Freiburger Schriften zur Hydrologie
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Band/volume 3: BUCHER B. (1994):
Optimierung von Grundwasserme▀netzen mit dem Kriging-Verfahren
In many countries groundwater plays an important role in public and industrial
Groundwater problems in many areas, caused by overuse or pollution, indicate
clearly, that groundwater has to be managed and protected carefully.
In order to prevent or to solve these problems, insight in the behavior
of groundwater is necessary. This is done by groundwater observation wells,
where the water level and the water quality can be measured. But in many
cases point measurements at observation wells are not sufficient. To get
the required spatial information, estimates of the variable at unmeasured
locations have to be made. Of course the reliability of the estimates
depends on the density of the monitoring network.
Until now, little research hasbeen done into quantifying the relationship
between network density and accuracy of the estimated values. Therefore
the objective of the present study is to test several methods for evaluating
the quality of existing groundwater monitoring networks and to give guidelines
for their optimization.
Several Kriging methods have been chosen to analyse the monitoring networks:
Ordinary Kriging, Universal Kriging, Kriging with generalized covariances,
Cokriging and Kriging in combination with a deterministic groundwater
flow model. Knowing the spatial structure of the variable by calculating
the semivariogram, Kriging methods provide not only estimated values at
unmeasured locations they give also a measure of their accuracy (standard
deviation of the estimation error).
It should be taken"into account, that the accuracy of the estimated
values do not depend directly on the measured- values but on the semivariogram
and the configuration of the measurement points. Therefore it is possible
to evaluate the effect of changes in the network (for example additional
observation wells) on the estimation error before actual measurements
are carried out. Therefore Kriging methods are considered a suitable tool
to analyse and optimize monitoring networks.
The Kriging approaches have been applied to a catchment of ca. 120 km2
called "Obere Schwalm" in the Lower Rhine area. There the groundwater
network for monitoring water levels consists of 138 observation wells.
Sampies for analysing groundwater quality have been taken at 31 sites.
Based on these point measurements, spatial interpolation was carried out.
To understand the uncertainty of the contours on the maps, the standard
deviation of the estimation error has been plotted too.
In a next step some measurement points were removed from the data sets
and fictitious points were added to simulate the effect of network changes
on the reliability of the estimated values. Especially the developed diagram
is instructive, showing for a given variable the general relationship
between the network density (regular grid) and the standard deviation
of the estimation error.
Based on this diagram, it can be easily realized, if a more dense monitoring
network would lead to a substantial increase in spatial information or
not. Thus in the studied area a network density of more than one weIl
per km2 to determine groundwater levels in a regional scale is not advisable.
Otherwise the measurement effort would greatly increase obtaining only
a minor decrease of the standard deviation of estimation error.
The analysis of the existing network for sampling groundwater quality
in the study area results in a general uncertainty to a high degree of
the estimated values. The main reason for that is a pronounced Nugget-Effect
(discontinuity at the origin of the semivariogram), which occured in most
of the chemical parameters.
The comparison of the different Kriging methods indicates, that not only
more observation weHs, but also advanced methods are able to improve the
reliabilty of the estimation. This is valid for the Cokriging approach
too. It allows to use information on other spatially correlated variables,
wh ich are sampled generally better.
In this study the elevation data of the ground surface was used to estimate
the groundwater table with the Cokriging system. Moreover, data on electrical
conductivity of groundwater was used to estimate the concentration of
some solutes (for instance calcium) too. In both cases the Cokriging method
yields smaller estimation errors than the ordinary Kriging approach.
However, Kriging combined with a deterministic groundwater flow modelied
to the smallest standard dev,iation of estimation error. Including the
physical knowledge about groundwater flow and further hydrogeological
information (for example transmissivity, recharge, withdrawals) is very
effectiv, particularly when the monitoring network is sparse.
Ordinary Kriging, wh ich is easier to use, is advisable for analysing
groundwater networks only when further useful informations are not available.
Otherwise it tends to overestimate the standard deviation of the estimation
error. In other words, it underestimates the real quality of the network.
The application of the Kriging methods require a sufficient number of
measurement points. At least 30 measured locations should be available
to get a meaningful semivariogram. The dilemma, that analysing and optimizing
of a network is only possible, when many observation wells already exist,
could be overcome by regionalisation of the semivariograms. Further research
in this field is recommended.
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