Groundwater Data Requirement and Analysis C. P. Kumar Scientist ‘F’ National Institute of Hydrology Roorkee – 247667 (India) Outline Introduction Data Requirement for Groundwater Studies Groundwater Data Acquisition Processing of Groundwater Data Interpolation of Hydrological Variables Geostatistical Analysis using ArcGIS Groundwater Data Management and Analysis Tools Introduction Why should we devote resources for assessing groundwater conditions? Groundwater is a vital natural resource for our country… • A major source of drinking water and irrigation water supply • Groundwater baseflow sustains streamflow during low flow periods • Dependence on groundwater is rapidly increasing • There’s a lot of stress on groundwater resource – contamination, over-pumping… Groundwater is an important, but often overlooked component of the hydrologic cycle… • Groundwater and surface water are in reality an interconnected resource. • Water management decisions that ignore the contributions of, or impacts to, groundwater are not sustainable in the long run. Accurate and reliable groundwater resource information (including quality) is critical to planners and decision-makers. Huge investment in the areas of ground water exploration, development and management at state and national levels aims to meet the groundwater requirement for drinking and irrigation and generates enormous amount of data. We need to focus on improved data management, precise analysis and effective dissemination of data. Data Requirement for Groundwater Studies ALL GROUND-WATER HYDROLOGY WORK IS MODELING A Model is a representation of a system. Modeling begins when one formulates a concept of a hydrologic system, continues with application of, for example, Darcy's Law or the Theis equation to the problem, and may culminate in a complex numerical simulation. The success of any groundwater study, to a large measure, depends upon the availability and accuracy of measured/recorded data required for that study. Therefore, identifying the data needs and collection/monitoring of required data form an integral part of any groundwater exercise. The first phase of any groundwater study consists of collecting all existing geological and hydrological data on the groundwater basin in question. Any groundwater balance or numerical model requires a set of quantitative hydrogeological data that fall into two categories: * Data that define the physical framework of the groundwater basin * Data that describe its hydrological framework Physical Framework 1. Topography 2. Geology 3. Types of aquifers 4. Aquifer thickness and lateral extent 5. Aquifer boundaries 6. Lithological variations within the aquifer 7. Aquifer characteristics Hydrological Framework 1. Water table elevation 2. Type and extent of recharge areas 3. Rate of recharge 4. Type and extent of discharge areas 5. Rate of discharge The data required for a groundwater flow modelling study under physical framework are: Geologic map and cross section or fence diagram showing the areal and vertical extent and boundaries of the system. Topographic map at a suitable scale showing all surface water bodies and divides. Details of surface drainage system, springs, wetlands and swamps should also be available on map. Land use maps showing agricultural areas. Contour maps showing the elevation of the base of the aquifers and confining beds. Isopach maps showing the thickness of aquifers and confining beds. Maps showing the extent and thickness of stream and lake sediments. These data are used for defining the geometry of the groundwater domain under investigation, including the thickness and areal extent of each hydrostratigraphic unit. Under the hydrogeologic framework, the data requirements for a groundwater flow modelling study are: Water table and potentiometric maps for all aquifers. Hydrographs of groundwater head and surface water levels. Maps and cross sections showing the hydraulic conductivity and/or transmissivity distribution. Maps and cross sections showing the storage properties of the aquifers and confining beds. Spatial and temporal distribution of rates of evaporation, groundwater recharge, groundwater pumping etc. Groundwater Data Acquisition Some data may be obtained from existing reports of various agencies/departments, but in most cases additional field work is required. The observed raw data obtained from the field may contain inconsistencies and errors. Before proceeding with data processing, it is essential to carry out data validation in order to correct errors in recorded data and assess the reliability of a record. Amongst the hydrologic stresses including groundwater pumping, evapotranspiration and recharge, groundwater pumpage is the easiest to estimate. Field information for estimating evapotranspiration is likely to be sparse and can be estimated from information about the land use and potential evapotranspiration values. Recharge is one of the most difficult parameters to estimate. Values of transmissivity and storage coefficient are usually obtained from data generated during pumping tests and subsequent data processing. For modelling at a local scale, values of hydraulic conductivity may be determined by pumping tests if volume-averaged values are required. In the field, in-situ hydraulic conductivity may be measured by Guelph Permeameter. For unconsolidated sand-size sediment, hydraulic conductivity may be obtained from laboratory permeability tests using permeameters. Laboratory analyses of core samples tend to give lower values of hydraulic conductivity than are measured in the field. Monitoring of Groundwater Levels A network of observation wells and/or piezometers are established to obtain data on the - o Depth and configuration of the water table o Direction of groundwater movement o Location of recharge and discharge areas In any drainage investigation, the highest and the lowest water table positions, as well as the mean water table during a hydrological year are important. For this reason, water level measurements should be made at frequent intervals. The interval between readings should preferably not exceed one month. All measurements in a study area should, as far as possible, be made on the same day because this gives a complete picture of the water table. Monitoring of Groundwater Quality The objectives of the water quality monitoring network are to: o Detect water quality changes with time o Identify potential areas that show rising trend o Detect potential pollution sources o Study the impact of land use and industrialization on groundwater quality Substantial costs are incurred to obtain and analyze samples. Field costs for drilling, installing, and sampling monitoring wells and laboratory costs for analyzing samples are not trivial. Comprehensive data analysis and evaluation by a knowledgeable professional should be the final quality assurance step . The frequency of sampling required in a ground-water-quality monitoring program is dictated by the expected rate of change in the concentrations of chemical constituents. For monitoring concentrations of major ions and nutrients, and values of physical properties of ground water, twice yearly sampling should be sufficient. More frequent sampling should be considered if the types and conditions of any upgradient sources of these compounds are changing. Monitoring of ground-water quality should be a long-term activity. Processing of Groundwater Data Processing of Groundwater Data Before any conclusions can be drawn about the cause, extent, and severity of an area’s groundwater related problems, the raw groundwater data on water levels and water quality have to be processed. This data then have to be related to the geology and hydrogeology of the area. The results, presented in graphs, maps, and cross-sections, will enable a diagnosis of the problems. The following graphs and maps have to be prepared that are discussed hereunder: o Groundwater hydrographs o Water table-contour map o Depth-to-water table map o Water table-fluctuation map o Head-differences map o Groundwater-quality map A proper interpretation of groundwater data, hydrographs, and maps requires a coordinate study of a region’s geology, soils, topography, climate, hydrology, land use, and vegetation. Groundwater Hydrographs When the amount of groundwater in storage increases, the water table rises; when it decreases, the water table falls. This response of the water table to changes in storage can be plotted in a hydrograph. Groundwater hydrographs show the water-level readings, converted to water levels below ground surface, against their corresponding time. A hydrograph should be plotted for each observation well or piezometer. It is important to know the rate of rise of the water table, and even more important, that of its fall. July Aug Sept Oct Nov Dec Jan Feb Mar Apr May June Groundwater hydrographs also offer a means of estimating the annual groundwater recharge from rainfall. This, however, requires several years of records on rainfall and water tables. An average relationship between the two can be established by plotting the annual rise in water table against the annual rainfall. Extending the straight line until it intersects the abscissa gives the amount of rainfall below which there is no recharge of the groundwater. Any quantity less then this amount is lost by surface runoff and evapotranspiration. Water Table – Contour Map A water table - contour map shows the elevation and configuration of the water table on a certain date. To draw the water table-contour lines, we have to interpolate the water levels between the observation points, using the linear interpolation method. A proper contour interval should be chosen, depending on the slope of the water table. For a flat water table, 0.25 to 0.50 m may suit; in steep water table areas, intervals of 1 to 5 m or even more may be needed to avoid overcrowding the map with contour lines. A water table-contour map is an important tool in groundwater investigations because, from it, one can derive the gradient of the water table (dh/dx) and the direction of groundwater flow, which is perpendicular to the water table-contour lines. The topographic base map should contain contour lines of the land surface and should show all natural drainage channels and open water bodies. For the given date, the water levels of these surface waters should also be plotted on the map. Only with these data and data on the land surface elevation can water table contour lines be drawn correctly. For a proper interpretation of a water table-contour map, one has to consider not only the topography, natural drainage pattern, and local recharge and discharge patterns, but also the subsurface geology. More specifically, one should know the spatial distribution of permeable and less permeable layers below the water table. For instance, a clay lens impedes the downward flow of excess irrigation water or, if the area is not irrigated, the downward flow of excess rainfall. A groundwater mound will form above such a horizontal barrier. Depth-to-Water Table Map A depth-to-water table map shows the spatial distribution of the depth of the water table below the land surface. A suitable contour interval may be 50 cm. The regions of map where the groundwater level is between 0-2 m depicts the area having drainage problems. Based on measurement results for a year, the map drawn using the lowest water table levels indicates to which extent the groundwater falls in a year. The section where the water table level is between 0-1 m determines the areas in which groundwater exists in the root-zone throughout a year. The depth and shape of the first impermeable layer below the water table strongly affect the height of the water table. Water Table - Fluctuation Map A water table - fluctuation map is a map that shows the magnitude and spatial distribution of the change in water table over a period (e.g. a season or a whole hydrological year). A water table-fluctuation map is a useful tool in the interpretation of drainage problems in areas with large water table fluctuations. The change in water table in fine-textured soils will differ from that in coarse-textured soils, for the same recharge or discharge. Head - Differences Map A head-differences map is a map that shows the magnitude and spatial distribution of the differences in hydraulic head between two different soil layers. We calculate the difference in water level between the two piezometers, and plot the result on a map. After choosing a proper contour interval (e.g. 0.10 or 0.20 m), we draw lines of equal head difference. The map is a useful tool in estimating upward or downward seepage. Groundwater - Quality Maps A groundwater-quality map (for example, electrical-conductivity map) is a map that shows the magnitude and spatial variation in the salinity of the groundwater. The EC values of all representative wells (or piezometers) are used for this purpose. Groundwater salinity varies not only horizontally but also vertically. It is therefore advisable to prepare an electrical- conductivity map not only for the shallow groundwater but also for the deep groundwater. In electrical conductivity maps, critical groundwater salinity is taken as 5000 micromhos/cm, although it changes according to species of the crop to be grown. By plotting all the EC values on a map, lines of equal electrical conductivity (equal salinity) can be drawn. Preferably the following limits should be taken: less than 100 micromhos/cm, 100 to 250; 250-750; 750 to 2500; 2500 to 5000; and more than 5000. Other limits may, of course, be chosen, depending on the salinity found in the waters. Other types of groundwater-quality maps can be prepared by plotting different quality parameters (e.g. Sodium Adsorption Ratio (SAR) values). The groundwater in the lower portions of coastal and delta plains may be brackish to extremely salty, because of sea- water encroachment. In the arid and semi-arid zones, shallow water table areas may contain very salty groundwater because of high rates of evaporation. Irrigation in such areas may contribute to the salinity of the shallow groundwater through the dissolution of salts accumulated in the soil layers. Interpretation of Hydraulic Head and Groundwater Conditions Measurements of hydraulic head, normally achieved by the installation of a piezometer or well point, are useful for determining the directions of groundwater flow in an aquifer system. In the above figure, three piezometers installed to the same depth enable the determination of the direction of groundwater flow and, with the application of Darcy’s law, the calculation of the horizontal component of flow. In the above figure, two examples of piezometer nests are shown that allow the measurement of hydraulic head and the direction of groundwater flow in the vertical direction to be determined either at different levels in the same aquifer formation or in different formations. Interpolation of Hydrological Variables A fundamental problem of Hydrology is that our models of hydrological variables assume continuity in space (and time), while observations are done at points. The elementary task is to estimate a value at a given location, using the existing observations. Hydrological data have variability in space and time. • Spatial variability is observed by a sufficient number of stations • Time variability is observed by recording time series • Spatial variability can be in different range of values or in different temporal behaviour A continuous field v = v(x,y,z,t) is to be estimated from discrete values vi = v(xi,yi,zi,ti) Global estimation: characteristic value for area Point estimation: estimation at a point P = P(x,y) We need data AND a conceptual model, how these data are related, (i.e. a conceptual model of the process) If the process is well defined, only few data are needed to construct the model Example A groundwater table in a confined, homogeneous, Q ⎛ r2 ⎞ h( r2 ) − h( r1 ) = ln⎜ ⎟ isotropic aquifer under steady 2πT ⎜ r1 ⎟ ⎝ ⎠ state discharge from a well is described by the Thiem well formula. Theoretically, the observation of two groundwater heads at different distances from the well is sufficient to reconstruct the complete groundwater surface. Hydrological variables are random and uncertain Geostatistical Methods Mostly 2D consideration v = v(x,y,t) Regionalisation and Interpolation Regionalisation: Identification of the spatial distribution of a function g, depending on local information as well as by transfer of information from other regions by transfer functions. Regionalisation therefore means to describe spatial variability (or homogeneity) of • Model parameters • Input variables • Boundary conditions and coefficients Regionalisation includes the following tasks: • Representation of fields of hydrological parameters and data (contour maps) • Smoothing spatial fields • Identification of homogeneous zones • Interpolation from point data • Transfer of point information from one region to others • Adaptation of model parameters for the transfer from point to area Interpolation Given z = z(x,y) at some points we want to estimate z0 at (x0, y0) z z2 z0 ? z3 z1 y (x3,y3) (x0,y0) (x2,y2) (x1,y1) x Weighted linear combination - n z = z0 = ˆ ˆ ∑w z i =1 i i The methods differ in the way how they establish the weights. Global and Local Interpolation An interpolation method is working globally, if all data points are evaluated in the interpolation. Local interpolation techniques use only data points in a certain neighbourhood of the estimated point. y y0 z0 r x0 x Deterministic or Statistical Interpolation Deterministic methods attempt to fit a surface of given or assumed type to the given data points • Exact • Smoothing Statistical (stochastic) methods Choice of Interpolation Method Depends primarily on the nature of the variable and its spatial variation. Examples: Rainfall, groundwater, soil physical properties, topography Example: Groundwater Data Groundwater tables have smooth surface, but trend! Hydrogeological information is highly random, has faults, few points with “good” data Deterministic Interpolation Methods Polynomials Spatial join (point in polygon) Thiessen polygons TIN and linear interpolation Spline Inverse Distance Weighting (IDW) Polynomials n n fs (x, y) = ∑ ∑ n •General: f s ( x) = ∑ ci x i cij xi y j i =0 i =0 j =0 •Plane: f s ( x, y ) = c0 + c1 x + c2 y •Second f s ( x, y ) = c0 + c1 x + c2 y + c3 x 2 + c4 xy + c5 y 2 Order: n(n + 3) nk = +1 f(x) •Number of 2 coefficients •Over- and undershoots x1 x2 x3 x4 x Spatial Join (point in polygon) Assign spatial properties by spatial join Thiessen Polygons Thiessen polygons A point in the domain receives the value of the closest data point Step-wise function # # # # # # # # # Interpolation of elevation surface using Thiessen Polygons Thiessen Polygons TIN and Linear Interpolation Surface is approximated by facets of plane triangles Continuous surface, but discontinuous 1st derivative 42.0 # 45.0 36.0 # # 50.0 # #55.0 74.0 # #82.0 # # 70.0 65.0 Splines Spline estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points. Conceptually, it is like bending a sheet of rubber to pass through the points while minimizing the total curvature of the surface. Inverse Distance Weighting (IDW) N z ( xi , yi ) ∑ hβ i =1 z ( x0 , y0 ) = ˆ i ,0 hi , 0 = d i2, 0 + δ 2 N 1 ∑ hβ i =1 i , 0 Default method in many software packages β = 2 Controlled by exponent β Stochastic (Geostatistical) Interpolation Analysis of the spatial correlation in the random component of a variable Optimum determination of weights for interpolation Semi-variance Regionalized variable theory uses a related property called the semi-variance to express the degree of relationship between points on a surface. The semi-variance is simply half the variance of the differences between all possible points spaced a constant distance apart. (Semi-variance is a measure of the degree of spatial dependence between samples) Semi-variance :The magnitude of the semi- variance between points depends on the distance between the points. A smaller distance yields a smaller semi-variance and a larger distance results in a larger semi-variance. Calculating the Semi-variance (Regularly Spaced Points) Consider regularly spaced points distance (d) apart, the semi-variance can be estimated for distances that are multiple of (d) (Simple form): 1 Nh γ ( h) = ∑ (z − z ) i+h 2 2N i i =1 h Semi-variance 1 Nh γ ( h) = ∑ (z − z ) i+h 2 2N i i =1 h Zi is the measurement of a regionalized variable taken at location i , Zi+h is another measurement taken h intervals away Nh is number of points Semi-variogram The plot of the semi-variances as a function of distance from a point is referred to as a semi- variogram or variogram. Semi-variogram The semi-variance at a distance d = 0 should be zero, because there are no differences between points that are compared to themselves. However, as points are compared to increasingly distant points, the semi-variance increases. Semi-variogram The range is the greatest distance over which the value at a point on the surface is related to the value at another point. The range defines the maximum neighborhood over which control points should be selected to estimate a grid node. Characteristics of the Semi-variogram (and therefore of the data) Nugget: variance at zero distance which should be zero but isn’t… Range: Distance at which max. variance is reached (data considered decorrelated) Sill: Level of max. variability Anisotropy might thus be manifested by varying range with direction (constant sill; so- called geometric anisotropy). This is observed with the elevation data. 1 Experimental semi- variogram γ * (h) = ∑=(hZ (u i ) − Z (u j )) 2 2 N ( h ) ui −u j Things nearby tend to be more similar than things that are farther apart 350 181 181 186 183 222 200 153 180 300 124 201 181 126 159 177 250 167 200 Variogram 80 84 86 106 150 2450 84 38 100 50 0 0 200 400 600 800 1000 1200 1400 1600 1800 Lag Distance Theoretical semi-variogram: fit function through empirical semi-variogram 350 300 250 Variogram 200 150 100 50 0 0 200 400 600 800 1000 1200 1400 1600 1800 Lag Distance Variogram - Spherical It is a ‘model’ semi-variogram and is usually called the spherical model. a is called the range of influence of a sample. C is called the sill of the semi-variogram. ⎧ ⎛ 3 h 1 h3 ⎞ ⎪C ⎜ − ⎟ where h ≤ a γ ( h) = ⎨ ⎜ 2 a 2 a 3 ⎟ ⎝ ⎠ ⎪C where h ≥ a ⎩ Variogram - Exponential γ ( h) = C 1 − e ( −h a ) Spherical and Exponential with the Spherical and Exponential with the same same range and sill sill and the same initial slope Semi-variogram from ArcGIS This is an example of a variogram produced using ArcGIS's Geostatistical Analyst. Interpolation by Kriging Kriging is named after the South African engineer, D. G. Krige, who first developed the method. Kriging uses the semi-variogram, in calculating estimates of the surface at the grid nodes. Interpolation by Kriging Kriging goes through a two-step process: 1. Variograms and covariance functions are created to estimate the statistical dependence (called spatial autocorrelation) values, which depends on the model of auto-correlation (fitting a model), 2. Prediction of unknown values Kriging yields the estimated value AND the estimation variance Standard deviation of estimated Estimated conductivity conductivity 5474000 5474000 105 5473500 5473500 18 100 5473000 5473000 17 95 5472500 90 5472500 16 85 5472000 5472000 15 80 5471500 75 5471500 14 70 5471000 5471000 13 65 5470500 5470500 12 60 5470000 55 5470000 11 3410500 3411000 3411500 3412000 3412500 3413000 3413500 3414000 3410500 3411000 3411500 3412000 3412500 3413000 3413500 3414000 Interpolation of elevation surface using Kriging Kriging Geostatistical Analysis using ArcGIS A linkage between GIS and spatial data analysis is considered to be an important aspect to explore and analyze spatial relationships. The GIS methodology for the spatial analysis of the groundwater levels involves the following steps: (a) Exploratory spatial data analysis (ESDA) using ArcGIS software for the data (e.g. groundwater level) to study the following: Data distribution Global and local outliers Trend analysis (b) Spatial interpolation for data using ArcGIS software, while kriging is applied by involving the following procedures: Semivariogram and covariance modelling Model validation using cross validation Surfaces generation of the groundwater level data Flow Chart of the Geostatistical Analysis Steps Groundwater Data Management and Analysis Tools Following are some of the software packages used for groundwater data management and analysis. AquaChem: AquaChem is an integrated software package developed specifically for graphical and numerical analysis of geochemical data sets. AquaChem also includes a direct link to the popular PHREEQC program for geochemical modeling. AquiferTest Pro: Graphical analysis and reporting of pumping test and slug test data. EnviroInsite: EnviroInsite is a desktop, groundwater visualization package for analysis and communication of spatial and temporal trends in multi- analyte, environmental groundwater data. GW Contour: Data interpolation and contouring program for groundwater professionals that also incorporates mapping velocity vectors and particle tracks. HydroGeo Analyst: Groundwater and borehole data management and visualization technology. RockWorks: Geological data management, analysis & visualization.