8.4 Analysis of Groundwater Flow Systems
Hydrogeologic investigations have specific goals defined to answer questions related to applied groundwater projects or to meet research objectives. Meeting these goals requires an understanding of the geologic framework forming the aquifer system, physical and hydraulic boundary conditions, as well as the locations, rates and timing of groundwater sources (e.g., recharge, stream leakage) and sinks (e.g., pumping, evapotranspiration). In most cases, it is necessary to determine the groundwater flow system behavior under both steady-state and transient conditions, and to prepare a water budget.
Developing Potentiometric Maps and Cross Sections
A key component of evaluating groundwater flow conditions is the construction of potentiometric maps of unconfined and confined aquifers and, in complex groundwater systems, representations of multiple aquifers and aquitards. Head measurements obtained from field investigations are used to interpret horizontal and vertical groundwater flow directions and rates, and the potential for exchange between aquifers and aquitards. Interpretation of the mapped gradients and behavior of groundwater flow can shed light on the aquifer conditions including changes in hydraulic conductivity, aquifer thickness, and can be used to identify the location of recharge and discharge areas. Challenges to presenting, developing and interpreting potentiometric information are included in this section.
Potentiometric Maps, Cross Sections and Flow Nets
Strictly speaking, a potentiometric map or cross section is a representation of the distribution of head (head values and equipotential lines). When flow lines are added to sets of equipotential lines the potentiometric map becomes a flow net (Figure 77). However, it may be referred to as a potentiometric map, water table map or a flow net. As presented in the previous sub sections, a set of parallel flow lines encompasses a flow tube. Conceptually, the discharge through flow tubes is constant under steady state conditions. Potentiometric maps can have an infinite number of flow tubes as there are as many tubes as there are pairs of flow lines. Most maps or cross sections show a number of flow tubes to represent general groundwater flow conditions (Figure 77a).

Although the term flow net can refer to any map or cross section with equipotential lines and flow lines, flow nets constructed under a series of rigorous rules (scaled flow nets) can be used to quantitatively examine groundwater flux (Figure 77b). Scaled flow nets can be hand drawn or produced using groundwater models. They are used in both map view and cross section view to compute the volume of water that would discharge into excavations or under berms or dams, and to design drainage systems.
Considerations When Developing Potentiometric Maps and Cross Sections
Potentiometric maps represent flow in the horizontal plain and they are often used to represent conditions in a single hydrogeologic unit or aquifer. Flow within an aquifer or between aquifers can be represented by the construction of vertical cross sections and/or multiple potentiometric maps.
To generate a potentiometric map of a groundwater system, care must be taken to assure that piezometers and wells used to collect data represent horizontal flow conditions (or near-horizontal conditions). In most groundwater systems, water flows horizontally in large portions of the aquifers. Figure 78 shows the equipotential lines and a flow line in an unconfined aquifer. Horizontal flow is represented by the shallow wells screened near the water table and by any of the wells where equipotential lines are near vertical (vertical equipotential lines indicate horizontal flow). Wells screened at variable depths in the recharge area and discharge area reflect vertical flow with lower heads in deeper wells in the recharge area and higher heads in deeper wells in the discharge area. Potentiometric maps need to exclude the data from these deeper wells in order to portray a reasonable representation of near-horizontal flow in the system. Cross-sectional representations would use all of the data to show vertical components of flow (Figure 78).

Maps of potentiometric surfaces are also used to represent flow in confined aquifers. In confined systems, the aquifer is constrained by confining beds and has substantially higher hydraulic conductivity than confining beds, so near-horizontal flow occurs in much of the system (vertical equipotential lines) when the confined aquifer is a horizontal layer. When confined aquifers dip, flow is near parallel to the aquifer boundaries. The exception to flow being parallel to the aquifer boundaries in confined aquifers occurs in recharge and discharge areas where vertical gradients are present as is the case in unconfined systems (Figure 79). When producing a potentiometric map for confined aquifers, it is generally appropriate to exclude head data from deeper wells located in the recharge and discharge areas so the flow lines will represent flow parallel to the aquifer boundaries. It is sometimes useful to represent areas containing vertical gradients by shading areas of a potentiometric map and labelling them as areas where gradients are upward or downward.

Construction of flow nets representing cross-sectional views rely on monitoring well data from wells screened at multiple depths (Figure 78 and Figure 79). Cross section flow nets are constructed as scaled sections without vertical exaggeration in the direction of flow (Figure 80). They must be constructed in the direction of groundwater flow in map view (section W-E of Figure 80a and b) so that flow is parallel to the plane of the drawing. This ensures meaningful flow lines because there is no flow in or out of the plane of the drawing. If cross sections are constructed at some angle other than parallel to groundwater flow, they will not represent vertical flow conditions along the flow path even though a vertical distribution of head can be plotted on the section (e.g., the W-NE section of Figure 80c and d).


Head data used for construction of potentiometric maps and cross sections need to be accompanied by the following information to assure the data are representative of the appropriate aquifer or cross section of earth materials:
- well completions, including depths and the extent of the casing open to the aquifer;
- types and configuration of aquifers and aquitards penetrated; and,
- location of recharge/discharge areas as well as areas of groundwater pumping, which can cause vertical gradients.
Representing Steady State and Transient Conditions
Steady state is represented by data collected over a period of time when heads and gradients are not changing. At smaller sites, a single hydrogeologist (or a team of people) makes all head measurements on the same day. When study areas are much larger, the data may be collected within the same week, or some other short period of time. The data sets are then represented as a snapshot in time when conditions are constant (e.g., March 15, 2020; or March 2019 to May 2019, average water levels). If data are collected over a period when the water table or potentiometric surface is changing in a consistent way (e.g., declining 2 cm per day) then either the data sets need to be corrected for this change (by generating comparable values for a short time period that are adjusted to a single day or week), or an error analysis should be generated. Often, well hydrographs that reflect groundwater level changes over time are recorded during the data collection period and can be referred to for data adjustments or error analyses. In large regional studies, where head changes in the down gradient direction are large, transient head errors may not impact interpretations of flow directions and fluxes because changes are small (a few centimeters) compared to the spatial variation in heads (meters).
If the system is changing in an irregular way (e.g., localized groundwater mounds or depressions are growing or shrinking) only the most general conclusions can be made using steady-state assumptions. In such cases a transient analysis should be undertaken.
Transient representations of changes in head distributions and flow paths are most often represented as a time series or “snapshots” of head distributions on maps and cross sections (e.g., a potentiometric map for each month; or a period of lowest water levels and highest water levels). These data sets and representations illustrate the system dynamics by documenting the timing and magnitude of changes. When head changes over time are small, it may be appropriate to generalize the system as steady state. However, when values change significantly over time, transient conditions should be presented.
Influence of Variation in Hydraulic Conductivity and Cross-Sectional Area on Head Distribution and Flow Pattern
As discussed in Section 4, construction of potentiometric maps and cross sections allow for the interpretation of groundwater flow directions. Gradients observed on maps and cross sections can be analyzed to shed light on: variations in aquifer thicknesses and hydraulic conductivity distributions; the locations of recharge and discharge areas; and the addition or loss of water along a flow path. The impact of these conditions on hydraulic gradient along a one-dimensional flow path are illustrated in Figure 81.

Similar concepts can be illustrated in two dimensions. To initiate the thought process, envision the steady state head distribution in an isotropic and homogeneous aquifer of constant thickness. The gradient would be constant in space and equipotential lines would be evenly spaced (Figure 82a). When equipotential lines are not evenly spaced, (e.g., the gradients are changing in space) there is an underlying reason (as indicated by Darcy’s law). The changing gradient could be due to a change in hydraulic conductivity (Figure 82b(1)) and/or cross sectional area (Figure 82b(2)), or due to water entering the aquifer as recharge or as leakage from an underlying/overlying zone (Figure 82b(3)).
When parallel flow lines converge and diverge, again the relationships defined by Darcy’s law can be used to hypothesize possible subsurface conditions. The change in width between the flow lines might reflect a change in hydraulic conductivity, cross-sectional area, and/or an increase or decrease of the discharge within the flow tube resulting from recharge or leakage to/from an adjacent formation (Figure 83).
Changes in gradients can also be caused by increasing the flow of water into the groundwater system in some areas (e.g., recharge), and decreasing the flow via discharge, pumping of wells, or direct groundwater evapotranspiration (Figure 82b(3) and Figure 83c).


Addition of steady recharge along the flow path results in a steepening of the gradient and/or a widening of the flow tube. Steady-state leakage of water out of an aquifer to, for example, an underlying aquifer results in a decreased gradient and/or a narrowing of the flow tube. When water is withdrawn from a well at a steady rate of pumping for an extended period of time, the head in the aquifer is lowered in a curved conical shape and recharge is captured in the area around the pumping well (Figure 84). This causes water to flow towards the well to sustain the rate of water discharging from the pump. The change in head in the potentiometric or water table surface is referred to as a cone of depression of the head field (or a drawdown cone). The cone of depression grows with time as water is released from storage in the aquifer and eventually the withdrawal rate is balanced by inflow in the form of leakage from overlying/underlying aquifers, capture of surficial recharge water, and/or inflow from (or decrease of outflow to) a surface water body such as a lake or river.

Putting the Concepts Together
Flow nets are created from head data collected in the field. The head data need to be representative of nearly horizontal flow in map view, or of a flow path in cross section. In addition to head data, the type, thickness and composition of aquifers including estimates of hydraulic conductivities are also collected as part of a hydrogeological investigation. These data are paired with flow nets to interpret causes of changes in observed gradients and flow paths yielding valuable insight to the nature of the groundwater flow system.