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  1. 1. Government of India & Government of The Netherlands DHV CONSULTANTS & DELFT HYDRAULICS with HALCROW, TAHAL, CES, ORG & JPS VOLUME 8 DATA PROCESSING AND ANALYSIS OPERATION MANUAL – PART III DATA PROCESSING AND ANALYSIS
  2. 2. 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 2-1 2.2 CONTOUR MAPS 2-1 2.3 RASTER MAPS 2-2 2.4 TIME SERIES / HYDROGRAPHS 2-3 2.5 OTHER DERIVED MAPS 2-4 3 EXAMPLE OF THE PREPARATION OF A CONTOUR MAP 3-1 3.1 PREPARATION OF BASIC DATA 3-1 3.2 CONTOURS OF THE DEPTH TO THE GROUNDWATER LEVEL 3-3 3.3 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 4-1 4.2 WATER TABLE/PIEZOMETRIC ELEVATION CONTOURING 4-1 4.2.1 CHOICE OF ALGORITHM 4-1 4.2.2 MANUAL MODIFICATIONS 4-4 4.3 WATER LEVEL DEPTH CONTOURING 4-4 4.3.1 CHOICE OF ALGORITHM 4-4 4.3.2 MANUAL MODIFICATIONS 4-5 4.4 WATER LEVEL FLUCTUATION CONTOURING 4-5 4.4.1 CHOICE OF ALGORITHM 4-5 4.4.2 MANUAL MODIFICATIONS 4-5 4.5 COMPUTATION OF VELOCITY FIELD 4-5 4.6 VALIDATION OF WATER LEVEL DATA 4-6 4.7 SUGGESTED READING 4-6 5 GROUNDWATER LEVEL TIME SERIES 5-1 5.1 INTRODUCTION 5-1 5.2 IDENTIFICATION OF THE DYNAMIC EQUILIBRIUM 5-1 5.3 IDENTIFICATION OF TEMPORAL TRENDS 5-2 5.3.1 DECLINING TREND 5-2 5.3.2 RISING TREND 5-2 5.3.3 PROJECTION OF DYNAMIC EQUILIBRIUM 5-3 5.4 IDENTIFICATION OF LINEAR INTER-DEPENDENCIES 5-3 5.4.1 IDENTIFICATION OF REPRESENTATIVE WELLS 5-3 5.4.2 ESTIMATION OF TIDAL EFFICIENCY 5-3 5.4.3 ESTIMATION OF BAROMETRIC EFFICIENCY 5-4 5.5 IDENTIFICATION OF LAGGED INTER-DEPENDENCIES 5-4 5.5.1 GENERAL 5-4 5.5.2 INTER-DEPENDENCE BETWEEN RAINFALL AND WATERTABLE 5-5 5.6 IDENTIFICATION OF OUTLIERS 5-5 5.6.1 MEAN ANNUAL HYDROGRAPH 5-6 5.6.2 TRENDS OF MACRO MEANS 5-6 5.6.3 INTERRELATED WELLS 5-6 5.7 IDENTIFICATION OF TRUE HYDROGRAPH 5-6 5.7.1 IDENTIFICATION OF SIGNIFICANT CYCLES 5-7 5.7.2 ANALYSIS OF HYDROGRAPH RECESSION 5-7 5.8 SUGGESTED READING 5-8 6 GROUNDWATER MODEL INPUT 6-1
  3. 3. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 1-1 1 DATA PROCESSING The Groundwater Estimation and Management System (GEMS) allows for the preparation of maps and the execution of calculations based on the basic data contained in the database. Such data processing is useful and appropriate for the analysis of the past, present and future condition of the available water resources, but may easily produce misleading results, when sufficient knowledge of the 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 been successfully validated, may be identified by the added validation flag or code. Only data with the required level of validation should be used in further data processing. The data validation therefore is an 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. In case of gaps in the data, statistical analyses may not yield results, because a continuous dataset is required. Filling in the gaps by generating simulated numbers is an option, to allow the use of the statistical methods in time-series analysis. However with data processing, emphasis should be put on the sites from where continuous time-series are available. The user should understand the limitations of the data before processing the data. For example the density of the data points should be sufficient to represent the hydrogeological feature, such as the groundwater level, when preparing for a contour map. In case the number of data points is insufficient then the contour map should not be generated. Having confidence in the basic data and in the results of the data processing is a prerequisite when using data from an information system. The basic data should only be used if sufficient confidence exist in the quality and completeness of this data. Furthermore the results of data processing activities always 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 from basic data to derived data is given in Chapter 2. The contouring of groundwater levels is explained in detail in Chapter 3. The analysis of groundwater level time series is explained in Chapter 4. Finally in Chapter 5 the preparation of input to groundwater models is given. Background information on spatial contouring and time series analysis is provided in the Reference Manual of this Volume.
  4. 4. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 2-1 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 of certain properties over a certain area. The basic data are generally point and polygon data. The point data represent the locations of the hydrogeological stations, such as the location of wells or hydromet stations. The polygon data represent maps which are either prepared by the staff operating the information 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 the locations of these stations and also showing measurements taken at these stations. These maps are useful 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 of a value derived from the measurements. For example a contour map can be prepared of the groundwater levels measured in the groundwater observation wells. However, such a map will not be realistic when effects are not accounted for of features in-between the measuring stations, for example of a river. Additional information therefore has to be incorporated to produce a meaningful map. 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, see Figure 2.2.
  5. 5. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 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 are incorrect. In Figure 2.3 one measurement has a significant effect on the shape of the contours. The value may be wrong but it may also be a correct value. The use of this value in contouring should be considered before preparing the final contour map. Figure 2.3: The observation point with a measured value of 4.4 has a significant effect on the position of the contours 2.3 RASTER MAPS After generating a contour map a raster map may be created. The raster map contains values for a grid with uniformly distributed points. The raster map allows for the presentation of the derived values by 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 6.3 6.4 5.7 4.6 4.5 3.5 3 6 5 4 2.9 5.1 4.6 4.3 5.8 5.3 5.4 6.3 6.4 5.7 4.6 4.5 3.5 3 6 5 4 7.2 4.1 4.9 4.4 ? 5.1 6.1 6.8 6.4 5.9 6.3 5.4 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 6.1 6.8 6.4 5.9 6.3 5.4 4.4 4.0 2.6 2.7 2.0 3.5 3 7 6 5 4
  6. 6. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 2-3 When working with rasters it is possible to carry out spatial calculations. For example the difference in groundwater level between pre-monsoon and post-monsoon may be calculated in a raster by subtracting the raster with the groundwater level for the post-monsoon conditions from the raster with the groundwater level for the pre-monsoon conditions. Multiplying the derived raster with the area of the raster cells and the specific yield of the aquifer will give the total groundwater volume increase during 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 in a hydrograph. Such a graph may combine multiple variables, such as the groundwater level of a well and rainfall quantities, measured in a nearby station see Figure 2.5 (a). The graph may also include a trend 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 simple inspection 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 groundwater level data is neither very flat nor very steep. When only depth of water is available then the vertical scale should be reversed, so that it increases from top to bottom, corresponding to the intuitive picture of rising and falling water levels. X = Post-monsoon groundwater level Pre-monsoon groundwater level Specific yield (Sy) Change in groundwater storage ∆ h (a) (b)
  7. 7. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 2-4 The hydrograph of a monitoring well or other geohydrological structure may also be presented in a map directly by showing multiple time series graphs (Fig 2.6). In combination with a map layer of the aquifer type such a map will be instructive in presenting the variation and trend of the groundwater levels 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)
  8. 8. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 2-5 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
  9. 9. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 2-6 Figure 2.8 Examples of a geological map Figure 2.9 example of a lithological map Example of the preparation of a contour map
  10. 10. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-1 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 the groundwater 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 level elevation for the period of January 2001. All measurements taken during the month of January of the year 2001 have been used. Using data from such a period is allowed in the case of a small variation of 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 - 590.955 128.661 152.1 637.985 -
  11. 11. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-2 The surface elevation points were derived from the database by using the altitude at the location of the 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 the basic data before starting with the data processing, to find incorrect values which may disturb the map preparation. 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 on the 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 the locations 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 value should 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 data validation procedures are carried out thoroughly on a monthly and annual basis, as prescribed for HIS, and only use is made of the authenticated data of the database in the Data Storage Centre such an activity, thoroughly would not be necessary. Nevertheless, it is always required to ensure yourself about 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 well coordinates, location is in the sea Location in the sea removed from the dataset Bay of Bengal Bay of Bengal
  12. 12. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-3 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 or other. Any outliers still present in the basic data should show by a concentration of contours line (see Figure 3.3, left). Check the locations causing these outliers and correct the value or if correction is not possible, 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 adding information in the form of data points or contours with a fixed value and subsequently generating the contours 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 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 Incorrect measurement Incorrect measurement removed
  13. 13. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-4 Figure3.4: Adding defined contour lines to improve contouring • Combine the contours with a map-layer of the drainage system (this combination is only relevant for groundwater levels from aquifers which are in direct contact with the surface water drainage system and if surface water levels are known). • Contours crossing the surface water drainage lines of rivers and streams should have the same value as the depth of the surface water level below ground surface; this may be achieved by adding 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. The correction of the contours by adding control points or lines is not straightforward and should be done with the greatest care, because the depth to the groundwater level is usually unknown. In general, it is advised to correct the groundwater depth contours for ground surface elevation by manual correction. • Combine the contours with a map-layer with the locations of groundwater abstraction (this action is 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 groundwater abstraction. Locations with a high abstraction rate should show in the contour map. Add control points with the depth to the groundwater level in case the groundwater depth is known at the abstraction. Take care that depths near abstractions only are applied to the usually small area 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 depth to the groundwater level should again be combined with the map-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 drawing software-package to edit the lines. The same map-layers as mentioned in Step 4 may be used to identify the areas where contours are to be corrected or added manually: • Combine the contours with a map-layer of the topographic boundaries: correct any contour lines which 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 line added with value 0 at coast line Contour lines generated from observed water levels only
  14. 14. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-5 • Combine the contours with a map-layer of the drainage system: correct any contour lines which do not conform to the drainage lines. Figure 3.5 correction of contours may be possible near the major drainage lines. This was not done for this example. Figure 3.5: Groundwater level contour lines and drainage system map-layer • The angle of the contour line to the drainage line may be corrected in case it is known that rivers are infiltrating or draining, see Figure 3.6. Figure 3.6: Groundwater level contour lines crossing a river or a stream • 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. As mentioned above, the manual correction of the contours is not straightforward and should be done with the greatest care, because the depth to the groundwater level is usually unknown. • Combine the contours with a map-layer with the locations of groundwater abstraction (this action is 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 groundwater abstraction. Locations with a high abstraction rate should show in the contour map. Edit contour lines 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 a title 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
  15. 15. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-6 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 or other. Any outliers still present in the basic data should show by a concentration of contour lines. Check the locations causing these outliers and correct the elevation of the measuring point or the depth to the groundwater 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 adding information in the form of data points or contours with a fixed value and subsequently generating the contours 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 value of the surface water level at the coastline of lakes. • Combine the contours with a map-layer of the drainage system (this combination is only relevant for groundwater levels from aquifers, which are in direct contact with the surface water drainage system and if surface water levels are known). • Contours crossing the surface water drainage lines of rivers and streams should have the same value as the value of the surface water level; this may be achieved by adding control points at the 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 should be done with the greatest care, because the elevation of the groundwater level is usually unknown. In general it is advised to correct the groundwater elevation contours for ground surface elevation by manual correction. • Combine the contours with a map-layer with the locations of groundwater abstraction (this action is relevant only when preparing the map at a scale of 1:100,000 or larger). The elevation of the groundwater level is expected to be larger in areas with groundwater abstraction. Locations with a high abstraction rate should show in the contour map. Add control points with the elevation of the groundwater level in case the groundwater elevation is known at the abstraction. Take care that elevations near abstractions only are applied to the usually small area 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 the map-layers to identify areas where the contours are to be edited. The manual editing is done by
  16. 16. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 3-7 editing the grid from which the contours are generated or by transferring the contour lines to a drawing software-package to edit the lines. The same map-layers as mentioned in Step 4 may be used to identify the areas where contours are to be corrected or added manually: • Combine the contours with a map-layer of the topographic boundaries: correct any contour lines which do not conform to the topographic features. • Combine the contours with a map-layer of the drainage system: correct any contour lines which do not conform to the drainage lines. The angle of the contour line to the drainage line may be corrected in case it is known that rivers are infiltrating or draining. • 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. As mentioned above, the manual correction of the contours is not straightforward and should be done with the greatest care, because the elevation of the groundwater level is usually unknown. • Combine the contours with a map-layer with the locations of groundwater abstraction (this action is 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 groundwater abstraction. Locations with a high abstraction rate should show in the contour map. Edit contour lines 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 a title and a legend.
  17. 17. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-1 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 Volume 8 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 an opportunity to edit the contours manually. Apart from producing water level contours, the user may use this capability to perform a variety of calculations including validation of the regional water level data. The present chapter aims at assisting the user of the software in performing these important tasks. The choice of algorithm for an automatic production of the contours is governed by the following considerations: • Theoretically, Kriging is applicable only to localised variations devoid of any regional trend, i.e., to stationary data. However, the assumption of stationarity applies not to the entire data but only to the 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 contours beyond the domain of the data points. • Universal Kriging may contour variations comprising a gradual and regular regional trend. This algorithm, 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 producing contours of localised and regional variations. However, it must be appreciated that the trend is computed purely from statistical considerations and as such, needs to be corroborated. Following criteria could be considered for such a corroboration: - In case of moderately developed unconfined aquifers and leaky confined aquifers with low hydraulic resistance, the slope of the water table/piezometric surface may generally be close to the topographical slope. - The regional trend of the piezometric elevation may be governed by the static piezometric head 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, are available: - If it is possible to isolate a phenomenon causing the trend, choose a trend based upon the phenomenon’s understanding. Subtract this trend from the observed data to obtain stationary residuals. Contour the stationary residuals by Kriging and add back the trend to the resultant contours to obtain the final contours. - If it is possible to divide the data set into smaller sub-regions within which the trend is negligible, 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 adopted for 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, usually mean 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 are the spatial trend and the data noise. An additional consideration, in the context of water level contouring, could be the subsurface flow across the boundary. The implications of these
  18. 18. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-2 considerations in the context of contouring water table/piezometric elevation (above a common datum) are as follows. Spatial trend The regional trend of water table/piezometric elevation is essentially a hydraulic gradient that is, slope of the water table or the piezometric surface. If the gradient is uniform, the trend is linear. On the other hand a spatially varying gradient leads to a non-linear trend, linear or mildly non-linear trend may be considered as gradual. Causative factors: A hydraulic gradient in an aquifer could be caused, apart from the topographical slope, by any one or more of the following hydrogeological features: • Head assigned boundary conditions: Such conditions arise if an aquifer is bounded by a hydraulically connected water body say a river or a reservoir. At the interface of the aquifer and the water body, the water table shall be the stage i.e., water elevation of the water body. This of course ignores the surface of seepage. Thus, if an aquifer is bounded on the two sides by two hydraulically connected water bodies having markedly different stages, then a hydraulic gradient at 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 significant hydraulic gradients. Figure 4.2: Flow through an unconfined aquifer to a well
  19. 19. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-3 • Confined conditions: Confined aquifers may have their recharge and pumping zones quite away from each other. This leads to sloping of the piezometric surface from the recharge area towards the 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-linear by this condition. The variation of aquifer parameters could be caused by various factors like hydrogeological structures, variable degree of weathering, change in thickness of aquifer units etc. In this context it is noteworthy, that an unconfined aquifer displaying a sloping water table over a horizontal lower impervious layer, has a spatially varying transmissivity even if the hydraulic conductivity is uniform. Thus, the regional trend (if any) in an unconfined aquifer shall be usually non-linear. • Effect of transmissivity: A low transmissivity may generally inhibit the regional trends caused by the features described above. This is due to poor hydraulic connections between various sites of the aquifer. For illustration, consider a homogenous aquifer bounded on the two sides by hydraulically connected rivers having markedly different stages. The resulting hydraulic gradient at steady state will be independent of the hydraulic conductivity or transmissivity. However, if the aquifer has very low transmissivity the steady state may never be reached. This means that in practice, the river stage may effect the water table only up to a short distance and may produce no regional trend. On the other hand if the transmissivity is very high, a steady state may be reached 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 averaged head over the entire aquifer thickness.
  20. 20. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-4 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) may be known at times. The use of Spline functions can assimilate this information into the contours and hence can ensure appropriate gradients at the boundary. 4.2.2 MANUAL MODIFICATIONS Water table/piezometric elevation contours permit an elaborate interpretation and as such, the algorithm-based contours may be evaluated and anomalies, if any may be corrected manually. The criteria for interpretation/evaluation are as follows. Head assigned boundary Such a boundary is activated at the interface between the aquifer and a hydraulically connected water body 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 water body equals the iso-level of the contour. • In case the exchange of water between the water body and the aquifer is significant, the contours in the vicinity of the boundary may be nearly parallel to it and thus, may merge with it rather abruptly. • If a hydraulically connected river is known to receive a baseflow contribution from the aquifer, the contours 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, a water 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 low transmissivity/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. 4.3.1 CHOICE OF ALGORITHM Water level depth data are far less likely to have a regional trend than the water elevation data. They mostly comprise local trends. As such, Kriging may usually be applicable. If the data do display a trend, it is likely to be gradual and hence Universal Kriging may be applicable. However, there may be no way of corroborating the computed trend.
  21. 21. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-5 A direct contouring of noisy water level depth data is not advised. The trend surface analysis may not apply, since there may not be any regional trend and local trends may be indistinguishable from the noise. In such a case, the raster data of depth and hence the depth contours may be produced indirectly by contouring the noisy water elevation data and then subtracting the resultant raster data from the topographical raster data. 4.3.2 MANUAL MODIFICATIONS Unlike the contours of water elevation, the algorithm-produced depth contours permit only a limited interpretation and as such, the scope of evaluation and hence of manual correction may be rather limited. The contours may nevertheless be modified to ensure a compatibility between the water level depth 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 routinely produced. These along with the contours of specific yield permit an estimation of the storage fluctuations, necessary for performing a lumped water balance. These may also be useful for calibrating a distributed aquifer response model. 4.4.1 CHOICE OF ALGORITHM Water level fluctuation data, like the depth data, may mostly comprise local trends with little or no regional trend. Hence in the context of the depth data, Kriging or Universal Kriging may usually be applicable. 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 trend surface analysis may not apply, since there may not be any regional trend and local trends may be indistinguishable from the noise. In such a case, the raster data of fluctuation and hence the fluctuation contours may be produced indirectly by contouring the noisy water elevation data at the beginning and the end of the period and then subtracting the resultant raster data of the former from the latter. 4.4.2 MANUAL MODIFICATIONS Contours of water elevation fluctuation permit a moderate interpretation (that is, more than what is permitted 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 be modified to ensure a compatibility between the water level fluctuation and fluctuation of the water surface in a hydraulically connected water body. Further, recourse may be taken to the fact that other things 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 of the attribute at any specified point. Thus, raster data of hydraulic gradients can be generated. These data together with the raster data of hydraulic conductivity can be used for estimating the velocity distribution, in accordance with Darcy’s law.
  22. 22. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 4-6 4.6 VALIDATION OF WATER LEVEL DATA Automatic contouring is essentially based upon interpolation by a chosen algorithm. This interpolation capability also permits identification of outliers, i.e., such data points that are statistically inconsistent with the rest of the data. An outlier may occur on account of some local phenomenon, which are not extensive enough to be picked up by the algorithm. However, the other possibility is that the data may be erroneous. Thus though an outlier may be viewed with a suspicion, it may not be straight away rejected. As such, it may be worth while to check it’s one time data like spatial coordinates and reduced level of the measuring point/ground level at the site. If no errors are detected and the inconsistency is detected consistently at various discrete times, it may be worth-while to investigate the possible causative phenomena. The following procedure, known as jack knifing may be adopted for detecting the outliers. This is a structured technique for identifying outliers and requires a statistical assessment of the precision of the interpolation. Kriging and Universal Kriging provide such an assessment at each point and as such, are ideally suited. Trend surface analysis, on the other hand provides an average assessment of the precision over the entire domain of the data points and thus, is moderately suitable. Spline functions 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 Surface and 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 Natural Resources Characterization (ed. G. Verly, et al.), D. Reidel Publishing Company, 1984.
  23. 23. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-1 5 GROUNDWATER LEVEL TIME SERIES 5.1 INTRODUCTION A water level time series comprises multiple- time data of water table/ piezometric head from a single observation well/ piezometer, arranged in a chronological order. The data may be elevations above a datum (usually MSL) or depths (usually below ground level). The time series thus comprises sequential annual hydrographs of the water elevation or depth. Water level time series manifests the net 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 the dedicated software described in the Reference Manual, Chapter 3, provided the data are available at an adequate frequency. However, the frequency of manual monitoring of GW levels (usually two to four times a year under Indian practice) is generally inadequate. The wide scale deployment of automatic water level recorders (DWLRs) implemented through the Hydrology Project, shall provide comprehensive and almost continuous water level time series. As such, the available frequency shall be 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. At the dynamic equilibrium (known alternately as stable state or dynamic steady state) the annual hydrographs over the years are from the same population. This requires stationarity of the mean (first order stationarity) and stationarity of shape (second order stationarity), both at a resolution of one year. A water level series will display first order stationarity if the volumetric balance exists, that is, the net annual withdrawals equal the net annual recharge. Further, the second order stationarity will be displayed if apart from the volumetric balance, the spatial and temporal distributions of the withdrawals, recharge and boundary conditions (e.g., stage of hydraulically connected streams in the vicinity) follow the same annual pattern over the years. Subjecting the time series to the Stationarity analysis described in the Reference Manual, Section 2.3 can 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 series are subjected to the tests of first and second order stationarity. A dynamic equilibrium may be inferred if these tests for stationarity are found to hold. In practice, a true dynamic equilibrium may never be reached, since there would always be inevitable variations of withdrawals, recharge and boundary conditions from year to year. However, if these variations are small in comparison to the respective long-term mean (i.e., display low coefficients of variation) a near- dynamic equilibrium may be reached. This would imply that though there are some variations from year to year, there is no long-term rising/declining trend of the annual mean and the shape of the hydrograph is not undergoing any distortion. Such a state may be inferred if the tests for stationarity are at least nearly satisfied. In case the test for first order stationarity is violated, a rising or falling trend of the annual mean may be inferred. In case the test of stationarity for the mean is satisfied, but the test for second order stationarity is violated, it may be inferred that though, the volumetric balance is being maintained, the withdrawal/recharge/boundary condition patterns have undergone a change during the span of the time series.
  24. 24. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-2 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 the hydrograph may display a rising or a falling trend. On the other hand, if this test holds but the test for second order stationarity is violated, the annual mean may be devoid of a trend but one or more of the other attributes may be displaying a trend. These trends in either of the attributes can be identified in the 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 is significantly different from zero, that is, whether there is any trend. If a trend is found (that is, if the slope coefficient is found to be significantly different from zero), apply the F test to determine whether 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 a linear polynomial is found to be adequate, the decline of the attribute continues at a constant rate that is (-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). If c is positive, the decline rate shall reduce over the years, till it attains a value of zero after (-b)/2c years. 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) or also due to reduction in pumpage or increase in vertical recharge. The stabilised attribute shall be as follows: 2 c2 b c c2 b bay       −+      −+= (5.1) 5.3.2 RISING TREND The preceding discussion in respect of the declining trend can be extended to the rising trend scenario. Thus a positive value of b indicates a rising trend. In case a linear polynomial is found to be adequate, the rise of the attribute continues at a constant rate, that is b per year. If a second-degree polynomial is found to be necessary, the rate of decline shall be (b + 2cx). If c is negative, the rise rate shall reduce over the years, till it attains a value of zero after b/[2(-c)] years. This implies that the rise is associated with one or more stabilizing phenomena (like decrease in influent seepage, increase in outflow to streams, increase in evapotranspiration) or there is an increase in pumpage or decrease in vertical recharge, over the years. The expression for the stabilised attribute is the same as given above in the context of falling trend.
  25. 25. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-3 Increase in lateral outflow accompanying a rising trend is generally more pronounced than the corresponding decrease in lateral flow accompanying a falling trend due to the increase in transmissivity as the water table rises. Similarly, the accompanying increase in the evapotranspiration is quite likely to be significant. Thus, a second-degree polynomial with negative c shall usually be found to be necessary. However, in case a linear polynomial is found to be adequate, it may be concluded 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 that the time series is converging to a dynamic equilibrium. The annual hydrograph at the dynamic equilibrium can be described in terms of stabilised macro means to be computed as described in the preceding sub-section. By carrying out such analysis on time series data from various wells in a region, the spatial distribution of the stabilized macro means can be obtained and contoured and hence the regional dynamic equilibrium projected. However, such a projection shall be purely statistical in nature, that is, derived statistically from the past trends contained in the time series. Thus, it would hold only if these trends persist for a long enough time. These trends may however undergo a change on account of the following modifications, which may result from certain natural phenomena or human activities: • Modification of the annual volume of pumpage/recharge or/and their spatial/temporal distributions. • 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 series analysis. Nevertheless, modelling the response of aquifer to the new trends of recharge, pumpage and 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 by estimating 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 adjacent wells can be treated as representative of the neighbourhood and thus, may be termed as representative wells. Data from such wells can serve as an index for the entire neighbourhood and may be targeted for a quick assessment of the impact of exceptional phenomenon like severe drought or cyclones. Such wells can be identified by estimating the unlagged cross correlations between the time series of water level data from various pairs of adjacent wells and identifying the pairs having significant positive correlations. 5.4.2 ESTIMATION OF TIDAL EFFICIENCY Tidal efficiency (TE) is defined as the ratio of the piezometric head fluctuation resulting exclusively from tides, to the causative fluctuation of the tide level. It’s estimate can provide a tentative value of specific storage (SS) in accordance with the following equation:
  26. 26. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-4 )TE1/(SS −γθβ= where γ is the specific weight of water, θ is the porosity of aquifer and β is the inverse of the bulk modulus 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 piezometric time series wherein the piezometric fluctuations are exclusively due to the tide. This, along with the subsequent 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 occurred exclusively on account of the tide. 2. Compute the cross-correlations between the piezometric and the TL time series, for each of the identified 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 the tide 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 resulting exclusively from the atmospheric pressure fluctuations, to the causative fluctuation of the atmospheric pressure 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 of atmospheric pressure and piezometric head. However, it is necessary to identify such segments of the piezometric head time series wherein the piezometric fluctuations are exclusively on account of the atmospheric pressure fluctuation. This, along with the subsequent estimation of the barometric efficiency may be implemented in the following steps: 1. Identify the possible time periods during which the piezometric fluctuations may have occurred exclusively on account of the atmospheric pressure fluctuation. 2. Compute the cross-correlations between the piezometric elevation and the atmospheric pressure time 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 atmospheric pressure 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 piezometric elevation 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 be identified by estimating cross correlations between their respective time series (refer Reference
  27. 27. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-5 Manual, Section 2.2.) at different lags, considered feasible. The lag at which the cross correlation is highest 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 estimation of 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 to identify 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 occurred exclusively on account of the recharge from the rainfall. 2. Stipulate a possible variation range for the time lag between the rainfall and the consequent recharge 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. The mean of the corresponding lags in each category may be taken as the time lags between the rainfall 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 and the 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 be available 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 statistically inconsistent with the rest of data. An outlier may represent some discrete or short-lived phenomenon. However, the other possibility is that the data may be erroneous. Thus though an outlier may be viewed with suspicion, it may not be straight away rejected. As such, it may be worth while to investigate the possible causative phenomena. Identification of the outliers should start with a manual inspection of hydrographs and thereafter, computerised statistics may be applied.
  28. 28. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-6 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 be validated, 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 selected discrete 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 the range (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 for identification 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)]; n being 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 the corresponding observed and regressed values. 4. Estimate the standard residues of each data point. A standard residue of a data point is defined as the ratio of the corresponding residue to the standard error. 5. Assuming the standard residues to be normally distributed with zero mean and unit standard deviation, the data whose standard residues are outside the range + 2 (or 3) may be treated as outliers 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 linearly interdependent, 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). Water level 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 true hydrograph. Usually the true hydrograph at macro scale, may comprise an annual cycle displaying a relatively fast rise from trough to peak, followed by a short fast recession and finally a prolonged slow recession till the trough. However, some exceptional phenomena like extreme exploitation, artificial
  29. 29. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-7 recharge, discontinuation of pumpage may modify this trend. Further, at micro level, it may also comprise 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 cycle occurring in the time series. It is caused mainly by the annual periodicities of - rainfall/irrigation recharge, stage of hydraulically connected rivers, pumpage etc. Subjecting the time series to spectral analysis (refer Reference Manual, Section 2.4) can identify these 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 the intrinsic 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. The recession 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 and the diffusivity (T/S). Thus, an analysis of such a recession can provide a preliminary estimate of the diffusivity, 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 the corresponding annual cycle of the driving head by shifting the datum to stage of the draining stream during the period of the recession. 2. Plot the recession curve (log of the driving head versus the time). The curve may reveal two or more straight lines segments. The first one, usually steep and short, may represent a fast recession. A relatively flat and long segment, representing a moderate/slow recession usually follows this. 3. Assuming a linear relation between log of the driving head and the time, carry out a regression analysis of the dominant segment of the recession. Hence compute the depletion time. The time for one log cycle (to the base ten) change in the driving head, divided by 2.3, is termed as the depletion time. 4. The depletion time, in general can be expressed as (k.L2 .T/S); where L is the distance of the sampled well from the draining stream along the flowline and k is a constant depending upon the boundary conditions. It could vary from 0.405 (drainage on both sides of the well) to 1.0 (drainage only on one side). The analysis described above holds for the recession of the outflow hydrograph also. The outflow may manifest as stream flow during dry season (when the entire stream flow may be derived from groundwater drainage) or as spring flow. The flow time series if available, may also be analyzed in a similar way. This may provide a means of corroborating the estimate of diffusivity arrived at by analyzing the driving head time series.
  30. 30. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 5-8 5.8 SUGGESTED READING • Jacob, C. E., Correlation of Groundwater Levels and Precipitation on Long Island, New York Part I - Theory. Transactions American Geophysical Union, Twenty Fourth Annual Meeting 1943, Part II, Section of Hydrology Reports and Papers, 564-573, 1944. • Jacob, C. E., Correlation of Groundwater Levels and Precipitation on Long Island, New York Part II - Correlation of Data. Transactions American Geophysical Union, Twenty Fifth Annual Meeting 1944, Part VI, Section of Hydrology Papers, 928-950, 1944. • Law, Albert G., Stochastic Analysis of Groundwater Level Time Series in the Western United States. Hydrology Papers, Colorado State University, Fort Collins, Colorado; No. 68, May 1974. • Bear, Jacob, Hydraulics of Ground water. McGraw Hill, Israel, 1979.
  31. 31. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 6-1 6 GROUNDWATER MODEL INPUT A groundwater model may be set up to simulate the hydrogeological conditions of an area in order to understand the hydrogeological processes taking place and in order to make calculations of future developments. There are different types of groundwater models. In this case the processing of subsurface data is explained for a model with horizontal layers. The data of the subsurface for such a model may be obtained from the information system. A general description of the steps involved in preparing such a model are described below. Suppose the groundwater model will consist of a number of horizontal layers, how will the information for 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 the model layers. The lithological logs of the boreholes (see Figure 6.1) in the area are processed identifying in each log the interfaces corresponding with the layers of the hydrogeological model. The interfaces should be coded in each log in order to retrieve these from the logs. Each interface will have a code and a depth assigned to it. The interfaces will be stored in a separate log, which will be called the hydrogeological column. Figure 6.1: Llithological log Step 2 The objective of Step 2 is to create rasters representing the depth of each interface. The interface depths from the hydrogeological columns are combined to create multiple rasters of the interface depth. The rasters are created by contouring the depths of each interface, see Figure 6.2. 0 1 2 3 1 2 3 4
  32. 32. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 6-2 Interface 0 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 the layer 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 layer thickness. In a groundwater model the permeability and storage properties of the layers are required to carry out the groundwater flow calculations.
  33. 33. Operation Manual – Data Processing and Analysis (GW) Volume 8 – Part III Data Processing and Analysis March 2003 Page 6-3 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 a constant value of value of the horizontal permeability or with a raster containing the spatially varying value of the horizontal permeability, see Figure 6.4. The vertical resistivity of a badly permeable layer is obtained by dividing the layer thickness by a constant value of the vertical permeability or by a raster containing the spatially varying value of the vertical 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 horizontal layers is completed. NBMNBNBMNB

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