Integration of radiative transfer–machine learning for physiological mapping of leaf chlorophyll and anthocyanin in cotton

1 Introduction

Accurate evaluation of the biophysical and biochemical properties of crops is crucial for comprehensive analysis of plant health and optimization of management strategies to maximize productivity. Leaf Chlorophyll Content (LCC) and Anthocyanin (Anth) are vital indicators of photosynthetic efficiency, adaptation to environmental stress, and plant nutritional status (Bista et al., 2024; 2025; Gitelson et al., 2001; Saha et al., 2025). Traditionally, assessing these biochemical indicators has relied on destructive sampling followed by sophisticated laboratory analyses (Kganyago et al., 2021; Thenkabail et al., 2018). While these methods yield highly accurate results, they can be quite labor-intensive and time-consuming, limiting their application in precision crop management. In contrast, advancements in remote sensing technologies, including hyperspectral imaging, have introduced innovative non-invasive options (Bheemanahalli et al., 2023; Cheng et al., 2025; Singh et al., 2025). These advanced techniques facilitate the comprehensive spectral data collection across a wide range of wavelengths, enabling the assessment of crop traits over extensive regions (Singh et al., 2023; Verma et al., 2024). This capability enables an efficient and appropriate appraisal of crop health and overall management practices (Han et al., 2022; Singh et al., 2020).

Uncrewed aerial systems (UASs) are transforming agricultural monitoring by incorporating hyperspectral and multispectral sensors (Singh et al., 2023; Shrestha et al., 2023). These sensors gather data with remarkable spatial resolution and across a wide spectral range, making them more effective than traditional ground-based measurements and broader satellite observations (Aasen et al., 2018; Bendig et al., 2014). This functionality enables a deeper understanding of crop health and management conditions. However, to convert the reflectance data into practical insights into crop traits, it is crucial to utilize advanced biophysical models and inversion techniques. Radiative transfer models (RTMs) are essential to this process. The PROSPECT model family has been widely used to simulate the optical properties of leaves, which are influenced by both biochemical components, such as chlorophyll content, and structural factors, such as leaf thickness (Féret et al., 2017; Jacquemoud and Baret, 1990). These models help bridge the gap between observed reflectance data and the intrinsic physiological traits of the vegetation. By employing RTMs, forward simulations predict how variations in leaf features affect the reflectance signature, while inverse retrieval methods determine these features from measured reflectance (Schiefer et al., 2021; Verrelst et al., 2019a). This dual functionality renders RTMs vital for improving the accuracy of crop monitoring and assessment in precision agriculture (Shiklomanov et al., 2016). Despite significant progress in RTM-based and hybrid RTM–ML approaches, several limitations remain. RTM inversion is inherently ill-posed, often resulting in unstable solutions due to spectral redundancy and sensitivity to measurement noise (Locherer et al., 2015; de Sa et al., 2021). While machine learning methods have been increasingly integrated to address these challenges, many existing studies focus on ideal or low-noise conditions and do not systematically evaluate model robustness under varying noise levels (Verrelst et al., 2019a; Liang et al., 2021). Additionally, limited attention has been given to integrating UAS-based multispectral imagery with leaf-level hyperspectral data within a unified RTM–ML framework. These gaps restrict the operational applicability and generalizability of current approaches for reliable crop trait retrieval (Rivera et al., 2014).

The RTM inversion process, despite its strong physical basis, is often ill-posed due to spectral redundancy and sensitivity to measurement noise (Verrelst et al., 2015). As a result, retrieving reliable vegetation parameters from reflectance data remains challenging. To mitigate these limitations, machine learning algorithms have been increasingly integrated with RTMs, enabling more flexible and data-driven parameter estimation (Verrelst et al., 2019a; Liang et al., 2021). Platforms such as the Automated Radiative transfer Models Operator (ARTMO) facilitate this integration by streamlining model simulation, calibration, and inversion using advanced regression techniques (Rivera et al., 2014). Existing studies have demonstrated the potential of RTM-based and hybrid RTM–ML approaches for retrieving vegetation biochemical properties. For instance, RTM inversion methods provide physically interpretable estimates but often suffer from instability and non-uniqueness due to spectral redundancy and noise sensitivity (Verrelst et al., 2015). In contrast, machine learning approaches offer improved predictive performance and computational efficiency; however, they are often data-dependent and may lack generalizability across sensors, crop types, and environmental conditions (Liang et al., 2021). Hybrid RTM–ML frameworks attempt to combine the strengths of both approaches, yet many studies rely on simulated or low-noise datasets and do not adequately assess model robustness under realistic noise conditions. Furthermore, few studies have explored integrating UAS-based multispectral data with leaf-level hyperspectral measurements within such frameworks. These limitations highlight the need for a more robust and transferable approach for reliable crop trait estimation. Therefore, the objectives of this study were to 1) develop an integrated framework that combines UAS-based multispectral imagery, leaf-level hyperspectral data, and PROSPECT-D simulations to estimate LCC and Anth in cotton, 2) evaluate the performance of multiple machine learning regression algorithms for RTM inversion, 3) assess the robustness and reliability of retrieval models under varying noise conditions, and 4) generate spatial maps of LCC and Anth to support precision crop management.

2 Materials and methods

2.1 Study area

The field experiment was carried out at R. R. Foil Plant Science Research Center, Mississippi State University, Mississippi, U.S. (33.47° N, 88.78° W) from May to October 2024. A total of 320 cotton genotypes, including 318 diverse germplasm accessions and two commercial cultivars were used in the study. These diverse genotypes were selected to maximize variability in canopy structure and leaf biophysical properties, which is essential for robust calibration and evaluation of radiative transfer models across a wide range of canopy structural and biophysical conditions. Seeds of germplasm accession were obtained from the Germplasm Resources Information Network (GRIN) database (https://www.grin-global.org/). The experiment was laid out in an augmented block design with 12 blocks. Each block consisted of 30 longitudinal, parallel rows, each 1.52 m long, with 0.92 m spacing between rows. Blocks were separated by 0.61 m. Each row represented the experimental unit. Accordingly, 30 rows per block comprises 28 accessions and 2 checks, except for the 11th block, which comprises only 10 accessions and checks. Plant-to-plant spacing of 12.7 cm was maintained in all rows. The augmented design was used to efficiently accommodate multiple genotypes within the field layout and capture their variability. As the study focused on modeling and parameter estimation, no formal statistical comparisons among genotypes were conducted based on the design. The genotypes were grown under rainfed conditions without supplemental irrigation. Adequate fertility was maintained by applying nitrogen (N), phosphorus (P), and potash (K), at 120:50:80 kg ha⁻¹, respectively. Weeds were controlled manually throughout the growing period. The field was evaluated daily to record phenological progression. At the reproductive stage, manual and aerial imagery were collected.

2.2 Data collection

Ground-truth data were collected 64 days after sowing, when more than 80% of the genotypes reached the flowering stage. Leaf pigment such as chlorophyll and anthocyanin content, were recorded using two MPM-100 (Opti-Sciences, Hudson, NH, United States) simultaneously. Three uniform plants were selected from each row, and measurements were taken by clamping the leaf sensor head onto the first fully expanded leaf from the apex of the plant during morning hours (08:00–12:00). The MPM-100 estimates chlorophyll content using leaf transmittance in the far-red and near-infrared regions, whereas anthocyanin content is derived from fluorescence ratio measurements. The leaves were harvested after ground-truth measurements, collected in insulated polystyrene boxes containing ice packs, and transported to the laboratory for spectral scanning. Leaf spectra from all genotypes were collected with a PSR + spectrometer (Spectral Evolution, United States) over the 350–2,500 nm range at 1 nm resolution. Leaves were scanned using the leaf clip accessory (Spectral Evolution, United States) attached to the PSR + spectrometer. The leaves are clipped between the jaws of the leaf clip to minimize external light interference. Instrument calibration was maintained by acquiring white reference measurements at 10-min intervals using a calibrated white reference panel (Spectralon®, Labsphere Inc., United States), ensuring consistency and correcting any temporal drift in sensor response. Ten scans per measurement were averaged to produce the final spectrum. In total, 1920 scans were obtained from 960 leaf samples (320 genotypes x 3 replicates), with two replicate scans per sample (960 × 2 scans). Ground-based pigment measurements and spectral scanning were conducted during the same field campaign to ensure temporal consistency between in situ observations and aerial imagery. A drone-mounted five-band multispectral camera (Rededge MX, Micasense Inc., Seattle, United States) was flown the day after ground-truth measurements at an altitude of 61 m (200 ft) above ground level, yielding a spatial resolution of approximately 4 cm. The data were collected to match the manual data collection within ±2 h of local solar noon. Although UAS data were collected 1 day after ground measurements, the impact of temporal mismatch was considered minimal due to the relatively stable pigment state of cotton leaves at the flowering stage. No significant rainfall or stress occurred between acquisitions, and environmental conditions remained consistent. Previous studies have shown that pigment traits exhibit limited short-term variability under stable conditions, supporting the assumption of temporal consistency. The total rainfall during the experimental period was 132 mm, whereas the average minimum and maximum temperatures were 32.32 °C and 20.33 °C, respectively. The weather data was obtained from the Delta Agricultural Weather Center (https://deltaweather.extension.msstate.edu/).

2.3 Data analysis

A combined approach integrating in situ measurements and remote sensing techniques was used to assess cotton pigment traits, including LCC and Anth levels. This involved integrating leaf measurements, radiometric reflectance data, and machine-learning inversion methods. The collected data not only provided reference observations for validation but also served as input for radiative transfer modeling. The parameter ranges used for the PROSPECT-D simulations are summarized in Table 1. This model simulates the optical properties of leaves by accounting for pigment concentrations, water content, and internal leaf structure, thereby generating reflectance and transmittance spectra. In this study, the inversion framework focused on retrieving chlorophyll and anthocyanin traits corresponding to the measured LCC and Anth indices obtained from the MPM-100 sensor. Within the PROSPECT-D model, these traits correspond to the pigment concentration parameters LCC (Leaf Chlorophyll Content) and Anth (anthocyanin content). Other PROSPECT-D parameters, including the leaf structure parameter (N), brown pigments (Cbrown), equivalent water thickness (Cw), and dry matter content (Cm), were constrained using literature-based ranges commonly reported for crop leaves to maintain physically realistic simulations (Jacquemoud and Baret, 1990; Féret et al., 2017; Verrelst et al., 2019a).

TABLE 1. PROSPECT-D input parameter ranges used for leaf optical property simulations.

LCC and Anth correspond to pigment concentration parameters used in the PROSPECT-D simulations and represent model equivalents of the measured LCC and Anth pigment indices obtained from the MPM-100 sensor, whose descriptive statistics are summarized in Table 2.

Forward simulations were conducted using the Automated Radiative Transfer Models Operator (ARTMO) platform, which allowed for the creation of synthetic spectra across a diverse range of pigment and water content levels. These generated spectra served as the foundation for a detailed training dataset used in model inversion. The RTM–ML inversion workflow consists of two main steps: forward simulation and inverse modeling. In the forward step, the PROSPECT-D model is used to generate a large set of synthetic spectra by varying key leaf biochemical and structural parameters within predefined ranges. This synthetic dataset represents a wide range of possible spectral responses associated with different pigment concentrations. In the inverse step, machine-learning regression models are trained on simulated spectra as inputs and the corresponding model parameters as outputs. Once trained, these models are applied to observed hyperspectral and UAS multispectral data to estimate leaf pigment traits. This approach allows the model to learn complex relationships between spectral reflectance and biochemical properties, thereby enabling robust retrieval of crop traits from remote sensing data. Leaf-level reflectance data were captured with a PSR + spectroradiometer in the laboratory. The spectral data were then resampled to match the resolutions of both PROSPECT-D simulations and UAS multispectral imagery, ensuring consistency and comparability among modeled, field, and drone-acquired datasets. Inverse modeling was performed using Machine Learning Regression Algorithms (MLRA) within ARTMO to identify statistical relationships between reflectance spectra and measured traits. Six machine learning regression algorithms available within the ARTMO MLRA toolbox were selected to evaluate their performance for pigment trait retrieval. These algorithms represent different regression paradigms commonly used in radiative transfer model inversion studies, including distance-based learning (KNN), linear multivariate regression (PLSR), kernel-based methods (Gaussian Kernel Regression), tree-based approaches (Regression Trees and Boosting Trees), and signal-to-noise–based methods (Kernel Signal-to-Noise Ratio). The purpose of selecting these algorithms was to compare diverse modeling strategies for retrieving biochemical traits from simulated spectral data. Kernel Ridge Regression (KRR) was not included in this analysis because the study focused on a representative subset of algorithms implemented within the MLRA workflow for comparative evaluation. The field spectroradiometer data and UAS reflectance measurements acted as predictor variables, while the leaf pigments and water content were treated as response variables. The inversion models were optimized by minimizing cost functions, selecting the best-performing models based on statistical criteria such as the correlation coefficient (r), root mean square error (RMSE), and Normalized root mean square error (NRMSE). NRMSE was calculated by normalizing RMSE to the mean of the observed values. Because normalization uses the dataset mean, differences in NRMSE among algorithms may appear relatively small even when correlation coefficients differ substantially. Hyperparameter tuning for each machine learning algorithm was performed within the ARTMO framework using iterative optimization to identify parameter combinations that minimize RMSE. Model performance was evaluated using cross-validation techniques to ensure generalizability. Overfitting was controlled through model complexity constraints (e.g., tree depth, kernel regularization) and by incorporating training noise to improve robustness. Spectral and parameter noise were introduced during model calibration within the ARTMO framework to simulate measurement uncertainties and improve model generalization. The reported noise values correspond to the optimal noise configurations identified for each regression algorithm during model optimization rather than fixed experimental conditions. The optimized MLRA models were subsequently used to analyze UAS imagery to spatially retrieve crop traits. This method produced high-resolution maps of chlorophyll and anthocyanin, offering insights into crop physiological status at the field scale and enhancing precision agriculture practices (Figure 1).

In addition to trait retrieval, the spatial representation of pigment distributions derived from UAS imagery provides an opportunity to examine within-field variability. Although the primary focus of this study was on genotype-level trait estimation, the generated high-resolution maps highlight the potential of this approach to capture fine-scale spatial heterogeneity in crop physiological status. Such information can support precision agriculture applications and improve the interpretation of genotype responses under varying field conditions.

3 Results

3.1 Spectral simulation

Spectral simulations were performed using forward modeling techniques within the ARTMO framework. Figure 2 illustrates the simulated directional reflectance spectra of cotton leaves under various pigment conditions. Changes significantly influenced the spectral variability noted in the 400–850 nm range in chlorophyll and anthocyanin concentrations. An increase in chlorophyll led to a considerable reduction in reflectance within the visible spectrum, particularly in the blue (450–500 nm) and red (650–680 nm) absorption ranges, while boosting reflectance in the near-infrared (700–850 nm) region due to enhanced internal scattering in the leaf mesophyll. The presence of anthocyanin also affected the spectral characteristics, mainly in the green (around 550 nm) and red-edge (680–720 nm) regions, where higher levels led to noticeable spectral alterations associated with their roles in photoprotection and excess light absorption. The interaction between chlorophyll and anthocyanin produced a diverse range of spectral signatures, as depicted in the color-coded matrix, with different pigment combinations accounting for much of the variability observed in the reflectance curves. Notably, leaves with higher anthocyanin content showed reduced reflectance in the visible spectrum, even with moderate chlorophyll levels, whereas leaves with significant chlorophyll concentrations consistently exhibited strong absorption features regardless of anthocyanin levels. These results highlight the distinct contributions of both pigments to spectral variability, with chlorophyll dominating absorption in the blue and red regions, while anthocyanin primarily influences reflectance in the green and red-edge regions. Figure 2a displays directional reflectance spectra (RN) plotted against wavelength, spanning approximately 480–850 nm. Each distinct colored line represents a unique combination of biochemical or structural conditions. The coloration of the lines indicates variations in leaf biochemical composition, with warmer hues (reds) typically signifying elevated pigment levels, while cooler hues (blues and greens) suggest reduced pigment levels. Throughout all observed conditions, reflectance remains comparatively low within the visible spectrum, followed by a pronounced increase in the near-infrared range (≥700 nm), a phenomenon consistent with the spectral characteristics typical of vegetation. Figure 2b illustrates a parameter space employing color coding to represent the combined effects of anthocyanin levels (x-axis) and leaf chlorophyll content (y-axis). The color gradient indicates increasing values of the combined pigment state, ranging from lower pigment concentrations (yellow-green shades) to higher pigment concentrations (blue, purple, and red shades). Each hue in this figure corresponds to the spectral colors presented in Figure 2a, thereby establishing a direct correlation between pigment composition and the associated reflectance patterns. The observed spectral responses are consistent with established relationships between leaf pigments and reflectance behavior reported in vegetation spectroscopy studies. Although a formal quantitative sensitivity or correlation analysis was not performed, the wavelength-specific trends clearly demonstrate the influence of chlorophyll and anthocyanin on spectral variability.

3.2 Implementation of noise

To evaluate the robustness of the inversion framework to realistic measurement uncertainties, spectral and parameter noise were introduced during model evaluation. These noise levels simulate potential errors associated with sensor measurements and parameter variability. Spectral noise was introduced as small random variations in reflectance values to simulate measurement uncertainty associated with sensors, while parameter noise was applied as variations in the input variables of the PROSPECT-D model to represent uncertainty in biochemical and structural parameters. These noise components were incorporated within the ARTMO framework during model evaluation to assess the robustness of the inversion approach under realistic uncertainty conditions. Model performance, as represented by the color scale in Figures 3(a,b), varied across different combinations of spectral and parameter noise. For leaf chlorophyll content (Figure 3a), performance values ranged approximately from 20 to 60, whereas for anthocyanin (Figure 3b), values ranged from approximately 0.5–0.9. Lower noise levels, shown in the bottom-left section of the heatmap, were associated with higher accuracy, indicating that the inversion framework is most reliable when both spectral measurements and parameter inputs are precise. Conversely, high levels of spectral and parameter noise, found in the top-right section, significantly undermined retrieval accuracy, illustrating the collective impact of uncertainties from measurement errors and input variability. The shift from blue to yellow highlights the model’s sensitivity to noise, with spectral noise having a slightly greater effect than parameter noise. Based on the observed patterns, model performance remained relatively stable under low noise conditions (approximately 0–5), whereas higher noise levels (>10) resulted in a noticeable decline in prediction accuracy. This indicates that the inversion framework performs reliably under low-noise conditions but becomes increasingly sensitive as noise levels increase. By explicitly accounting for these error sources, the method ensures that the derived crop traits accurately reflect true physiological patterns, thereby increasing confidence in the robustness of the research findings. Descriptive statistics of the field-measured pigment indices used as ground-truth data for model calibration and validation are summarized in Table 2. The table presents the minimum, maximum, mean, and standard deviation values of leaf chlorophyll content (LCC) and anthocyanin (Anth) measured using the MPM-100 sensor across the sampled cotton genotypes. While formal statistical significance testing was not performed, the observed trends consistently demonstrate the sensitivity of model performance to increasing spectral and parameter noise levels.

TABLE 2. Descriptive statistics of leaf chlorophyll content (LCC) and anthocyanin (Anth) measured using the MPM-100.

3.3 Machine learning

3.3.1 Leaf chlorophyll content (LCC)

Inverse modeling was performed using the Machine Learning Regression Algorithms (MLRA) toolbox available in the ARTMO platform. This study utilized six different machine learning methods: K-nearest neighbors’ regression, partial least squares regression, Gaussian kernel regression, kernel signal-to-noise ratio regression, regression trees, and boosting trees. Each method provided distinct advantages that influenced model performance under varying noise conditions. The dataset was split into two sections: 70% for calibration and 30% for validation. A 70/30 calibration–validation split was adopted to maintain an independent validation dataset for model evaluation. Although ARTMO also provides k-fold and leave-one-out cross-validation options, the split-sample approach was selected to ensure a clear separation between training and validation datasets. The performance of various Machine linear regression algorithms (MLRAs) under different levels of spectral and parameter noise is outlined in Table 3 for LCC. Among the tested methods, Gaussian kernel regression showed comparatively better performance, achieving higher correlation and lower error metrics (r = 0.82, RMSE = 0.24, NRMSE = 30.89) under the evaluated conditions. Kernel signal-to-noise ratio regression also performed well (r = 0.78), although it had a slightly higher RMSE (0.26).

TABLE 3. ML Models’ performances during the calibration of LCC.

Conversely, K-nearest neighbors (KNN) regression achieved moderate accuracy (R = 0.50), whereas regression trees (r = 0.44) and boosting trees (r = 0.36) showed comparatively poorer predictive performance in noisy environments. Partial least squares regression (PLSR) yielded moderate results (r = 0.42) but was less effective than the kernel-based methods. Overall, kernel-based methods demonstrated better performance than tree-based and linear approaches under the tested noise conditions (Table 3). Although confidence intervals were not explicitly calculated, the consistency of performance metrics (r, RMSE, and NRMSE) across different noise levels and models provides a reliable indication of model stability and prediction performance. Although differences in NRMSE values among models are relatively small, model evaluation was based on a combination of performance metrics (r, RMSE, and NRMSE), and the consistent trends across these metrics provide a more reliable basis for comparing model performance under varying noise conditions.

3.3.2 Anthocyanin

In assessing anthocyanin content, Gaussian Kernel Regression demonstrated strong performance compared to other methods, achieving an R value of 0.78, an RMSE of 0.23, and an NRMSE of 28.62, as detailed in Table 4. These results indicate a strong fit to the data and high predictive accuracy. Additionally, the Kernel Signal-to-Noise Ratio Regression model demonstrated competent performance with an R value of 0.65, effectively distinguishing the signal from noise. In contrast, Partial Least Squares Regression (PLSR) showed moderate effectiveness with an r value of 0.54, indicating limitations in estimating anthocyanins. Regression tree models, with an r value of 0.62, surpassed estimates for chlorophyll, suggesting their strength in capturing nonlinear relationships in pigment data. However, K-Nearest Neighbors (KNN) and boosting trees exhibited limited effectiveness, with r values of 0.33 and 0.43, respectively, indicating sensitivity to noise. Overall, estimating anthocyanin content proved more challenging than chlorophyll estimation, as reflected in lower r values across most algorithms. Nonetheless, kernel regression methods consistently outperformed other techniques, illustrating their robustness in pigment analysis.

TABLE 4. ML Models’ performances during the calibration of Anth.

3.3.3 Parameter retrieval (validation)

Validation was conducted using 30% of the dataset that was not used for model calibration. The findings show that the models developed were dependable in estimating both LCC and Anth levels. For LCC, the regression analysis resulted in a correlation coefficient (r) of 0.74 (Figure 4a). Likewise, for Anthocyanin, the model attained an r value of 0.71 (Figure 4b). The scatterplots (Figures 4a,b) demonstrate a close correlation between predictions and actual data, with points closely clustered around the 1:1 line, indicating minimal bias and strong generalization. These results affirm that the combination of UAS multispectral data, radiative transfer modeling, and machine learning facilitates reliable extraction of crop biochemical parameters in real field settings. This solid validation underscores the effectiveness of the approach for precision agriculture applications, especially for monitoring crop physiological conditions and identifying spatial variability within fields.

4 Parameter mapping

The use of uncrewed aerial system (UAS) data for analyzing crop parameters has provided valuable insights into plant health across various agricultural fields. The findings showed that chlorophyll levels varied notably, ranging from 0.2 to 0.6. This variation signifies different levels of photosynthetic efficiency, which is vital for assessing how effectively each field harnesses sunlight for energy. Such insights enable farmers to pinpoint areas that may require extra attention or resources to improve growth (Figure 5). Conversely, Anthocyanin levels showed a more subtle variation, ranging from 0.01 to 0.09. Although these levels are less distinct, they are crucial for evaluating the overall health and vitality of the crops. Anthocyanins are important for photosynthesis and help shield plants from stress by neutralizing free radicals. As a result, understanding these values provides a comprehensive overview of the crops’ nutritional condition, ultimately enabling informed predictions of potential yields. This detailed comprehension of plant health, guided by UAS data, underscores the significance of precision agriculture in boosting crop productivity and sustainability (Figure 5).

5 Discussion

This research demonstrates that integrating UAS-based multispectral data with radiative transfer modeling and machine learning provides a reliable, non-invasive method for estimating key biochemical traits of cotton (chlorophyll and anthocyanin pigment). The forward simulations produced with the PROSPECT-D model successfully captured the anticipated spectral responses of cotton leaves across the visible and red-edge regions, where pigment-driven absorption is strongest. To reduce potential discrepancies between simulated and observed spectra, the PROSPECT-D simulations were constrained using field-measured leaf hyperspectral data collected with the PSR + spectroradiometer. The simulated spectra were further resampled to match the spectral configuration of the UAS multispectral sensor, ensuring consistency between modeled and observed reflectance data. The simulated reduction in reflectance with increasing chlorophyll levels, along with the notable impact of anthocyanins at green and red-edge wavelengths, aligns with well-established physiological and optical principles (Féret et al., 2017; Gitelson et al., 2001). This hybrid RTM–machine learning framework demonstrates the potential of combining physically based modeling with data-driven approaches for non-destructive crop monitoring. Such integration provides an efficient pathway for translating leaf-level spectral information into field-scale insights using UAS multispectral imagery.

Radiative transfer models (RTMs) provide a meaningful link between plant characteristics and reflectance; however, inverting these models poses challenges due to spectral redundancy and noise sensitivity (Chen et al., 2024; Ishaq et al., 2023). This study demonstrates that integrating machine learning techniques with RTM simulations can effectively address these challenges. Among the methods assessed, Gaussian Kernel Regression consistently performed best for retrieving LCC and Anth, particularly in noisy environments. This method’s strong performance can be attributed to the ability of kernel-based techniques to model complex nonlinear relationships between spectral reflectance and biochemical traits, while also being relatively robust to noise through implicit smoothing in the feature space. An additional advantage of Gaussian Process Regression is its ability to provide predictive uncertainty estimates. Although uncertainty maps were not generated in the current analysis, incorporating pixel-wise uncertainty information could provide valuable insight into the spatial confidence of retrieved pigment traits and represents an important direction for future research. Although NRMSE differences among models appear relatively small, the higher correlation coefficient achieved by Gaussian Kernel Regression indicates a stronger ability to capture the nonlinear relationship between spectral reflectance and pigment traits. These results align with previous research (Atzberger and Richter, 2012; Fenghua et al., 2017; Liang et al., 2021; Singh et al., 2022; Verrelst et al., 2019b) and further validate the robustness of these methods when implemented within a physically grounded modeling framework. In comparison, KNN and tree-based models showed weaker performance, indicating greater susceptibility to noise and limited generalization of complex spectral–biochemical interactions.

The study also conducted a thorough evaluation of spectral and parameter noise, providing valuable insights into the framework’s reliability. As anticipated, increased noise levels reduced retrieval accuracy, underscoring the need for high-quality spectral data and precise parameterization. Spectral noise was shown to affect results slightly more than parameter noise, underscoring the importance of sensor quality, calibration, and data preprocessing in UAS-based multispectral investigations. By addressing these uncertainties, the study offers a more realistic view of model functionality in field conditions rather than idealized scenarios. Independent validation using separate field measurements revealed strong correlations between predicted and actual pigment values, with correlation coefficients of 0.74 for LCC and 0.71 for anthocyanins. These findings suggest that the developed models generalize reasonably well beyond the calibration dataset and fall within the range reported in previous UAS-based studies (Cheng et al., 2022; Han et al., 2022; Tao et al., 2020). The marginally lower performance for anthocyanins is expected due to their typical lower concentrations and subtler effects on reflectance compared to chlorophyll. Nonetheless, the accuracy achieved indicates the framework’s capacity to capture meaningful physiological variations in both pigments.

When positioned within the broader literature on hybrid radiative transfer model–machine learning (RTM–ML) approaches for pigment retrieval, the validation accuracies obtained in this study (r = 0.74 for LCC and r = 0.71 for Anth) should be interpreted as moderate rather than exceptional. These values fall within the commonly reported range for RTM–ML studies (r ≈ 0.70–0.90), although studies incorporating hyperspectral data or canopy-level RTMs often report higher accuracies. Several recent studies have reported higher chlorophyll retrieval accuracies when canopy radiative transfer models such as PROSAIL or related canopy-aware approaches are incorporated into hybrid inversion frameworks (Atzberger and Richter, 2012; Liang et al., 2021; Verrelst et al., 2019b). These studies often integrate canopy structural information such as LAI, canopy architecture, or vegetation indices, which helps improve model performance. Kernel-based algorithms, including Gaussian Process Regression (GPR) and related methods, have also been widely shown to perform well in RTM inversion studies (Fenghua et al., 2017; Singh et al., 2022). A likely explanation for the comparatively lower performance observed in the present study is the leaf-to-canopy scaling limitation, where canopy reflectance is influenced not only by leaf optical properties but also by structural factors such as canopy architecture, leaf angle distribution, and soil background, which can weaken the direct relationship between simulated leaf-level spectra and observed canopy reflectance. Specifically, the PROSPECT-D model simulates leaf optical properties, whereas the inversion was applied to canopy-level UAS multispectral imagery, where reflectance is additionally influenced by canopy architecture, leaf angle distribution, soil background, and shadowing effects. Canopy-scale RTM frameworks are better suited to account for these structural influences and have therefore demonstrated improved pigment retrieval performance in several recent studies (Liang et al., 2021; Verrelst et al., 2019b).

The spatial maps generated from UAS imagery further illustrate the practical benefits of this approach. Variability in LCC and anthocyanin levels across the field reflects differences in plant physiological status attributed to genetic variation, nutrient availability, or micro-environmental factors. These high-resolution maps are beneficial for reliable phenotyping of large panels and precision crop management, including site-specific management decisions and early stress detection. Compared with conventional destructive sampling methods, this approach offers a scalable, repeatable alternative for monitoring crop health throughout the growing season. While the proposed RTM–ML framework demonstrates promising performance, several sources of uncertainty should be considered when interpreting the results. The inversion process relies on simulated spectral–trait relationships, which may not fully capture the complexity of real-world canopy reflectance, particularly under varying illumination and background conditions. Additionally, the use of multispectral data limits the spectral resolution available for pigment retrieval, potentially reducing sensitivity compared to hyperspectral approaches. The absence of explicit canopy structural parameters may also contribute to uncertainty in scaling leaf-level simulations to canopy-level observations. Furthermore, the robustness of machine learning models is influenced by the representativeness of the training dataset, and model performance may vary when applied to different environmental conditions or crop systems.

Despite these positive outcomes, some limitations should be acknowledged. Ground measurements and UAS imagery were collected during the same field campaign, with aerial imagery acquired 1 day after ground sampling. While this short temporal difference is unlikely to significantly affect pigment–reflectance relationships, it may introduce minor variability that could influence model accuracy and temporal transferability under dynamic field conditions. The analysis focused on a single crop and a specific growth stage, which may limit the generalizability of the models to other crops, growth stages, and environmental conditions, thereby affecting their broader applicability in operational precision agriculture. In addition, the dataset included a diverse panel of 320 cotton genotypes, which may exhibit variability in leaf structure, thickness, and pigment composition. Such genotypic differences can influence spectral responses and may affect the transferability of the developed models across genetic groups. Although the PROSPECT-D model represents leaf optical properties, canopy reflectance observed by UAS sensors is influenced by structural factors such as leaf angle distribution, canopy architecture, and soil background reflectance. In this study, machine learning algorithms were used to bridge the scaling between leaf-level spectral simulations and canopy-level observations. Nevertheless, the absence of explicit canopy structural parameters (e.g., LAI) may introduce additional uncertainty in canopy-scale retrievals. Future studies will integrate canopy radiative transfer models such as PROSAIL to further improve the physical representation of canopy reflectance. Future research should expand this framework to cover multiple growth stages, incorporate canopy-level models, and integrate multi-temporal UAS observations to enhance robustness and applicability across diverse agricultural systems. These limitations highlight the need for multi-temporal data, canopy-level modeling, and cross-site validation to improve the robustness and practical applicability of the proposed framework.

6 Conclusion

This research demonstrates the potential of integrating UAS-based remote sensing, radiative transfer modeling, and machine learning to non-invasively retrieve crop biochemical parameters. By implementing the PROSPECT-D model within the ARTMO framework and evaluating various regression algorithms, we developed a robust pipeline capable of estimating chlorophyll and anthocyanin across different noise levels. Gaussian Kernel Regression proved to be the most effective technique, with a moderate predictive accuracy during calibration (r = 0.82) for LCC and (r = 0.78) for Anth. Validation with 30% of the dataset further demonstrated robust correlations with ground-truth data (r = 0.74 for LCC; r = 0.71 for Anth), underscoring the method’s reliability in field applications. UAS-based parameter mapping revealed distinct spatial variability in LCC and Anth, demonstrating the framework’s ability to provide high-resolution insights into crop physiological status. Such comprehensive monitoring is vital for precision agriculture, facilitating enhanced nutrient management, early stress identification, and targeted interventions. In summary, the results underscore the potential of integrating hyperspectral data, radiative transfer models, and machine learning as a scalable, precise, and non-invasive method for monitoring crop traits. Future investigations should broaden this framework to include additional biochemical parameters, incorporate multi-temporal analyses, and examine its applicability across various crop types and agroecosystems.

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Footnotes

Edited by: Zhenghong Yu, Guangdong Polytechnic of Science and Technology, China

Reviewed by: Manojit Chowdhury, Visva-Bharati University, India

Jian Wang, Chinese Academy of Agricultural Sciences, China