Fractional Differential Method For Near Surface Remote Sensing Estimation Of Heavy Metals In Soil

Estimation of soil heavy metals based on spectral data is an important direction of monitoring soil heavy metal pollution using remote sensing technology.Among them,spectral reflectance is based soil heavy metal inversion research is also a relatively mature research system.In the process of using spectral data to invert soil heavy metals,the precision of spectral data preprocessing has a significant impact on the precision of the final model estimation.In the actual data preprocessing,after first order differential and reflectance curve of second order differential transformation has great difference with the original spectral curve,direct use of integer order differential for data processing,more tiny information between and among ignore and to a certain extent will lead to access to information is not complete,and the negative influence on the precision of the estimation model.The calculation of fractional differential pays more attention to the change process of the first and second order differential.By refining the spectrum,the difference of the spectrum is increased,so that the data information can be used more effectively.However,in the spectrum research direction,the development of fractional differential is still relatively slow,and the related research is still relatively lack,so this study introduced the concept of fractional differential in the spectral preprocessing.After the mathematical transformation,the fractional differential calculation of various mathematical forms is carried out,and the subtle soil heavy metal information in the spectral data is deeply mined.Through the analysis,a possibility is explored,that is,to add the fractional differential method in the remote sensing research,so as to achieve better monitoring effect of soil heavy metal.In this study,the plains in the north of Longkou was determined as the study area.in the area of soil heavy metals As and Pb As the research object,in combination with the determination of the laboratory parameters such As heavy metal content and spectral index,using the fractional order differential processing results,the characteristics of spectra and spectral index As the independent variables,heavy metals As and Pb respectively As the dependent variable,based on partial least squares method,the estimation model of building,and model verification.Based on the discussion of fractional differential and modeling and verification of soil heavy metals,the conclusion is drawn:(1)In this paper,three indexes including range,coefficient of variation and correlation coefficient of reflectance and heavy metals were selected to analyze the relationship between them and the fractional order differential order,and the influence of fractional order differential on spectral data was studied.This study found that(1)With the fractional order differential of the order number from 0 to 2 the change of the order,the poor on the fractional order value is very close to the integer order on poor value,poor value infinite close to zero,it shows that to score after differential spectral reflectance spectra happened to the discrete degree is reduced,its distribution is also concentrated near the zero,this change makes it easier to access to effective information simple.(2)When the order of fractional differential increases gradually from 0 to 1,the correlation coefficient curve also changes.When the order changes from 1 to 2,the correlation coefficient curve has a great fluctuation,indicating that the autocorrelation between the spectra is significant.(3)For the four mathematical transformations of the original spectral data R,reciprocal RT,logarithmic LT and logarithmic reciprocal AT,it is found that they have no weak variation bands,and with the increase of the differential order,the number of moderate variation bands shows a trend of first decline,then rise,and then decline,and the order corresponding to some extreme points are all in the fractional order.Through the analysis of the above three indexes,it can be seen that the fractional order differential directly affects the variation of indexes such as range,correlation coefficient and coefficient of variation,and makes the depth mining of data easier by refining the spectrum.(2)64 soil samples will be collected in the study area according to the ratio of 3:1was divided into modeling set(n=43)and the validation set(n=21),according to the condition of large and significant correlation to selection of the spectral reflectance of soil samples,as a characteristic spectrum,then selected spectra and spectral index as the independent variable,heavy metal As and Pb respectively as the dependent variable,and modeling PLSR.In our use of 0 to 2 order differential value of 168 soil heavy metal estimation model,a total of 39 model effect is good,the RPD is greater than 2,compare RMSEC,R_C~2,RMSEP,R_P~2 and RPD found that for heavy metals As,1.8 order differential data based on the logarithmic data the established model is best,the optimal result,the precision of the model evaluation index RMSEC=1.2,R_C~2=0.703,RMSEP=0.32,R_P~2=0.842 and RPD=2.271.For heavy metal Pb,according to the data processing after logarithmic transformation of LT,when its fractional order is 1.9,the model established is the best and the effect is the best.The precision evaluation indexes of the model are RMSEC=13.26,R_C~2=0.718,RMSEP=4.31,R_P~2=0.803 and RPD=2.328.For the PLSR models established by the original spectral data R,reciprocal RT,logarithmic LT,logarithmic reciprocal AT and heavy metals,most of the optimal models achieved the best results in the fractional order.It is indicated above that the accuracy of modeling can be improved after the processing of spectral data by fractional order differentiation.Therefore,we introduce fractional differential in the preprocessing,which can be used to refine the spectral data,so as to significantly improve the accuracy and stability of modeling.