Biophysical parameter estimation of crops from polarimetric synthetic aperture radar imagery with data-driven polynomial chaos expansion and global sensitivity analysis

Data-driven machine learning regression methods are easy to implement and applicable to a wide-range of data in biophysical parameter estimation and have become a common approach in the remote sensing field. Among the regression methods, polynomial chaos expansion (PCE) is one of the reliable and interesting ones due to its tight relationship with uncertainty quantification. One of the advantages of PCE is that global sensitivity analysis (GSA) with Sobol's method can be analytically computed from polynomial coefficients if the input space is statistically independent. However, most of the phenomena include dependent features either statistically or physically. Though the physical independence is provided between inputs, they must be statistically uncorrelated. Therefore, an independent and uncorrelated input space must be created before the regression analysis. In this paper, we performed PCE-based regression analysis for the estimation of biophysical parameters of crops. The study was conducted in the experimental fields of field pea, barley, canola, and oat of the AgriSAR2009 campaign. The input parameters of the regression model were formed by creating polarimetric features derived from RADARSAT-2 imagery. The estimated biophysical parameters were based on the discrete in situ measurements of leaf area index (LAI) and normalized difference vegetation index (NDVI), scattered semi-randomly in each crop field. We implemented neighbourhood component analysis (NCA) to create an independent and uncorrelated input space by eliminating correlations. Finally, we investigated the importance of features, which drive the PCE-based regression models applying GSA with Sobol's method. Besides the individual effects of each feature, their interactions were found significant.