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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.

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

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?

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 2/20

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?

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 2/20

1. Problems

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 3/20

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?

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 3/20

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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 4/20

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?

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 4/20

2. Data Analysis

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 5/20

2. Data Analysis

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 5/20

2. Data Analysis

Simple dual Kriging

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 6/20

2. Data Analysis

Simple dual KrigingAssume

γ(λ) =1

2〈(u(x) − u(x + λ))2〉

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 6/20

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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 7/20

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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 7/20

2. Data Analysis

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 8/20

2. Data Analysis

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 9/20

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 9/20

2. Data Analysis

RCr,Ni = 0.72

RCd,Pb = 0.66

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 10/20

2. Data Analysis

Concentration contour of Cd

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 11/20

2. Data Analysis

Concentration contour of Pb

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 12/20

2. Data Analysis

Generalized Correlation Coefficient

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 13/20

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].

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 13/20

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)′

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 14/20

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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 15/20

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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 15/20

2. Data Analysis

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

(to be done)

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 16/20

3. Modeling

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 17/20

3. Modeling

Convection Model

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 17/20

3. Modeling

Convection Model

∂u

∂t+ ∇q = 0

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 17/20

3. Modeling

Convection Model

∂u

∂t+ ∇q = 0

q = −ku∇h

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 17/20

3. Modeling

Convection Model

∂u

∂t+ ∇q = 0

q = −ku∇h

∂u

∂t− k∇h · ∇u − ku∇2h = 0

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 17/20

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)

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 18/20

3. Modeling

Finding pollution regions

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 19/20

3. Modeling

Finding pollution regions

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

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 19/20

3. Modeling

Finding pollution regions

∀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.

Report on Evaluation of Environmental Quality and Evolution in Urban Soils of Qingdao City – p. 19/20

Finding Pollution Regions

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

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