Estimation of desert soil organic carbon content based on hyperspectral data preprocessing with fractional differential

Abstract: Soil organic carbon (SOC) is a crucial soil property which has attracted wide attention in the field of global change. This is especially true in the arid and semi-arid regions. In recent years, it is a hot topic to estimate SOC content by hyperspectral remote sensing technology, however, it is hard to estimate SOC content in desert area precisely when it is less than 2%. Existing work, including related research history and current status, has mostly focused on integer differential, which yet might influence the effective information detection and cause the loss of spectral information to some extent. Therefore, this study aimed to bring fractional order differential algorithm into the preprocessing of hyperspectral data. With 103 surface soil samples collected from the Ebinur Lake basin in Xinjiang Uighur Autonomous Region, China, the SOC contents and reflectance spectra were measured in the laboratory. After removing the marginal bands (350-400 and 2401-2500 nm) and smoothed by Savitzky-Golay filter, the raw hyperspectral reflectance (R) data were transformed by 4 mathematical methods, i.e., the reciprocal, logarithm, logarithm-reciprocal and root mean square method, respectively. Secondly, their 0-2 order differentials (taking 0.2-order as step) were calculated by Grünwald-Letnikov fractional differential equation. And then, we computed the correlation coefficients between each fractional order differential value of R, its 4 mathematical transformation forms and SOC content. After choosing the feature bands whose correlation coefficient passed the significance test at 0.01 level, 103 samples were divided into 2 parts: 69 for model calibration and 34 for validation. Subsequently, partial least squares regression (PLSR) was employed to build the hyperspectral estimation models of SOC content. And then, root mean square error of calibration (RMSEC), determination coefficient of calibration (R2c), root mean square error of prediction (RMSEP), determination coefficient of predicting (R2p) and relative prediction deviation (RPD) were used for accuracy assessment. The results showed that: 1) Fractional order differential algorithm could refine the correlation coefficient curves between the SOC content and the raw hyperspectral reflectance in the wavelength ranges of 450-600, 640-700 and 1400-1500 nm, and also reduce the information loss to some extent; 2) With the order increasing, the number of bands whose correlation coefficient passed the significance test at 0.01 level firstly increased and then decreased, but the number of bands did not reach the maximum at the same order, and some differences occurred; 3) Comparing the predictive effects of 55 SOC estimating models calibrated by PLSR, the model based on 1.6-order differential of logarithm transform was much better than others, and had better performance in predicting SOC content in the study area (RMSEC=2.433 g/kg, R2c=0.786, RMSEP=2.263 g/kg, R2p=0.825, RPD=2.392). And indeed, the models based on fractional order differentials were more robust and accurate than the conventional integer differential ones. Over all, it is a fairly satisfactory preprocessing method of hyperspectral data in the quantitative study on soil nutrients by means of remote sensing. In order to achieve more universal and stable inversion model, the next step is to enlarge the sampling area and the number of soil samples as much as possible to improve and perfect the soil hyperspectral database.