Estimating Soil Salt Content Using Fractional Derivatives and Optional Spectral Indices in the Ebinur Lake Oasis, Northwestern China

  • Fei ZhangEmail author
  • Xiaoping Wang
  • Hsiang-te Kung
  • Verner Carl Johnson
Original Article


Derivative spectroscopy is a powerful mathematical tool that provides more useful information of spectral data than untreated data. Visible and near-infrared diffuse reflectance spectroscopy (VIS-NIR) has shown levels of accuracy comparable to conventional laboratory methods for estimating soil properties. The VIS-NIR spectrum is one of the most important data acquisition technologies for digital soil mapping, precision agriculture, and soil resource surveys. The objective of this study was to develop a soil salt content model using the fractional-order derivatives of field-measured spectral data paired with ground measurements. The results showed the following: There was a significant correlation between the single-band reflectance spectra and the soil salt content, and as the derivative order increased, reflectance values first increased and then decreased, with a peak value, R = 0.525, in the 1.2-order derivative. Strong correlations between the estimation of soil salt content and the derivative spectral data of the difference index (DI), ratio index (RI), and normalized difference index (NDI) were also produced by the 1.2-order derivative. R values for the DI, RI, and NDI were 0.818, 0.8624, and 0.8297, respectively. Selected bands with the highest correlation values from the 1.2-order derivative spectral data of the R1428, DI (R1426 / R2151), RI (R1429 − R2024), and NDI (R1526 − R2470)/(R1526 + R2470)] were used to build a model to estimate soil salt content, which showed an R2 value of 0.53 and low RMSE and SD values. The 15 samples of the data were then used to validate the single-band model, R1428, and the combination models, DI (R1426 / R2151), RI (R1429 − R2024), and NDI [(R1526 − R2470)/(R1526 + R2470)], which demonstrated that the R2 values were greater than 0.8. The RMSE and SD values were low, and the value of the RPD was greater than 1.4. This study demonstrated the potential of using fractional derivatives rather than integer derivatives for soil salt content estimation. By making full use of hyperspectral data, fractional derivatives could enrich data preprocessing methods and unearth information about spectral emissions that are lost by integer derivatives. Although this study is a straightforward application of the fractional derivative method, it provides a reference for the estimation of other parameters with hyperspectral technology.


Fractional derivative Ebinur Lake oasis Soil salt content Hyperspectral index 



The authors wish to thank the referees for providing helpful suggestions to improve this manuscript. The authors wish to thank Professor Abduwasit Ghulam (Saint Louis University) have helped us to improve the manuscript carefully. Please see the revised version of the paper.

Funding Information

The research was carried out with the financial support provided by the Xinjiang Local Outstanding Young Talent Cultivation Project of National Natural Science Foundation of China (U1503302).


  1. 1.
    K. Baderia, A. Kumar, G.K. Singh, Hybrid method for designing digital FIR filters based on fractional derivative constraints. ISA. Trans. 58, 493–508 (2015)CrossRefGoogle Scholar
  2. 2.
    V. de Paul Obade, L. Rattan, Assessing land cover and soil quality by remote sensing and geographical information systems (GIS). Catena 104, 77–92 (2013)CrossRefGoogle Scholar
  3. 3.
    J.L. Ding, D.L. Yu, Monitoring and evaluating spatial variability of soil salinity in dry and wetseasons in the Werigan-Kuqa Oasis, China, using remote sensing and electromagnetic induction instruments. Geoderma 2014, 316–322 (2014)CrossRefGoogle Scholar
  4. 4.
    A. El Harti, R. Lhissoua, K. Chokmani, et al., Spatiotemporal monitoring of soil salinization in irrigated Tadla plain (Morocco) using satellite spectral indices. Int. J. Appl. Earth Obs. Geoinf. 50, 64–73 (2016)CrossRefGoogle Scholar
  5. 5.
    Y.C. Gao, J.N. Wang, S.H. Guo, Y.L. Hua, T.T. Li, et al., Effects of salinization and crude oil contamination on soil bacterial community structure in the Yellow River Delta region, China. Appl. Soil Ecol. 86, 165–173 (2015)CrossRefGoogle Scholar
  6. 6.
    R. Gerbbers, V.I. Adamchuk, Precision agriculture and food security. Science 327, 828–831 (2010)CrossRefGoogle Scholar
  7. 7.
    Hamzeh, A.A. Naseri, Behzad, S.K. Alavi Panah, Estimating salinity stress in sugarcane fields with spaceborne; hyperspectral vegetation indices. Int. J. Appl. Earth Obs. Geoinf. 21(1), 282–290 (2013)CrossRefGoogle Scholar
  8. 8.
    A. Harti, R. Lhissou, K. Chokmani, Spatiotemporal monitoring of soil salinization in irrigated Tadla ain (Morocco) using satellite spectral indices. Int. J. Appl. Earth Obs. Geoinf. 2016(50), 64–73 (2016)CrossRefGoogle Scholar
  9. 9.
    W. Ji, Z. Shi, Q. Zhou, L.Q. Zhou, VIS-NIR reflectance spectroscopy of the organic matter in several types of soil. J. Infrared Millim Waves 31(3), 277–282 (2012) (In Chinese)CrossRefGoogle Scholar
  10. 10.
    Jin X L, Du J, Liu H J, Wang Z M, Song K S, Remote estimation of soil organic matter content in the Sanjiang Plain, Northest China: The optimal band algorithm versus the GRA-ANN model. Agric For Meteorol 218–219, 250–260 (2006)Google Scholar
  11. 11.
    Z.X. Leng, L.M. Ge, X.L. Nurbey Pan, Functional district of Ebinur Lake watershed based on GIS. South North Water Transf. Water Sci. Technol. 4(1), 33–35 (2006)Google Scholar
  12. 12.
    Y. Li, H. Tang, H. Chen, Fractional-order derivative spectroscopy for resolving simulated overlapped Lorenztian peaks. Chemom. Intell. Lab. Syst. 107, 83–89 (2011)CrossRefGoogle Scholar
  13. 13.
    J. Li, L. Pu, M. Zhu, R. Zhang, The present situation and hot issues in the salt-affected soil research. Act Geograph. Sin. 67(9), 1233–1245 (2012) (In Chinese)Google Scholar
  14. 14.
    X. Li, Y. Zhang, Y. Bao, Exploring the best hyperspectral features for LAI estimation using partial least squares regression. Remote. Sens. 6, 6221–6241 (2014)CrossRefGoogle Scholar
  15. 15.
    H.M. Ozaktas, B. Barshan, D. Mendlovic, Convolution and filtering in fractional Fourier domains. Opt. Rev. 1(1), 15–16 (1994)CrossRefGoogle Scholar
  16. 16.
    Y.I. Pankova, A.F. Novikova, A. Kontoboytseva, in Developments in Soil Salinity Assessment and Reclamation, ed. by S. A. Shahid, M. A. Abdelfattah, F. K. Taha. The new map of soil salinity and regularities in distribution of salt-affected soils in Russia (Springer-Verlag, Berlin, 2013), pp. 99–111CrossRefGoogle Scholar
  17. 17.
    J. Peng, H. Liu, Z. Shi, Regional heterogeneity of hyperspectral characteristics of salt-affected soil and salinity inversion. Trans. Chin. Soc. Agric. Eng. 30(17), 167–174 (2014) (In Chinese)Google Scholar
  18. 18.
    V. Poenaru, A. Badea, S.M. Cimpeanu, Multi-temporal multi-spectral and radar remote sensing for agricultural monitoring in the Braila plain. Agric. Agric. Sci. Proscenia 6, 506–516 (2015)Google Scholar
  19. 19.
    Y. Pu, W. Wang, J. Zhou, Y. Wang, H. Jia, Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation, Science in China. Series F. Inf. Sci. 51(9), 1319–1339 (2009)zbMATHGoogle Scholar
  20. 20.
    F. Rui, Z. Yushu, W. Yu, Analysis of the relationship between the spectral characteristics of maize canopy and leaf area index under drought stress. Acta Ecol. Sin. 33, 301–307 (2013)CrossRefGoogle Scholar
  21. 21.
    P.A. Sanchez, S. Ahamed, F. Carre, et al., Digital soil map of the world. Science 325, 680–681 (2009)CrossRefGoogle Scholar
  22. 22.
    E. Scudiero, T.H. Skaggs, L. Dennis, Corwin. Comparative regional-scale soil salinity assessment with near-ground apparent electrical conductivity and remote sensing canopy reflectance. Ecol. Indic. 2016(70), 276–284 (2016)CrossRefGoogle Scholar
  23. 23.
    V.E. Tarasov, On chain rule for fractional derivatives communications in. Nonlinear Sci. Num. Simul. 30(1), 1–4 (2016)Google Scholar
  24. 24.
    S. Tonglu, L. Jianjun, H. Zhi, Tunable continuous-wave terahertz radiation system based on photomixing. Chin. J. Lasers. 41(4), 0411001 (2014)CrossRefGoogle Scholar
  25. 25.
    X. Wang, F. Zhang, K. Hsiang-Te, H. Yu, Spectral response characteristics and identification of typical plant species in Ebinur lake wetland national nature reserve (ELWNNR) under a water and salinity gradient. Ecol. Indic. 81, 222–234 (2017)CrossRefGoogle Scholar
  26. 26.
    J. Xu, F. Xinlu, G. Liang, et al., Fractional differential application in preprocessing infrared spectral data. Control Instrum. Chem. Ind. 39(3), 347–351 (2012)Google Scholar
  27. 27.
    I. Yahiaoui, A. Douaoui, Q. Zhang, A. Ziane, Soil salinity prediction in the lower Cheliff plain (Algeria) based on remote sensing and topographic feature analysis. J. Arid. Land 7, 794–805 (2015)CrossRefGoogle Scholar
  28. 28.
    G. Yang, L. Lu, C. He, et al., Baseline correction method for Raman spectra based on generalized Whittaker smoother. Chin. J. Lasers. 42(9), 0915003 (2015)CrossRefGoogle Scholar
  29. 29.
    F. Zhang, T. Tashpolat, V.C. Johnson, H. Kung, Evaluation of land desertification from 1990 to 2010 and its causes in Ebinur Lake region, Xinjiang China. Environ. Earth Sci. 73, 5731–5745 (2015)CrossRefGoogle Scholar
  30. 30.
    B. C. O’Kelly, Accurate determination of moisture content of organic soils using the oven drying method. Drying Technology 22(7), 1767–1776 (2004)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Fei Zhang
    • 1
    • 2
    Email author
  • Xiaoping Wang
    • 1
    • 2
  • Hsiang-te Kung
    • 3
  • Verner Carl Johnson
    • 4
  1. 1.Key Laboratory of Smart City and Environmental Modeling of Higher Education Institute, College of Resources and Environment SciencesXinjiang UniversityUrumqiChina
  2. 2.Key Laboratory of Oasis EcologyXinjiang UniversityUrumqiChina
  3. 3.Department of Earth SciencesThe University of MemphisMemphisUSA
  4. 4.Department of Physical and Environmental SciencesColorado Mesa UniversityGrand JunctionUSA

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