Estimating equivalent water thickness of apple leaves using hypersecptral data based on EFAST and PLS

Abstract: Equivalent water thickness (EWT) is an important parameter for evaluating the growth status and yield of fruit tree. The objectives of this study were (i) to establish and verify a model for the EWT of the apple leaves, in which the regression models, the extended Fourier amplitude sensitivity test - partial least squares (EFAST-PLS), and the normalized difference infrared water index (NDIWI) model were tested, and (ii) to compare the performances of the proposed models respectively using the EFAST-PLS and the NDIWI model. Spectral reflectance of leaves and concurrently the apple leaves' EWT parameters were acquired in Tai'an area, Shandong, China during apple growth seasons of 2012-2013. Firstly, the apple leaves' EWT sensitivity was analyzed through the EFAST and the PROSPECT model; the results showed that the first order sensitivity index of the EWT of apple leaves for spectral reflectance was larger in 3 wavelengths, i.e. 900-1 700, 1 701-2 200, and 2 201-2 500 nm, and the largest first order sensitivity index of the EWT value of apple leaves existed at the wavelength of 1 425, 1 900 and 2 500 nm. Secondly, the EWT of apple leaves was estimated by PLS and NDIWI; the results showed that the coefficient of determination (R2) was 0.5628 and 0.2831 and the norm root mean square error (NRMSE) was 0.0625 and 0.08 respectively, and the R2 was 0.2471, 0.1232 and 0.2401 and the NRMSE was 0.0819, 0.0884 and 0.0823 using the reflectance of the single wavelength of 1 425, 1 900 and 2 500 nm, respectively. Lastly, in order to validate the accuracy of the EWT model of apple leaves, the measured value and predicted value were compared between PLS, NDIWI and empirical regression of single wavelength. The results indicated that the apple leaves' EWT measured value and EWT predicted value had better relationship using PLS and NDIWI regression, while the relationship between the apple leaves' EWT measured value and EWT predicted value was worse using single wavelength regression. For PLS, NDIWI, and single wavelength regression of 1 425, 1 900 and 2 500 nm, the R2 was 0.3012, 0.2478, 0.4297, 0.2356 and 0.1777, respectively, the NRMSE was 0.1317, 0.0902, 0.0936, 0.1 and 0.1027, respectively, and the NRMSE was 0.0016, 0.0011, 0.0011, 0.0012 and 0.0012 g/cm2, respectively. Both the modeling and verification showed that for the EWT model of apple leaves, using PLS and NDIWI regression was better than using single wavelength regression. The reason was the EFAST-PLS model coupled a number of sensitive spectral bands for apple leaves' EWT, and the accumulation of sensitive bands improved the EWT accuracy of apple leaves in estimation and reduced the influence of environment factors on apple leaves' EWT; PLS regression can solve data correlation while NDIWI and single wavelength cannot solve, but NDIWI computes simply so that it can solve the apple leaves' EWT. The results indicate that the EFAST-PLS model has great potential for the EWT estimation of apple leaves; however, the NDIWI also has merit.