28].
As a result, the method for linking a physical model with the kernel-driven BRDF model provides potentials to accurately retrieve canopy biophysical/structural variables, particularly from the global routine BRDF parameter products generated by the kernel-driven BRDF model. Despite its great potential mentioned above, it is also necessary to investigate the limitations of this method, because the linked models usually have their own specific parameterization method in modeling inhomogeneity of the land surface. As one of the popular physical BRDF models, the PROSAIL model is designed based on radiative transfer theory, where only the leaves are included with a random azimuth distribution [
3,
29], and one of intrinsic limitations in its capacity may arise from simulating heterogeneous canopies showing clumping at several scales [
1]. For semi-empirical, kernel-driven models such as the RTLSR model, although both of the radiative transfer process and the geometric-optical mutual shadowing have been considered, the substantial simplification into several so-called kernels [
30,
31] may make the models inflexible to provide a fit to any type of reasonable shape, but rather are constrained by the predetermined BRDF shapes of these kernels [
32]. Therefore, such limitations behind the model mechanism may yield inconsistent BRDF results once they are linked in terms of the input-output chain, which probably leads to uncertainties and errors in their applications.
In this study, the BRF and albedo simulations derived by linking the PROSAIL model with the kernel-driven Ross-Li models are compared for the first time to examine their consistency in BRFs. First, 20,000 sets of BRFs were produced through the simulation method by the PROSAIL model, which covered various optical and structural parameters of vegetation canopies and contained 397 angles for each data set. Then, these data were input into the kernel-driven models for calculating the BRFs in the same solar and viewing geometries. The albedos were then calculated from the BRFs of both models. Finally, we compared the two models in terms of their BRFs and albedos and examined how vegetation parameters affect such a model link. To further strengthen such an investigation, 21 sets of multiangle reflectances were also used in this study. Finally, we conclude this study with a summary of the findings.
4. Discussion
In this study, the directional reflectance and albedo results of PROSAIL simulations as well as a variety of types of observations and their inversions using the hotspot-revised RTCLSR/RTCLTR model were compared for the first time, and good global agreement was observed, despite a few extreme discrepancies. The AFX was utilized to explore the scattering types among diverse canopies of PROSAIL simulations. Furthermore, the sensitivity of the model consistency to the vegetation structure was investigated to obtain a better understanding of the model linking. Additionally, the albedo, which is an essential factor in the models, was considered for further comparison to offer advice regarding albedo inversion by combining the two models.
The generally similar BRDF results of the RTCLSR model and the optimal RTCLTR model may be due to the robustness of the MODIS operational LSR model. Therefore, the commonly used RTCLSR model can be used in future model coupling. The case study results involving a common canopy exhibited good overall agreement, indicating that model coupling can be performed when only typical vegetation is considered. Despite the extreme error in the directional reflectance (
Figure 3), 88.6% and 79.0% of canopies can meet tolerances of 0.02 and 0.05 in the red and NIR bands, respectively. On one hand, the kernel-driven model has proven to be reliable for various canopies [
56,
62,
63], and therefore such a consistency is not surprising. On the other hand, however, discrepancies between these two models remain and may be caused by the differences in model theory, as discussed in the introduction. In addition, the diverse combinations of vegetation parameters required to cover complete canopies may be responsible for these differences because unreasonable combinations that do not exist in the real world may be included. However, no better way of performing a complete analysis has been developed to date, and the method of random combination has been widely applied in comprehensive analyses [
43,
44]. Therefore, further studies of the interactions among vegetation variables are necessary to guide the experimental design. Nonetheless, we have obtained an overall understanding of the consistency between the two models within the capacity of the PROSAIL model, and these findings will facilitate further studies on joining these two models. In terms of the field measurements, the RTLSR model presents better fitting compared to the PROSAIL model, which may imply that the semi-empirical kernel-driven models have more potentials in flexibly fitting actual multiangle observations than the physical models that require the parameterization of various biophysical/structural and spectral variables as inputs. In addition, more discrepancies were observed in the result for the field data than that of the 20,000 simulations, which may be related to the uncertainties during the BRF measurements and vegetation parameter matching.
To further explore the reasons underlying these discrepancies, the links between the vegetation structure and model differences were analyzed in detail, and canopy parameters, including LAI, ALA and
, were shown to be sensitive in the red band. Similarly, LAI and ALA can also affect the fit-RMSE in the NIR band. At the leaf level, variations can only be observed as
changes. This result suggests that the largest effect on model discrepancy occurs at the canopy level, especially for ALA, and that the canopy structure can significantly affect reflectance in the red and NIR bands, as shown in previous studies [
1]. Because of the equal variation derived from the uniform sampling of every parameter, the sensitivity analysis can be considered reliable. Hence, the analyses of canopies with small LAI and C
ab values and those with large ALA and
values suggest that we should be cautious when combining the two models in the red band and that further examination is required for both large LAIs and erectophile canopies in the NIR band. Notably, a real vertical leaf is limited [
29]. This limitation may affect the validation of PROSAIL model simulations and, subsequently, comparisons such as those performed in this study. Moreover, large ALAs (erectophile canopy) generally cause a dramatic change in the BRDF shape [
29], for which a large hotspot is generally observed. Our group is working on a hotspot correction for the geometric-optical scattering kernel, and a reexamination of these discrepancies is likely necessary using the updated model.
Parameter inversion is a potential application of linking these two models. The two models used in this study benefit from both the complete description of the vegetation structure in the PROSAIL model and the robust BRDF simulation and inversion of the kernel-driven model. In this study, we examined the parameter consistency in terms of albedo as an example. The highly consistent albedo reflects reliable model coupling for estimation and evaluation. Limited to the five SZAs used for BSA comparison, the BSA consistency must be further examined for other SZAs. Similarly, good consistency was observed for the 21 sets of field BRDF observations, in which the lower agreement may be due to error that occurs during the post-processing of the vegetation parameter matching and the uncertainty of from BRF measurements themselves. Based on the parameter matching, the retrieved and measured LAIs were compared. The result shows good consistency with a high R
2 of 0.8584 and a total RMSE of 0.95, which can probably meet the precision of current LAI products (around ±1.0) from MODIS and CYCLOPES sensors [
64]. Such an attempt for the LAI retrieval may initially demonstrates the feasibility of PROSAIL inversion by linking the two models. The three coefficients
,
and
included in the MODIS BRDF product are promising for estimating vegetation parameters, such as in the CI [
25,
26] and canopy height [
28], as discussed in the introduction. In addition, the AFX has been applied to extract prior BRDF archetypes and can capture the main BRDF variety, which is potentially related to the vegetation architecture [
38,
39,
40]. Thus, these BRDF factors could be added as constraints for parameter retrieval using the PROSAIL model in the future, where the relationships between these BRDF parameters and the vegetation structure can be further studied. Notably, the model consistency analysis in this study provides meaningful guidance for such studies. We preliminarily analyzed the sensitivity of retrieved Ross-Li model coefficients against PROSAIL parameters by using the Extended Fourier amplitude sensitivity test (EFAST) method. The result is consistent with
Figure 5, which suggests that sensitive parameters on BRDF effect occurs at the canopy level, especially for the ALA. Additionally, real data, such as sufficient measurements of LAI and ALA as well as other vegetation parameters, can be used to verify the results of these comparisons during their estimations. The strategy of comparison of BRDF for linking different models proposed in this study is still applicable for many other physical BRDF models beyond the PROSAIL model, and it would be promising to estimate various vegetation structure related to the physical models from satellite BRDF data by considering the BRDF consistency of model linking.
5. Conclusions
In this study, the potential in linking two widely used models (i.e., a semi-empirical, hotspot-revised, kernel-driven model, including the RTCLSR and RTCLTR models, and the physical PROSAIL model) was comprehensively investigated in terms of BRDF and albedo. A typical canopy was first exemplified in the comparison in viewing hemispherical and principal planes to examine the potential in linking the two models. In total, 20,000 sets of parameter combinations were applied in a comprehensive analysis based on the PROSAIL model and were used to generate the PROSAIL multiangle reflectance and albedo. Then, BRDF and albedo values were obtained using the kernel-driven model. Finally, the reflectance and albedo values of the two models were compared, and the correlations between vegetation parameters and model discrepancy were further explored. To further strengthen the investigation, 21 sets of field BRDF observations that cover a variety of land surface classes were also introduced into the study.
Overall, similar results were observed for the RTCLTR and RTCLSR models. This finding indicates that the MODIS operational LSR model provides a robust inversion technique, although the LTR model is considered to be the optimal version of the LSR model [
36]. Globally, the two models agree well in terms of directional reflectance for diverse canopies (R
2 > 0.92), where 88.6% and 79.0% of fit-RMSEs are within tolerances of 0.02 and 0.05, respectively, in the two bands. This indicates great potential for linking these two models for potential applications, such as for developing inversion procedures to accurately retrieve vegetation properties from the satellite BRDF parameter product generated by the kernel-driven BRDF model. Limitations may arise from the few inconsistencies in BRFs between the two models in a large VZA beyond 70°, which somewhat depends on the variation of SZAs. In terms of reflectance anisotropy, geometric-optical scattering was dominant in the red band, whereas volumetric scattering was usually dominant in the NIR band. Model differences slightly increase for extreme case of volume scattering (large AFX values), especially in the NIR band. Additionally, attention should be paid to small LAI and C
ab values and large ALA and
values in the red band, and large LAI and ALA values in the NIR band, which tend to result in more errors when linking the two models, especially for erectophile canopies. Great potential in linking the two models should arise based on the good agreement in albedo (R
2 > 0.98), and 99.98% and 97.99% of the WSA deviations were less than 0.02 in the two bands. At an SZA of 30°, the BSA tends to perform best among all simulations. In addition, a similar result was found for the 21 sets of field BRDF observations, which presents more consistency between the two models than the result of the 20,000 PROSAIL simulations. This may contribute to the real measurements of BRDF and vegetation structure.
The overall good consistency between the two models suggests a great potential for linking these two models for parameter estimation, especially from the BRDF parameter product generated by the kernel-driven BRDF model, except for extreme cases that involve a few types of canopies. Therefore, future research should focus on the application of prior BRDF knowledge derived from the kernel-driven model, such as global BRDF parameters (e.g., MCD43A) and AFX BRDF archetypes, in conjunction with the PROSAIL inversion to devise an inversion relationship between vegetation structure and model BRDF parameters, based on the findings in this study.