download-manuals-ground water-manual-gw-volume8operationmanualdataprocessingpartiii

Government of India & Government of The Netherlands

DHV CONSULTANTS &DELFT HYDRAULICS withHALCROW, TAHAL, CES,ORG & JPS

VOLUME 8DATA PROCESSING AND ANALYSIS

OPERATION MANUAL – PART III

DATA PROCESSING AND ANALYSIS

Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III

Data Processing and Analysis March 2003 Page i

Table of Contents

1 DATA PROCESSING 1-1

2 FROM BASIC DATA TO DERIVED DATA 2-1

2.1 BASIC DATA 2-12.2 CONTOUR MAPS 2-12.3 RASTER MAPS 2-22.4 TIME SERIES / HYDROGRAPHS 2-32.5 OTHER DERIVED MAPS 2-4

3 EXAMPLE OF THE PREPARATION OF A CONTOUR MAP 3-1

3.1 PREPARATION OF BASIC DATA 3-13.2 CONTOURS OF THE DEPTH TO THE GROUNDWATER LEVEL 3-33.3 CONTOURS OF THE ELEVATION OF THE GROUNDWATER LEVEL 3-5

4 SPATIAL CONFIGURATION OF THE GROUNDWATER LEVEL 4-1

4.1 GENERAL CONSIDERATIONS FOR CHOICE OF ALGORITHM 4-14.2 WATER TABLE/PIEZOMETRIC ELEVATION CONTOURING 4-1

4.2.1 CHOICE OF ALGORITHM 4-14.2.2 MANUAL MODIFICATIONS 4-4

4.3 WATER LEVEL DEPTH CONTOURING 4-4


4.4 WATER LEVEL FLUCTUATION CONTOURING 4-5


4.5 COMPUTATION OF VELOCITY FIELD 4-54.6 VALIDATION OF WATER LEVEL DATA 4-64.7 SUGGESTED READING 4-6

5 GROUNDWATER LEVEL TIME SERIES 5-1

5.1 INTRODUCTION 5-15.2 IDENTIFICATION OF THE DYNAMIC EQUILIBRIUM 5-15.3 IDENTIFICATION OF TEMPORAL TRENDS 5-2

5.3.1 DECLINING TREND 5-25.3.2 RISING TREND 5-25.3.3 PROJECTION OF DYNAMIC EQUILIBRIUM 5-3

5.4 IDENTIFICATION OF LINEAR INTER-DEPENDENCIES 5-3

5.4.1 IDENTIFICATION OF REPRESENTATIVE WELLS 5-35.4.2 ESTIMATION OF TIDAL EFFICIENCY 5-35.4.3 ESTIMATION OF BAROMETRIC EFFICIENCY 5-4

5.5 IDENTIFICATION OF LAGGED INTER-DEPENDENCIES 5-4

5.5.1 GENERAL 5-45.5.2 INTER-DEPENDENCE BETWEEN RAINFALL AND WATERTABLE 5-5

5.6 IDENTIFICATION OF OUTLIERS 5-5

5.6.1 MEAN ANNUAL HYDROGRAPH 5-65.6.2 TRENDS OF MACRO MEANS 5-65.6.3 INTERRELATED WELLS 5-6

5.7 IDENTIFICATION OF TRUE HYDROGRAPH 5-6

5.7.1 IDENTIFICATION OF SIGNIFICANT CYCLES 5-75.7.2 ANALYSIS OF HYDROGRAPH RECESSION 5-7

5.8 SUGGESTED READING 5-8

6 GROUNDWATER MODEL INPUT 6-1


Data Processing and Analysis March 2003 Page 1-1

1 DATA PROCESSING

The Groundwater Estimation and Management System (GEMS) allows for the preparation of mapsand the execution of calculations based on the basic data contained in the database. Such dataprocessing is useful and appropriate for the analysis of the past, present and future condition of theavailable water resources, but may easily produce misleading results, when sufficient knowledge ofthe basic data or the data processing methods is missing.

It is therefore important when executing data processing activities to have knowledge on:

• The quality of the data with respect to the representation of the actual situation.

• The completeness of the data; what data is missing?

• The possibilities and limitations in the use of the data.

The quality of the data is expressed by the results of the validation activities. Data, which has beensuccessfully validated, may be identified by the added validation flag or code. Only data with therequired level of validation should be used in further data processing. The data validation therefore isan important preparatory activity before data processing takes place.

The completeness of the data is important with respect to the analysis of the time-dependent data. Incase of gaps in the data, statistical analyses may not yield results, because a continuous dataset isrequired. Filling in the gaps by generating simulated numbers is an option, to allow the use of thestatistical methods in time-series analysis. However with data processing, emphasis should be put onthe sites from where continuous time-series are available.

The user should understand the limitations of the data before processing the data. For example thedensity of the data points should be sufficient to represent the hydrogeological feature, such as thegroundwater level, when preparing for a contour map. In case the number of data points is insufficientthen the contour map should not be generated.

Having confidence in the basic data and in the results of the data processing is a prerequisite whenusing data from an information system. The basic data should only be used if sufficient confidenceexist in the quality and completeness of this data. Furthermore the results of data processing activitiesalways must be checked before using them for presentation or for other purposes.

In this volume data processing techniques are demonstrated. A general overview of the process frombasic data to derived data is given in Chapter 2. The contouring of groundwater levels is explained indetail in Chapter 3. The analysis of groundwater level time series is explained in Chapter 4. Finally inChapter 5 the preparation of input to groundwater models is given. Background information on spatialcontouring and time series analysis is provided in the Reference Manual of this Volume.



77 78 79 80 81 82 83 84

13

14

15

16

17

18

19

Adilabad

Anantapur

Chitoor

Cuddapah

East Godavari

Guntur

Hyderabad

Karimnagar

Khammam

Krishna

Kurnool

Mahbubnagar

Medak

Nalgonda

Nellore

Nizamabad

Prakasam

Srikakulam

Visakhapatnam

Vizianagaram

Warangal

West Godavari

2 FROM BASIC DATA TO DERIVED DATA

2.1 BASIC DATA

With an information system based on a GIS it is very easy to create maps showing the distribution ofcertain properties over a certain area. The basic data are generally point and polygon data. The pointdata represent the locations of the hydrogeological stations, such as the location of wells or hydrometstations. The polygon data represent maps which are either prepared by the staff operating theinformation system, such as a groundwater recharge map, or which are obtained from other agencies,such as a soil map or a geological map.

The basic data in the database relates mainly to point data. Maps can easily be prepared showing thelocations of these stations and also showing measurements taken at these stations. These maps areuseful in showing the quantity and density of the available basic data.

Figure 2.1: Example of a location map of groundwater level and quality monitoring network

2.2 CONTOUR MAPS

Contour maps may be generated with a GIS to show the spatial distribution of the measurements or ofa value derived from the measurements. For example a contour map can be prepared of thegroundwater levels measured in the groundwater observation wells. However, such a map will not berealistic when effects are not accounted for of features in-between the measuring stations, forexample of a river. Additional information therefore has to be incorporated to produce a meaningfulmap. This is generally only possible with the information system by editing the contours manually,after combining the generated contours with map layers containing the important features, seeFigure 2.2.



Figure 2.2: The presence of a river should not be overlooked when generating contours

Also a contour map can give a wrong representation when one or more of the observed values areincorrect. In Figure 2.3 one measurement has a significant effect on the shape of the contours. Thevalue may be wrong but it may also be a correct value. The use of this value in contouring should beconsidered before preparing the final contour map.

Figure 2.3: The observation point with a measured value of 4.4 has a significant effect on theposition of the contours

2.3 RASTER MAPS

After generating a contour map a raster map may be created. The raster map contains values for agrid with uniformly distributed points. The raster map allows for the presentation of the derived valuesby classifying the values, and assigning each class with a separate symbol and/or color.

2.9

5.1

4.6

4.3

5.8

5.3

5.4

6.36.4

5.7

4.64.5

3.5

3

6

5

4

2.9

5.1

4.6

4.3

5.8

5.3

5.4

6.36.4

5.7

4.64.5

3.5

3

6

5

4

7.2

4.1

4.9

4.4 ?

5.1

6.16.8

6.4

5.9

6.35.4

4.4

4.0

2.6

2.7

2.0

3.5

3

7 6 5 4

7.2

4.1

4.9

4.4

5.1

6.16.8

6.4

5.9

6.35.4

4.4

4.0

2.6

2.7

2.0

3.5

3

7 6 5 4



When working with rasters it is possible to carry out spatial calculations. For example the difference ingroundwater level between pre-monsoon and post-monsoon may be calculated in a raster bysubtracting the raster with the groundwater level for the post-monsoon conditions from the raster withthe groundwater level for the pre-monsoon conditions. Multiplying the derived raster with the area ofthe raster cells and the specific yield of the aquifer will give the total groundwater volume increaseduring the monsoon period. In this calculation also the specific yield may be a raster.

Figure 2.4: Example of spatial calculations with rasters

2.4 TIME SERIES / HYDROGRAPHS

The time dependent data of a monitoring well or other geohydrological structure may be presented ina hydrograph. Such a graph may combine multiple variables, such as the groundwater level of a welland rainfall quantities, measured in a nearby station see Figure 2.5 (a). The graph may also include atrend line to indicate the long-term variation of the groundwater level see Figure 2.5 (b).

Figure 2.5: Examples of DWLR hydrograph

Water level hydrographs are very useful for the visual presentation of water level data, for the simpleinspection of the reliability of the water level data and for the preparation of a groundwater level map(Fig 2.5). The scale of the hydrograph should be selected such that the variation of the groundwaterlevel data is neither very flat nor very steep. When only depth of water is available then the verticalscale should be reversed, so that it increases from top to bottom, corresponding to the intuitive pictureof rising and falling water levels.

X =

Post-monsoon groundwater level

Pre-monsoon groundwater level

Specific yield (Sy) Change in groundwater storage

∆ h

(a) (b)



The hydrograph of a monitoring well or other geohydrological structure may also be presented in amap directly by showing multiple time series graphs (Fig 2.6). In combination with a map layer of theaquifer type such a map will be instructive in presenting the variation and trend of the groundwaterlevels in the area.

2.5 OTHER DERIVED MAPS

Examples of derived maps include:

- groundwater level maps,

- groundwater quality maps,

- groundwater production maps, and

- other maps.

Some examples of derived maps are presented in the Figure 2.6 to 2.9:

Groundwater level maps:

• Observation well densities• Depth to water level• Groundwater level elevation• Groundwater level fluctuation

for

• Pre-monsoon• Post-monsoon conditions

Figure 2.6: Example of a ground water level contour map(depth to water level)



Groundwater quality maps:

• Water classification• Groundwater salinity• Drinking water suitability• Irrigation water suitability

Figure 2.7:Example of groundwater quality map

Groundwater production maps:

• Well densities• Present production• Potential production

Other maps:

• Geohydrological areas/units with time series graphs• Lithological map using lithological sections• Geology



Figure 2.8 Examples of a geological map Figure 2.9 example of a lithological map Example ofthe preparation of a contour map



3 EXAMPLE OF THE PREPARATION OF A CONTOUR MAP

3.1 PREPARATION OF BASIC DATA

In this section an example is given of the preparation of a contour map from groundwater level data.The data is obtained from the database by selecting locations in Andhra Pradesh. Part of thegroundwater level data is shown in table 3.1.

X-coord. Y-coord. Date Water level Altitude

(mbgl) (m amsl)

78.308 14.947 26/Jan/2001 0.05 -

78.620 14.911 26/Jan/2001 0.77 -

79.854 13.691 26/Jan/2001 1.26 43.93

80.658 16.121 08/Jan/2001 1.44 7.88

80.153 15.469 19/Jan/2001 1.58 2.58

79.746 16.882 27/Jan/2001 1.73 110.34

82.897 17.926 03/Jan/2001 1.95 79.12

78.422 18.350 23/Jan/2001 2.03 211.40

79.797 13.400 25/Jan/2001 2.15 -

Table 3.1: Part of the groundwater level data used in this example

The contour map will be prepared of the depth to the groundwater level and of the groundwater levelelevation for the period of January 2001. All measurements taken during the month of January of theyear 2001 have been used. Using data from such a period is allowed in the case of a small variationof the groundwater level.

Step 1 Prepare the required map-layers

Map-layers are required for the data processing and data presentation. If available, the following map-layers may be used (see Figure 3.1):

• Administrative boundaries

• Topographic boundaries: coast lines, mountain ridges

• Drainage system, including rivers, streams, ponds, tanks and lakes

• Surface elevation contours or surface elevation points

• Locations of groundwater abstraction

Figure 3.1: Administrative boundaries, surface elevation points and drainage system

77 78 79 80 81 82 83 84

13

14

15

16

17

18

19

77 78 79 80 81 82 83 84

13

14

15

16

17

18

19 249.125

683.605

7.88

592.835

693.968

640.24

503.375

-

439.72

424.18

20.2

-

144.36

290.44

127.407

79.12

-

306.185

-

241.308

-

278.93

433.59

136.43

49.72

273.25

90.1

50.106

141.227

271.535

-

252.347

109.48

-

-

275.84

-

-

117.72

-70.35

83.27

-878.39

8.634

58.48

598.445

180.29

-

861.89

50.79

-

184.03

-

-

319.93

-

201.36-

235.1

450.3

344.155

355.125

99.23

292.8355

8.215

-

590.955

128.661

152.1637.985

-



The surface elevation points were derived from the database by using the altitude at the location ofthe observation wells. The altitude is not known at all locations as can be seen from Table 3.1.

Step 2 Check the basic data

The preparation of the map should start with checking the basic data. It is important to screen thebasic data before starting with the data processing, to find incorrect values which may disturb the mappreparation. The checking of the data should involve:

1. Checking the coordinates :• by plotting the well locations on a map with administrative boundaries; any location falling

outside the area boundaries should be corrected or deleted.

Figure 3.2: Example of a well location with incorrect coordinates

• by visually checking for duplicate coordinate pairs; this may be done by sorting the data onthe coordinates. There are two possibilities:− the duplicate coordinate pairs have the same date and time; in this case the duplicate

location(s) should be removed;− the duplicate coordinate pairs do not have the same date and time; in this case the

average value of the measured groundwater level should be assigned to one of thelocations and the duplicate location(s) should be removed.

2. Checking the date and time of the measurement:• by visually checking for dates and times outside the period of January 2001.

3. Checking the groundwater level measurements:• by visually checking for values outside the expected range; this may be done by sorting the

data; check these values with the hydrograph for the relevant locations. Any incorrect valueshould show as an outlier on the hydrograph.

Note: the check of the basic data is an essential step before any map preparation. If the regular datavalidation procedures are carried out thoroughly on a monthly and annual basis, as prescribed forHIS, and only use is made of the authenticated data of the database in the Data Storage Centre suchan activity, thoroughly would not be necessary. Nevertheless, it is always required to ensure yourselfabout the quality of the data. the corrected data should be saved in a new file.

77 78 79 80 81 82 83 84

13

14

15

16

17

18

19

77 78 79 80 81 82 83 84

13

14

15

16

17

18

19

Wrong wellcoordinates,location is inthe sea

Location inthe searemovedfrom thedataset

Bay of Bengal Bay of Bengal



3.2 CONTOURS OF THE DEPTH TO THE GROUNDWATER LEVEL

Step 3 Derive contours of the depth to the groundwater level

The contours are generated using the available software, like Vertical Mapper / MapInfo, Surfer orother.

Any outliers still present in the basic data should show by a concentration of contours line (see Figure3.3, left). Check the locations causing these outliers and correct the value or if correction is notpossible, remove the location from the file.

Generate the contours again after removing or correcting the outliers (see Figure 3.3 right).

Figure3.3: Identifying incorrect measurements by contouring

Step 4 Edit the contours by adding defined contour lines

The generated contours of the depth to the groundwater level should be combined with the map-layers to identify areas where the contours are to be edited. The first editing should be done by addinginformation in the form of data points or contours with a fixed value and subsequently generating thecontours again. The following map-layers may be used to identify the areas with incorrect contours:

• Combine the contours with a map-layer of the topographic boundaries;

• Contours generated in the sea or in lakes should be removed; this may be done by adding acontour line with the value 0 at the coastlines (see Figure 3.4).

76 77 78 79 80 81 82 83 84 85

12

13

14

15

16

17

18

19

20

76 77 78 79 80 81 82 83 84 85

12

13

14

15

16

17

18

19

20

Incorrectmeasurement

Incorrectmeasurementremoved



Figure3.4: Adding defined contour lines to improve contouring

• Combine the contours with a map-layer of the drainage system (this combination is only relevantfor groundwater levels from aquifers which are in direct contact with the surface water drainagesystem and if surface water levels are known).

• Contours crossing the surface water drainage lines of rivers and streams should have the samevalue as the depth of the surface water level below ground surface; this may be achieved byadding control points at the location of the drainage lines.

• Combine the contours with a map-layer of the surface elevation.

• The depth to the groundwater level is expected to be larger in areas with a high elevation. Thecorrection of the contours by adding control points or lines is not straightforward and should bedone with the greatest care, because the depth to the groundwater level is usually unknown. Ingeneral, it is advised to correct the groundwater depth contours for ground surface elevation bymanual correction.

• Combine the contours with a map-layer with the locations of groundwater abstraction (this actionis relevant only when preparing the map at a scale of 1:100,000 or larger).

• The depth to the groundwater level is expected to be larger in areas with groundwaterabstraction. Locations with a high abstraction rate should show in the contour map. Add controlpoints with the depth to the groundwater level in case the groundwater depth is known at theabstraction. Take care that depths near abstractions only are applied to the usually small areainfluenced around the abstraction.

Generate the contours again after adding the contours and control points.

Step 5 Edit the contours manually

The generated contours of the depth to the groundwater level should again be combined with themap-layers to identify areas where the contours are to be edited. The manual editing is done byediting the grid from which the contours are generated or by transferring the contour lines to a drawingsoftware-package to edit the lines.

The same map-layers as mentioned in Step 4 may be used to identify the areas where contours are tobe corrected or added manually:

• Combine the contours with a map-layer of the topographic boundaries: correct any contour lineswhich do not conform to the topographic features.

76 77 78 79 80 81 82 83 84 85

12

13

14

15

16

17

18

19

20

76 77 78 79 80 81 82 83 84 85

12

13

14

15

16

17

18

19

20

Contour lineadded withvalue 0 atcoast line

Contour linesgeneratedfrom observedwater levelsonly



• Combine the contours with a map-layer of the drainage system: correct any contour lines whichdo not conform to the drainage lines. Figure 3.5 correction of contours may be possible near themajor drainage lines. This was not done for this example.

Figure 3.5:Groundwater level contour lines and drainagesystem map-layer

• The angle of the contour line to the drainage line may be corrected in case it is known that riversare infiltrating or draining, see Figure 3.6.

Figure 3.6:Groundwater level contour lines crossing a river or astream


• The depth to the groundwater level is expected to be larger in areas with a high elevation. Asmentioned above, the manual correction of the contours is not straightforward and should bedone with the greatest care, because the depth to the groundwater level is usually unknown.


The depth to the groundwater level is expected to be larger in areas with groundwaterabstraction. Locations with a high abstraction rate should show in the contour map. Edit contourlines in case the groundwater depth is known at the abstraction.

Save the corrected contours after the manual correction and prepare the map for presentation with atitle and a legend.

3.3 CONTOURS OF THE ELEVATION OF THE GROUNDWATER LEVEL

When preparing a map of the groundwater level elevation the procedure is the same for Step 1 and 2.The contours are generated for the groundwater elevation which is derived from:

Infiltrating riverDraining river

76 77 78 79 80 81 82 83 84 85

12

13

14

15

16

17

18

19

20



Altitude (measuring point, meter above msl) – Water level (meter below ground level)

From Step 3 the procedure is as follows:

Step 3 Derive contours of the elevation of the groundwater level

The contours are generated using the available software, like Vertical Mapper / MapInfo, Surfer orother.

Any outliers still present in the basic data should show by a concentration of contour lines. Check thelocations causing these outliers and correct the elevation of the measuring point or the depth to thegroundwater level or, if correction is not possible, remove the location from the file.

Generate the contours again after removing or correcting the outliers.

Step 4 Edit the contours by adding defined contour lines

The generated contours of the elevation of the groundwater level should be combined with the map-layers to identify areas where the contours are to be edited. The first editing should be done by addinginformation in the form of data points or contours with a fixed value and subsequently generating thecontours again.

The following map-layers may be used to identify the areas with incorrect contours:

• Combine the contours with a map-layer of the topographic boundaries.• Contours generated in the sea or in lakes should be removed; this may be done by adding a

contour line with the value 0 at the coastline of the sea or by adding a contour line with the valueof the surface water level at the coastline of lakes.

• Combine the contours with a map-layer of the drainage system (this combination is only relevantfor groundwater levels from aquifers, which are in direct contact with the surface water drainagesystem and if surface water levels are known).

• Contours crossing the surface water drainage lines of rivers and streams should have the samevalue as the value of the surface water level; this may be achieved by adding control points atthe location of the drainage lines.

• Combine the contours with a map-layer of the surface elevation.• The elevation of the groundwater level is expected to be larger in areas with a high elevation.

The correction of the contours by adding control points or lines is not straightforward and shouldbe done with the greatest care, because the elevation of the groundwater level is usuallyunknown. In general it is advised to correct the groundwater elevation contours for groundsurface elevation by manual correction.


The elevation of the groundwater level is expected to be larger in areas with groundwaterabstraction. Locations with a high abstraction rate should show in the contour map. Add controlpoints with the elevation of the groundwater level in case the groundwater elevation is known atthe abstraction. Take care that elevations near abstractions only are applied to the usually smallarea influenced around the abstraction.

Generate the contours again after adding the contours and control points.

Step 5 Edit the contours manually

The generated contours of the elevation of the groundwater level again should be combined with themap-layers to identify areas where the contours are to be edited. The manual editing is done by



editing the grid from which the contours are generated or by transferring the contour lines to a drawingsoftware-package to edit the lines.

The same map-layers as mentioned in Step 4 may be used to identify the areas where contours are tobe corrected or added manually:

• Combine the contours with a map-layer of the topographic boundaries: correct any contour lineswhich do not conform to the topographic features.

• Combine the contours with a map-layer of the drainage system: correct any contour lines whichdo not conform to the drainage lines. The angle of the contour line to the drainage line may becorrected in case it is known that rivers are infiltrating or draining.


• The elevation of the groundwater level is expected to be larger in areas with a high elevation. Asmentioned above, the manual correction of the contours is not straightforward and should bedone with the greatest care, because the elevation of the groundwater level is usually unknown.


• The depth to the groundwater level is expected to be larger in areas with groundwaterabstraction. Locations with a high abstraction rate should show in the contour map. Edit contourlines in case the groundwater depth is known at the abstraction.

Save the corrected contours after the manual correction and prepare the map for presentation with atitle and a legend.



4 SPATIAL CONFIGURATION OF THE GROUNDWATER LEVEL

4.1 GENERAL CONSIDERATIONS FOR CHOICE OF ALGORITHM

The contouring capability of the dedicated software is presented in the Reference Manual, to Volume8 chapter 1. For using this capability, the user has to first select an algorithm from a built-in array.Subsequently, upon an algorithm-assisted automatic production of the contours, the user has anopportunity to edit the contours manually. Apart from producing water level contours, the user mayuse this capability to perform a variety of calculations including validation of the regional water leveldata. The present chapter aims at assisting the user of the software in performing these importanttasks.

The choice of algorithm for an automatic production of the contours is governed by the followingconsiderations:

• Theoretically, Kriging is applicable only to localised variations devoid of any regional trend, i.e., tostationary data. However, the assumption of stationarity applies not to the entire data but only tothe selected neighbourhood (see Reference Manual, Sections 1.3 and 1.5).

• Kriging is not a good extrapolator, and as such, should not be used for producing contoursbeyond the domain of the data points.

• Universal Kriging may contour variations comprising a gradual and regular regional trend. Thisalgorithm, apart from providing contours, also permits an estimation of the trend.

• Since Universal Kriging accounts for and computes the trend, it may be used for producingcontours of localised and regional variations. However, it must be appreciated that the trend iscomputed purely from statistical considerations and as such, needs to be corroborated. Followingcriteria could be considered for such a corroboration:

- In case of moderately developed unconfined aquifers and leaky confined aquifers with lowhydraulic resistance, the slope of the water table/piezometric surface may generally beclose to the topographical slope.

- The regional trend of the piezometric elevation may be governed by the static piezometrichead at an upstream point of the basin and the stage of the outfall at the downstream end.

• In case the computed trend seems to be erratic, the following options in the order of priority, areavailable:

- If it is possible to isolate a phenomenon causing the trend, choose a trend based upon thephenomenon’s understanding. Subtract this trend from the observed data to obtainstationary residuals. Contour the stationary residuals by Kriging and add back the trend tothe resultant contours to obtain the final contours.

- If it is possible to divide the data set into smaller sub-regions within which the trend isnegligible, then perform Kriging separately on each sub-region.

- Use Spline functions.- If the attribute data are known to comprise noise, i.e., random and unsystematic gauging

errors or interference effects from production, then trend surface analysis may be adoptedfor contouring the regional variations.

4.2 WATER TABLE/PIEZOMETRIC ELEVATION CONTOURING

Contours of water table/piezometric elevation (that is, the height above a common datum, usuallymean sea level) are required for estimating lateral flow directions and rates.

4.2.1 CHOICE OF ALGORITHM

It is clear from the preceding section that the main considerations for the choice of an algorithm arethe spatial trend and the data noise. An additional consideration, in the context of water levelcontouring, could be the subsurface flow across the boundary. The implications of these



considerations in the context of contouring water table/piezometric elevation (above a commondatum) are as follows.

Spatial trend

The regional trend of water table/piezometric elevation is essentially a hydraulic gradient that is, slopeof the water table or the piezometric surface. If the gradient is uniform, the trend is linear. On the otherhand a spatially varying gradient leads to a non-linear trend, linear or mildly non-linear trend may beconsidered as gradual.

Causative factors: A hydraulic gradient in an aquifer could be caused, apart from the topographicalslope, by any one or more of the following hydrogeological features:

• Head assigned boundary conditions: Such conditions arise if an aquifer is bounded by ahydraulically connected water body say a river or a reservoir. At the interface of the aquifer andthe water body, the water table shall be the stage i.e., water elevation of the water body. This ofcourse ignores the surface of seepage. Thus, if an aquifer is bounded on the two sides by twohydraulically connected water bodies having markedly different stages, then a hydraulic gradientat the steady state is inevitable.

Figure 4.1: Flow through an unconfined aquifer bounded by surface water

• Localised pockets of intense pumpage or recharge: Such conditions can lead to significanthydraulic gradients.

Figure 4.2: Flow through an unconfined aquifer to a well

��

��

��

��

��

��

��



• Confined conditions: Confined aquifers may have their recharge and pumping zones quite awayfrom each other. This leads to sloping of the piezometric surface from the recharge area towardsthe pumping area.

Figure 4.3: Flow through a confined aquifer

• Spatial variation of aquifer parameters: Such a condition itself may not lead to a trend. However,if above contributory factors exist, the spatial trend caused by them may be rendered non-linearby this condition. The variation of aquifer parameters could be caused by various factors likehydrogeological structures, variable degree of weathering, change in thickness of aquifer unitsetc. In this context it is noteworthy, that an unconfined aquifer displaying a sloping water tableover a horizontal lower impervious layer, has a spatially varying transmissivity even if thehydraulic conductivity is uniform. Thus, the regional trend (if any) in an unconfined aquifer shallbe usually non-linear.

• Effect of transmissivity: A low transmissivity may generally inhibit the regional trends caused bythe features described above. This is due to poor hydraulic connections between various sites ofthe aquifer. For illustration, consider a homogenous aquifer bounded on the two sides byhydraulically connected rivers having markedly different stages. The resulting hydraulic gradientat steady state will be independent of the hydraulic conductivity or transmissivity. However, if theaquifer has very low transmissivity the steady state may never be reached. This means that inpractice, the river stage may effect the water table only up to a short distance and may produceno regional trend. On the other hand if the transmissivity is very high, a steady state may bereached quite quickly. This means that the river stages may define the regional gradient.

Data noise

This could originate from the following:

• Measurement errors,

• Temporal effects,

• Clogging of the piezometer,

• Interpretation error, such as water level in a partially penetrating well taken as vertically averagedhead over the entire aquifer thickness.

��

��

��

��



Subsurface flow across the boundary

The information on the rate of the subsurface flow (volume per unit time per unit boundary length)across the boundary and hence the hydraulic gradient (the flow rate divided by the transmissivity) maybe known at times. The use of Spline functions can assimilate this information into the contours andhence can ensure appropriate gradients at the boundary.

4.2.2 MANUAL MODIFICATIONS

Water table/piezometric elevation contours permit an elaborate interpretation and as such, thealgorithm-based contours may be evaluated and anomalies, if any may be corrected manually. Thecriteria for interpretation/evaluation are as follows.

Head assigned boundary

Such a boundary is activated at the interface between the aquifer and a hydraulically connected waterbody like river, reservoir, lake, etc. Such hydraulic connection may usually hold for unconfined and,less frequently for leaky confined aquifers. Deeper confined aquifers would very rarely be connected.The contours must honour the following requirements at the boundary:

• A contour intersects the boundary at a location where the stage (above the datum) of the waterbody equals the iso-level of the contour.

• In case the exchange of water between the water body and the aquifer is significant, the contoursin the vicinity of the boundary may be nearly parallel to it and thus, may merge with it ratherabruptly.

• If a hydraulically connected river is known to receive a baseflow contribution from the aquifer, thecontours in its vicinity must reflect a fall of watertable towards the river and vice versa.

Impervious boundary

An impervious boundary could either be a physical barrier like a dyke or a hydraulic barrier, that is, awater divide. The contours must join such a boundary normally.

Transmissivity variations

For the same horizontal flow, the contour spacing shall be narrower in regions of lowtransmissivity/hydraulic conductivity and vice versa.

4.3 WATER LEVEL DEPTH CONTOURING

Contours of water level depth (below ground) are produced for a routine analysis aimed at evaluation,planning and management of groundwater resource.


Water level depth data are far less likely to have a regional trend than the water elevation data. Theymostly comprise local trends. As such, Kriging may usually be applicable. If the data do display atrend, it is likely to be gradual and hence Universal Kriging may be applicable. However, there may beno way of corroborating the computed trend.



A direct contouring of noisy water level depth data is not advised. The trend surface analysis may notapply, since there may not be any regional trend and local trends may be indistinguishable from thenoise. In such a case, the raster data of depth and hence the depth contours may be producedindirectly by contouring the noisy water elevation data and then subtracting the resultant raster datafrom the topographical raster data.


Unlike the contours of water elevation, the algorithm-produced depth contours permit only a limitedinterpretation and as such, the scope of evaluation and hence of manual correction may be ratherlimited. The contours may nevertheless be modified to ensure a compatibility between the water leveldepth and the depth of the water surface below the bank in a hydraulically connected water body.

4.4 WATER LEVEL FLUCTUATION CONTOURING

Contours of water level fluctuation in a given period (usually, monsoon and dry seasons) are routinelyproduced. These along with the contours of specific yield permit an estimation of the storagefluctuations, necessary for performing a lumped water balance. These may also be useful forcalibrating a distributed aquifer response model.


Water level fluctuation data, like the depth data, may mostly comprise local trends with little or noregional trend. Hence in the context of the depth data, Kriging or Universal Kriging may usually beapplicable. It may, however, be difficult to corroborate the trend computed through Universal Kriging.

As for the depth data, a direct contouring of noisy water level fluctuation data is not advised. The trendsurface analysis may not apply, since there may not be any regional trend and local trends may beindistinguishable from the noise. In such a case, the raster data of fluctuation and hence thefluctuation contours may be produced indirectly by contouring the noisy water elevation data at thebeginning and the end of the period and then subtracting the resultant raster data of the former fromthe latter.


Contours of water elevation fluctuation permit a moderate interpretation (that is, more than what ispermitted with the depth contours but not as elaborate as with the water elevation contours). Hence,there is a moderate scope of evaluation and hence of manual correction. The contours may bemodified to ensure a compatibility between the water level fluctuation and fluctuation of the watersurface in a hydraulically connected water body. Further, recourse may be taken to the fact that otherthings being equal, regions of low specific yield display larger fluctuations and vice versa.

4.5 COMPUTATION OF VELOCITY FIELD

The contouring algorithms incorporated in the dedicated software permit an estimation of gradients ofthe attribute at any specified point. Thus, raster data of hydraulic gradients can be generated. Thesedata together with the raster data of hydraulic conductivity can be used for estimating the velocitydistribution, in accordance with Darcy’s law.



4.6 VALIDATION OF WATER LEVEL DATA

Automatic contouring is essentially based upon interpolation by a chosen algorithm. This interpolationcapability also permits identification of outliers, i.e., such data points that are statistically inconsistentwith the rest of the data.

An outlier may occur on account of some local phenomenon, which are not extensive enough to bepicked up by the algorithm. However, the other possibility is that the data may be erroneous. Thusthough an outlier may be viewed with a suspicion, it may not be straight away rejected. As such, itmay be worth while to check it’s one time data like spatial coordinates and reduced level of themeasuring point/ground level at the site. If no errors are detected and the inconsistency is detectedconsistently at various discrete times, it may be worth-while to investigate the possible causativephenomena.

The following procedure, known as jack knifing may be adopted for detecting the outliers. This is astructured technique for identifying outliers and requires a statistical assessment of the precision ofthe interpolation. Kriging and Universal Kriging provide such an assessment at each point and assuch, are ideally suited. Trend surface analysis, on the other hand provides an average assessmentof the precision over the entire domain of the data points and thus, is moderately suitable. Splinefunctions do not provide this assessment and are therefore, unsuitable.

A brief description of the method is as follows:

• Consider a single data point.• Remove (that is, jack-knife) this data point from the data set.• Interpolate the value at the location of the removed data point using an appropriate algorithm.

Also compute the standard error of the interpolation.• Compute the deviation of the observed value from the interpolated value in a statistical sense, as

follows:- Calculate the deviation, i.e., modulus of the difference between the observed and

interpolated values;- Divide the deviation by the standard error of interpolation. This is known as absolute

normalized deviation (AND).• Repeat the above procedure in respect of every data point.• Assuming AND to be normally distributed with zero mean and unit standard deviation, the data

points for which AND is greater than some threshold value, say 3 or 4, are labelled as outliers.

4.7 SUGGESTED READING

• Bardossy, A. (Ed), Geostatistical Methods: Recent Developments and Applications in Surfaceand Subsurface Hydrology. Proceedings of an International Workshop held at Karlsruhe,Germany, from 17 to 19 July 1990, UNESCO (IHP IV), Paris 1992.

• Isaaks, Edwards H. and Srivastava, R. Mohan, An Introduction to Applied Geostatistics.Oxford University Press, 1989.

• Neuman, S.P., Role of Geostatistics in Subsurface Hydrology. In Geostatistics for NaturalResources Characterization (ed. G. Verly, et al.), D. Reidel Publishing Company, 1984.



5 GROUNDWATER LEVEL TIME SERIES

5.1 INTRODUCTION

A water level time series comprises multiple- time data of water table/ piezometric head from a singleobservation well/ piezometer, arranged in a chronological order. The data may be elevations above adatum (usually MSL) or depths (usually below ground level). The time series thus comprisessequential annual hydrographs of the water elevation or depth. Water level time series manifests thenet impact of time series of rainfall, pumpage, river stage etc. on the groundwater system and is thus,of a primary interest to a hydrogeologist.

The water level time series are amenable to a comprehensive analysis through the tools of thededicated software described in the Reference Manual, Chapter 3, provided the data are available atan adequate frequency. However, the frequency of manual monitoring of GW levels (usually two tofour times a year under Indian practice) is generally inadequate. The wide scale deployment ofautomatic water level recorders (DWLRs) implemented through the Hydrology Project, shall providecomprehensive and almost continuous water level time series. As such, the available frequency shallbe high enough to permit a variety of analyses including those described in the following sections.

5.2 IDENTIFICATION OF THE DYNAMIC EQUILIBRIUM

A time series of water level data can be viewed as an ensemble of sequential annual hydrographs. Atthe dynamic equilibrium (known alternately as stable state or dynamic steady state) the annualhydrographs over the years are from the same population. This requires stationarity of the mean (firstorder stationarity) and stationarity of shape (second order stationarity), both at a resolution of oneyear.

A water level series will display first order stationarity if the volumetric balance exists, that is, the netannual withdrawals equal the net annual recharge. Further, the second order stationarity will bedisplayed if apart from the volumetric balance, the spatial and temporal distributions of thewithdrawals, recharge and boundary conditions (e.g., stage of hydraulically connected streams in thevicinity) follow the same annual pattern over the years.

Subjecting the time series to the Stationarity analysis described in the Reference Manual, Section 2.3can identify the state of dynamic equilibrium. The segment length may be taken as one year. Thus,the time series is divided into the constituent annual hydrographs. These segments of the time seriesare subjected to the tests of first and second order stationarity. A dynamic equilibrium may be inferredif these tests for stationarity are found to hold.

In practice, a true dynamic equilibrium may never be reached, since there would always be inevitablevariations of withdrawals, recharge and boundary conditions from year to year. However, if thesevariations are small in comparison to the respective long-term mean (i.e., display low coefficients ofvariation) a near- dynamic equilibrium may be reached. This would imply that though there are somevariations from year to year, there is no long-term rising/declining trend of the annual mean and theshape of the hydrograph is not undergoing any distortion. Such a state may be inferred if the tests forstationarity are at least nearly satisfied.

In case the test for first order stationarity is violated, a rising or falling trend of the annual mean maybe inferred. In case the test of stationarity for the mean is satisfied, but the test for second orderstationarity is violated, it may be inferred that though, the volumetric balance is being maintained, thewithdrawal/recharge/boundary condition patterns have undergone a change during the span of thetime series.



5.3 IDENTIFICATION OF TEMPORAL TRENDS

An annual water level hydrograph may be characterised by the following attributes:

• Annual mean

• Annual highest

• Annual lowest

• Macro (say monthly) means

In case the test for first order stationarity is violated, the annual mean and other attributes of thehydrograph may display a rising or a falling trend. On the other hand, if this test holds but the test forsecond order stationarity is violated, the annual mean may be devoid of a trend but one or more of theother attributes may be displaying a trend. These trends in either of the attributes can be identified inthe following steps:

• Split the time series into a sequence of annual hydrographs.

• Compute the desired attribute of each hydrograph.

• Generate a time series comprising the computed attribute values arranged chronologically.

• Fit a regression line to this time series and apply the test to check if the slope coefficient issignificantly different from zero, that is, whether there is any trend. If a trend is found (that is, ifthe slope coefficient is found to be significantly different from zero), apply the F test to determinewhether the trend is linear or quadratic (refer Reference Manual, Section 2.3.2).

It is usually not desirable to explore polynomials of a degree higher than two.

5.3.1 DECLINING TREND

A negative value of b, i.e., slope coefficient (refer Section 3.3.2) indicates a declining trend. In case alinear polynomial is found to be adequate, the decline of the attribute continues at a constant rate thatis (-b) per year. If a second-degree polynomial is found to be necessary, the rate of decline shall be[(-b) - 2cx], where c is the coefficient of the quadratic term (refer Reference Manual, Section 2.3.2). Ifc is positive, the decline rate shall reduce over the years, till it attains a value of zero after (-b)/2cyears. The reduction in the decline rate could be due to one or more of the stabilising phenomena(like increase in influent seepage, decrease in outflow to streams, decrease in evapotranspiration) oralso due to reduction in pumpage or increase in vertical recharge. The stabilised attribute shall be asfollows:

2

c2

bc

c2

bbay

−+

−+= (5.1)

5.3.2 RISING TREND

The preceding discussion in respect of the declining trend can be extended to the rising trendscenario. Thus a positive value of b indicates a rising trend. In case a linear polynomial is found to beadequate, the rise of the attribute continues at a constant rate, that is b per year. If a second-degreepolynomial is found to be necessary, the rate of decline shall be (b + 2cx). If c is negative, the rise rateshall reduce over the years, till it attains a value of zero after b/[2(-c)] years. This implies that the riseis associated with one or more stabilizing phenomena (like decrease in influent seepage, increase inoutflow to streams, increase in evapotranspiration) or there is an increase in pumpage or decrease invertical recharge, over the years. The expression for the stabilised attribute is the same as givenabove in the context of falling trend.



Increase in lateral outflow accompanying a rising trend is generally more pronounced than thecorresponding decrease in lateral flow accompanying a falling trend due to the increase intransmissivity as the water table rises. Similarly, the accompanying increase in the evapotranspirationis quite likely to be significant. Thus, a second-degree polynomial with negative c shall usually befound to be necessary. However, in case a linear polynomial is found to be adequate, it may beconcluded that the length of the time series is not long enough to permit the extrapolation.

5.3.3 PROJECTION OF DYNAMIC EQUILIBRIUM

If macro (say monthly) means display rising or falling trends at attenuating rates, it can be inferred thatthe time series is converging to a dynamic equilibrium. The annual hydrograph at the dynamicequilibrium can be described in terms of stabilised macro means to be computed as described in thepreceding sub-section.

By carrying out such analysis on time series data from various wells in a region, the spatial distributionof the stabilized macro means can be obtained and contoured and hence the regional dynamicequilibrium projected. However, such a projection shall be purely statistical in nature, that is, derivedstatistically from the past trends contained in the time series. Thus, it would hold only if these trendspersist for a long enough time. These trends may however undergo a change on account of thefollowing modifications, which may result from certain natural phenomena or human activities:

• Modification of the annual volume of pumpage/recharge or/and their spatial/temporaldistributions.

• Modification of the stage of the hydraulically connected water bodies.

The dynamic equilibrium corresponding to the modified trends can not be projected by the time seriesanalysis. Nevertheless, modelling the response of aquifer to the new trends of recharge, pumpageand the boundary conditions can make such projections.

5.4 IDENTIFICATION OF LINEAR INTER-DEPENDENCIES

Linear inter-dependence between two concurrent time-dependent phenomena can be identified byestimating unlagged cross correlations between their respective time series (refer Reference Manual,Section 2.2). A significant cross correlation may indicate a close linear inter-dependence.

5.4.1 IDENTIFICATION OF REPRESENTATIVE WELLS

Wells whose time series are significantly cross-correlated with time series of most of the adjacentwells can be treated as representative of the neighbourhood and thus, may be termed asrepresentative wells. Data from such wells can serve as an index for the entire neighbourhood andmay be targeted for a quick assessment of the impact of exceptional phenomenon like severe droughtor cyclones.

Such wells can be identified by estimating the unlagged cross correlations between the time series ofwater level data from various pairs of adjacent wells and identifying the pairs having significantpositive correlations.

5.4.2 ESTIMATION OF TIDAL EFFICIENCY

Tidal efficiency (TE) is defined as the ratio of the piezometric head fluctuation resulting exclusivelyfrom tides, to the causative fluctuation of the tide level. It’s estimate can provide a tentative value ofspecific storage (SS) in accordance with the following equation:



)TE1/(SS −γθβ=

where γ is the specific weight of water, θ is the porosity of aquifer and β is the inverse of the bulkmodulus elasticity of water.

Tidal efficiency may be estimated by a composite analysis of the concurrent time series of tide level(TL) and the piezometric head. However, it is necessary to identify such segments of the piezometrictime series wherein the piezometric fluctuations are exclusively due to the tide. This, along with thesubsequent estimation of the tidal efficiency may be implemented in the following steps:

1. Identify the possible time periods during which the piezometric fluctuations may have occurredexclusively on account of the tide.

2. Compute the cross-correlations between the piezometric and the TL time series, for each of theidentified time periods.

3. Identify such time periods for which the computed cross-correlations are positive and significant.

4. Assume the following linear relation between piezometric elevation (h) and the tide level (H):

5. h = TE.H + constant

6. Estimate the TE by carrying out a regression analysis of the piezometric elevation data and thetide level data from the time periods identified in Step 3.

5.4.3 ESTIMATION OF BAROMETRIC EFFICIENCY

The barometric efficiency (BE) is defined as the ratio of the piezometric head fluctuation resultingexclusively from the atmospheric pressure fluctuations, to the causative fluctuation of the atmosphericpressure expressed as head of water. Its estimate can provide a tentative value of specific storage(SS) in accordance with the following equation:

BE/SS γθβ=

Barometric efficiency may be estimated by a composite analysis of the concurrent time series ofatmospheric pressure and piezometric head. However, it is necessary to identify such segments ofthe piezometric head time series wherein the piezometric fluctuations are exclusively on account ofthe atmospheric pressure fluctuation. This, along with the subsequent estimation of the barometricefficiency may be implemented in the following steps:

1. Identify the possible time periods during which the piezometric fluctuations may have occurredexclusively on account of the atmospheric pressure fluctuation.

2. Compute the cross-correlations between the piezometric elevation and the atmospheric pressuretime series for each of the identified time periods.

3. Identify such time periods for which the computed cross-correlations are negative and significant.

4. Assume the following linear relation between piezometric elevation (h) and the atmosphericpressure head (H). H is the atmospheric pressure divided by the specific weight of water.

5. h = constant - BE.H

6. Estimate the barometric efficiency by carrying out a regression analysis of the piezometricelevation data and the atmospheric pressure head data from the time periods identified in Step 3.

5.5 IDENTIFICATION OF LAGGED INTER-DEPENDENCIES

5.5.1 GENERAL

Linear time-lagged inter-dependence between two concurrent time-dependent phenomena can beidentified by estimating cross correlations between their respective time series (refer Reference



Manual, Section 2.2.) at different lags, considered feasible. The lag at which the cross correlation ishighest may represent the lag between two phenomena. If the highest cross correlation is significant,a linear inter-dependence (with the identified lag) between the two phenomena may be concluded.Thus, such an analysis apart from establishing the inter-dependence, may also permit an estimationof the lag.

5.5.2 INTER-DEPENDENCE BETWEEN RAINFALL AND WATERTABLE

For establishing a quantitative inter-dependence between rainfall and water table, it is necessary toidentify such well sites at which the water table is relatively unaffected by the boundary conditions.The time series of water table data from such wells may be analysed in the following steps:

1. Identify the possible time periods during which the water table fluctuations may have occurredexclusively on account of the recharge from the rainfall.

2. Stipulate a possible variation range for the time lag between the rainfall and the consequentrecharge to the water table.

3. Discretize the range by a finite number of lags.4. Compute the lagged cross-correlations between the water table and the rainfall time series in

each of the identified time periods with the pre-selected time lags.5. Plot correlograms for each of the time periods.6. Identify for each time period the optimal lag, that is, the lag at which the cross-correlation is the

highest on the positive side.7. Identify such periods for which the highest positive cross-correlation is significant. The water table

in such periods may be deemed to have fluctuated exclusively on account of the rainfall recharge.8. Divide the identified periods into two categories, that is, those occurring at the beginning of a rainy

season and those occurring well within it. The lag in the former shall generally be higher. Themean of the corresponding lags in each category may be taken as the time lags between therainfall and the consequent recharge in early and the latter parts of the rainy season.

9. Lag the water table series in the identified periods by the corresponding identified lags.10. Assume the following linear relation between the lagged water table elevation (h) and the rainfall

(R): h = Infiltration index * R / Specific yield + constant

11. Estimate the Infiltration index by carrying out a regression analysis of the lagged water table andthe rainfall data and assuming an appropriate value of specific yield.

Interpolation of the rainy season water table elevations at times when only the rainfall data may beavailable can also be estimated by co-Kriging (refer Reference Manual, Section 2.5).

5.6 IDENTIFICATION OF OUTLIERS

The time series analysis permits identification of outliers, i.e., data points that are statisticallyinconsistent with the rest of data.

An outlier may represent some discrete or short-lived phenomenon. However, the other possibility isthat the data may be erroneous. Thus though an outlier may be viewed with suspicion, it may not bestraight away rejected. As such, it may be worth while to investigate the possible causativephenomena.

Identification of the outliers should start with a manual inspection of hydrographs and thereafter,computerised statistics may be applied.



5.6.1 MEAN ANNUAL HYDROGRAPH

Detection of outliers by this approach shall involve the following steps:

• Split up the water level time series into the constituent annual hydrographs.

• Superpose the hydrographs over each other.

• Select the discrete times (say end of each month) of the year at which the data are to bevalidated, avoiding abrupt changes of the water level between two successive discrete times.

• Estimate the mean (m) and standard deviation (s) of water level data at each of the selecteddiscrete times.

• Generate the hydrograph of the computed means (m) with upper and lower envelopes at 95%and 99% confidence level. These envelopes respectively are (m + 2s) and (m + 3s).

• A recorded water level at any discrete time falling outside the envelopes [that is, outside therange (m - 2s or 3s) to (m + 2s or 3s)] may be treated as an outlier.

5.6.2 TRENDS OF MACRO MEANS

The procedure (refer Section 5.3) involved in identification of temporal trends can be extended foridentification of outliers as follows:

1. Establish a relation between macro mean of a specific period (say month) and the year number.2. Estimate the standard error of the fit as follows:

- In case a linear relation is found to be adequate, the standard error shall be [MRV1/(n-2)]; nbeing the number of the data points (that is, number of years).

- In case a quadratic relation is found to be necessary, the standard error shall be [MRV2/(n-3)].

3. Estimate the residues at all data points. Residue at a data point is the difference between thecorresponding observed and regressed values.

4. Estimate the standard residues of each data point. A standard residue of a data point is definedas the ratio of the corresponding residue to the standard error.

5. Assuming the standard residues to be normally distributed with zero mean and unit standarddeviation, the data whose standard residues are outside the range + 2 (or 3) may be treated asoutliers with a confidence level of 95% (or 99%).

5.6.3 INTERRELATED WELLS

The procedure (refer Section 5.4.1) of identifying pairs of wells whose data are linearlyinterdependent, can be extended to identify the outliers as follows:

1. Identify a pair of wells whose data are significantly interrelated.

2. Carry out a regression analysis between the time series of water level data from the two wells,assuming an already concluded linear relation between the two water levels.

3. Estimate the standard residue at each discrete time of the time series (refer Section 4.6.2).

4. Identify the discrete times at which the standard residues lie outside the range + 2 (or 3). Waterlevel data from one or both the wells at such discrete times may be treated as outliers with 95%(or 99%) confidence level.

5.7 IDENTIFICATION OF TRUE HYDROGRAPH

The high frequency data monitored through the DWLRs shall lead to an identification of the truehydrograph. Usually the true hydrograph at macro scale, may comprise an annual cycle displaying arelatively fast rise from trough to peak, followed by a short fast recession and finally a prolonged slowrecession till the trough. However, some exceptional phenomena like extreme exploitation, artificial



recharge, discontinuation of pumpage may modify this trend. Further, at micro level, it may alsocomprise shorter cycles like seasonal, barometric, tidal etc. in the form of kinks.

5.7.1 IDENTIFICATION OF SIGNIFICANT CYCLES

A water level time series may thus, comprise a few high frequency (say daily, fortnightly, seasonal)cycles superposed over a dominant annual cycle. The annual cycle is usually the strongest cycleoccurring in the time series. It is caused mainly by the annual periodicities of - rainfall/irrigationrecharge, stage of hydraulically connected rivers, pumpage etc.

Subjecting the time series to spectral analysis (refer Reference Manual, Section 2.4) can identifythese cycles. The steps shall be as follows:

1. Level the time series.

2. Subject the levelled time series to spectral analysis and identify various cycles.

3. Assimilate the pre-computed trends of mean and standard deviation into the cycles, to obtain theintrinsic cycles of the time series.

The annual cycle, so identified shall be devoid of the high frequency (short-term) cycles.

5.7.2 ANALYSIS OF HYDROGRAPH RECESSION

The recession of a hydrograph comprises it’s declining phase, that is, from peak to the trough. Therecession may result from processes like natural drainage to the hydraulically connected streams,pumpage and evapotranspiration.

A recession predominantly resulting from the natural drainage, is related to the aquifer geometry andthe diffusivity (T/S). Thus, an analysis of such a recession can provide a preliminary estimate of thediffusivity, which in turn may lead to the estimation of the transmissivity or the storage coefficient,knowing the other. The steps of the computation are as follows:

1. Isolate the intrinsic annual cycle from the time series (refer Section 5.7.1). Derive thecorresponding annual cycle of the driving head by shifting the datum to stage of the drainingstream during the period of the recession.

2. Plot the recession curve (log of the driving head versus the time). The curve may reveal two ormore straight lines segments. The first one, usually steep and short, may represent a fastrecession. A relatively flat and long segment, representing a moderate/slow recession usuallyfollows this.

3. Assuming a linear relation between log of the driving head and the time, carry out a regressionanalysis of the dominant segment of the recession. Hence compute the depletion time. The timefor one log cycle (to the base ten) change in the driving head, divided by 2.3, is termed as thedepletion time.

4. The depletion time, in general can be expressed as (k.L2.T/S); where L is the distance of thesampled well from the draining stream along the flowline and k is a constant depending upon theboundary conditions. It could vary from 0.405 (drainage on both sides of the well) to 1.0 (drainageonly on one side).

The analysis described above holds for the recession of the outflow hydrograph also. The outflow maymanifest as stream flow during dry season (when the entire stream flow may be derived fromgroundwater drainage) or as spring flow. The flow time series if available, may also be analyzed in asimilar way. This may provide a means of corroborating the estimate of diffusivity arrived at byanalyzing the driving head time series.



5.8 SUGGESTED READING

• Jacob, C. E., Correlation of Groundwater Levels and Precipitation on Long Island, New York PartI - Theory. Transactions American Geophysical Union, Twenty Fourth Annual Meeting 1943, PartII, Section of Hydrology Reports and Papers, 564-573, 1944.

• Jacob, C. E., Correlation of Groundwater Levels and Precipitation on Long Island, New York PartII - Correlation of Data. Transactions American Geophysical Union, Twenty Fifth Annual Meeting1944, Part VI, Section of Hydrology Papers, 928-950, 1944.

• Law, Albert G., Stochastic Analysis of Groundwater Level Time Series in the Western UnitedStates. Hydrology Papers, Colorado State University, Fort Collins, Colorado; No. 68, May 1974.

• Bear, Jacob, Hydraulics of Ground water. McGraw Hill, Israel, 1979.



6 GROUNDWATER MODEL INPUT

A groundwater model may be set up to simulate the hydrogeological conditions of an area in order tounderstand the hydrogeological processes taking place and in order to make calculations of futuredevelopments. There are different types of groundwater models. In this case the processing ofsubsurface data is explained for a model with horizontal layers. The data of the subsurface for such amodel may be obtained from the information system. A general description of the steps involved inpreparing such a model are described below.

Suppose the groundwater model will consist of a number of horizontal layers, how will the informationfor such layers be derived from the information system?

Step 1

The objective of Step 1 is to create columns with interfaces corresponding with the interface of themodel layers.

The lithological logs of the boreholes (see Figure 6.1) in the area are processed identifying in each logthe interfaces corresponding with the layers of the hydrogeological model. The interfaces should becoded in each log in order to retrieve these from the logs. Each interface will have a code and a depthassigned to it. The interfaces will be stored in a separate log, which will be called the hydrogeologicalcolumn.

Figure 6.1:Llithological log

Step 2

The objective of Step 2 is to create rasters representing the depth of each interface. The interfacedepths from the hydrogeological columns are combined to create multiple rasters of the interfacedepth. The rasters are created by contouring the depths of each interface, see Figure 6.2.

��

01

2

3

1

2

3

4



��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

Interface0

1

2

3

Derived hydrogeological columns Rasters with depth to interface

1

2

3

Rasters with depth to interface Rasters with layer thickness

Layers

Figure 6.2: Rasters with depth to interface

Step 3

The objective of Step 3 is to create rasters of the thickness of the model layers.

The rasters with the layer thickness are obtained by determining the difference in depth between thelayer interfaces. This is done easily by subtracting the rasters of the interface depth see Figure 6.3.

Figure 6.3: Rasters with layer thickness

Step 4

The objective of Step 4 is to combine the hydrogeological properties of the layers with the layerthickness.

In a groundwater model the permeability and storage properties of the layers are required to carry outthe groundwater flow calculations.



X =

Layer thickness (m) Horizontal permeability (m/day) Transmissivity (m2/day)

/ =

Layer thickness (m) Vertical permeability (m/day) Resistivity (days)

The transmissivity of the water bearing layers is obtained by multiplying the layer thickness with aconstant value of value of the horizontal permeability or with a raster containing the spatially varyingvalue of the horizontal permeability, see Figure 6.4.

The vertical resistivity of a badly permeable layer is obtained by dividing the layer thickness by aconstant value of the vertical permeability or by a raster containing the spatially varying value of thevertical permeability, see Figure 6.4.

Figure 6.4: Determination of Rasters for transmissivity and resistivity

With these four steps the hydrogeological schematization for a groundwater model with horizontallayers is completed.

NBMNBNBMNB

download-manuals-ground water-manual-gw-volume8operationmanualdataprocessingpartiii

Technology

data validation

derived data

data processing methods

preparation of basic

timedependent data

validation of water

number of data points

timeseries analysis