A robust method to estimate foliar phosphorus of rubber trees with hyperspectral reflectance

Rapid and accurate estimation of leaf phosphorus content (LPC) from hyperspectral reflectance is vital for nutrient diagnosis of rubber trees (Hevea brasiliensis). Determination of the most related variables from the hundreds or thousands of hyperspectral wavelengths is the key to develop a robust and accurate estimation model. However, few studies focused on using variable selection algorithm to extract meaningful spectral bands in estimating LPC of plants. The objectives of this study were to select the characteristic wavelengths related to LPC of rubber trees and to identify a suitable method for predicting LPC of rubber trees. In the current study, a hybrid approach namely Monte Carlo-uninformative variable elimination (MC-UVE) in combination with successive projections algorithm (SPA) (MC-UVE-SPA) was proposed to select the most informative spectral wavelengths for estimating the LPC of rubber trees. A total of 108 leaf samples were collected from the fields in two years (2014 and 2017). Out of these samples, seventy-eight were used as model calibration dataset, while the remaining thirty were served as an independent prediction dataset. Thirty-one spectral wavelengths of 390, 437, 438, 547, 611, 706, 713, 727, 747, 1144, 1146, 1387, 1405, 1686, 1735, 1800, 1801, 1886, 2071, 2241, 2243, 2252, 2299, 2301, 2416, 2426, 2449, 2452, 2464, 2465, and 2492 nm were selected from the original 2150 wavelengths by using the MC-UVE-SPA algorithm, and finally seven wavelengths including 2449, 2243, 1686, 1405, 1144, 713 and 437 nm were used as input variables for the multiple linear regression (MLR) model and artificial neural network (ANN). Performances of MLR and ANN were compared with the partial least squares regression (PLSR) which used the full spectra (full-PLSR) and the MC-UVE derived wavelengths (MC-UVE-PLSR) as input variables respectively. Results showed that MLR and ANN models exhibited good performance both in terms of calibration (values of normalized root mean square error of calibration (nRMSEC) were 9.597%, and 7.314% for MLR and ANN, respectively) and prediction (values of normalized root mean square error of prediction (nRMSEP) were 7.960%, and 7.754% for MLR and ANN, respectively). On the other hand, MC-UVE-PLSR only presented better calibration performance (value of nRMSEC was 6.153%); while its predictive accuracy decreased markedly in the prediction dataset (value of nRMSEP was 9.340%). The full-PLSR yielded the lowest calibration and prediction results (values of nRMSEC and nRMSEP were 11.251% and 10.547%, respectively). Furthermore, despite the fact that nRMSEP value of MLR (7.960%) was slightly higher than that of ANN (7.754%), considering that MLR was much simpler and easier to be interpreted, MC-UVE-APA-MLR can be used for estimating LPC of rubber trees. The overall results demonstrated that MC-UVE-SPA was a promising approach for wavelength selection and MC-UVE-SPA-MLR was a robust and accurate model for estimating LPC of rubber trees.