1. Introduction
Satellite-based optical remote sensing from missions such as ESA’s Sentinel-2 (S2) have emerged as valuable tools for continuously monitoring the Earth’s surface, thus making them particularly useful for quantifying key cropland traits in the context of sustainable agriculture [
1]. Upcoming operational imaging spectroscopy satellite missions will have an improved capability to routinely acquire spectral data over vast cultivated regions, thereby providing an entire suite of products for agricultural system management [
2]. The Copernicus Hyperspectral Imaging Mission for the Environment (CHIME) [
3] will complement the multispectral Copernicus S2 mission, thus providing enhanced services for sustainable agriculture [
4,
5]. To use satellite spectral data for quantifying vegetation traits, it is crucial to mitigate the absorption and scattering effects caused by molecules and aerosols in the atmosphere from the measured satellite data. This data processing step, known as atmospheric correction, converts top-of-atmosphere (TOA) radiance data into bottom-of-atmosphere (BOA) reflectance, and it is one of the most challenging satellite data processing steps e.g., [
6,
7,
8]. Atmospheric correction relies on the inversion of an atmospheric radiative transfer model (RTM) leading to the obtaining of surface reflectance, typically through the interpolation of large precomputed lookup tables (LUTs) [
9,
10]. The LUT interpolation errors, the intrinsic uncertainties from the atmospheric RTMs, and the ill posedness of the inversion of atmospheric characteristics generate uncertainties in atmospheric correction [
11]. Also, usually topographic, adjacency, and bidirectional surface reflectance corrections are applied sequentially in processing chains, which can potentially accumulate errors in the BOA reflectance data [
6]. Thus, despite its importance, the inversion of surface reflectance data unavoidably introduces uncertainties that can affect downstream analyses and impact the accuracy and reliability of subsequent products and algorithms, such as vegetation trait retrieval [
12]. To put it another way, owing to the critical role of atmospheric correction in remote sensing, the accuracy of vegetation trait retrievals is prone to uncertainty when atmospheric correction is not properly performed [
13].
Although advanced atmospheric correction schemes became an integral part of the operational processing of satellite missions e.g., [
9,
14,
15], standardised exhaustive atmospheric correction schemes in drone, airborne, or scientific satellite missions remain less prevalent e.g., [
16,
17]. The complexity of atmospheric correction further increases when moving from multispectral to hyperspectral data, where rigorous atmospheric correction needs to be applied to hundreds of narrow contiguous spectral bands e.g., [
6,
8,
18]. For this reason, and to bypass these challenges, several studies have instead proposed to infer vegetation traits directly from radiance data at the top of the atmosphere [
12,
19,
20,
21,
22,
23,
24,
25,
26]. Though the latter studies exemplify the diversity of TOA-based trait retrieval methods that have been proposed, the overarching rationale is that the direct retrieval of radiance data presents the advantage of circumventing the complex process of atmospheric correction, thereby mitigating the potential transmission of errors to subsequent retrieval processes.
Regardless of the specific methodological implementation, all those proposed TOA-based retrieval studies have in common that they account for the fundamental physical principles governing radiative transfer [
12,
19,
21,
22,
23,
25,
26]. This entails the integration of a vegetation RTM with an atmospheric RTM [
20,
27,
28,
29]. Atmospheric RTMs systematically model the atmospheric influences on surface-reflected radiance, thus calculating the interaction of radiation with the atmosphere while accounting for diverse gaseous absorptions under assumptions of anisotropic or Lambertian surfaces [
30]. Some of the most relevant atmospheric models include the MODerate resolution atmospheric TRANsmission (MODTRAN) [
31], the Second Simulation of a Satellite Signal in the Solar Spectrum (6SV) [
32], and the libRadtran (Library for Radiative Transfer) [
33]. The principle of TOA-based trait retrievals lies in the coupling of vegetation RTMs with such an atmospheric RTM, with the latter explicitly modelling the atmospheric effects on the radiance received by the sensor. This coupling enables the generation of a LUT of TOA radiance simulations, which forms the foundation for subsequent retrieval strategies or sensitivity analysis studies. For instance, the theoretical validation of TOA-based trait retrieval was established through a global sensitivity analysis [
20,
34]; atmospheric parameters demonstrate sensitivity in distinctive, largely nonoverlapping spectral bands, such as those associated with ozone column concentration and water vapour. Furthermore, the spectral signal experiences comparatively minimal impact from most atmospheric variables when contrasted with the more influential canopy or leaf-level variables. These vegetation variables, particularly prominent in the visible and shortwave infrared regions, exert a predominant effect, thus implying that, in principle, they can be retrieved directly from TOA radiance data [
20,
34].
Building upon these theoretical foundations, recent experimental studies have demonstrated that hybrid retrieval methods can function as powerful processors to process TOA radiance data into quantifiable vegetation variables [
29,
35,
36,
37,
38]. In essence, hybrid methods combine RTM simulations with machine learning regression algorithms (MLRAs). These methods are usually applied to the processing of BOA reflectance data e.g., [
39,
40,
41,
42], where hybrid models achieved accurate estimations of plant functional traits due to their robustness, transferability, and fast processing (see reviews in [
43,
44,
45]). Yet recently, pursuing the hybrid strategy, some studies inferred vegetation traits directly from TOA satellite imagery with adequate spectral coverage but with only a limited number of bands, such as Copernicus Sentinel-2 or Sentinel-3 [
29,
35,
36,
37,
38]. The core algorithm of these hybrid models is usually the Bayesian MLRA Gaussian process regression (GPR) [
46]. GPR is typically preferred in hybrid models because of its proven excellent prediction accuracies and insights in relevant bands e.g., [
41,
42,
47,
48,
49]. Furthermore, associated model uncertainties can be derived from the GPR models, which is useful to understand the quality of the variable prediction when transferring models to different sites and under diverse conditions e.g., [
36,
50].
While the studies have demonstrated the effectiveness of hybrid or TOA-based models, their application has been limited to the processing of multispectral or BOA data. Recently, satellite imaging spectroscopy missions have been designed and partly launched, thereby possessing hundreds of spectral bands that provide a vast amount of data of high detail and accuracy. In addition to CHIME, these missions include the launched PRecursore IperSpctrale de la Missione Applicativa (PRISMA) [
51], the Environmental Mapping and Analysis Program (EnMAP) [
52], and the planned Surface Biology and Geology (SBG) [
53]. In light of the challenges associated with atmospheric correction and the recent successes in developing TOA-based hybrid retrieval models, the natural progression would be to explore and develop hyperspectral TOA-based hybrid models.
Altogether, given the upcoming era of imaging spectroscopy, this work is determined to develop TOA-based hybrid retrieval models that enable the accurate and fast processing of hyperspectral images directly from TOA radiance data, thus bypassing the need for an atmospheric correction. Specifically, we aim to address some of the most relevant vegetation traits in the field of agriculture, such as the leaf area index (LAI), the canopy water content (CWC), the fraction of absorbed active photosynthetic radiation (FAPAR), the fractional vegetation cover (FVC), and the canopy chlorophyll content (CCC). It has recently been demonstrated that these traits can be successfully retrieved from atmospherically corrected imaging spectroscopy reflectance data using hybrid GPR models [
49]. As a next step, we aim to provide evidence that these traits can be directly predicted from hyperspectral TOA radiance data, which brings us to the following objectives: (1) to develop and evaluate TOA-based hybrid GPR models for estimating vegetation traits using simulated hyperspectral TOA data and (2) to assess the generalisability of the TOA-based hybrid models to different imaging spectroscopy datasets, including PRISMA and EnMAP imagery. Finally, (3) we will address the feasibility of the TOA-based hybrid retrieval schemes for upcoming global imaging spectroscopy missions, such as CHIME.
4. Discussion
Despite the widespread practice of applying retrieval models to atmospherically corrected images, in this study, we explored the development of hybrid models capable of directly analyzing hyperspectral TOA radiance imagery. Essentially, such an approach saves the atmospheric correction processing time and avoids potential errors derived from this process. This TOA-based retrieval approach has been laid out here in support of the upcoming CHIME and evaluated with the scientific hyperspectral precursor mission data from PRISMA and EnMAP. To the best of our knowledge, this is the first study estimating multiple vegetation traits from satellite hyperspectral radiance data using a hybrid workflow. Though comparison studies at the TOA scale are lacking, our results can be compared against retrievals achieved at the BOA scale. The following sections discuss the key aspects achieved in this study. Firstly, we examine the RTM and sensors’ data comparison (
Section 4.1); secondly, we examine the retrieval performance with the hybrid workflow applied to the BOA and TOA (
Section 4.2); thirdly, we examine the Gaussian processes regression and delivered uncertainty (
Section 4.4); and quarterly, we examine the variable-specific mapping using PRISMA and EnMAP imagery (
Section 4.3). Lastly, the limitations and further research opportunities are discussed in
Section 4.5).
4.1. RTM and Sensor Data Comparison
When aiming to move towards a routine processing of hyperspectral data into vegetation traits across the globe, the implemented retrieval algorithm has to be accurate, robust, and fast, preferably with the provision of uncertainty intervals alongside the estimates [
43]. To this end, hybrid models have been evaluated as the most promising, thereby combining physically based RTMs with the flexibility of machine learning algorithms [
44]. In this context, the ability to generate realistic data from RTMs is crucial for developing highly effective hybrid models. This was achieved by both optimizing in the spectral domain, through PCA dimensionality reduction [
49], and through optimising the training dataset. In addition to applying a realistic sampling design within the RTM parameter spaces, this can be accomplished by further optimising the selection of RTM training samples through the AL procedure, as has been extensively demonstrated and discussed in previous studies [
47,
48,
49,
73]. Using AL supports, we can accomplish the establishment of a representative training dataset, which is the main prerequisite for the successful training of the retrieval models. Furthermore, the RTM spectral output should be configured according to the band settings of the imagery where the hybrid model will be applied to [
39,
49]. The usage of a proper RTM setting allows for the simulation of diverse, yet realistic vegetation scenarios, which better represent real scenarios. The primary objective of this study was to develop hybrid models tailored to the capabilities of the upcoming CHIME satellite. Since the CHIME mission is still in its development phase and a proven atmospheric correction method is unavailable, we explored the development of hybrid models directly at the TOA scale and benchmarked them against BOA-based models. Anticipating the availability of CHIME data, the developed models were evaluated using PRISMA and EnMAP imagery. PRISMA and EnMAP image spectral bands were resampled to align with the spectral range of previously validated CHIME models, thereby ensuring compatibility with the sensor specifications [
49].
Having a consistent band setting between the RTM training and satellite-recorded data at both the BOA and TOA scales,
Section 2.7 provided descriptive statistical comparisons of the spectra for both PRISMA and EnMAP sensors to validate their spectral similarity (
Figure 3 and
Figure 4). These illustrations showcase the similarity between the simulated and satellite-recorded spectra, thereby implying that the hybrid models can correctly interpret and convert the spectral data into vegetation traits both at the BOA and TOA levels.
4.2. Retrieval Performance at BOA and TOA Scales
The hybrid models developed in this study combine the strengths of physical and statistical models to achieve both portability and robustness. At the same time, the PCA dimensionality reduction step ensures optimal exploitation of the spectral domain, while the AL step ensures optimal selection of the RTM training samples [
49]. As a novelty compared to previous studies, in this study both optimization steps were applied to the BOA and TOA scales. For the traits LAI, CCC, and CWC, both the BOA and TOA models were adequately validated against field data (e.g.,
ranging between 0.69 and 0.92). Moreover, a slight tendency emerged favoring superior estimates derived from the TOA scale for the canopy variable LAI. It is noteworthy that previous studies conducted by Estévez et al. [
29,
35] using Sentinel-2 data also demonstrated superior LAI retrieval performance at the TOA scale as opposed to the BOA scale. At the same time, the BOA validation showed slightly higher accuracies for the other analyzed variables. However, the TOA scale demonstrated comparable accuracy levels, thus highlighting its competitive performance. The high TOA-based accuracies could be attributed to the potential degradation of BOA hyperspectral data quality during the multiple processing stages involved in converting the L1C product to L2A, which could have negatively impacted retrieval accuracy [
11].
Related to this topic, hybrid models often add some degree of noise to the training dataset, e.g., [
29,
35,
39,
86]. This spectral degradation of the training dataset can lead to an improvement in the validation statistics, as it mitigates the tendency of overfitting the model toward synthetic RTM data. In our TOA-based models, combining canopy simulations with atmospheric simulations might likewise have acted somewhat as a noise perturbation factor of the vegetation RTM spectra, i.e., this perturbation similarly mitigates the tendency of overfitting.
Also, the observed moderate discrepancies between the BOA and TOA and the field validation data require further explanation. On the one hand, these discrepancies may be attributed to the use of different RTMs for the atmospheric simulation versus the atmospheric correction in the PRISMA and EnMAP processors, which causes a net effect similar to radiometric calibration errors. While in this study libRadtran was used to generate the TOA training dataset, both PRISMA’s and EnMAP’s atmospheric corrections are based on MODTRAN [
87,
88]. This suggests that further work should ensure consistency among the atmospheric RTMs used for the generation of the training dataset and in the atmospheric correction processors. On the other hand, as previously mentioned, the spectral resampling to a common spectral configuration (CHIME) introduces additional noise in the PRISMA/EnMAP images, particularly in the vicinity of gas absorption regions. This noise is enhanced by effects such as spectral calibration errors and smile. Although major absorption bands have been filtered out (
Section 2.3) to reduce the impact of this noise, residual H
O and O
bands were still present in the data and might have contributed to an increased noise level in the data.
4.3. Machine Learning Regression Model and Uncertainty
The work presented here is the natural continuation of a research line that focuses on the development of GPR-based hybrid models e.g., [
29,
35,
36,
37,
38]. GPR allows for the development of hybrid models with accurate predictions and valuable estimations of uncertainty for each test spectrum. Following the results achieved in
Table 4 and
Table 5, it can be deduced that GPR achieves good performance along the considered metrics.
The training time for GPR hybrid models is a significant factor to consider. As the training time grows cubically as a function of the training samples [
89], it typically exceeds the application time by several orders of magnitude. However, in the context of real-world operational applications, where timely retrieval estimations are paramount, the prediction time emerges as the more critical parameter. GPR hybrid models, despite their relatively lengthy training process, excel in their application performance, thereby enabling them to swiftly process new incoming spectra and rendering them highly suitable for routine global mapping applications. This trade-off between training time and application efficiency makes GPR hybrid models particularly well suited for scenarios demanding the rapid retrieval of new spectra.
Another aspect of GPR that makes it a highly appealing MLRA for operational contexts is its built-in uncertainty estimation. GPR not only provides an estimation but also generates a corresponding normal distribution. This normal distribution is characterized by its standard deviation, which serves as an uncertainty estimate for the mean retrieval value. Uncertainty estimates are crucial for the effective interpretation of GPR model outputs, as they enable per-pixel evaluation of the performance of the model [
50]. Furthermore, uncertainty estimations are particularly valuable in operational contexts where models cannot be validated for all locations. For instance, uncertainty information from (future) Copernicus products is usually requested to support the application of the data and products in various contexts, such as policy and climate modelling, e.g., [
90]. Therefore, it should be an obligatory part of the provided products.
Here, the uncertainty estimation provided in
Figure 7 indicates that our models are more proficient at estimating vegetation traits on spectra where vegetation density is high. Notably, the LAI, CCC, and CWC uncertainties were larger on the left side of the axis. This trend could be attributed to the increasing influence of soil in the spectra of pixels with lower vegetation density. This behavior is supported by the FVC and FAPAR uncertainty values, as these models were optimised and validated only against RTM-generated data (i.e., with less influence of soil in the turbid medium model SCOPE), and their uncertainty estimates appear to be less attributed to vegetation density.
4.4. Variable-Specific Mapping in PRISMA and EnMAP Sensors
Inspecting both the PRISMA- and EnMAP-based trait maps in
Figure 8 and
Figure 9, it can be concluded that TOA-based mapping is possible for both data sources. Particularly, the FAPAR and FVC led to meaningful maps with strong similarity towards their BOA-based counterparts. At the same time, it is also noteworthy that the PRISMA TOA-based LAI, CCC, and CWC maps were not completely behaving as expected, with a general tendency toward overestimation over nonvegetated surfaces. This can be attributed to various error sources. First, the spectral resampling to CHIME resolution might derive higher errors due to the coarser spectral resolution of PRISMA (∼15 nm) compared to EnMAP (6.5–10 nm). Second, the GPR models were trained by adding bare soil spectra to the training dataset. These soil spectra might not be suitable for the specific image acquisition by PRISMA. This factor warrants consideration during the development of future models.
In the broader context, the efficiency of the models in processing full TOA images within minutes underscores their feasibility for large-scale applications. The consistent mapping results between the BOA and TOA scales, along with the low uncertainties, emphasise the practical utility of these models for real-world applications such as precision agriculture, land cover monitoring, and ecosystem assessment. Discussing the larger implications of our findings, the consistent performance of the TOA-based models across multiple hyperspectral sensors signifies their applicability and scalability. The trait mapping results, particularly for the FAPAR and FVC, hold significance for monitoring vegetation health and productivity. These findings contribute valuable information for environmental monitoring, land management, and policy formulation.
It also deserves remarking that the cropland characteristics at the canopy level were often inferred more accurately from space than leaf-level traits such as the LCC [
91]. Our findings for the L1C and L2A scales clearly showed that tendency, which was also supported by a few related studies examining Sentinel-2 data [
66,
92,
93]. Xie et al. [
66] suggested that this can be caused by the compensating effects between the LAI and LCC, which could account for the lower retrieval accuracy at the leaf level. The precision with which leaf biochemicals may be retrieved from canopy reflectance may also be influenced by the signal’s intensity or signal propagation, which is primarily determined by structural characteristics like the LAI [
94,
95].
4.5. Limitations and Further Research Opportunities
Reviewing our research objectives, the developed hybrid GPR models successfully addressed the challenge of canopy trait mapping from hyperspectral imagery at the TOA level. However, a few limitations had to be addressed, and some warrant further exploration to enhance the accuracy and robustness of the retrieval models. For instance, to overcome the lack of in situ observations for the FAPAR and FVC, we increased the number of simulated samples from 500 (as for the LAI, CCC, and CWC) to 1000, thus enhancing the generalisation capability and robustness of the models.
A notable limitation of the study is that only canopy-level traits were mapped. Some initial tests with leaf-level variables showed rather low performance. These findings align with the results of previous studies, thus demonstrating that leaf-level variables are more challenging to retrieve with sufficient accuracy using TOA-based data [
35,
36]. The superior performance of our canopy-scale retrievals for the CCC and CWC can be attributed to the role of LAI in leaf-to-canopy upscaling. The LAI represents the density of leaves and, as such, the contrast between vegetated and nonvegetated fractions of the surface. Indeed, the LAI is recognized as one of the strongest drivers of spectral variability across the entire VNIR and SWIR spectral range [
20].
To further improve model efficiency, follow-up research could investigate potential improvements both in the employed algorithm and the optimization of the number of principal components. Alternative machine learning approaches could be explored to enhance the obtained results, such as employing large-scale formulations of GPR [
46,
96]. Multioutput regression models might also ensure physical correlations between the traits, thereby enhancing the robustness of the models [
97]. Other methods such as multifidelity [
98] can improve the efficiency of the retrieval while improving the accuracy of the output product. Additionally, the use of more advanced three-dimensional RTMs, such as DART e.g., [
99] could be leveraged to generate more data and feed these large-scale approaches to construct more accurate models. To further broaden the applicability and implementation on other hyperspectral missions and in a range of geographical settings would significantly enhance the generalisability of the models e.g., [
100]. Additionally, incorporating additional trait variables would provide a more comprehensive understanding of the vegetation dynamics and their underlying mechanisms across the globe e.g., [
101].
Another relevant aspect of research is applying the developed models to hyperspectral time series data. These, however, are not yet available from current missions. This would allow us to track the temporal evolution of vegetation traits in various ecosystems. Additionally, expanding the scope of the study to include different crop types within the study region, and their various phenological stages would further enhance its value. Also, investing in the portability of the models would be beneficial to further advance this work. In the upcoming era of big data, it is expected that these TOA-based hybrid GPR models can be implemented into cloud computing platforms [
102], thus opening the processing chain to the broader community without the need to download TOA radiance imagery. Finally, it is important to note that all the developments and models presented here can be relatively easily reproduced. The satellite data used in the study are open (upon registration), and the hybrid models can be replicated through the ALG tool and ARTMO toolbox (both downloadable at
http://artmotoolbox.com/ (accessed on 26 March 2024)). Likewise, the provided tools facilitate customization for any applicable sensor by enabling the training of GPR models with resampled TOA spectral data tailored to the desired spectral band configuration.