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DIRECTIONAL
VARIOGRAPHY AND ASSESSMENT OF
THE CHARACTERISTICS OF A CONTAMINATION SOURCE OF AN AQUIFER: IS IT A POSSIBLE
TASK?
G. PASSARELLA
(*), M. VURRO (*), V. D'AGOSTINO(**) AND and M. BENEDINI(***)
(***)
Istituto di Ricerca Sulle Acque, CNR, Roma, Italy.
(**) Tecnopolis,
Novus Ortus, Valenzano, Italy;
(*) Istituto di
Ricerca Sulle Acque, CNR, Bari, Italy.
via F. De
Blasio, 5 - 70123 Bari, Italy
tel.
+39-080-5313354; fax +39-080-5313365; e-mail: passarella@area.ba.cnr.it
ABSTRACT
The geometric characteristics
of a contamination source in an aquifer are a very important element for
managing, monitoring and cleaning
polluted groundwater. This paper
outlines a methodology to evaluate the configuration of the sources using a
geostatistical approach, based on the directional variography. The proposed
method has been tested using the results of three simulated cases and the
values of concentration of several pollutants sampled in 36 wells. Directional
experimental variograms have been plotted, for each variable, and theoretical
models with their parameters (range and sill) have been fitted. The radar plots
of the values of the sills explain the different typology of the sources. In
particular, linear sources produce a butterfly
shape radar plot, punctual sources produce a rounded shape radar plot and sparse, punctual sources produce an
almost irregular shape radar plot.
The analysis of directional variography can have practical usability in
screening field measurements aimed at the identification of contamination
sources.
KEYWORDS
Keywords: Geostatistics,
Directional Variography, Groundwater, Pollution
INTRODUCTION
Problems related
to groundwater pollution are of increasing importance, particularly in regions
where the scarcity and deterioration of surface water render subsurface
resources the most important source of drinkable water. The knowledge of the
characteristics of a contamination source of groundwater is an important
element in environmental problems. Inferences of the a posteriori identification of the source of an aquifer
contamination are relevant to define choices and procedures in monitoring and
cleaning polluted systems [4]. Geostatistical techniques have been used to
evaluate the distribution of hydrogeological parameters in specific areas [5,
7, 13]. Recently some investigations have addressed the inferences of spatial
correlation for physical and chemical parameters using the above techniques [2,
3].
This paper
discusses the possibility of using directional variography to evaluate the typology
of groundwater contamination sources. The hydrogeological knowledge of the test
site coupled with an understanding of the physics of the studied phenomena
allow an interpretation of the experimental directional variograms obtained,
which yields an insight of the pollution sources.
DIRECTIONAL
VARIOGRAPHY
Estimation
requires a model of how the phenomenon behaves at locations were it has not
been sampled. Few earth science applications are understood in sufficient
detail to permit a deterministic approach to estimation. There is a lot of
uncertainty about what happens at unsampled locations. The geostatistical
approach is based on a probabilistic model that recognizes these inevitable
uncertainties. In such a probabilistic framework, the available sample data are
viewed as the result of some random process. In practice, geostatistics adopts
a stationary random function, Z(x), as model and specifies only its variogram.
Using the variogram a weaker form of stationarity is sufficient. In fact, in
such a case the (second order) stationarity is not assumed for Z(x) but rather
for the first-order differences (Z(x+h)-Z(x)); this is called intrinsic
hypothesis [8]. The variogram function g(h) is defined by
(1)
where var indicates the variance of the
increments of Z(x).
The process of
variograms construction and modeling is called variography.
Starting from
point values, say z(x1),...,z(xn) at n locations x1,...,xn
in a two-dimensional space, an estimator of g(h) is represented by the
experimental variogram g*(h) defined as follows:
(2)
where n(h) is the
number of data pairs in each interval of distances. The knowledge on the data
value and position is useful to calculate the experimental variogram, to choose
the variogram model and to determine the model parameters.
A typical behavior
for g*(h) starts at 0 and reaches the maximum (or sill)
value g*(a) = C,
for h a. The value h = a is called range and
represents the maximum separation distance for which sample pairs remain correlated
in the mean. In some cases, when h
approaches zero, a non-zero value of g*(h) = C0 is sought. This limiting
value C0 is called the nugget. With or without nugget effects
the sill value depends on the variogram model used. Journel and Huijbregts [8]
suggest avoiding automatic variogram model selection and curve fitting. When
the variography concerns multiple directions for the lag-vector h, it is
called directional variography. Using directional variography it is possible to
investigate anisotropic data. In the isotropic case the variable is studied
irrespective of directions and the variogram depends only on the modulus of the
lag-vector h. In the anisotropic
case, spatial variability in multiple directions is considered and the
variogram depends on the choice of the direction.
Since nugget
values do not vary with the direction, unlike range or sill values, the
variogram depends only on these two parameters. Therefore, anisotropies can be
determined by viewing radar plots of sills (zonal anisotropy) and ranges
(geometric anisotropy) in different directions.
APPLICATION
TO CASES OBTAINED BY NUMERICAL SIMULATIONS
Directional
variography has been applied to the results of numerical simulations of fate of
a generic pollutant in an aquifer considering different types of sources. The
simulations were performed using a numerical model reported by Bear and
Verruijt [1], which considers mean advection and hydrodynamic dispersion.
The modeled domain
was a very simple two-dimensional domain having an area of about 56 km2.
It was discretized by a mesh of 961 nodes and 900 elements and all the
hydrogeological parameters (i.e. porosity and hydraulic conductivity) were
considered to be constant all over the domain (perfectly isotropic porous
medium). The flow field was the same for all the simulations (Vx=1
m/sec and Vy=0 m/sec) and constant in time (steady state flow
conditions).
In the first
simulation, the source of contamination was assumed linear, and placed along
the western side. It produced a continuous pollutant input having concentration
equal to 1 g/cm3. The second simulation dealt with a continuous
point source. The concentration was again set to 1 g/cm3. The third
simulation was characterized by eleven, randomly placed, continuous sources
with concentrations ranging from 0.1 g/cm3 through 20 g/cm3.
The pollutant was considered as a tracer (not reactive and not density
dependent) and the total simulation time was set long enough to ensure a good
spread of the tracer over the considered domain.
For each
simulation, a random sampling procedure [6] was used to extract about 16,000
data pairs from the over 460,000 pairs available. This ensures the existence
and validity of the variograms [8]. Volpi and Gambolati [11] demonstrated that
data samples, extracted from numerical simulations, can be analyzed by using
variograms.
LINEAR SOURCE
LINEAR SOURCE
During the
simulation, the iso-concentration curves were almost parallel to the linear
source of pollution and the concentration values decreased along the flow
direction (from West to East). The directional analysis was performed computing
the experimental variograms of the tracer concentration, in directions 0°+k30°
(k=0,..,5), with tolerance of 15°. The experimental variograms were almost
regular because of the uniform concentration distribution over the modeled
area. The experimental directional variograms were fitted using the gaussian
model. The directional representation (radar plots) of the variogram parameters
(ranges and sills) is shown in figure 1. The butterfly
shape of the radar plot of sills indicates a wide variability, along the
flow direction, and a small variability in the transversal one. The ranges show
a large correlation length parallel to flow while a discontinuity (i.e. pure
nugget effect) at the origin may be found in the transverse direction.
Figure 1: Radar plots of ranges and sills of the
results obtained from numerical simulation with a linear source.
The butterfly shape of the radar
plot of sills indicates a wide variability, along the flow direction, and a
small variability in the transversal one. The ranges show a large correlation
length parallel to flow while a discontinuity (i.e. pure nugget effect) at the
origin may be found in the transverse direction.
Figure 1
Figure 2: Radar plots of ranges and sills of the
results obtained from numerical simulation of point source.
POINT
SOURCE
The results of
this simulated case show a typical symmetric and regular plume, elongated
through the flow direction (from West to East). Experimental variograms were
fitted by spherical models. The thin transversal dimension of the plume
produced a very small number of samples, having values different from zero, in
directions from 60° through 120°. Ranges and sills in directions 0°+k30°
(k=0,..,5) are shown in radar plots (Figure 2).
The
constant values of sills in each direction are rather evident and this behavior
is due to the maximum concentration variability which is almost constant in
every direction. The radar plot of ranges has a spindle shape and, similarly to the previous case, it is elongated
in the direction of flow. Again it can be observed that ranges are larger in
the flow direction than in the transversal one.
Figure 2
SPARSE POINT
SOURCES
The random
placement of sources represents a situation of disordered pollution, which is not due to a single and determined
source. The directional variograms are highly influenced by the random sources
of concentration. The experimental variograms were fitted, again, using the
gaussian model and the radar plots of sills and ranges are shown in figure 3. A
somewhat irregular shape of the sills
diagram is shown, while the ranges plot still have a spindle shape in the direction of the flow.
Figure 3
DISCUSSION
DISCUSSION
The observation
and discussion on the results of the directional variography, performed on the
simulated cases of pollution, gave rise to the following questions:
1)
from a theoretical standpoint, is it correct to affirm that the shape of
the radar plot of directional sills
is representative of the characteristics of the source of pollution?
2)
If the answer to the first question is affirmative, is it possible to
apply this method to real cases? The boundary and initial conditions imposed to
the simulated system were defined in order to make it as ideal as possible. Real cases are characterized by extremely
variable flow conditions and concentration values and cannot be schematized in
an easy frame.
3)
Finally, if this method can be accepted theoretically and would be
useful for application to real cases, is it possible to improve it by using it
to evaluate not only the source type but also its position over the
investigated area?
Figure 3. Radar plots of ranges and sills of the
results obtained from numerical simulation of sparse point sources.
The answer to the
first question should be easily given. If we ask if the directional variography
is a correct approach to the directional analysis of the spatial behavior of an
environmental parameter we must answer
yes. If the question is: "is the interpretation of the observed
results correct and generalized?", the answer should be: probably. The
observation of the results above reported do not demonstrate the existence of a
unique function linking the shape of the radar plots of the sills to the type
of source of contamination, nor provide an automatic procedure to blindly
evaluate them. However, the shape of the radar plots of sills seems not to be
in conflict with the a priori
knowledge of the phenomena and with the expected behavior of the pollutants.
The final answer to the first question can be: this method seems a good qualitative indicator of the typology of the
contamination source.
To respond to the
second question we have applied the method to a study area where monitored
values of concentration of different parameters in groundwater have been
sampled. In particular three parameters were considered characterized by behaviors similar to that simulated; chloride ion, due to sea water
intrusion, was considered produced by a linear source of pollution (i.e. the
coast), ammonia concentrations were
considered representative of a diffuse source of pollution and polyphenols concentrations were assumed
to be produced by sparse point sources in the study area (i.e. olive oil wastewater discharges)
[12]. the shape of the radar plots of sills seems to be, again, in
agreement with the a priori knowledge
of the phenomena and with the expected behavior of the pollutants. In the
following section there is a brief description of the study area and of the
results produced by the analysis of chloride
ions concentration.
Concerning the
third and last question, no answers are available up today. We are going to be
convinced that we could use this method, supported by temporal information, to
outline the probable location of the pollution source .
APPLICATION
TO A REAL CASE
The investigated
area covers about 76 km2, around Bisceglie, a small town in
south-eastern Italy. Groundwater flows in a karst aquifer, in Mesozoic
carbonatic rocks of the Apulian platform. The aquifer is fractioned into
several levels; it is mostly semi-confined and has the mean flow direction
perpendicular to the coastal line. Previous studies [10] have shown that
changes in magnitude and direction of the flow field are limited in time. In
proximity to the sea, saltwater intrusion occurs in the aquifer with a
significant degree of salinity stratification observed. Groundwater quality is
threatened, apart from seawater intrusion, also by presence of potential sources of contamination related to
uncontrolled dumping of solid urban wastes in relict sites. Furthermore, waste
water from different origins is discharged to an ephemeral stream. Lopez et al.
[9] report the results of a sampling in 36 wells distributed over the area,
using accurate standard sampling and analyzing techniques. As reported above,
analyses where made for chlorides, ammonia
and poliphenols. For the sake of simplicity, only the chloride behavior
is described here.
Chlorides in the
coastal aquifer are mainly due to sea water intrusion. Experimental variograms
were calculated every 30° with tolerance of 15°. The variograms qualitatively
show a gaussian behavior and a gradual shift from a low variability, in
directions 120° through 180°, to a high variability in directions 30° through
90°. A radar plot (Figure 4) shows, for each direction, the estimated value of
the sills and the ranges.
Figure 4: Radar
plots of ranges and sills of the values of concentration of chloride ions.
The
butterfly shape, with major axis in
direction 60° and minor axis in direction 150°, clearly shows an anisotropic
behavior of the chloride ion data. Since concentrations of chloride ion are due
to sea water intrusion, the concentration gradient is perpendicular to the
coastal line. The observed anisotropy of the variogram plots indicates that the
source of pollution is linear and
perpendicular to the mean flow direction. The same conclusion can be
drawn, considering the ranges plots.
Figure 4
CONCLUSION
The observation of
the results of the directional variography performed on simulated values of
concentration, of an ideal pollutant,
in an ideal groundwater domain,
brought the authors of this work to make themselves several questions on the
practical applicability of directional variography in order to evaluate the
characteristics of the source that produces an observed pollution. In
particular, representing the values of directional
sills and ranges on a radar plot, it can be observed that the shape of
these plots can give some information on the type of source that produced the
pollution and on the mean direction of flow. A stretched (high zonal
anisotropy) and a rounded (zonal
isotropy) shape indicates a linear and,
respectively, a point or area source of contamination. The area source can be
considered as a point if it is much smaller than the extension of the test
site. Moreover the radar plot of sills tends to regularly degenerate to a point
(pure nugget) when the area source is larger than the extension of the test
site. Finally, in the case of sparse, randomly placed point sources of
contamination the radar plot of sills has an irregular shape. The directional
analysis conducted on range values (geometrical anisotropy) seems to be
representative of the mean direction of the groundwater flow. A limitation of
the proposed approach is that the tool has to be coupled to the essential
knowledge of the hydrogeological characteristics of the site and to the
physical and chemical process uncertainties (i.e. initial and boundary
conditions, time varying parameters). The radar plots of sills obtained through
mathematical simulations have been compared with those produced by the
directional analysis of concentration data from field sampling and the results
seem to confirm the goodness of the method. Obviously, the results reported in
this paper do not demonstrate the
existence of a unique function linking the shape of the radar plots of the
sills to the type of contamination source, nor provide an automatic procedure
to blindly evaluate them. However, directional variography of groundwater
quality seems to outline several practical implications related to the
possibility of evaluating the typology of the contamination sources. In
particular, the shape of the radar plots of sills does not conflict with the a priori knowledge of the phenomena and
with the expected behavior of the pollutants. Above all, it seems a good
qualitative indicator of the typology of the contamination source. Although the
applicability of the proposed approach is somewhat limited by the need of a
knowledge of the physical and chemical nature of transport process, we can
conclude that our application bears significant implications for field studies.
In particular, future development of this study can be directed toward the
evaluation of using it to evaluate not only the source type but also its
position over the investigated area. Unfortunately, no answers, to this idea,
are available up today, but the authors
are going to be convinced that using this method, supported by temporal
information, could provide a good tool for outlining the probable location of
the pollution source.
REFERENCES
1. Bear, J. and
Verruijt, A., (1990). "Modeling
Groundwater Flow and Pollution", D. Reidel Publ. Co., Dordrecht.
2. Bellin, A.,
Rinaldo, A., Bosma, W.J.P., Van Der Zee, S.E.A.T.M. and Rubin, Y., (1993).
Linear equilibrium adsorbing solute transport in physically and chemically
heterogeneous porous formations: 1. Analytical solutions, Water Resour. Res., 29,
4019-4030.
3. Bosma, W.J.P.,
Bellin, A., Van Der Zee, S.E.A.T.M. and Rinaldo, A., (1993). Linear equilibrium
adsorbing solute transport in physically and chemically heterogeneous porous
formations: 2. Numerical results, Water Resour.
Res., 29, 4031-4043.
4. Dagan, G., (1989).
"Flow and Transport in Porous
Formation". Springer-Verlag, Berlin.
5. De Marsily, G.,
(1986). "Quantitative Hydrogeology:
Groundwater Hydrology for Engineers". Academic Press, New York.
6. Englund, E. and
Sparks, A., (1988), "GEO-EAS. User's
Guide". U.S. Environ. Protec. Agency EPA600/4-88/033, Las Vegas, NE.
7. Hess, K.M., Wolf,
S.H. and Celia, M.A., (1992). Large-scale natural gradient tracer test in sand
and gravel, Cape Cod, Massachusetts. 3. Hydraulic conductivity variability and
calculated macrodispersivity, Water
Resour. Res., 28,
2011-2027.
8. Journel, A.G. and
Huijbregts, C.J., (1978). "Mining
Geostatistics". Academic Press, London.
9. Lopez, A., Vurro,
M., Limoni, P.P. and Maggiore, M., (1994). Definition of protected areas for drinking water well: a field study, in "Transport and Reactive Processes in
Aquifers". Ed. Dracos, T. and Stauffer, F., Balkema, Rotterdam, 263-268.
10. Maggiore, M., (1993). Aspetti
idrogeologici degli acquiferi pugliesi
in relazione alla ricarica artificiale, Quaderni
IRSA. v. 94, 6.1‑6.32.
11. Volpi, G. and Gambolati, G.,
(1978). On the use of a main trend for the kriging technique in hydrology, Adv. in Water Resources., 1, 345-349.
12. Vurro M., Passarella G.,
D'Agostino V., (1994). Valutazione della Sorgente di Inquinamento di una Falda
Idrica Sotterranea Tramite l'Analisi Geostatistica Strutturale. Ingegneria Sanitaria - Ambientale,
settembre-dicembre, 27-38.
13. Woodbury, A.D. and Sudicky,
E.A., (1991). The geostatistical characteristics of Borden aquifer, Water Resour. Res. 27,
533-546.
Figure
1: Radar plots of ranges and sills of the results obtained from numerical
simulation with a linear source
Figure 2: Radar plots of ranges and sills of the
results obtained from numerical simulation of point source.
Figure 3. Radar plots of ranges and sills of
the results obtained from numerical simulation of sparse point sources.
Figure 4: Radar plots of ranges and sills of the
values of concentration of chloride ions.