Quantitative Inversion Model of Total Potassium in Desert Soils based on Multiple Regression Combined with Fractional Differential
An-Hong Tian, Jun-San Zhao, Hei-Gang Xiong, and Cheng-Biao Fu
(Received March 28, 2018; Accepted August 8, 2018)
Keywords: fractional differential, total potassium, multiple regression, desert soil, inversion model
Potassium is an important nutrient element for plant growth. The traditional integer-order differential transformation methods at first order and second order tend to reduce the accuracy of the total potassium content quantitative inversion model, and there are few reports on the use of the fractional differential algorithm for the prediction of soil total potassium content. In this paper, the use of the fractional differential algorithm to predict total potassium content is introduced. Field soils collected in the Xinjiang Uygur Autonomous Region from May 9 to 23, 2017, were used as the data sources. Firstly, we calculated the correlation between spectral reflectance and total potassium content for the original spectrum (R) and the root mean square spectrum (√R) under different fractional differential orders. Secondly, bands whose maximum absolute correlation coefficient was greater than 0.5 were selected as sensitive bands. R had seven bands: 562, 596, 1177, 2155, 2156, 2364, and 239nm. √R had six bands: 596, 1177, 2155, 2156, 2364, and 2398 nm. Finally, a multiple regression analysis method was employed to quantitatively estimate the optimal model. The ratio of performance to deviation (RPD) evaluation index of a good model should be greater than or equal to 1.4. The simulation results showed that the optimal models for R and √R were the 0.8 order differential and the 0.6-order differential, respectively. The corresponding PRD values were 1.700182 and 1.783319,respectively. We found that the prediction model of √R was more accurate.
Corresponding author: Jun-San Zhao