Application of kriging in ground
RS & GIS
M.Tech 1st year 2nd Sem
Basic principles of Kriging
• Literature Review
• Case Study1
• Case Study 2
Groundwater is one of the major sources of water.
Management of this resource is very important to meet the
increasing demand of water for domestic, agricultural and
Various management measures need to know the spatial
and temporal behaviour of groundwater. .
• In recent years, the importance of groundwater as a natural
resource has been increasingly recognized throughout the
• Groundwater is essentially a renewable resource generated
within the global water circulation system.
• Keeping the water-table at a favourable level is quite
• Two factors pertaining to ground water is
Rise in ground water table
Decline in ground water table
Rising of the water-table for various reasons can cause adverse
effects on human health and environment as well as crop
The problem of falling water tables is common in urban areas.
In order to observe water-table continuously, groundwater
observation wells are used and monthly measurements are
In a scattered groundwater observation net, geostatistical
methods can be used to determine the values for the points
where measurements are not made.
Basic principles of kriging
Optimise interpolation by
dividing spatial variation into
• Kriging uses the
estimates of the surface at the
Fig.1 Fig showing how spatial
variation can be considered in
The semivariance is simply half the
variance of the differences between all
possible points spaced a constant
Semivariance is a measure of the degree
of spatial dependence between samples.
The magnitude of the semivariance
between points depends on the distance
between the points. A smaller distance
yields a smaller semivariance and a larger
distance results in a larger semivariance.
Fig 2. fig showing all possible pairs
for semivariance calculation.
-Calculation of semivariance
where γ*(h) = estimated value of the semivariance for lag h;
N(h) is the number of experimental pairs separated by vector h;
z(xi) and z(xi +h) = values of variable z at xi and xi+h,respectively
xi and xi+h = position in two dimensions .
The plot of the semivariances as a function of distance from a
point is referred to as a semivariogram or variogram.
Fig 3 . Semivariogram
Inverse Square distance method
The weights λi are inversely
proportional to the square of
distance from the estimation
Fig.4 Inverse square distance
Nicolaos et al.(2005) presented the application of kriging aiming at optimisation of
groundwater observation networks.
Various analysis methods are applied in this study in order to demonstrate the
potential of improvement of the quality of the observation network.
Vijay et al.(2006) discussed the application of kriging, for the spatial analysis of
Kriged groundwater table contour maps are compared with the groundwater
table contour maps prepared using the Inverse Distance Method
The results proved that Kriging is considered as the best as it resulted in less error.
Moukana et al. (2007) conducted two studies in establishing relationship between
decline in groundwater levels and changes in land cover.
Firstly changes in land cover with a high degree of accuracy via satellite image
analysis were detected. Then Groundwater residuals were used in kriging to
obtain kriging maps.
Both were combined via Multi Regression model to identify the main factor of
land cover change contributing to the decline in ground water levels over the
Yang et al.(2008) discussed the Kriging approach combined with hydrogeological
analysis (based on GIS) for the design of groundwater level monitoring network.
The effect of variogram parameters (i.e., the sill, nugget effect and range) on
network has been analyzed.
Kholghi et al. (2009) examined the efficiency of the ordinary kriging
and adaptive network-based fuzzy inference system (ANFIS) in
interpolation of groundwater level in an unconfined aquifer.
The results showed that ANFIS model is more efficient in estimating
the groundwater level than ordinary kriging.
Collection of data sets
Preparation of experimental
Fitting theoretical model
Case study 1
• Title : Kriging of groundwater levels
• Authors : Vijay et al.(2006)
• Study Area : Rajasthan
• Objective of this case study :
To represent spatial variability of the groundwater levels which
are characterised by preparing experimental semivariograms
followed by Kriging and validation tests.
data pertaining to pre-
monsoon (June) and
over the years from
1985 to 1990 covering
an area of 2100 sq. km
Fig.6 Plan of canal network and location
of observation wells
Ground water level contour maps
Groundwater levels and estimation variances were
calculated by kriging.
These estimated level values are used to draw the
contour maps of groundwater levels and estimation
Fig .8 Groundwater level contours(m) by
Fig.9 Estimation Variance (sq.m) by kriging
Case study 2
Title : Geostatistical model for correlating declining groundwater
levels with changes in land cover detected from analyses of
Authors : Moukana et al. (2007)
Study Area : Kumamoto Plain in central Kyushu, southwest
Objective of the study Area :
To construct a spatial model of actual temporal changes in
groundwater levels related to changes in land-cover uses and
specify the main factors influencing these changes.
Fig 11 : Location of study area Kumamoto Plain, southwest
Japan, and locations of groundwater observation wells.
Satellite images from Landsat 5 Thematic Mapper (TM) and
Landsat 7 Enhancement Thematic Mapper Plus (ETM+) were
used in this study.
Digital elevation map (DEM) dataset to select suitable ground-
control points for image registration and identify land-cover
use for image classification (Geographical Survey Institute of
Japan) were used in this study.
Construction Ministry of Japan (CMJ: 12 wells)
Kumamoto City Office (KCO: 14 wells)
Fig.12 Flow chart of methods used to spatially quantify changes in groundwater
levels using geostatistics and relate these trends to changes in land-cover use
determined from analyses of Landsat 5 TM and Landsat 7 ETM+ images.
Changes in land cover detected by linear spectral method
Fig 13 : Results of image classification by linear spectral mixture algorithm
for five classes of land-cover use for five selected images.
Geostatistical analysis of groundwater-level data
1.Identification and removal of trend components
2.Spatial estimation by ordinary kriging
1.Identification and removal of trend components
The groundwater levels yt at time t are time-series data that can
be decomposed into three fundamental components,trend Tt,
seasonal St, and residual Ɛt.
To understand the Tt pattern repartition,two descriptive statistical
tests were adopted
• Kendall’s tau test
Fig.14 comparison of measured and calculated
groundwater levels using best cross-regression models.
2.Spatial estimation by ordinary
Fig.16 Kriging estimated maps forgroundwater residual levels
over study area for five periods.
Multivariate regression model
• To validate the multivariate regression model in terms of clarifying the
relationship between declining groundwater levels and changes in
land cover, a cross-validation method is used between the observed
and estimated groundwater residual Et at the 14 KCO wells.
• The correlation coefficients between the observed and estimated
residual levels by the multivariate regression model at 14 wells for the
cross-validation range from 0.95 to 0.98.
Fig.17 Comparison of kriged maps of groundwater
residual levels with images classified into five classes of
land-cover use by LSM
From the discussed case studies it was inferred that kriged
groundwater levels satisfactorily matched the observed
Spatial models of the residuals using ordinary kriging were
effective in evaluating the influence of land-cover use on
groundwater levels, which highlighted the significant decline
in groundwater levels.
More realistic than most other interpolation methods.
Hence Kriging provides the best linear unbiased estimation for
spatial interpolation of groundwater levels.
Jean Aurelien Moukanaa, Katsuaki Koike(2007), “Geostatistical
model for correlating declining groundwater levels with changes
in land cover detected from analyses of satellite images”,
Computers & Geosciences 34 (1527–1540).
Kholghi.M & Hosseini S.M,(2009), “Comparison of Groundwater
Level EstimationUsing Neuro-fuzzy and Ordinary Kriging”, Environ
Model Assess 14 (729–737).
Nicolaos Theodossiou, Pericles Latinopoulos (2006), “Evaluation
and optimisation of groundwater observation networks using the
Kriging methodology”, Environmental Modelling & Software 21
Peter Burrough A. and Rachael McDonnell A.,”Principles of
Geographical Information Systems”,Oxford Publications.
Vijay Kumar and Remadevi (2006), “Kriging of Groundwater
Levels” Journal of Spatial Hydrology Vol.6, No.1 Spring edition (81-
YANG Feng-guang, CAO Shu-you, LIU Xing-nian,YANG Ke-
jun(2008), “ Design of groundwater level monitoring network with
ordinary kriging”,Journal of Hydrodynamics 20 (339-346).