Initial Conditions and Contouring of Hydraulic Head

2.6.1 Initial Conditions and Contouring of Hydraulic Head

In the world of groundwater modeling, the term initial conditions refers to the three- dimensional distribution of observed hydraulic heads within the groundwater system, which is the starting point for transient (time-dependent) modeling simulations. These hydraulic heads (water table of unconfined aquifers and potentiometric surface of con- fined aquifers) are the result of various boundary conditions acting upon the system during a certain time period. The initial distribution of the hydraulic heads for transient modeling can also be the calibrated solution of a steady-state model, which is the closest match to the field-observed heads when assuming constant boundary conditions and no change in storage. In a broad sense, any set of field-measured or calibrated hydraulic heads can serve as the starting point for further analysis, including for transient ground- water modeling. Ideally, the initial conditions should be as close as possible to the state of

a long-term equilibrium between all natural water inputs and outputs from the system, or with as little anthropogenic (artificial) influences as possible: the so-called predevelop- ment conditions (Fig. 2.52). However, in many cases there is insufficient hydraulic head data for such natural conditions, which causes various difficulties with data interpolation and extrapolation, including uncertainties associated with any assumed predevelopment boundary conditions.

Whatever the case may be regarding the selection of initial conditions, contouring of the hydraulic head data is the first important step. Contour maps of the water table (un- confined aquifers) or the piezometric surface (confined aquifers) are made in the majority of hydrogeologic investigations and, when properly drawn, represent a very powerful tool in aquifer studies. Although commonly used for determination of groundwater flow directions only, contour maps, when accompanied with other data, allow for the analyses and calculations of hydraulic gradients, flow velocity and flow rate, particle travel time, hydraulic conductivity, and transmissivity. In addition, the spacing and the orientation (shape) of the contours directly reflect the existence of flow boundaries. When interpret- ing contour maps, one should always remember that it is a two-dimensional representa- tion of a three-dimensional flow field, and as such it has limitations. If the groundwater system of interest is known to have significant vertical gradients, and enough field infor- mation is available, it is always wise to construct at least two contour maps: one for the shallow depth and one for the deeper depth. As with geologic and hydrogeologic maps in general, a contour map should be accompanied with several cross-sections showing locations and vertical points of the hydraulic head measurements with posted data, or ideally showing the contour lines on the cross sections as well. Probably the most in- correct and misleading case is developed when data from monitoring wells screened at different depths in an aquifer with vertical gradients are lumped together and contoured as one “average” data package. A perfect example would be a fractured rock or karst aquifer with thick residuum (regolith) deposits and monitoring wells screened in the residuum and at various depths in the bedrock. If data from all the wells were lumped

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F IGURE 2.52 Potentiometric surface of the Upper Floridan aquifer in the area of Savannah, GA, and Hilton Head Island, SC. Top: Predevelopment conditions (datum is NGVD 29); bottom: recorded in

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i+1

h i-1

Equipotential lines

F IGURE 2.53 Flow net is a set of equipotential lines and streamlines which are perpendicular to each other. The equipotential line connects points with the same groundwater potential, i.e., hydraulic head h. The streamline is an imaginary line representing the path of a groundwater

same. Equipotential lines are more widely spaced where the aquifer is more transmissive.

together and contoured, it would be impossible to interpret where the groundwater is actually flowing for the following reasons: (1) the residuum is primarily an intergranular porous medium in unconfined conditions (it has water table), and horizontal flow direc- tions may be influenced by local (small) surface drainage features; (2) the bedrock has discontinuous flow through fractures at different depths, which is often under pressure (confined conditions), and may be influenced by regional features such as major rivers or springs. The flow in two distinct porous media (the residuum and the bedrock) may therefore be in two different general directions at a particular site, including strong verti- cal gradients from the residuum toward the underlying bedrock. Creating one “average” contour map for such system does not make any hydrogeologic sense (Kresic, 2007a).

The contour map of the hydraulic head is one of two parts of a flow net: flow net in

a homogeneous isotropic aquifer is a set of streamlines and equipotential lines, which are perpendicular to each other (see Fig. 2.53). Streamline (or flow line) is an imaginary line representing the path of a groundwater particle as it flows through the aquifer. Two streamlines bound a flow segment of the flow field and never intersect, i.e., they are roughly parallel when observed in a relatively small portion of the aquifer. The main requirement of a flow net is that the flow rate between adjacent pairs of streamlines is the

aquifer, providing that the hydraulic conductivity and the aquifer thickness are known. Equipotential line is a horizontal projection of the equipotential surface—everywhere at that surface the hydraulic head has a constant value. Two adjacent equipotential lines (surfaces) never intersect and can also be considered parallel within a small aquifer portion. These characteristics are the main reason why a flow net in a homogeneous, isotropic aquifer is sometimes called the net of small (curvilinear) squares. In general,

GroundwaterSystem

the following simple rules apply for graphical flow net construction in heterogeneous, isotropic systems (Freeze and Cherry, 1979):

1. Flow lines and equipotential must intersect at right angles throughout the sys- tem.

2. Equipotential lines must meet impermeable boundaries at right angles.

3. Equipotential lines must parallel constant-head boundaries.

4. The tangent law must be satisfied at geologic boundaries (see Fig. 2.47).

5. If the flow net is drawn such that squares are created in one portion of one formation, squares must exist throughout that formation and throughout all formations with the same hydraulic conductivity. Rectangles will be created in formations of different conductivity.

The last two rules make it extremely difficult to manually draw accurate quantita- tive flow nets in complex heterogeneous systems. If a system is anisotropic in addition, it would not be feasible to draw an adequate flow net manually in most cases. How- ever, drawing an approximate contour map (flow net without streamlines) manually is always recommended since it allows the interpreter to incorporate the understanding of various hydrogeologic complexities. Complete reliance on contouring with computer programs could lead to erroneous conclusions since they are unable to recognize interpre- tations apparent to a groundwater professional such as presence of geologic boundaries, varying porous media, influence of surface water bodies, or principles of groundwa- ter flow. Thus, manual contouring and manual reinterpretation of computer-generated maps are essential and integral parts of hydrogeologic studies. Although some advocates of computer-based contouring argue that it is the most “objective” method since it ex- cludes possible “bias” by the interpreter, little can be added to the following statement: if something does not make hydrogeologic sense, it does not matter who or what created the senseless interpretation.

The ultimate tool for creating contour maps, tracking particles as they flow through the system, and calculating flow rates for any part of a groundwater system, is a numeric model, which can incorporate and test all known or suspected heterogeneities, bound- aries, and anisotropy, in all the three dimensions. Figures 2.54 to 2.56 show output from a model used to test influence of varying hydraulic conductivity and anisotropy on tracks of particles released at certain locations in the aquifer.

When analyzing initial conditions, several synoptic data sets collected in different time periods should be used in order to better understand the system and select what appears to be a “representative” spatial distribution of the hydraulic heads. In addition to recordings from piezometers, monitoring wells, and other water wells, every effort should be made to record elevations of water levels in the nearby surface streams, lakes, ponds, and other surface water bodies. Information about hydrometeorologic conditions (e.g., rainfall) prior to the time of hydraulic head measurements is also important for understanding possible influence of recharge episodes on groundwater flow directions and fluctuations of the hydraulic heads. All this information is essential for making a correct contour map.

One of the most important aspects of constructing contour maps in alluvial aquifers is to determine the relationship between groundwater and surface water. In hydraulic

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X X =K Y

F IGURE 2.54 Hydraulic head contour lines and particle tracks (dashed) in an isotropic,

homogeneous aquifer of uniform hydraulic conductivity (K 1 ).

K 2 = 4K 1

K X =K

F IGURE 2.55 Influence of a geologic boundary (heterogeneity) on contour lines and particle tracks. The shaded area has four times higher hydraulic conductivity than the rest of the flow field. Aquifer

is isotropic (the hydraulic conductivity is same in X and Y directions).

GroundwaterSystem

K Y K X = 4K Y

F IGURE 2.56 Influence of anisotropy on particle tracks (dashed lines). The hydraulic conductivity in X direction is four times higher than in Y direction.

terms, the contact between an aquifer and a surface water body is an equipotential boundary. In case of lakes and wetlands, this contact can be approximated with the same hydraulic head. In case of flowing streams, the hydraulic head along the contact decreases in the downgradient direction. If enough measurements of a stream stage are available, it is relatively easy to draw the water table contours near the river and to finish them along the river-aquifer contact. However, often little or no precise data is available on river stage and, at the expense of precision, it has to be estimated from a topographic map or from the monitoring well data by extrapolating the hydraulic gradients until they intersect the river. Figure 2.57 shows some of the examples of surface water-groundwater interaction represented with the hydraulic head contour lines.

In highly fractured and karst aquifers, where groundwater flow is discontinuous (it takes place mainly along preferential flow paths such as fractures and karst con- duits), Darcy’s Law does not apply and flow nets are not an appropriate method for the flow characterization. However, contour maps in such aquifers are routinely made by many professionals who often find themselves excluding certain “anomalous” data points while trying to develop a “normal-looking” map. Contour maps showing regional (say, on a square-mile scale) flow-pattern in a fractured rock or karst aquifer may be jus- tified since groundwater flow generally is from recharge areas toward discharge areas and the regional hydraulic gradients will reflect this simple fact. The problems usually arise when interpreting local flow patterns, as schematically shown in Fig. 2.58.