Introduction of Variable Correlation for the Improved Retrieval of Crop Traits Using Canopy Reflectance Model Inversion

Abstract

Look-up table (LUT)-based canopy reflectance models are considered robust methods to estimate vegetation attributes from remotely sensed data. However, the LUT inversion approach is sensitive to measurements and model uncertainties, which raise the ill-posed inverse problem. Therefore, regularization options are needed to mitigate this problem and reduce the uncertainties of estimates. In this study, we introduce a new method to regularize the LUT inversion approach to improve the accuracy of biophysical parameters (leaf area index (LAI) and fractional vegetation cover (fCover)). This was achieved by incorporating known variable correlations that existed at the test site into the LUT approach to correlate the model variables of the Soil–Leaf–Canopy (SLC) model using the Cholesky decomposition algorithm. The retrievals of 27 potato plots obtained from the regularized LUT (LUTreg) were compared with the standard LUT (LUTstd), which did not consider variable correlations. Different solutions from both types of LUTs (LUTreg and LUTstd) were utilized to improve the quality of the model outputs. Results indicate that the present method improved the accuracy of LAI estimation, with the coefficient of determination R2 = 0.74 and normalized root-mean-square error NRMSE = 24.45% in LUTreg, compared with R2 = 0.71 and NRMSE = 25.57% in LUTstd. In addition, the variability of LAI decreased in LUTreg (5.10) compared with that in LUTstd (12.10). Hence, our results give new insight into the impact of adding the correlation between variables to the LUT inversion approach to improve the accuracy of estimations. In this study, only two correlated variables (LAI and fCover) were examined; in subsequent studies, the full correlation matrix based on the Cholesky algorithm should be explored.

Comparison of Crop Trait Retrieval Strategies Using UAV-Based VNIR Hyperspectral Imaging

“…Extending a previous study [ 30 ], we generated two LUTs (LUTstd and LUTreg) with a size of 17,280 simulations. The input model variables of the standard LUT (LUTstd) were independent of each other, following the uniform and multivariate normal distribution function.…”

“…More details about the implementation of the Cholesky method (LU) and LHS to correlate the model inputs using the ground measurements can be found in [ 30 , 76 ]. The simulated spectra of both LUTs (LUTstd and LUTreg) were resampled, corresponding to the 40 bands of the Gamaya OXI VNIR-40.…”

“…In an attempt to solve the inverse problem, averaging similar input variable combinations with the smallest differences between the measured and simulated spectra were calculated using the mean or median [25,81,82]. However, the median of 300 LUT entries was used as an optimal solution, as has been pointed out previously [30].…”

“…Overall, this study set out to investigate the performances of statistical, physical, and hybrid methods under variable illumination for estimating LAI, fCover, and CCC from UAV-based hyperspectral data throughout the growth cycle of a potato crop. The following specific objectives are addressed: (1) To test whether the regularized LUT (LUTreg) developed in the study of Abdelbaki et al [30], which was shown to work on a single observation date, using field spectroradiometer measurements, can yield an improvement in the variables of interest; (2) to compare the LUTreg with statistical and hybrid methods in the estimation process; and (3) to assess if using information on illumination conditions during image acquisition can improve the accuracy of estimates.…”

“…To alleviate the ill-posed inverse problem and increase the accuracy of retrieval, different regularization schemes have been suggested, as described in [ 29 ]. In a recent study [ 30 ], the usage of correlated variables using the Cholesky method was proposed, in order to regularize a look-up table inversion approach (LUTreg). Using prior information on the cross-correlations between variables (e.g., LAI, CCC, and fCover), which can be collected from field measurements, may reduce the probability of unrealistic parameter combinations and simulated spectra [ 31 ].…”