Transcript Bayesian maximum entropy solution of the stochastic

Spatiotemporal mapping of
ground water pollution in a Greek
lignite basin, using Geostatistics
K. Modis,
National Technical University of Athens, GREECE
SWEMP 2010 – 25-05-2010, Prague, CzechRepublic
Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Contents
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


Scope
The data
Mapping
Conclusions
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Scope
3
Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Objective

The objective of this work
is to apply Bayesian
Maximum Entropy (BME)
analysis, in order to
estimate the spatiotemporal
distribution of ground water
contamination in an area of
northwestern Greece.
Scope
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Variables of Interest


Our interest is focused on the presence of
ammonium, nitrite and nitrate ions.
52% of the samples exceed the TAC for
ammonium, 10% for nitrites and 3% for
nitrates.
Pollutant
Mean (mg/l)
Max (mg/l)
TAC (mg/l)
Ammonium
1.41
136
0.50
Nitrites
0.49
25
0.50
Nitrates
8.93
151
50
Scope
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
What is BME

The spatiotemporal distribution of groundwater pollution is studied within the
framework of the BME analysis, which is a
versatile extension of classical geostatistical
methods that can use a variety of physical
input, as well as hard and soft (uncertain)
observations.
Scope
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
The data
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Available Data

During the period from
2000 to 2007, 633
water samples from a
set of 64 boreholes
were taken at various
time periods. A number
of samples (usually
quarterly) are available
for each borehole,
varying from 1 to 30.
The data
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics

In general, pollutant
concentrations do not
seem to exhibit any
notable temporal trend
during the period of
monitoring.
Some
seasonal variations might
be present but they can
not be clearly quantified
The data
Ammonium (mg/l ).
Temporal Trend
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
3 tms 2004
3 tms 2005
3 tms 2006
time (trimesters)
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Why geostatistics

Regarding the problem of spatial and temporal
mapping of water contamination, the coarse
and irregular sampling pattern, especially if
combined with absence of evident seasonal
variations and temporal trends, does not
facilitate further processing of the data by use
of deterministic models. A mere statistical
analysis seems then appropriate
The data
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Detrending

Detrending of the dataset
was accomplished with
the application of a
Gaussian
kernel
transformation.
Subtraction of trend from
the original values leads
to a homogeneous S/TRF
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Basic Assumption

Our analysis considers the first (means) and
second (covariances) moments of the
rainfall S/TRF, hence we assume that it
follows a Gaussian distribution.
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Normality Assessment
500
400
Frequency
However,
the
data
distribution
histograms
were positively skewed.
Normality was assessed
by applying a normal
scores transformation to
the detrended data.
300
200
100
0
-50
50
Data
100
150
2
4
60
40
20
0
-4
Mapping
0
80
Frequency

-2
0
Data
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Covariance Model

A suitable permissible
covariance model was
selected to describe
the
spatiotemporal
systematic
dependencies of the
pollutant
concentrations, based
on the experimental
covariance from the
observations.
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Ranges of Influence

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A spatial range of
influence of 800 m
appears in all models.
In the temporal part, a
nested structure of two
spherical
models
is
evident in all pollutant
distributions with ranges
of 4 and 40 trimesters
respectively.
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Spatiotemporal mapping
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In the prediction stage we used the available
measurements as well as the aforementioned
structural models in order to produce spatial
maps of the probability that the pollutants
exceed the corresponding TACs, for all time
instances (trimesters) in the 8 year period.
These maps may be used in the future for the
assessment of the health risk due to elevated
groundwater pollutant concentrations in
cultivated areas.
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Examples
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Risk assessment model for ammonium from
2000 to 2007
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Examples
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6
x 10
1
0.8
0.6
4.48
0.4
4.475
0.2
x 10
8
4.485
y-coordinate (m)
y-coordinate (m)
4.485
-7
x 10
6
4.48
4
4.475
2
3.05

3.1
3.15
x-coordinate (m)
3.2
5
x 10
3.05
3.1
3.15
x-coordinate (m)
3.2
5
x 10
Risk assessment maps for nitrates on 4th trimester 2003
(left) and 1st trimester 2004 (right)
Mapping
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Concluions
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Conclusions (1)


The data in a hydrogeological data set
concerning pollution, may not be enough to
allow for deterministic estimation of a
possible seasonal behavior or a temporal
trend.
In that case, the application of the BME
theory which allows merging spatial and
temporal estimations in a single model may
be a solution to this problem.
Conclusions
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Conclusions (2)

In the case of Ptolemais mining area, results
reveal an underlying average yearly variation
pattern of pollutant concentrations. A second,
longer cycle, indicate a potential forecasting
range of up to 10 years.
Conclusions
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Conclusions (3)

Inspection of the produced spatiotemporal
maps shows a continuous increase in the risk
of ammonium contamination, while risk for
the other two pollutants appears in hot spots.
Conclusions
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Modis: Spatiotemporal mapping of ground water pollution in a Greek lignite basin, using Geostatistics
Thank you!
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