Post on 12-Jul-2020
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