Application of kriging in ground
water studies
By
S.Anusha
RS & GIS
M.Tech 1st year 2nd Sem
(NIT Warangal)
R.No:131871
.
Contents
• Introduction
 Basic principles of Kriging
 Semivariogram
 Variogram models
• Literature Review
• Methodology...
INTRODUCTION
 Groundwater is one of the major sources of water.
 Management of this resource is very important to meet t...
• In recent years, the importance of groundwater as a natural
resource has been increasingly recognized throughout the
wor...
 Rising of the water-table for various reasons can cause adverse
effects on human health and environment as well as crop
...
Basic principles of kriging
 Optimise interpolation by
dividing spatial variation into
three components
 Deterministic v...
Semivariance
 The semivariance is simply half the
variance of the differences between all
possible points spaced a consta...
Contd..
-Calculation of semivariance
where γ*(h) = estimated value of the semivariance for lag h;
N(h) is the number of ex...
Semivariogram
 The plot of the semivariances as a function of distance from a
point is referred to as a semivariogram or ...
Variogram models
Spherical
Exponential
Gaussian 10
Inverse Square distance method
11
 The weights λi are inversely
proportional to the square of
distance from the estimatio...
Literature Review
 Nicolaos et al.(2005) presented the application of kriging aiming at optimisation of
groundwater obser...
 Moukana et al. (2007) conducted two studies in establishing relationship between
decline in groundwater levels and chang...
 Kholghi et al. (2009) examined the efficiency of the ordinary kriging
and adaptive network-based fuzzy inference system ...
Methodology
Collection of data sets
Preparation of experimental
semivariograms
Fitting theoretical model
Kriging
Cross val...
Case study 1
• Title : Kriging of groundwater levels
• Authors : Vijay et al.(2006)
• Study Area : Rajasthan
• Objective o...
Study Area
17
Fig.5 Location of Study Area
Data aquisition
 groundwater level
data pertaining to pre-
monsoon (June) and
post-monsoon
(September) seasons
over the y...
Statistics of the data set
19
20
Fig .7 Experimental and fitted variogram for different
data sets
21
Cross validation results
22
Ground water level contour maps
 Groundwater levels and estimation variances were
calculated by kriging.
 These estimate...
24
Fig .8 Groundwater level contours(m) by
kriging method
25
Fig.9 Estimation Variance (sq.m) by kriging
method
26
Fig .10 Groundwater level contours(m) by
Inverse Square Distance Method
27
Case study 2
 Title : Geostatistical model for correlating declining groundwater
levels with changes in land cover detect...
Study Area
Fig 11 : Location of study area Kumamoto Plain, southwest
Japan, and locations of groundwater observation wells...
Data used:
 Satellite images from Landsat 5 Thematic Mapper (TM) and
Landsat 7 Enhancement Thematic Mapper Plus (ETM+) we...
Methodolgy
Fig.12 Flow chart of methods used to spatially quantify changes in groundwater
levels using geostatistics and r...
First Approach
 Changes in land cover detected by linear spectral method
Fig 13 : Results of image classification by line...
Second Approach
 Geostatistical analysis of groundwater-level data
1.Identification and removal of trend components
2.Spa...
Fig.14 comparison of measured and calculated
groundwater levels using best cross-regression models.
34
2.Spatial estimation by ordinary
kriging
35
Fig.16 Kriging estimated maps forgroundwater residual levels
over study area f...
Multivariate regression model
• To validate the multivariate regression model in terms of clarifying the
relationship betw...
Fig.17 Comparison of kriged maps of groundwater
residual levels with images classified into five classes of
land-cover use...
Summary
 From the discussed case studies it was inferred that kriged
groundwater levels satisfactorily matched the observ...
References
 Jean Aurelien Moukanaa, Katsuaki Koike(2007), “Geostatistical
model for correlating declining groundwater lev...
 Peter Burrough A. and Rachael McDonnell A.,”Principles of
Geographical Information Systems”,Oxford Publications.
 Vijay...
41
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APPLICATION OF KRIGING IN GROUND WATER STUDIES

  1. 1. Application of kriging in ground water studies By S.Anusha RS & GIS M.Tech 1st year 2nd Sem (NIT Warangal) R.No:131871 .
  2. 2. Contents • Introduction  Basic principles of Kriging  Semivariogram  Variogram models • Literature Review • Methodology • Case Study1 • Case Study 2 • Summary • References 2
  3. 3. 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. . 3
  4. 4. • 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 4
  5. 5.  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. 5
  6. 6. 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. 6 Fig.1 Fig showing how spatial variation can be considered in kriging
  7. 7. 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. 7 Fig 2. fig showing all possible pairs for semivariance calculation.
  8. 8. 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 . 8
  9. 9. 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 9
  10. 10. Variogram models Spherical Exponential Gaussian 10
  11. 11. Inverse Square distance method 11  The weights λi are inversely proportional to the square of distance from the estimation point as: Fig.4 Inverse square distance method.
  12. 12. 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. 12
  13. 13.  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. 13
  14. 14.  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. 14
  15. 15. Methodology Collection of data sets Preparation of experimental semivariograms Fitting theoretical model Kriging Cross validation 15
  16. 16. 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. 16
  17. 17. Study Area 17 Fig.5 Location of Study Area
  18. 18. 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 18 Fig.6 Plan of canal network and location of observation wells
  19. 19. Statistics of the data set 19
  20. 20. 20 Fig .7 Experimental and fitted variogram for different data sets
  21. 21. 21
  22. 22. Cross validation results 22
  23. 23. 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. 23
  24. 24. 24 Fig .8 Groundwater level contours(m) by kriging method
  25. 25. 25 Fig.9 Estimation Variance (sq.m) by kriging method
  26. 26. 26 Fig .10 Groundwater level contours(m) by Inverse Square Distance Method
  27. 27. 27
  28. 28. 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. 28
  29. 29. Study Area Fig 11 : Location of study area Kumamoto Plain, southwest Japan, and locations of groundwater observation wells. 29
  30. 30. 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) 30
  31. 31. 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. 31
  32. 32. 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. 32
  33. 33. 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 33
  34. 34. Fig.14 comparison of measured and calculated groundwater levels using best cross-regression models. 34
  35. 35. 2.Spatial estimation by ordinary kriging 35 Fig.16 Kriging estimated maps forgroundwater residual levels over study area for five periods.
  36. 36. 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. 36
  37. 37. Fig.17 Comparison of kriged maps of groundwater residual levels with images classified into five classes of land-cover use by LSM 37
  38. 38. 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. 38
  39. 39. 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). 39
  40. 40.  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). 40
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