Analysis of Soil Pollution Degree and Causes Based on Mathematical Model

Transcription

1 Analyss of Sol Polluton Degree and Causes Based on Mathematcal Model Zeng Yunhu (Correspondng author) College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: Zhang Yuanbao College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: Huang Shusheng College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: Gong Hongfe College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: Chen Yln College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: 16

2 Shen Shyue College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: Huang L College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: @qq.com Hu Wenjuan College of Intellgent Scence and Engneerng, Jnan Unversty No. 206, Qanshan Road, Xangzhou Dstrct, Zhuha Cty, Guangdong Provnce, Chna Tel: E-mal: @qq.com Receved: Sep. 15, 2018 Accepted: Sep. 27, 2018 Publshed: December 24, 2018 do: /jee.v URL: Abstract Takng the heavy metal polluton n the urban surface sol as the object, ths paper analyzes the degree of heavy metal polluton n dfferent areas n the cty and the man causes of polluton. Frstly, ths paper uses Krgng nterpolaton method to ncrease the sample data together wth Surfer software to draw the spatal dstrbuton map of eght heavy metals, and then compares the sngle factor ndex method and the geologcal accumulaton ndex-nemero ndex method to make a comprehensve evaluaton of the heavy metal polluton degree n dfferent areas of the cty. It s concluded that the polluton level n the area from slght to heavy s: mountan areas, park green areas, lvng areas, traffc areas, ndustral areas. Then, the man comprehensve ndex of heavy metals s extracted by the prncpal component analyss, and the spatal dstrbuton map of the man factors s drawn based on t. Accordng to the spatal dstrbuton map, the man cause of heavy metal polluton s the emsson of automoble exhaust and ndustral waste, whch provdes a relable theoretcal bass for the preventon and treatment of heavy metal polluton n the urban surface sol. Keywords: heavy metal polluton, Krgng nterpolaton, Surfer, sngle factor ndex method, prncpal component analyss 17

3 1. Introducton Heavy metal polluton n sol refers to excessve heavy metal concentraton caused by excessve deposton of mcroscale metal elements n sol due to human actvtes. Wth the rapd development of urban economy and the contnuous ncrease of urban populaton, the mpact of human actvtes on urban envronmental qualty has become ncreasngly promnent. The verfcaton of urban sol geologcal envronment anomales and how to apply the vast amount of data obtaned from the verfcaton to carry out urban envronmental qualty assessment as well as study the evoluton pattern of urban geologcal envronment under the nfluence of human actvtes have become the focus of attenton. At present, plenty of studes have been carred out on the evaluaton of heavy metal polluton levels n urban sol at home and abroad. However, overall the evaluaton of academa for the degree of heavy metal polluton n urban sols s manly through a sngle method such as the sngle factor ndex method, the geologcal accumulaton ndex method and the Nemero ndex (Xu, 2008). Meanwhle t s only the surface analyss of the obtaned polluton degree results, drectly to the cause of polluton, not through the scentfc and effectve model for analyss and verfcaton. For example, only the geologcal accumulaton ndex method and Excel tool are used to study the degree of heavy metal polluton n the sol, and then the cause of polluton s drectly obtaned through the result of polluton degree (Xu et al., 2012), or only the sngle factor polluton ndex method s used to analyze the degree of heavy metal polluton n ctes (Yue et al., 2012). Although some used sngle factor ndex method and Nmero comprehensve polluton ndex method to evaluate the polluton degree of sol heavy metal elements, the polluton reason s drectly obtaned accordng to the analyss result of polluton degree, wthout consderng the correlaton between heavy metals and usng effectve way to verfy the concluson (Gu, et al., 2013; L, et al., 2014). In fact, the sngle evaluaton method of urban sol metal polluton degree exstng today has ts own scope and defects. For example, the geologcal accumulaton ndex can reflect the natural varaton characterstcs of heavy metal dstrbuton, but only gvng the degree of polluton of a sngle heavy metal n the samplng pont; the Nemero ndex specfcally consders the most pollutng factor, avodng the nfluence of subjectve factors n the weght coeffcent n the weghted process, but does not consder the natural dstrbuton characterstcs of the man metal dstrbuton. Therefore, only usng a sngle evaluaton method to evaluate the degree of sol heavy metal polluton wll nevtably result n an unobtrusve or naccurate evaluaton result. Besdes, the spatal dstrbuton of some heavy metals may have a certan correlaton. Metal wth greater correlaton may have a certan relatonshp between source and orgn, and related heavy metals may nterfere wth each other durng analyss. Therefore, when we analyze the man reason of heavy metal polluton, the relatonshp between heavy metal polluton must be consdered. Ths paper, to evaluate the problem of heavy metal polluton n dfferent regons, combned wth the sngle factor ndex method and the geologcal accumulaton ndex-nemero ndex method, draws a comprehensve concluson showng the degree of heavy metal polluton n dfferent regons. At the same tme, n ths paper, the prncpal component analyss method s used to convert the eght heavy metal elements mentoned n the data nto several lnear 18

4 uncorrelated comprehensve ndcators, whch help to elmnate mutual nterference between metal elements and smplfy data processng. Fnally, accordng to the spatal dstrbuton map of the man factors, the man causes of heavy metal polluton are obtaned, makng up for the lmtatons of the prevous studes on the degree and causes of heavy metal polluton n urban sol, and provdng a relable theoretcal bass to prevent and control heavy metal polluton n urban surface sol. 2. Method 2.1 Data Acquston and Assumptons The orgnal data of the research object of ths paper s from the 2011 Natonal College Students Mathematcal Modelng Competton (Chna Socety for Industral and Appled Mathematcs, 2011). The samplng ponts n the orgnal data are from the man functonal areas of lvng areas, ndustral areas, mountan areas, man road areas and park green areas. The data sheet lsts the locaton of the samplng ponts, the alttude and nformaton of ts functonal areas, together wth the concentraton of the eght major heavy metal elements at the samplng pont and the background values of the eght major heavy metal elements. To facltate analyss and understandngs, we make the followng assumptons about the model: (1)The data gven n the topc s true and authentc; (2)No consderaton of the degradaton of heavy metals; (3)Assumng that the probablty of arflow occurrng n all drectons s the same, that s, the atmospherc propagaton characterstc s consdered to be sphercal dffuson; (4)Ignore the effect of gravty on heavy metal ons. Include n these subsectons the nformaton essental to comprehend and replcate the study. Insuffcent detal leaves the reader wth questons; too much detal burdens the reader wth rrelevant nformaton. Consder usng appendces and/or a supplemental webste for more detaled nformaton. 2.2 Krgng Interpolaton The fact of Krgng nterpolaton (Zhou,2016) s usng the orgnal data of the regonalzed varables and the structural characterstcs of the varogram and makng lnear unbased and optmal estmaton of the unknown samples. Due to trends and expectatons of the unknown data, a regonalzed varable valuaton method of unknown expectatons s chosen under ordnary Krgng estmaton. Here,The regonalzed varable Z( x ) conssts of expectaton m and resdual ex: ( ) Zx ( ) m ex ( ) (1) Among them, expectaton m s unknown and the expectaton of resdual ex ( ) s 0. The second-order statonary of the varable Z( x) s assumed to be: 19

5 Among them, ( h) s ts varogram. EZ [ ( x h) Zh ( )] 0 (2) Var[ Z( x h) Z( h)] 2 ( h) (3) The estmaton formula for the ordnary Krgng estmaton method s: Z * n ( x ) = l Z( ) 0 x = 1 (4) Among them, Z ( x0 ) s the estmate of estmated poston x 0,and the observaton value of known locaton x ; observatons to use. s the weght assgned to Z( x ) ; n s the estmated number of The equaton for ordnary Krgng estmaton s: n j= 1 n j = 1 l C ( x x ) m = C( x x ), l = 1 j j = 1,2,..., n (5) The estmated error varance s: 2.3 Evaluaton Model s 2 OK = u + n l C = 1 ( x x ) + C( 0) 0 (6) Sngle Factor Polluton Index Method It s a relatve dmensonless ndex used to evaluate sol polluton degree or sol envronmental qualty levels. The polluton degree of the sol s represented by a sngle factor, and then the comprehensve polluton ndex P s calculated. The comprehensve polluton ndex P s a combnaton of sngle polluton ndexes. Its formula s (L et al.,2008): P C S = (7) Among them, P s the polluton degree of heavy mental, C s the actual concentraton of pollutants, and S s the evaluaton crtera for pollutants, generally takng the secondary standard of norganc pollutants n sol envronmental qualty standards.. Fnally calculate the comprehensve polluton ndex P. The formula s as follows: 20

6 P = n P = 1 n (8) Geologcal Accumulaton Index - Nemero Index Method. Geologcal accumulaton ndex The geologcal accumulaton ndex s wdely used to study the quanttatve ndcators of heavy metal polluton n sedments and other materals (Yang et al.,2014). It not only consders the nfluence of natural geologcal processes such as sedmentary dageness on the background values, but also pays attenton to the mpact of human actvtes on heavy metal polluton. However, the ndex can only be used to ndcate the polluton degree of a certan heavy metal, not provdng comprehensve polluton degree of varous heavy metals. Its expresson s as follows: I j = C (9) log j BE j In the formula, I j s the geologcal accumulaton ndex of the j th heavy mental n the th regon, Cj s the actual measured value of the j th heavy mental n the th regon,and BE j s the background concentraton of the j th heavy mental. Besdes, 1.5 s the correcton factor and usually used to ndcate sedmentary characterstcs, rock geology, and other effects.. Nemero Comprehensve Polluton Index The Nemero ndex s a weghted multfactor envronmental qualty ndex consderng the extreme value or the maxmum value. It hghlghts the mpact of the most pollutng substances on the degree of polluton. The basc formula s: P max ave = (10) 2 In the formula, P s the Nemero Comprehensve Index n the th regon, max s the maxmum value of the sngle factor polluton ndex of each heavy metal n the th regon, ave s the average of the sngle factor polluton ndex of each heavy metal n the th regon.. Comprehensve evaluaton Substtutng the results obtaned n the formulae (9) nto (10), the ndcators for comprehensve evaluaton of the polluton elements n dfferent regons can be obtaned. 21

7 2.4 Polluton Cause Analyss Model Spearman Coeffcent Spearman coeffcent s a statstc that measures the degree of correlaton between gradng and orderng varables. For the orgnal grade data, the one-sde openng data, the data whose overall dstrbuton s unknown and the data that does not obey the normal dstrbuton, or meet the correlaton coeffcent of the product, the Spearman coeffcent formula s (Zhang et al.,2016): 2 6 d r = 1 3 n n (11) Prncpal Component Analyss. Standardzed processng Suppose the orgnal data matrx be: X x x x x x x p p = x x x n1 n2 np and use the followng formula: X j * ( X X j j ) = ( = 1,2,,p;j = 1,2,p) S j (12) In the formula, S j s the standard devaton, X j s the mean. The orgnal data s normalzed to elmnate the dmenson relaton between the varables, makng the data comparable.. Calculatng the egenvalues and egenvectors of the correlaton coeffcent matrx The correlaton coeffcent s calculated as: r w n = X k = 1 * kw X * kj ( n 1) ( w = 1,2,, pj ; = 1,2,, p) (13) In the formulae, rjw = r, wj r jj =1, and the ndcator j. Its matrx s: r wj s the correlaton coeffcent between the ndcator w 22

8 r11 r r21 r R = rp1 r p2 r1 p r2 p r pp. Calculatng the egenvalues and egenvectors Supposng that λ 1, λ 2,..., λ ( λ 1 > λ 2 >... > λ ) p p are the egenvalues of R and u, u,... u 1 2 p are the correspondng egenvectors, then there s the followng lnear transformaton relatonshp: y 1 ux 11 1 ux 12 2 ux 1p p y 2 u 21x 1 u 22x 2 u 2px p = = y = p u p1x + 1 u p 2x u ppx p v. Contrbuton rate and cumulatve contrbuton rate Contrbuton rate: cumulatve contrbuton rate: p ηt λt λ j j = 1 = ( t 1,2,, p) t t j j j = 1 j = 1 p α = λ λ ( t 1,2,, p) = (14) = (15) v. Calculatng prncpal component load ( ) = = λ (, j = 1,2, Λ, p) l p z x e, j j j (16) v. Calculatng each prncpal component score Z z z Λ z z z Λ z m m = M M M Λ n1 n2 nm z z z 23

9 3. Model Establshment and Soluton 3.1 Spatal Dstrbuton of Heavy Metals n Sol Based on Krgng Interpolaton Usng the Surfer software to the data n the attachment x and y, the concentraton of eght heavy metals are flled by Krgng nterpolaton method, and the three-dmensonal spatal dstrbuton map was drawn. Due to the space lmtaton, only concentraton of As, Cd s shown n Fgure 1, Fgure 2. Fgure 1. Spatal dstrbuton of as concentraton n the urban area Dfferent colors are used to ndcate the concentraton of As n the regon. The closer to red, the hgher the concentraton of As n the area. On the contrary, the closer to blue, the lower the concentraton of As n the area. It can be seen ntutvely from Fgure 1 that As s more concentrated n the central and southwestern part of the urban area, that s, the concentraton of As n the ndustral area and the traffc area s hgher. It can be seen from Fgure. 2 that Cd s more concentrated n the southwest drecton of the urban area, that s, the concentraton of Cd n the ndustral area s very hgh. 24

10 Fgure 2. Spatal dstrbuton of Cd concentraton n the urban area 3.2 Analyss of Polluton Degree of Heavy Metals n Dfferent Regons Soluton of Evaluaton Model. Solvng the sngle factor ndex method a) Constructng a sngle factor ndex matrx Calculate the average concentraton of each heavy metal n each regon, and then calculate the sngle factor ndex of each heavy metal n each regon accordng to formulae (7). The obtaned matrx s shown n Table 1: Table 1. Sngle factor ndex matrx Area As Cd (ng/g) Cr Cu Hg (ng/g) N Pb Zn b) Calculatng the comprehensve polluton degree ndex Calculate the sngle factor comprehensve polluton degree by usng the data n Table 1 by formula (8). The results are shown n Table 2: 25

11 Table 2. Sngle factor comprehensve polluton degree Area P Among them, the hgher the P value, the more serous the polluton. c) Gradng accordng to the comprehensve ndex polluton degree Accordng to the comprehensve ndex polluton degree gradng standards (Appendx II), the degree of polluton of each heavy metal substance n each regon and the comprehensve polluton degree of each regon can be evaluated. The results are shown n Table 3: Table 3. Comprehensve polluton degree Area Grade Rankng Among them, the grade represents the polluton degree n the regon, and the rankng represents the rankng of the polluton degree n the fve regons. By usng sngle factor ndex method to analyze each heavy metal n each regon, t was found that Zn and Cd were the most polluted n lvng areas and green areas; n addton to hgh Zn and Cd n the ndustral zone, the polluton degree of Cu and Hg s also qute hgh; the hghest degree of polluton n the mountan areas s Cd; the polluton degree n the traffc areas are hgh n order of Cd, Zn, Cu and Hg. Besdes, the comprehensve polluton degree of the fve regons from slght to hgh are ranked from mountan areas to park green areas, lvng areas, traffc areas and ndustral areas.. Heavy metal polluton degree model based on geologcal accumulaton ndex-nemero ndex a) Constructng a geologcal accumulaton ndex matrx Frstly, calculate the average concentraton of each heavy metal n each regon. Then, accordng to the geologcal accumulaton ndex formulae (9), the sngle factor ndexes I of each heavy metal substance n each regon s calculated. The results are shown n table 4: Table 4. Geologcal accumulaton ndex matrx Area As Cd (ng/g) Cr Cu Hg (ng/g) N Pb Zn

12 b) Calculatng comprehensve polluton ndcators usng the Nemero ndex Calculate the comprehensve polluton degree ndex P n each regon usng all the geologcal accumulaton ndexes n each regon n table 4 and mprove the basc Nemero formulae (10). The followng formula s obtaned: P I 2 2 I j max j ave (17) 2 In the formula, P s the comprehensve polluton ndex for the th regon, j max I s the maxmum value of the eght geologcal accumulaton ndexes n the regon, and I j s the average value of the eght geologcal accumulaton ndexes n the regon. Use the formulae (17) to obtan the comprehensve polluton ndex of the fve regons. The results are shown n Table 5: Table 5. Geologcal accumulaton - Nemero comprehensve polluton degree Area P Grade Rankng By analyzng each heavy metal n each regon by geologcal accumulaton ndex, t was found that the lvng area was serous polluted by Zn; the park green area was serously polluted by Hg; the ndustral area was serously polluted by Cd, Cu, Hg, Pb, Zn ; the mountan area was not polluted; the traffc area was serously polluted by Cu, Hg, Zn. In addton, the comprehensve polluton levels of the fve regons from low to hgh are followed by mountan areas, park green areas, lvng areas, traffc areas and ndustral areas, whch are the same as those obtaned by the sngle factor ndex method, ndcatng the accuracy of the fnal conclusons. 3.3 Soluton of Heavy Metal Polluton Analyss Model Verfcaton of Normal Dstrbuton Usng SPSS to process data (Lu et al., 2003), and verfy the normal analyss, due to space lmtatons, only the normal dstrbuton map of Hg, Zn s lsted here, as shown n Fgure 3 and Fgure 4 below. ave 27

13 Fgure 3. Normal dstrbuton test dagram of Hg element Fgure 4. Normal dstrbuton test dagram of Zn element It can be seen ntutvely from the fgure that the dstrbuton of heavy metal element concentraton does not satsfy the normal dstrbuton, so that the Spearman coeffcent can be used Verfcaton of Correlaton Analyss Verfcaton of correlaton analyss s to analyze whether there s a certan relatonshp between the varous heavy metals, that s, whether they can be consdered separately. Snce the heavy metal polluton ndcators do not obey the normal dstrbuton, the SPSS software s used to verfy the correlaton of the Spearman coeffcent. Some of the results are shown n Table 6. 28

14 Table 6. Correlaton verfcaton of several heavy metal polluton Spearman coeffcents Spearman As Cd (ng/g) Cr Cu As Cd (ng/g) Cr Cu Hg (ng/g) N Pb Correlaton coeffcent * ** ** ** ** ** sgnfcance N Correlaton coeffcent * ** ** ** ** ** sgnfcance N Correlaton coeffcent ** ** ** ** ** ** sgnfcance N Correlaton coeffcent ** ** ** ** ** ** sgnfcance N Among them, the ** marks the correlaton s sgnfcant at 0.01 (two-taled), and the * marks that the correlaton s sgnfcant at It can be seen from the table that there s a strong correlaton between varous heavy metals, such as Cr and N, Cd and Pb. Therefore, t s judged from the ngredents that they have strong correlatons n the source Prncpal Component Analyss a) Prncpal component ratonalty analyss KMO and Bartlett are used to verfy whether the orgnal varables are sutable for prncpal component analyss. The results are shown n Table 7. Table 7. Verfcaton of KMO and Bartlett Kaser-Meyer-Olkn Measurng samplng legtmacy.778 Bartlett's sphercal ch-square check Df sgnfcance From Table 7, the value of KMO s The orgnal hypothess of the Bartlett Sphercty test s that the correlaton coeffcent matrx s a unt matrx, and the Sg value s whch s less than the sgnfcant level of The orgnal hypothess s rejected, ndcatng that there s a correlaton between the varables and that s sutable for prncpal component analyss. 29

15 b) Determnng the prncpal component factors The number of prncpal component factors was determned by SPSS software. The results are shown n Table 8. Table 8. The quanttatve analyss of prncpal component factor Com Startng egenvalue Codfed sum of squares load pone nt Statstcs Accumulate d % Accumula te % Statstcs Accumula ted% Accumulate% It can be seen from the table that the cumulatve varance contrbuton rate of the frst sx factors s greater than 90%. Therefore, the frst sx factors are extracted as the prncpal factors. c) Calculatng the factor load value The prncpal component load value s acqured by calculatng the egenvectors, cumulatve contrbuton rate and other ndcators. And the Kaser normalzed orthogonal rotaton method s used to obtan the load values of rotated factors by factor rotaton. The values are as shown n Table 9. Table 9. Factor load value after rotaton component element Z-score: As Z-score: Cd (ng/g) Z-score: Cr Z-score: Cu Z-score: Hg (ng/g) Z-score: N Z-score: Zn Z-score: Pb Analyss of the causes of heavy metal polluton To carry out the analyss better, the SPSS software s used to convert the table data 30

16 correspondng to the eght orgnal varables nto the data correspondng to the sx prncpal factors. Because there s a certan postve lnear relatonshp between the prncpal factor varable and the meta varable, t can determne the spatal dstrbuton of the orgnal varables based on the spatal dstrbuton of the prncpal factors. Due to space lmtatons, only the spatal dstrbuton of the frst two prncpal factors s shown here n Fgure 5 and Fgure 6. Fgure 5. Factor I spatal dstrbuton contour map Fgure 6. Factor II spatal dstrbuton contour map Accordng to the spatal dstrbuton contour map of Factor 1, the elements N and Cr are 31

17 closely related n source, and ther concentratons n the lvng area and traffc area are hgh. In real lfe, there are many overlappng parts n the two areas. Therefore, the analyss s that the excessve content of N and Cr s caused by the domestc sewage and automoble exhaust emssons. From the spatal dstrbuton contour map of factor 2, Cd and Pb are closely related n source, and the concentratons are hgh n the traffc area and ndustral area. The analyss s that t manly caused by the emsson of automoble exhaust and ndustral waste water. It can be seen from the spatal dstrbuton contour map of the factor 3 that the element Hg has a hgher concentraton n the traffc area and the ndustral area. However, n the lower left part of the fgure, an anomaly that spreads to one sde appears. The analyss s that the uneven Hg n the propagaton process may be due to the presence of wnd or ran eroson n a certan drecton. From the spatal dstrbuton contour map of Factor 4, t can be seen that the concentraton of element As n the traffc area and ndustral area s hgh. Combned wth the actual stuaton, the man source of As s the dscharge of ndustral As wastewater, whch s consstent wth the actual stuaton. Accordng to the spatal dstrbuton contour map of Factor 5, the concentraton of element Cu n the ndustral area s relatvely hgh. Combned wth the actual stuaton, t s known that Cu manly comes from the chemcal ndustry and the three wastes n the plastcs, prntng and dyeng ndustres, whch s consstent wth the actual stuaton. It can be seen from the spatal dstrbuton contour map of Factor 6 that the concentraton of element Zn s hgh n the lvng area and ndustral area. Combned wth the actual stuaton, t s known that the source of Zn s manly the dscharge of domestc sewage and ndustral wastewater, whch s consstent wth the actual stuaton It can be seen from the above results that the man source of heavy metal polluton s consstent wth the actual stuaton accordng to the spatal dstrbuton map of heavy metal concentraton. The content of varous heavy metals n the traffc area and ndustral area s relatvely hgh, and t s known that the emssons of automoble exhaust and ndustral wastes are the major sources of heavy metal polluton. At the same tme, the concentraton of Cr and N s hgher n the traffc area and s also affected by the lvng area. The analyss s that the polluton s manly caused by automoble exhaust gas (the domestc sewage also accounts for a part of the proporton). The concentraton of Cd and Pb s relatvely hgh n the traffc area and ndustral area. And analyss s that t manly caused by automoble exhaust and ndustral waste gas or ndustral sewage. The concentraton of Hg s relatvely hgh n the traffc area and ndustral area. The concentraton of As relatvely hgh n the traffc area and ndustral area. The concentraton of Cu s hgh n the ndustral area and lvng area, and t s also hgh n the traffc area manly due to the ndustral prntng producton. The concentraton of Zn s hgher n the lvng area and traffc area. 32

18 4. Concluson In ths paper, at frst, the Krgng nterpolaton method s used to lnearly estmate the concentraton of heavy metals n the unsampled regon, so that t can ncrease the sample sze objectvely. Based on ths, the spatal dstrbuton maps of eght heavy metals are obtaned. At the same tme, the sngle factor ndex method and the geologcal accumulaton ndex-nemero ndex method are ntroduced to evaluate the degree of heavy metal polluton n dfferent regons. It s found that ther descrptons of the polluton degree are smlar, and the comprehensve polluton ndex s compared to obtan the polluton degree of dfferent areas. The degree from slght to heavy s: mountan areas, park green areas, lvng areas, traffc areas, ndustral areas. Subsequently, the correlaton analyss of the eght heavy metal elements gven n the ttle s carred out. Wth the premse of ensurng that many varables were fully explaned by a few factors, prncpal component analyss s used to transform them nto several lnear and rrelevant comprehensve ndcators. It s used to elmnate mutual nterference between metal elements and smplfy data processng. Fnally, accordng to the spatal dstrbuton map of the prncpal factors, t s known that the man cause of heavy metal polluton s the emsson of automoble exhaust and ndustral waste, whch provdes theoretcal bass and gudng sgnfcance for preventng and treatng heavy metal polluton n urban sol. However, the research n ths paper has some shortcomngs because the data gven by the ttle s lmted, whch are emboded n: (1)The number of samplng ponts gven n the queston s small, whch causes a large error after nterpolaton. (2)The data provded s sampled n a grd of one klometer wthout specfc geographcal dstrbuton. Therefore, when analyzng polluton sources, t has certan ambguty because t s based on nterpolaton. Acknowledgments Ths work was supported by the Natonal Natural Scence Foundaton of Chna ( ), the Fundamental Research Funds for the Central Unverstes ( ), Key Project of Guangdong Natural Scence Foundaton (2016A ), 2015 Guangdong Specal Support Scheme (2014TQ01X706), Hgh-level Talent Scheme of Guangdong Educaton Department ( ), the Guangdong Natural Scence Foundaton (2017A ). References Chna Socety for Industral and Appled Mathematcs. (2011). Hgher Educaton Club Cup Natonal Contest on Mathematcal Modelng for College Students. [Onlne] Avalable: Gu, Y-Qu., Shen, Je-Je., & Yao, Wen-Xu. (2013). Analyss of Heavy Metal Polluton n the Surface Sol of Cty. Journal of Xchang Unversty (Natural Scence Edton), 27(1). Mar

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