Application of kriging in ground

water studies

By

S.Anusha

RS & GIS

M.Tech 1st year 2nd Sem

(NIT Warangal)

R.No:131871

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Contents

• Introduction

Basic principles of Kriging

Semivariogram

Variogram models

• Literature Review

• Methodology

• Case Study1

• Case Study 2

• Summary

• References

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INTRODUCTION

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

industrial use.

Various management measures need to know the spatial

and temporal behaviour of groundwater. .

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• In recent years, the importance of groundwater as a natural

resource has been increasingly recognized throughout the

world.

• Groundwater is essentially a renewable resource generated

within the global water circulation system.

• Keeping the water-table at a favourable level is quite

significant.

• Two factors pertaining to ground water is

Rise in ground water table

Decline in ground water table

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Rising of the water-table for various reasons can cause adverse

effects on human health and environment as well as crop

production.

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

normally recorded.

In a scattered groundwater observation net, geostatistical

methods can be used to determine the values for the points

where measurements are not made.

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Basic principles of kriging

Optimise interpolation by

dividing spatial variation into

three components

Deterministic variation

Spatially autocorrelated

Uncorrelated noise

• Kriging uses the

semivariogram,in calculating

estimates of the surface at the

grid nodes.

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Fig.1 Fig showing how spatial

variation can be considered in

kriging

Semivariance

The semivariance is simply half the

variance of the differences between all

possible points spaced a constant

distance apart.

.

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.

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Fig 2. fig showing all possible pairs

for semivariance calculation.

Contd..

-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 .

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Semivariogram

The plot of the semivariances as a function of distance from a

point is referred to as a semivariogram or variogram.

Variogram parameters

Sill

Range

Nugget

Fig 3 . Semivariogram

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Variogram models

SphericalExponential

Gaussian 10

Inverse Square distance method

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The weights λi are inversely

proportional to the square of

distance from the estimation

point as:

Fig.4 Inverse square distance

method.

Literature Review

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

groundwater levels.

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.

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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

study area.

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.

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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.

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Methodology

Collection of data sets

Preparation of experimental

semivariograms

Fitting theoretical model

Kriging

Cross validation

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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.

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Study Area

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Fig.5 Location of Study Area

Data aquisition

groundwater level

data pertaining to pre-

monsoon (June) and

post-monsoon

(September) seasons

over the years from

1985 to 1990 covering

an area of 2100 sq. km

were selected

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Fig.6 Plan of canal network and location

of observation wells

Statistics of the data set

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Fig .7 Experimental and fitted variogram for different

data sets

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Cross validation results

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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

variance.

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Fig .8 Groundwater level contours(m) by

kriging method

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Fig.9 Estimation Variance (sq.m) by kriging

method

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Fig .10 Groundwater level contours(m) by

Inverse Square Distance Method

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Case study 2

Title : Geostatistical model for correlating declining groundwater

levels with changes in land cover detected from analyses of

satellite images.

Authors : Moukana et al. (2007)

Study Area : Kumamoto Plain in central Kyushu, southwest

Japan.

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.

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Study Area

Fig 11 : Location of study area Kumamoto Plain, southwest

Japan, and locations of groundwater observation wells.

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Data used:

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.

Groundwater-level data

Construction Ministry of Japan (CMJ: 12 wells)

Kumamoto City Office (KCO: 14 wells)

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Methodolgy

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.

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First Approach

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.

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Second Approach

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

• t-test

• Kendall’s tau test

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Fig.14 comparison of measured and calculated

groundwater levels using best cross-regression models.

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2.Spatial estimation by ordinary

kriging

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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.

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Fig.17 Comparison of kriged maps of groundwater

residual levels with images classified into five classes of

land-cover use by LSM37

Summary

From the discussed case studies it was inferred that kriged

groundwater levels satisfactorily matched the observed

groundwater levels.

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.

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References

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

(991-1000).

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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-

94).

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).

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