Spectroscopic retrieval of above-ground crop nitrogen content with a hybrid machine learning regression method

Proteins are the major nitrogen-containing biochemical constituents of plants. Since nitrogen (N) cannot be measured directly using remote sensing data, leaf protein content constitutes a valid proxy for this main limiting plant nutrient. In the past, mainly linear parametric algorithms, such as vegetation indices, have been employed to retrieve this non-state variable from optical reflectance data. Moreover, most studies solely relied on the relationship of chlorophyll content with nitrogen. In contrast, our study presents a hybrid model inversion scheme of a physically-based approach via protein retrieval combined with advanced machine learning regression. The leaf optical properties PROSPECT-PRO model, including the newly calibrated specific absorption coefficients (SAC) of proteins, was coupled with the canopy reflectance model 4SAIL to PROSAIL-PRO. A generic synthetic database of model input parameters with corresponding reflectance was simulated and used for training two different machine learning regression methods: a standard homoscedastic Gaussian Process (GP) and a variational heteroscedastic GP regression that accounts for signal-to-noise correlations. Both GP methods have the interesting feature of providing confidence intervals for the estimates. As part of multiple field campaigns, carried out in the scientific preparation framework of the Environmental Mapping and Analysis Program (EnMAP), spectra of maize and winter wheat were acquired to simulate EnMAP data and plant-organ-specific nitrogen measurements were destructively collected for validation. Both GP models yielded excellent performance in learning the nonlinear relationship between specific protein absorption bands and area-based above-ground N. They also performed similar or even outperformed other nonlinear nonparametric approaches. Physical validation of the estimates against in situ nitrogen measurements from leaves plus stalks yielded a root mean square error (RMSE) of 2.5 g/m². The variational heteroscedastic GP provided a more differentiated pattern of uncertainty with tighter confidence intervals within low-value regimes compared to the standard GP. The inclusion of fruit nitrogen content for validation deteriorated the results of all models, which can be explained by the inability of radiation in the optical domain to penetrate the thick tissues of maize cobs and wheat ears. Following some further validation exercises, we aim to implement GP-based algorithms for global agricultural monitoring of above-ground N derived from future satellite imaging spectroscopy data.