Abstract:

Objective The leaf area index (LAI) is a key biophysical parameter that reflects the canopy structure and photosynthetic capacity of crops. However, the inversion of winter wheat LAI from remote sensing data is often constrained by the limited availability of field measurements, leading to insufficient model generalization. Although radiative transfer model (RTM)-based simulations can expand the sample size, discrepancies between simulated and observed spectra persist due to simplified canopy and soil parameterizations. Conversely, purely data-driven generative models such as generative adversarial networks (GANs) can enhance sample diversity but often produce physically inconsistent samples in the absence of biophysical constraints. To address these issues, a physics-constrained PROSAIL-cGAN (conditional generative adversarial network) spectral sample augmentation method was proposed that integrated the PROSAIL model with cGAN to improve the accuracy and robustness of LAI inversion under small-sample conditions, generate physically realistic spectral-parameter pairs and provide reliable data support for remote sensing-based monitoring of winter wheat growth. Methods The study area was located in Zouping city, Shandong Province, a major winter wheat production region within the Huang-Huai-Hai Plain. A total of 133 field samples were collected during the jointing stage in April 2025 using an LAI-2200C canopy analyzer, with synchronous canopy spectra acquired. A Sentinel-2A Level-2A image from April 15, 2025, served as the remote sensing source, comprising 13 bands resampled to a spatial resolution of 10 m. The dataset was divided into training (70%) and validation (30%) subsets, with LAI values ranging from 1.646 to 7.505. The proposed method combined the PROSAIL radiative transfer model with a conditional GAN framework. First, PROSAIL was employed to simulate canopy reflectance and corresponding biophysical parameters, including chlorophyll content (C_ab), carotenoid content (C_ar), brown pigment content (C_brown), equivalent water thickness (C_w), dry matter content (C_m), LAI, and leaf inclination distribution (LIDFa). A multi-layer perceptron (MLP) surrogate model was then trained to approximate the forward mapping of PROSAIL, enabling differentiability for integration with deep learning architectures. The cGAN generator received random noise and physical parameters as conditional inputs to produce corresponding canopy reflectance, while the discriminator jointly evaluated authenticity and physical consistency. During adversarial training, physical constraints were incorporated into the generator's loss function to ensure biophysical realism. The generated samples were subsequently filtered based on parameter ranges and discriminator confidence scores. Kernel density overlap between real and generated LAI distributions was used to quantify their statistical consistency. Finally, the enhanced dataset was used to train random forest (RF) and extreme gradient boosting (XGBoost) regression models for the LAI inversion. Model performance was assessed using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE), and compared with three baselines: 1) field-measured modeling, 2) the PROSAIL lookup table (LUT) method, and 3) cGAN-only augmentation. Results and Discussions The surrogate MLP model accurately reproduced PROSAIL-simulated spectra, achieving R² 0.817, RMSE 0.008 5, and MAE 0.005 5, confirming its feasibility as a differentiable physical proxy. The cGAN-based augmentation achieved a LAI distribution overlap of 0.806 with the measured samples, whereas the PROSAIL-cGAN improved the overlap to 0.827, demonstrating enhanced physical realism and sample diversity. Model comparisons revealed substantial differences in performance. The LUT-based inversion yielded only R² 0.353 0 and RMSE 1.284 0, reflecting its limited adaptability to spectral heterogeneity. Direct regression using field data improved accuracy (R²=0.680 1 for XGBoost and 0.648 8 for RF). Incorporating cGAN-generated samples further enhanced model accuracy (R² 0.745 0 for RF and 0.739 0 for XGBoost). The PROSAIL-cGAN-enhanced RF model achieved the best overall performance, with R² 0.848 8, RMSE 0.540 9, and MAE 0.293 7. The sample-size sensitivity analysis demonstrated that as the number of field samples increased from 27 to 106, R² improved from 0.546 2 to 0.848 8 and RMSE decreased from 1.024 3 to 0.540 9. When the sample size exceeded 79, model performance stabilized, indicating strong robustness. Spatial mapping results showed that LAI values were higher in the central and northern regions (4~7) and lower in the southern mountainous areas (1.5~4), consistent with variations in soil fertility and field management practices. These findings validate the model's applicability for regional-scale monitoring of crop growth. Conclusions This study developed a physics-constrained PROSAIL-cGAN spectral sample augmentation method for winter wheat LAI inversion. By integrating a radiative transfer model, a conditional generative network, and a differentiable surrogate, the method effectively generated physically consistent and diverse spectral-parameter samples under small-sample conditions. The PROSAIL-cGAN-based RF model achieved a relatively high inversion accuracy, outperforming traditional LUT and field-only approaches. The proposed method successfully mitigated small-sample limitations, ensured physical interpretability, and improved model generalization. It provides a robust framework for the remote sensing inversion of crop canopy parameters, supporting precision agriculture and dynamic monitoring of crop growth. Future work will focus on optimizing sample generation strategies, integrating multi-temporal satellite data and additional physiological parameters, and coupling with deep or semi-supervised learning techniques to further enhance scalability and applicability across crops and regions.

Key words: physical constraint, PROSAIL, conditional generative adversarial network, sample augmentation, leaf area index, remote sensing inversion