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. Author manuscript; available in PMC: 2023 Nov 1.
Published in final edited form as: ISPRS J Photogramm Remote Sens. 2022 Nov;193:104–114. doi: 10.1016/j.isprsjprs.2022.09.003

Retrieval of carbon content and biomass from hyperspectral imagery over cultivated areas

Matthias Wocher a,*, Katja Berger b,c, Jochem Verrelst b, Tobias Hank a
PMCID: PMC7614045  EMSID: EMS159341  PMID: 36643957

Abstract

Spaceborne imaging spectroscopy is a highly promising data source for all agricultural management and research disciplines that require spatio-temporal information on crop properties. Recently launched science-driven missions, such as the Environmental Mapping and Analysis Program (EnMAP), deliver unprecedented data from the Earth’s surface. This new kind of data should be explored to develop robust retrieval schemes for deriving crucial variables from future routine missions. Therefore, we present a workflow for inferring crop carbon content (Carea), and aboveground dry and wet biomass (AGBdry, AGBfresh) from EnMAP data. To achieve this, a hybrid workflow was generated, combining radiative transfer modeling (RTM) with machine learning regression algorithms. The key concept involves: (1) coupling the RTMs PROSPECT-PRO and 4SAIL for simulation of a wide range of vegetation states, (2) using dimensionality reduction to deal with collinearity, (3) applying a semi-supervised active learning technique against a 4-years campaign dataset, followed by (4) training of a Gaussian process regression (GPR) machine learning algorithm and (5) validation with an independent in situ dataset acquired during the ESA Hypersense experiment campaign at a German test site. Internal validation of the GPR-Carea and GPR-AGB models achieved coefficients of determination (R2) of 0.80 for Carea and 0.80, 0.71 for AGBdry and AGBfresh, respectively. The mapping capability of these models was successfully demonstrated using airborne AVIRIS-NG hyperspectral imagery, which was spectrally resampled to EnMAP spectral properties. Plausible estimates were achieved over both bare and green fields after adding bare soil spectra to the training data. Validation over green winter wheat fields generated reliable estimates as suggested by low associated model uncertainties (< 40%). These results suggest a high degree of model reliability for cultivated areas during active growth phases at canopy closure. Overall, our proposed carbon and biomass models based on EnMAP spectral sampling demonstrate a promising path toward the inference of these crucial variables over cultivated areas from future spaceborne operational hyperspectral missions.

Keywords: EnMAP, AVIRIS-NG, Carbon content, Biomass, Gaussian process regression, Active learning

1. Introduction

Quantification and knowledge of carbon-based plant constituents are crucial for all terrestrial ecosystems. Since the terrestrial biosphere is a significant sink for atmospheric CO2, the carbon (C) stored in vegetation plays an important role for a balanced radiative budget and thus influences the global climate system (Kaminski et al., 2012; Denman et al., 2007; Paustian et al., 2019). Agricultural areas globally cover almost 40% of the terrestrial land surface, with one-third used as cropland, and two-thirds consisting of grasslands and pastures for grazing livestock (FAO, 2022). Hence, there is a significant contribution of cultivated areas to the global CO2storage in form of soil organic carbon, influencing the soil C budget (Paustian et al., 2019). Atmospheric CO2is transferred into biotic and pedologic C pools of the plant ecosystem, whereas C among others enters the soil via decomposition of roots or aboveground biomass (Jansson et al., 2021). Storing a vast amount of carbon, aboveground biomass thus presents a crucial ecological variable for evaluating potential changes of the climate system (Lu, 2006; Fang et al., 2021). For this reason, it has been defined as one of the Essential Climate Variables (ECV) by the Global Climate Observing System (GCOS WMO, 2022). In the last decades, an unprecedented amount of Earth observation (EO) data with increasing spatial, temporal, and spectral resolution capabilities became available providing unique opportunities for deriving biomass and carbon contents. A particular focus was on operational multispectral systems, such as the Copernicus Sentinel-2 sensors of the European Space Agency (ESA) or their predecessors. However, multispectral data are limited in their ability to provide substantial information about plant carbon contents, mostly because the relevant absorption features in the shortwave infrared (SWIR) cannot be resolved by these sensors. At present we are approaching a new era of spaceborne imaging spectrometers, being already launched, under design or planned (Ustin and Middleton, 2021). By means of these upcoming data streams, we will be able to timely monitor the state and dynamics of cultivated land in higher spectral detail, essential among others, for agricultural management systems (Hank et al., 2019). As opposed to multispectral data sources, hyperspectral sensors are capable of resolving subtle absorption features, such as those caused by specific pigments, proteins or carbon. Important scientific precursor missions include the PRecursore IperSpettrale della Missione Applicativa (PRISMA) (Loizzo et al., 2019), launched on 22nd March 2019, and the Environmental Mapping and Analysis Program (EnMAP) (Guanter et al., 2015), which entered into orbit on 1st April 2022. PRISMA and EnMAP will be followed by the operational NASA Surface Biology and Geology observing system (SBG) (National Academies of Sciences, 2018) and the Copernicus Hyperspectral Imaging Mission for the Environment (CHIME) (Nieke and Rast, 2019). Thus, new opportunities arise for the development of retrieval models for higher-level vegetation products from hyperspectral data.

In the last three decades, significant progress was achieved with improving leaf optical properties models, such as the PROSPECT family (Jacquemoud and Baret, 1990; Féret et al., 2008, 2017). Féret et al. (2021) recently introduced carbon-based constituents (CBC) in the PROSPECT-PRO model version, differentiating the spectral contribution of dry matter content into the signals caused by proteins and CBC. The authors demonstrated that CBC can be successfully estimated from the optical properties of both fresh and dry leaves. To obtain such agriculturally relevant traits from satellite data, upscaling of simulated leaf optical properties to the canopy level is required, which is typically done by combining leaf and canopy radiative transfer models (RTMs). For instance, the PROSPECT-PRO model was coupled with the Scattering by Arbitrarily Inclined Leaves model (4SAIL) (Verhoef and Bach, 2007) to PROSAIL-PRO by Berger et al. (2020) and by Verrelst et al. (2021b) to simulate canopy nitrogen content (CNC). Inversion of the model simulations is then required to estimate the crop properties of interest from received satellite signals. Traditional physically-based inversion, such as numerical optimization or look-up-table methods (Vohland et al., 2010; Kimes et al., 2000), relied on direct comparison of simulated against observed spectra through diverse cost functions (e.g., Verrelst et al., 2013a). However, the major drawback of these techniques is the high computational demand that makes them unsuitable for the real-time processing of large scenes, as they are now beginning to become available from hyperspectral satellites. Currently, efficient hybrid methods have become popular (Verrelst et al.,2015, 2019), where machine learning (ML) regression algorithms are trained over simulated databases generated by means of these RTMs (e.g., De Grave et al., 2020; Berger et al., 2020, 2021a; Verrelst et al., 2021b; Brede et al., 2020; Danner et al., 2021). Combining physical awareness with the inductive capabilities of data-driven ML approaches, these methods blend previous efforts and may soon be considered state-of-the-art for agricultural mapping activities and beyond (Svendsen et al., 2020; Baker et al., 2018; Verrelst et al., 2019; Machwitz et al., 2021). Straightforward parametric regressions making use of empirical relationships between spectral observations (or vegetation indices) and in situ measured variables (Glenn et al., 2008; Verrelst et al., 2015) may be easily implemented and are computationally fast. However, these models depend on a mathematically continuous relationship between the variable of interest and its corresponding absorptive signal. Once established, parametric regressions clearly under-exploit the available spectral information of hyperspectral data and in addition lack transferability to other instruments and sites both temporally and spatially (Wocher et al., 2020; Atzberger et al., 2011; Verrelst et al., 2019). In respect to ML algorithms, in particular the Bayesian approaches of Gaussian process regression (GPR) (Rasmussen and Williams, 2006) demonstrated high performances in the context of Earth observation regression problems (e.g., Camacho et al., 2021; Mateo-Sanchis et al., 2021; de Sáet al., 2021; Verrelst et al., 2011, 2020; Zhou et al., 2018). The high performance of GPR can be traced to theoretical and practical advantages specific to these algorithms, for instance, the design of appropriate covariance functions, enabling the inclusion of prior knowledge about the signal characteristics (Camps-Valls et al., 2016; Rasmussen and illiams,2006). GPR algorithms and established models further provide a particular advantage over other ML strategies: they deliver predictive variance or uncertainty intervals. In this way, the models provide quality information about their prediction capabilities, which is in particular interesting when transferring the models to other sites, sensors and vegetation types (Verrelst et al., 2013b). However, a drawback of GPR algorithms within hybrid retrieval schemes is that they come with a computational cost, especially when large training datasets are processed in the training phase (Rivera-Caicedo et al., 2017; Danner et al., 2021). This can be alleviated, for instance, by applying spectral dimensionality reduction, such as principal component analysis (PCA) (Jolliffe and Cadima, 2016). Nonetheless, reduction in the spectral domain alone may not suffice in view of the huge number of potentially redundant samples generated by RTMs. Therefore, optimization in the sampling domain is required as well. A solution to the sampling problem is given by semi-supervised approaches, also known as active learning (AL). Using diversity and uncertainty strategies, AL aims to optimize training datasets through intelligent sampling by means of an iterative procedure (Settles, 2009; Berger et al., 2021c). Several studies successfully implemented AL techniques within hybrid retrieval workflows, for instance to estimate leaf biochemical variables and upscaled canopy-traits from Sentinel-2 top-of-canopy (Salinero-Delgado et al., 2021) and top-of-atmosphere data (Estévez et al., 2022), crop nitrogen content (Verrelst et al., 2020, 2021b), non-photosynthetic crop biomass (Berger et al., 2021b) or multiple crop traits from the PRISMA (Tagliabue et al., 2022) or CHIME-simulated missions (Candiani et al., 2022). However, the majority of these studies incorporated the fully sampled ground datasets in the AL-tuning procedures, or found only a limited transferability of established models to independent datasets of other sites (Estévez et al., 2022). In view of the prioritization of specific variables by near-term operational missions, it remains to be investigated if hybrid models including AL heuristics can obtain sufficiently high and transferable retrieval performances.

Therefore, the objective of the current study was to evaluate the quantification and mapping of crop carbon content as well as wet and dry biomass from future EnMAP hyperspectral mission data. To achieve this, we employed in situ sampled field datasets from two different campaigns for model training, optimization, and independent testing, particularly focusing on the spectral configuration of the EnMAP sensor in preparation for future routine observations.

2. Materials and methods

2.1. Model building workflow

For the retrieval of crop carbon content (Carea), dry biomass (AGBdry) and wet biomass (AGBresh) a hybrid approach was applied. Fig. 1 schematically shows the workflow, which is itemized into seven main steps:

  1. preparing a training dataset with PROSAIL-PRO;

  2. reducing the dimensionality of full range spectral information using PCA;

  3. applying active learning methods to condense and optimize the training sample pool;

  4. training of GPR models and testing of internal model performance based on field campaign datasets;

  5. improving mapping capability by adding bare soil spectra to the training database and retraining GPR models;

  6. processing of airborne AVIRIS-NG spectrometric imagery;

  7. validating retrieved carbon and biomass contents based on independent in situ data.

Fig. 1.

Fig. 1

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Schematic workflow for carbon and biomass mapping.

In the next sub-sections, these steps will be described in detail.

2.2. Field campaign dataset for model training and validation

During the Munich-North-Isar (MNI) (Wocher et al., 2018) field campaigns in the years 2017, 2018, 2020, and 2021, hyperspectral signatures and plant traits from corn, winter wheat, and winter barley were collected weekly over the whole growing season on communal farmland 15 km north of Munich, Southern Germany. Spectral reflectance was measured from 350 to 2500 nm using an ASD FieldSpec 3 Jr at a height of one meter above the canopy. Field spectrometer data available at 1 nm spectral sampling interval was resampled to EnMAP band configuration according to pre-launch expected 242 spectral bands (423–2439 nm) (Guanter et al., 2015) with the further exclusion of nine bands in the visible to near-infrared (VNIR)-SWIR sensor overlap region (bands 89–98: 905–996 nm). This finally resulted in 233 bands at average full-width-half-maxima (FWHM) of 7.8 nm in the VNIR and 12.0 nm in the SWIR. Plant biomass samples were collected destructively, cutting an area of 0.25 m2 at soil level. AGBfresh and AGBdry weights were determined separately for leaves, stalks, and fruits. Total AGBfresh was weighed in the field and separately right after arrival in the laboratory. The samples then were oven-dried until constant weight for 24 h at 105 °C before AGBdry was determined. Furthermore, after milling of the samples, a CHNS-Analyzer (Elementar vario EL cube) was used to determine the carbon concentration (Cmass) of the samples in [%]. Afterwards, Carea in [g/m2] of leaves, stalks and fruits were calculated by multiplying AGBdry with Cmass. Based on preliminary tests and prior studies, model training and validation were focused on the sum of measured leaf + stalk contents as radiation is limited in penetrating thick tissues of plant fruit organs (refer to discussions in Wocher et al., 2018; Berger et al., 2020). Leaf area index (LAI) in [m2/m2] was determined using a LI-COR LAI-2200C Plant Canopy Analyzer. A statistical summary of available in situ data is shown in Table 1.

Table 1.

MNI site measured ranges (mean; standard deviation) and number of measurements (#N) for in situ leaf + stalk sums of Carea, AGBdry, AGBfresh, as well as LAI and BBCH growth stages determined according to Meier (2018). Values correspond to measurements with available spectral reflectance data.

Year Crop type BBCH [-] LAI [m2/m2] Carea [g/m2] AGBdry [g/m2] AGBfresh [g/m2]
2017 Winter wheat (#11) 25–87 1.6–6.2 (4.8; 1.6) 71–450 (338; 117) 70–988 (659; 316) 437–4059 (2993; 1332)
Corn (#8) 30–85 0.2–3.9 (2.3; 1.4) 13–392 (150; 204) 26–872 (460; 334) 165–4361 (2712; 1605)
2018 Winter wheat (#7) 28–87 1.5–6.2 (4.8; 1.6) 56–534 (289; 203) 127–1205 (456; 651) 560–3632 (2046; 1134)
Corn (#6) 32–83 1.8–3.6 (3.2; 0.7) 95–631 (425; 181) 236–1454 (964; 413) 2841–6720 (5496; 1376)
2020 Winter wheat (#13) 26–92 0.6–6.2 (3.9; 2.1) 28–579 (286; 176) 66–1313 (671; 388) 226–5706 (3211; 2042)
Corn (#9) 11–80 0.1–3.1 (1.4; 1.4) 1–507 (191; 222) 3–1170 (439; 512) 25–6950 (2740; 3162)
2021 Winter wheat (#7) 26–85 0.4–4.6 (2.0; 1.7) 18–533 (190; 204) 41–1268 (440; 480) 168–5689 (1705; 2098)
Winter barley (#5) 26–30 0.5–3.2 (1.5; 1.1) 29–169 (83; 54) 69–412 (132; 199) 319–2030 (943; 661)
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2.3. Hypersense experiment campaign

In the context of the ESA CHIME mission preparations, Next Generation Airborne Visible Infrared Imaging Spectrometer (AVIRIS-NG) airborne hyperspectral images were acquired over the Irlbach site (48°49’N, 12°44’E), southeast Germany on 30th May 2021 in an area of intensive agriculture (Fig. 2). The AVIRIS-NG instrument provides similar spectral properties as CHIME will have once in orbit. The campaign was managed by the University of Zurich, bringing the aircraft with the instrument from the USA to the Dübendorf airbase near Zurich in Switzerland. From there, measurement flights were performed with AVIRIS-NG over more than 20 test sites in Europe, among those the Irlbach site.

Fig. 2.

Fig. 2

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Location of the ESA CHIME site Irlbach in Southeastern Germany (Hypersense experiment campaign): false-color infrared section of AVIRIS-NG imagery covering winter wheat sampling points (crosses) on 30th May 2021. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The AVIRIS-NG sensor recorded reflectance in the range from 377–2501 nm in 425 bands (FWHM ≈ 5.5 nm) at 5.3 m ground sampling distance (GSD) (Chapman et al., 2019). To comply with established retrieval models, spectrometric imagery likewise was resampled to 233 EnMAP spectral bands. Parallel to the overflight in situ measurements of Carea, AGBdry, AGBfresh, as well as LAI-sampling were carried out in the same manner as for MNI site (see chapter 2.2). Note that access was only possible to winter wheat fields at similar growth stages (stem elongation phase, no ears), limiting measured cross-field data variability. Nevertheless, the campaign generated a dataset to validate the GPR models independently of the model building process combining spectrometric imagery and 20 in situ data points (Table 2) of six fields.

Table 2.

Irlbach site ranges (mean; sd) for 20 winter wheat measurements collected on 30th May 2021 of LAI and total Carea, AGBdyy, and AGBfresh (no ears were present in observed growth stage).

BBCH [-] LAI [m2/m2] Carea [g/m2] AGBdry [g/m2] AGBfresh [g/m2]
32 2.5–4.8 (3.5; 0.7) 230–522 (334; 70) 543–1220 (796; 160) 1882–4020 (2968; 512)
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2.4. Radiative transfer modeling and synthetic training database

For the hybrid model building process, first, a PROSAIL-PRO training database was generated. PROSAIL (Jacquemoud et al., 2009) combines the Leaf Optical Properties Spectra model PROSPECT (Jacquemoud and Baret, 1990) and the turbid medium canopy reflectance model 4SAIL: Scattering by Arbitrarily Inclined Leaves (Verhoef and Bach, 2007). The leaf RTM version PROSPECT-D (Féret et al., 2017) simulates reflectance and transmittance of leaves in the optical domain as a function of leaf pigments, i.e. chlorophyll a and b (Cab), carotenoids (Cxc), and anthocyanins (Canth), a leaf mesophyll structure parameter (N), brown pigments (Cbroum) and equivalent water thickness (Cw) as well as leaf dry matter content (Cm). In the latest recalibrated version PROSPECT-PRO (Féret et al., 2021), Cm was separated into nitrogencontaining proteins (Cp) and carbon-based constituents (CBC), which include both non-structural carbohydrates (sugars and starch) as well as lignin, cellulose, and hemicellulose, each having a specific carbon content (Ma et al., 2018). Therefore, in order to retrieve carbon content from spectral observations, a conversion factor needs to be implemented. Based on measurements of Cmass during the MNI-campaigns and in accordance with similar findings of Ma et al. (2018), this factor is set to 2.31 (see Eq. (1), representing mean Cmass (43.3%) of leaves (43.8%), stalks (42.1%), and fruits (43.9%).

To upscale optical properties from leaf to canopy-level and to account for structural effects, the 4SAIL model was employed. 4SAIL simulates the bi-directional reflectance factor of a plant turbid medium (Jacquemoud et al., 2009) as a function of LAI, brightness of the underlying soil (psoil), average leaf inclination angle (ALA) or optionally, ellipsoidal leaf inclination distribution (LIDF), and hot spot size (hspot) for a given illumination and viewing geometry (observation zenith angle (OZA), relative azimuth angle (rAA) between sun and sensor, and the solar zenith angle (SZA)).

For the simulation and correct representation of diverse crop states, parameters were varied over a wide value range (Table 3). Ranges were set based on prior knowledge of the authors and previous studies (Wocher et al., 2020; Verrelst et al., 2021b; Berger et al., 2021c,a; Danner et al., 2021). The key parameters CBC and LAI were sampled according to a Gaussian distribution to realistically reflect measured patterns during the growth cycle. This sampling strategy is common practice in retrieval studies and leads to valid and generic models, as e.g. demonstrated by Berger et al. (2018b). For the acquisition angles, fixed values in nadir view at 40° SZA were assumed to prevent the occurrence of hot spot effects in simulated spectra. To allow the global applicability of the models, all other parameters were sampled uniformly. Since both LAI and CBC show an impact on reflectance over the entire optical domain, the full spectral range is considered for model training. In terms of practical applicability, data homogeneity, as well as reduction of computational effort, PROSAIL 1 nm reflectance output was resampled to EnMAP spectral resolution @233 bands. Due to a large number of parameter variations, the training database size was set to 3000 members. To further reduce inherent unrealistic combinations of input parameters within the training database (Yebra and Chuvieco, 2009), entries with Cp > CBC were considered implausible and were deleted, resulting in a model training database of 2868 members.

Table 3.

Parameter ranges for generating the PROSPECT-PRO + 4SAIL (PROSAIL-PRO) training database. Specified ranges are uniformly (range) or Gauss-distributed (mean; sd), and single values are fixed.

PROSPECT-PRO parameters Range Notation [Unit] 4SAIL parameters Range Notation [Unit]
N 1.0–3.0 [–] LAI 0.01–6.5 (4.0; 2.0) [m2/m2]
Cab 0–60 [μg/cm2] ALA 30–70 [deg]
Cw 0.001–0.06 [g/cm2] hspot 0.01–0.5 [–]
Cp 0.0–0.0025 [g/cm2] SZA 40 [deg]
CBC 0.0–0.03 (0.01; 0.02) [g/cm2] OZA 0 [deg]
Cbrown 0.0–0.8 [–] rAA 0 [deg]
Cxc Cab-dependenta [μg/cm2] psoil 0.0–1.0 [–]
Canth 0.0–2.0 [μg/cm2]
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a

According to Wocher et al.(2020).

Thus, to derive canopy carbon and biomass from imaging spectroscopy data the corresponding PROSPECT-PRO parameters were upscaled according to Eqs. (1), (2), and (3).

Carea =CBC⋅LAI⋅10,0002.31[g/m2] (1)
AGBdry=(Cp+CBC)⋅LAI⋅10,000[g/m2] (2)
AGBfresh =(Cp+CBC+Cw)⋅LAI⋅10,000[g/m2] (3)

As a last step, simulated Carea, AGBdry, and AGBfresh distributions were compared and verified against in situ leaf + stalk sums to ensure broad coverage of simulated against measured value ranges. PROSAIL-PRO training database generation was performed using the ‘Create Look-up-Table’ tool provided within the open source software EnMAP-Box 3 (Van der Linden et al., 2015) ‘Agricultural Applications’ (Hank et al., 2021).

2.5. Spectral and sampling optimization

To boost processing speed, PCA was applied. PCA is a useful technique to reduce the dimensionality of datasets which in the case of hyperspectral reflectance data manifests in radiometric collinearity issues (Kumar, 1975; Verrelst et al., 2019) between multiple close adjacent spectral bands. ith PCA, measured and simulated reflectance spectra are converted into a lower-dimensional feature space, maximizing algorithmic interpretability and minimizing information loss (Jolliffe and Cadima, 2016; Verrelst et al., 2016; Rivera-Caicedo et al., 2017). In accordance with previous studies that used PCA to retrieve vegetation traits from hyperspectral data (De Grave et al., 2020; Verrelst et al., 2021a; Morata et al., 2021; Pascual-Venteo et al., 2022), the number of principal components (PCs) was set to #20. Pascual-Venteoet al. (2022) demonstrated that the first components may provide significant relevance, but the most important features are located in higher components, depending on the targeted variable. Hence, this number is considered as an acceptable trade-off between a sufficient representation of full optical range spectral variability and calculation effort during model training (Morata et al., 2021). Prior internal tests also showed that the inclusion of more than 20 PCs did not contribute to further error reduction.

Training databases created by random sampling of model input parameters result in redundancies of both the contained spectral representations and within the parameter set itself. Furthermore, large training databases drastically decrease the processing speed of the training process and inherently imply an aggravation of parameter ill-posedness, i.e. the probability of multiple different parameter sets defining similar spectral responses. To counteract these issues, AL techniques (Verrelst et al., 2020; Berger et al., 2021c) were deployed. Specifically, two algorithms were tested. First, the Euclidean distance-based diversity (EBD) strategy proved suitable both in terms of processing speed and accuracy (Douak et al., 2013), whereas sampling candidates are selected based on the squared Euclidean distance to a sample already contained in the training set. Second, the variance-based pool of regressors (PAL) strategy was applied. PAL predicts the target value by means of a respective ML regression algorithm based on multiple training subsets, computes the variance of the predictions by the resulting regressors, and finally adds the samples with the greater disagreements. Although PAL proved to require more computing time then other AL methods, it often performed superior in terms of retrieval accuracy (Douak et al., 2013; Verrelst et al., 2016). Both EBD and PAL were initialized based on 2% (N = 58) randomly selected members of the training database and with a maximum selection of 300 spectra as a stopping criterion. These thresholds were chosen according to internal tests, experience of the authors and recommendations of prior studies (Verrelst et al., 2020, 2021b; Berger et al., 2021c). With each sample added, overall accuracy against in situ data was evaluated by the root mean square error (RMSE). By this crosscheck, only samples that contribute to an improved RMSE are included in the reduced database. The iteration continued until all samples of the training database were evaluated.

Adequate and accurate mapping of Carea, AGBdry, and AGBfresh using full scenes of future satellite imagery is the primary focus of this study. Hence, subsequent to the initial internal model performance evaluation, 24 bare soil spectra with defined respective variable contents of zero were selected from the AVIRIS-NG image and were added to the training database. The number of 24 spectra was chosen in accordance with the study by Verrelst et al. (2021b). In this way, mapping uncertainties due to unknown soil signatures can be reduced by augmenting the models’ ability to distinguish between bare soil and sparsely vegetated pixels.

2.6. Machine learning regression algorithm

The regression algorithm used within this study was based on GPR as formulated by Rasmussen and Williams (2006). Along with proven solid performances, as demonstrated in various previous studies (Verrelst et al., 2011, 2015; Camps-Valls et al., 2019; Pipia et al., 2021; Berger et al., 2021b), GPR provides analytical estimates of predictive uncertainties together with variable estimates. Due to their probabilistic handling of regression tasks in a Bayesian framework, the provision of relative uncertainties as prediction intervals renders GPR particularly attractive for solving highly non-linear regression problems within remote sensing data analysis (Verrelst et al., 2019). Analyzing these prediction intervals enables useful insights into uncertainties of model parameterization and input data. Moreover, information about uncertainties can be used to assess the transferability of the models to other locations and times (Verrelst et al., 2013a). A downside of GPR is its limited ability to process large samples of several thousand within reasonable running time due to its time complexity of 𝒪(n3) by inversion of a n×n matrix (Rasmussen and Williams, 2006). Although previous studies suggested training datasets of only 1000 samples (Lázaro-Gredilla et al., 2013; Berger et al., 2021b), in preliminary tests, this number turned out to be too small to cover the possible spectral variability produced by the here considered PROSAIL-PRO parameter range definitions. Since one training database as a single generally valid baseline for all three target variables (and potentially others) is aimed, the decision was made to increase the size of the training database to 3000. This size still led to tolerable processing times of ∼12 min on an Intel i7-107002.9 GHz when using a standard configuration of a squared exponential covariance (kernel) function Gaussian process. The implementation of GPR models, as well as PCA dimensionality reduction, AL strategies, and mapping, were provided within the Automated Radiative Transfer Models Operator (ARTMO) machine learning regression algorithms (MLRAs) toolbox (Verrelst et al., 2012).

3. Results

3.1. AL-tuning and validation over MNI site

First of all, the selected PROSAIL-PRO spectra were compressed into 20 PCs to efficiently reduce the processing speed for GPR models. In the second step, AL was applied to optimize the training datasets in the sampling domain for the GPR algorithm and model-building process. The predictive power of the models is assessed using absolute RMSE and normalized RMSE (nRMSE [%] = RMSE/measured value range ×100) for model intercomparison, as well as the coefficient of determination (R2) to evaluate goodness-of-fit. Fig. 3 illustrates the RMSE convergence results of PAL and EBD methods regarding retrieval of MNI in situ data during GPR training. For all three variables of interest, PAL performed better than EBD with highest discrepancy for AGBfresh, where PAL reached a RMSE of 1153g/m2 compared to 1236 g/m2 with EBD (Fig. 3c) after iterative selection of 300 samples. For Carea (Fig. 3a) and AGBdry (Fig. 3b), PAL reduced RMSE from initially 190 and 423 g/m2 to 85 (EBD: 88) and 190 g/m2 (EBD: 198), respectively. Although the PAL sequence needed ∼10 times longer than EBD to select the most suitable spectral samples from the training database, it was chosen as the optimal AL method due to its consistent best performance. Overall, AL reduced the size of the training database from 2868 samples by 88% to 358 samples.

Fig. 3.

Fig. 3

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RMSE convergence for Carea (a) AGBdry (b) and AGByrelh (c) applying EBD and PAL methods on a full PROSAIL-PRO training database (i.e., 2868 samples) against MNI in situ data.

The performances of the models against MNI in situ data after reduction of the training database using PAL are shown in Fig. 4. For Carea and AGBdry good results were obtained (R2 = 0.80; nRMSE = 13% for both; Fig. 4a and b). For AGBfresh (Fig. 4c) retrieval performance is lower but still acceptable (R2 = 0.71; nRMSE = 16%). Generally, the GPR models succeeded in estimating all three variables, but with a slight tendency to underestimate higher contents. Particularly for AGBfresh, this underestimation may be connected to saturation effects of high specific concentrations in the respective measured spectral signals. Regarding GPR uncertainty intervals, for most data points, predicted value ranges are relatively stable with a coefficient of variation (CV) below 35%. Note that naturally, high CV values mostly correspond to low absolute values. However, some points with high relative uncertainty in the higher value range may indicate that in situ measured quantities poorly correspond to the spectral acquisition on that particular day and spot. Despite these predictive uncertainties, GPR is able to successfully incorporate these data points into the regression scheme. Besides, the models’ performances were clearly affected by the abundant availability of in situ data covering four full seasons (N = 66). The attempt of using only two years (2017 and 2018; N= 32) for training and keeping the years 2020 and 2021 (N = 34) for validation, yielded lower performing GPR models for Carea (R2= 0.71) and AGBdry (R2 = 0.65), and even failed for AGBfresh (R2=0.01).

Fig. 4.

Fig. 4

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GPR validation results against MNI in situ data for Carea (a), AGBdry (b), and AGBfresh (c) using GPR retrieval models built on optimized PCA and PAL training databases. Relative uncertainty is expressed as coefficient of variation (CV), i.e. standard deviation/mean × 100 [%]. CV frequency distributions are indicated as colored bars. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.2. Optimizing GPR-Carea and GPR-biomass models for mapping activities

The GPR retrieval models were prepared for mapping by including 24 bare soil spectra in each PAL-reduced training database. The GPR algorithms were then retrained based on the optimized training datasets composed of 382 samples (random 58 initial 2% + 300 PAL-selected + 24 bare soils) for each of the three variables. Results are shown in Fig. 5. In spite of increased nRMSE and point spread for Carea (R2 = 0.76; nRMSE = 17%; Fig. 5a) and AGBdry (R2 = 0.72; nRMSE = 18%; Fig. 5b), underestimation of high contents does no longer occur. Additionally, mean relative uncertainties decreased by 40% for Carea and 38% for AGBdry, being indicative of the models’ improved ability to differentiate between soil spectral influence, the crop signal, and particularly the signal of crop senescence. However, this does not apply for AGBfresh (Fig. 5c), where prediction performance with added bare soil spectra changed only marginally and the tendency to underestimation is not resolved. Here, mean relative uncertainty decreased by 12%.

Fig. 5.

Fig. 5

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Performance of final GPR-Carea (a), GPR-AGBdry, (b), and GPR-AGBfreah (c) models against MNI in situ data and predictive relative uncertainties. CV frequency distributions are indicated as colored bars. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.3. Validation over Irlbach site

Subsequent to retraining with added bare soil spectra, the GPR-Carea, GPR-AGBdry, and GPR-AGByfresh models were applied to AVIRISNG imagery (spectrally resampled to EnMAP). The resulting maps show that all three variables were derived with appropriate plausibility (Fig. 6a, b, c (left)). Due to the small GSD of 5.3 m, which was maintained from the airborne campaign and was not converted to EnMAP 30 m spatial resolution, the results adequately reflect within- field heterogeneities attributable to expositional and/or soil related site factors as well as to row sowing structure of the fields. Furthermore, fine cross-field variations of the mapped contents can be identified. As it can also be recognized in the probability density histograms, high contents indicate lush green cereal crops (mostly winter wheat and winter barley), as typically present in this region at the end of May. Also, many fields are still barely vegetated (corn and sugar beet). Yet, the retrieval models succeeded in discerning bare soil from recently sprouted crops, notable as fine lines of low particular contents in these fields.

Fig. 6.

Fig. 6

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Mapping results and relative uncertainties (CV) for Carea (a) AGBdry (b), and AGBfresh (c) with spatial probability density distributions applying established GPR-Carea and GPR-Biomass models on EnMAP resampled AVIRIS-NG imagery of Irlbach site from 30th May 2021.

Relative uncertainties are presented in Fig. 6a, b, c (right). Uncertainties for green fields were consistently low (< 40%, yellow colored), and low uncertainties of unambiguously identified bare soil pixels illustrate the importance of adding bare soil spectra to the training database. High degrees of relative uncertainty (> 50%, red to > 100%, blue colored) mostly occurred in scarcely vegetated areas where, nonetheless, absolute contents were correctly recognized as low. However, high uncertainties prevailed in areas which spectrally were not considered by the training database, such as anthropogenic structures and forests.

Comparison of pixel-based estimates and in situ measured quantities (Fig. 7) shows that regarding the mean estimates, all three variables tended to be overestimated with nRMSEs for Carea = 29%, AGBdry = 25%, and AGBfresh = 36%. However, considering that biomass measurements of winter wheat at similar growth stages feature such large variations themselves, these variations are well reflected by the range of the estimates. Only for AGBdry maximum estimated values appear limited resulting in underestimation of high in situ measured contents (Fig. 7b). ith respect to absolute RMSEs, these were even lower by 20% for Carea (85 g/m2), 36% for AGBdry (170 g/m2), and 35% for AGBjfresh (770 g/m2) than compared to the final training results (Fig. 5).

Fig. 7.

Fig. 7

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Validation of the carbon and biomass maps obtained for the Irlbach area against winter wheat in situ data for Carea (a), AGBdry (b), and AGBfresh (c). Single measurements are displayed as small crosses, measurement and estimation means and standard deviations are shown as large crosses.

4. Discussion

In this study, we adapted a hybrid workflow for the retrieval of plant carbon content as well as dry and wet biomass from simulated EnMAP data. In the following, the key findings are discussed, involving: (1) active learning and spectral dimensionality reduction, (2) carbon and biomass mapping, and (3) opportunities and challenges for the EnMAP mission.

4.1. Active learning and spectral dimensionality reduction

A key result of our study is that all three retrieval models could be better optimized by applying the AL method PAL than EBD. This is contrasting to previous studies identifying the EBD method as the most accurate and fastest (e.g., Upreti et al., 2019; Verrelst et al., 2020), see also review by Berger et al. (2021c). Comparing both methods, we showed that EBD outperformed PAL with respect to computation time for the learning process but not in terms of optimization accuracy as was also demonstrated by Douak et al. (2013). This aspect should be considered when using kernel-based methods, such as GPR, for establishing operational retrieval models. Nonetheless, both approaches provided significant improvements over using full data sets and consequently, we can recommend the implementation of both, regressor uncertainty (e.g. PAL) or diversity AL methods (e.g. EBD), into hybrid workflows. The consideration of AL in the processing chain leads to small but representative training data sets (here 88% training database size reduction; 358 members instead of 2868) and thus to efficient and lightweight models to estimate the variables of interest. It must be noted that involving in situ data for tuning retrieval models may bring the drawback of decreasing the models’ transferability. However, obtained results revealed that our AL optimized models performed relatively well when transferring them to another location and sensor, as done here from handheld spectrometer measurements at the MNI site (data used for AL tuning) to EnMAP-resampled airborne AVIRIS-NG imagery at the Irlbach site (independent validation). Similar findings are reported by Tagliabue et al. (2022), who provided fairly robust and exportable AL-tuned models for multiple leaf and canopy level traits. Still, a more versatile validation in situ dataset covering diverse crop types sampled during different growth stages at different geographical sites would be required to ensure the generation of overall robust retrieval models. This so far has been limited by the monotemporal character of airborne campaigns and is likely to be resolved now as hyperspectral satellites will provide regular observations.

Multiple studies focused on hybrid retrieval algorithms in combination with PCA for the retrieval of various vegetation variables (e.g., Berger et al., 2021b; Candiani et al., 2022; Danner et al., 2021; De Grave et al., 2020; Tagliabue et al., 2022; Verrelst et al., 2020; Rivera-Caicedo et al., 2017; Pascual-Venteo et al., 2022). The feature transformation approach PCA provides the attractive property of converting full range spectral information from the imaging spectrometer into a defined number of unique components while disregarding the target variables. This leads to a richer dataset for the training of machine learning algorithms compared to selecting a few bands, based on feature extraction approaches (Rivera-Caicedo et al., 2017; Berger et al., 2020). However, the question of the optimal number of components to resolve a prediction problem remained to be clarified. In a recent study, this number was investigated, leading to the result that 18 components covered 99.95% of the variance (Pascual-Venteoet al., 2022). This confirmed prior studies demonstrating that 20 PCs represent an optimal compromise to ensure high retrieval performance for targeting diverse variables and at the same time avoiding the risks of exploring noisy data (Danner et al., 2021; Verrelst et al., 2021b; Morata et al., 2021).

In this study, we successfully applied GPR as a core retrieval algorithm, which shows potential to be implemented into the EnMAP-Box software to solve agriculturally relevant retrieval problems. GPR has provided outstanding performances in multiple studies (Verrelst et al., 2013b; Camps-Valls et al., 2016, 2018, 2019; Estévez et al., 2021, 2022) and also provides the particular capability of providing uncertainty estimates along with the estimations (Verrelst et al., 2013a). Nonetheless, other machine learning regression algorithms could be tested in a future setup, such as random forest regression or powerful designs of artificial neural networks, provided that uncertainty measures can be made available along with the model results.

4.2. Carbon and biomass mapping

Apart from a physical evaluation of our models, we also investigated the spatial portability of our approach through mapping of Carea, AGBdry, and AGBfresh over an agricultural area using airborne hyperspectral imagery.

Provided relative uncertainties add information about GPR model internal stability and confidence, as demonstrated in Fig. 6a, b, c (right). The consistent low uncertainties for green fields indicate a high degree of model reliability for cultivated areas during phases of active growth at canopy closure. Also, the obtained plausible low contents and low uncertainties for bare soil pixels that were returned by the models illustrate the importance of adding bare soil spectra to the training database. Note that adding bare soil spectra directly from the considered imagery may reduce transferability to other observations. However, preliminary mapping tests without consideration of bare soil spectra led to overestimated quantities with high uncertainties at bare soil locations. Anthropogenically influenced and forested areas provided lower confidence, i.e. higher uncertainty estimates, since these areas were not included by the training database, which was generated using PROSAIL-PRO assuming uniform turbid medium plant canopies (Berger et al., 2018a).

Given the high confidence of these maps, in principle, they can be further used within prognostic models for the simulation of terrestrial carbon fluxes. These models may strongly be supported by assimilating observational information, such as plant carbon content, resulting in reduced uncertainty of carbon balance simulations. Ingesting the spatial and temporal dynamics, which are contained in Earth Observation data into prognostic models, can provide a better understanding of the terrestrial carbon sinks. Results of these models then may contribute to efficient management strategies, such as in agriculture, to mitigate climate change and related severe effects on the environment (Kaminski et al., 2012). Future operational retrieval schemes can build upon the proposed workflow to monitor plant carbon content relevant to multiple topics in cropping systems. These include for instance improved knowledge about the potential of carbon farming, i.e. soil carbon sequestration methods as a negative emission strategy (Paustian et al., 2019; Jansson et al., 2021).

Dry biomass, also known as lignocellulosic biomass, further provides opportunities for the production of renewable liquid fuels (Welker et al., 2015). Hereby, thermochemical conversion can be used as an efficient method to convert biomass into biofuels (Zhang and Zhang, 2019). Since lignocellulosic material for biofuel and biochemical production may reduce CO2 emissions (Stigka et al., 2014), the spatiotemporal mapping over vast agricultural regions supports activities toward climate change mitigation.

4.3. Opportunities and challenges for the EnMAP mission

This work was carried out within the activities of the hyperspectral EnMAP mission preparation for agricultural applications (Hank et al., 2019; Danner et al., 2021). The German hyperspectral mission has been prepared for many years until the final launch on 1st April 2022. From experience with prior hyperspectral sensors, such as Hyperion installed on NASA’s EarthObserver-1 satellite, the signal-to-noise ratio (SNR) is of overriding importance for the usability of hyperspectral data. The development time of the EnMAP instrument, therefore, was repeatedly extended to ensure that EnMAP will be able to provide high-quality measurements from space, for instance, due to excellent SNR. In addition, for many environmental scientific and commercial applications, repeated observations of the same point on the Earth’s surface are crucial, requiring a mobile platform and stable geometry, which is also provided by the mission. Since the AVIRIS-NG imagery was spectrally resampled to EnMAP, we essentially present the first canopy carbon content and aboveground biomass maps as they can also be realized with the hyperspectral precursor. EnMAP also provides great opportunities due to its similarity with the PRISMA sensor. The joint observation capabilities of both instruments can increase the density of time series, which are dearly needed for agriculturally relevant products (Salinero-Delgado et al., 2021). The combined use of PRISMA and EnMAP data will be particularly advantageous for agricultural studies preparing for future operational missions, such as CHIME (Verrelst et al., 2021a,b; Candiani et al., 2022), which may provide further validation of the proposed workflow.

5. Conclusions

Hybrid modeling approaches have become a cornerstone for solving inference problems from Earth observation data due to their synergistic use of physical, expert and domain knowledge of mechanistic models, combined with the high flexibility, accuracy and consistency of machine learning algorithms. In our study, we explored such a hybrid design for deriving carbon and biomass content of croplands, succeeding in high transferability of the established models. For this, we trained GPR algorithms over simulated datasets generated by the PROSAIL-PRO model, employing PCA and active learning heuristics tuned on in situ data of the German MNI test site. The established models were transferred to an EnMAP resampled AVIRIS-NG scene of a similar agricultural area, achieving high mapping accuracy but moderate validation performance over a limited field data set with nRMSE ranging from 25% to 36%. These results point toward the need for further model adaptations and optimizations exploring field data sets of a larger variety of crop types and growth stages. Monitoring carbon temporarily stored in vegetation by means of hyperspectral Earth Observation data will support carbon farming, aiming to enhance the removal of CO2 from the atmosphere through conversion of plant material and soil organic matter to soil organic carbon.

We conclude that the suggested workflow presents an appealing path toward reliable mapping of plant carbon and cropland biomass by spaceborne imaging spectroscopy missions. We also anticipate that EnMAP data, along with complementary hyperspectral missions, will constitute a valuable and crucial source for the preparation of future operational missions providing high-priority crop products for multiple research fields and applications.

Acknowledgments

K.B. was mainly funded within the EnMAP scientific preparation program under the DLR Space Administration with resources from the German Federal Ministry of Economic Affairs and Climate Action, grant number 50EE1923. J.V. and K.B. were funded by the European Research Council (ERC) under the ERC-2017-STG SENTIFLEX project (grant agreement 755617) and Ramón y Cajal Contract (Spanish Ministry of Science, Innovation and Universities). This publication is also the result of the project implementation: “Scientific support of climate change adaptation in agriculture and mitigation of soil degradation” (ITMS2014+ 313011W580) supported by the Integrated Infrastructure Operational Programme funded by the ERDF. Further, the research was supported by the Action CA17134 SENSECO (Optical synergies for spatiotemporal sensing of scalable ecophysiological traits) funded by COST (European Cooperation in Science and Technology, www.cost.eu).

Footnotes

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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