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Report on

Evaluation of Environmental Qualityand Evolution in Urban Soils of

Qingdao City

Y. Cai, Z. Cai, L. Duan, C. Farmer, Z. Gu,S. Jaimungal, G. Li, J. Ockendon, H. Yang, Q. Ye

+S. Ding, Z. Hao, Q. Jiang, X. Guo, K. Kwon,

W. Liu, J. XuReport on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 0/20

1. Problems

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 1/20

1. Problems

What we know about the problem are:(1) the coordinates of 319 sample sites and some

environmental factors about the sample sites;(2) the concentrations of 70 elements in 319 sites.


1. Problems

(1) Is there a quantitative model describing theprimary heavy metals (such as Cd, Cr, Cu, Ni, Pb, Zn,Hg, and As) distributions and their relations?


1. Problems

(1) Is there a quantitative model describing theprimary heavy metals (such as Cd, Cr, Cu, Ni, Pb, Zn,Hg, and As) distributions and their relations?

What about for rare earths elements ormicroelements?


1. Problems

(2) As compared with the background values,could we find some pollution sources characteristicsfor heavy metals?


1. Problems

(2) As compared with the background values,could we find some pollution sources characteristicsfor heavy metals?

Could we construct an evolution model todescribe the process and make some prediction?


1. Problems

(3) The methods in being to evaluate soilgeological environment is mostly for single element,such as the methods of Igeo and EF, etc.


1. Problems

(3) The methods in being to evaluate soilgeological environment is mostly for single element,such as the methods of Igeo and EF, etc.

Could we find more effective ways to evaluateimpacts of human activities on the urban soilsenvironmental quality when consideringmulti-elements?


2. Data Analysis


2. Data Analysis

(1) Use geostatistics to interpolate themeasurements by Kriging with a variogram.


2. Data Analysis

Simple dual Kriging


2. Data Analysis

Simple dual KrigingAssume

γ(λ) =1

2〈(u(x) − u(x + λ))2〉

whereu(x) is concentration,λ is lag-vector.


2. Data Analysis

u(x) = m +N

∑

i=1

wiγ(x − xi)

N∑

i=1

wi = 1

u(xi) = u∗i , i = 1, 2, · · · , N

whereu∗i are measurements.


2. Data Analysis

u(x) = m +N

∑

i=1

wiγ(x − xi)

N∑

i=1

wi = 1

u(xi) = u∗i , i = 1, 2, · · · , N

whereu∗i are measurements.

m andwi (i = 1, 2, · · · , N ) can be determined.


2. Data Analysis

(2) Perform correlation analysis of the data fordifferent chemicals.


2. Data Analysis

Denoteci anddi by the concentrations of twoelements at(xi, yi).


2. Data Analysis

Denoteci anddi by the concentrations of twoelements at(xi, yi).

The correlation coefficient is

Rc,d =

∑

(ci − c)(di − d)√

∑

(ci − c)2

√

∑

(di − d)2


2. Data Analysis

RCr,Ni = 0.72

RCd,Pb = 0.66


2. Data Analysis

Concentration contour of Cd


2. Data Analysis

Concentration contour of Pb


2. Data Analysis

Generalized Correlation Coefficient


2. Data Analysis

Generalized Correlation Coefficient

Our problem involves many kinds of elements,such as heavy metal, rare earth, etc. So, in order toinvestigate the sources of pollution and thedistribution of these elements, we need to find theglobal correlation between two element groups. Herewe use the generalized correlation coefficient.[Yaoting Zhang, Generalized correlation coefficients and their

applications (in Chinese),Acta Mathematicae Applicatae Sinica, 1978,

1(4):312–320].


2. Data Analysis

Denotex andy are concentrations of two groupsof elements

Σxx = E(x − Ex)(x − Ex)′

Σyy = E(y − Ey)(y − Ey)′

Σxy = E(x − Ex)(y − Ey)′


2. Data Analysis

Denoteλi (i = 1, 2, · · · , n) are the eigenvaluesof Σ+

xxΣxyΣ+yyΣyx, whereΣ+

xx, Σ+yy are the

Moore-Penrose inverse of matrixΣxx andΣyy.


2. Data Analysis

Denoteλi (i = 1, 2, · · · , n) are the eigenvaluesof Σ+

xxΣxyΣ+yyΣyx, whereΣ+

xx, Σ+yy are the

Moore-Penrose inverse of matrixΣxx andΣyy.

1

n

n∑

i=1

λi

is the generalized correlation coefficient.


2. Data Analysis

(3) Perform correlation analysis betweeninterpolated data and the height fieldh(x).

(to be done)


3. Modeling


3. Modeling

Convection Model


3. Modeling

Convection Model

∂u

∂t+ ∇q = 0


3. Modeling

Convection Model

∂u

∂t+ ∇q = 0

q = −ku∇h


3. Modeling

Convection Model

∂u

∂t+ ∇q = 0

q = −ku∇h

∂u

∂t− k∇h · ∇u − ku∇2h = 0


3. Modeling

Characteristic

dx

dt= −k∇h

du

dt= ku∇2h

The solution is

u(x, t) = uT exp

(

−

∫ T

t

k∇2h(x(τ))dτ

)

(1)


3. Modeling

Finding pollution regions


3. Modeling


∀p, from interpolated datau(p, T ), we calculateu(x(t), t;p) (0 ≤ t ≤ T ) backwards in time along thecharacteristic curve throughp.


3. Modeling


∀p, from interpolated datau(p, T ), we calculateu(x(t), t;p) (0 ≤ t ≤ T ) backwards in time along thecharacteristic curve throughp.

Given a threshold of pollution concentrationu∗,for any givent (0 ≤ t ≤ T ), denote

Bt = {x(t) | u(x(t), t;p) ≥ u∗}

as the possible pollution regions att.


Finding Pollution Regions

k is unknown, however the formula can stillsuggestwhere the pollution originated but notwhen.


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