Potential Energy and Hydraulic Head

The flow of both surface water and groundwater is driven by differences in potential energy. In the case of surface water, flow occurs in response to differences in gravitational potential energy caused by elevation differences. In other words, water flows downhill, from high potential energy to low potential energy. In groundwater systems, things are a bit more interesting. Unlike surface water, which is in contact with the atmosphere and therefore rarely under pressure, water in groundwater systems is isolated from the land surface. This means that groundwater can also have potential energy associated with pressure. In extreme cases, water in confined aquifers may be under sufficient pressure to drive flow upward, against gravity. Artesian wells are one manifestation of this.

Fundamentally, groundwater and surface water are similar in that flow is in the “downhill” direction. But what does “downhill” mean in a groundwater system? To define the flow direction, we need to account for the two types of potential energy. Unfortunately, the potential energy of the water cannot be measured directly. However, we can measure a proxy for the potential energy by measuring the hydraulic head, or level to which water rises in a well (Figures 26 and 27). The hydraulic head combines two components: (1) potential energy contained by the water by virtue of its elevation above a reference datum, typically mean sea level; and (2) additional energy contributed by pressure. In a well, the value of hydraulic head represents the potential energy of the water at a particular point in three dimensions – at the depth where the well is open to the aquifer (Figures 26-27). This is analogous to a temperature reading taken at the tip of a thermometer, which provides a proxy for heat energy. Hydraulic head can be written as:

h = z + Ψ,

where z is the elevation energy, and Ψ is the pressure energy.

Figure 26. Diagram illustrating the two components of hydraulic head measured at point “A” where the well is screened and connected to the subsurface formation. The water rises in the well from point “A” to the measured water level because of pressure energy.

Source: Maureen Feineman, Pennsylvania State University

Figure 27. Examples of hydraulic head measured in an unconfined aquifer (point “A”) in which head is typically equal to the water table elevation at any location, and in a confined aquifer (point “B”). Note that the hydraulic head in “B” is above the top of the confined aquifer – indicating substantial pressure energy.
Click to expand to provide more information

Diagram of an aquifer with two wells diagram. Aquifer is layered from the top down: land surface, unsaturated zone, unconfined aquifer, confirming unit, confined aquifer, undefined interval, and sea level. The diagram shows examples of hydraulic head measure in an unconfined aquifer: Point A (bottom of well 1) sits in the unconfined aquifer zone slightly above the division between unconfined aquifer and confirming unit. The head for point A sits near the water table (between the unsaturated zone and the unconfined aquifer) at any location. Point B (bottom of well 2) sits in the top third of the confined aquifer level but its head at point B is in the unconfined aquifer—far above the top of the confined aquifer which indicates substantial pressure energy.

Source: US Geological Survey Circular 1217.

Hydraulic Head and the Direction of Groundwater Flow

In order to define groundwater flow directions and rates through aquifers, individual measurements of hydraulic head are combined to generate contour maps of water level – or potential energy (Figure 29). These maps define the potentiometric surface, which is much like a topographic contour map but defines the distribution of potential energy in the groundwater system. Each contour, or equipotential, represents a line of equal hydraulic head.

Video: Slag Heap Experiment (3:46 minutes)

To first approximation, groundwater flows down-gradient (from high to low hydraulic head). As is the case with surface water, or a ball rolling down a hill, the water flows in the direction of the steepest gradient, meaning that it flows perpendicular to equipotentials. There are exceptions to this – for example, if the hydraulic conductivity of the aquifer is much higher in one direction than another, or dominated by fractures with particular orientations, then these can redirect groundwater flow askew to the maximum gradient.

The potentiometric map also provides clues about the rate of groundwater flow. If you think back to Darcy material and our in-class activity from last week, you will recall that groundwater flow rate depends on the head gradient (i.e. the hydraulic gradient) and hydraulic conductivity. In a simple one-dimensional Darcy tube experiment, the head gradient is just the difference (h1-h2)/L. In two dimensions, the head gradient is defined by the slope of the potentiometric surface – just as the slope of the land surface is defined on a topographic map. The path that water takes in the aquifer, defined as a continuous line tracing the maximum gradient on a map of the potentiometric surface, is known as a flowline.

Figure 29. Potentiometric surface map of the Spring Creek Groundwater Basin ca. 1969.

Source: USGS Scientific Investigations Report 2005-5091

Well Hydrographs

Just as river hydrographs are used to record and visualize variations in flow with time (as discussed in Module 4), a well hydrograph is a time series of hydraulic head recorded in a well. This provides information about the fluctuation of hydraulic head (equivalent to the water table in an unconfined aquifer), which reflects the combined effects of temporal variations in climate, recharge, and pumping (Figures 30-31). The U.S. Geological Survey maintains a database of active monitoring wells [1] in major aquifer systems across the United States. Hydrographs provide information about seasonal patterns that may be associated with pronounced wet and dry seasons typical of some regions (for example, Central CA), as well as long-term trends driven by climate change, decadal-scale climate patterns like el nino, prolonged groundwater extraction, or human-induced modifications to natural recharge. We’ll cover examples of the latter two processes in the next section of the module (Module 6.2: Water budgets).

Figure 30. Hydrograph for 2022-2023 for a monitoring well near Sacramento, CA. The blue dashed line shows water level (hydraulic head) measured in depth below the land surface. The blue circles show measurements from field visits.

Source: USGS [2], 10/4/2014

Figure 31. Hydrograph for 2022-2023 for a monitoring well in Centre County, PA near State College. The blue line shows water level (hydraulic head) measured in depth below the land surface. The blue circles show measurements from field visits. The grey line shows 2002-2024 median water level below land surface.
USGS [3]

Video: Slag Heap Experiment (3:46)

Fluxes (Inflows and Outflows) in Groundwater Systems

Fluxes (inflows and outflows) in Groundwater Systems: In order to define the water balance or water budget of an aquifer system, the individual processes that bring water into or out of the system must be quantified (Figure 37 on the next page).

Common inflows of water to a groundwater system include:

• Infiltration through the vadose zone that is not intercepted by evaporation, transpiration, or bound in the unsaturated zone, and thus becomes recharge. Infiltration may be distributed over large areas, or may be focused beneath surface water bodies or at geological features (e.g., sinkholes). Recharge may occur naturally or can be induced or enhanced by excavation and removal of low-permeability soils, and the construction of recharge pits, typically lined or filled with permeable sands (Figure 38 on the next page).
• Injection at wells, either for disposal of treated wastewater or as part of managed aquifer storage and recovery (ASR) programs. The latter is growing in popularity as one way to “bank” excess water in times of surplus, for example, wet seasons or wet years, and then tap the stored water when needed. Although energy-intensive because it requires pumping, ASR is not affected by evaporative losses whereas reservoirs are.
• Groundwater flow from areas outside of the region of interest – areas that are either up-gradient or above or below (i.e. flow across a confining layer).

Outflows from groundwater systems typically include:

• Evaporation or transpiration; this typically occurs in areas where the water table is shallow. Although direct evaporation of water from the water table is possible (in detail, this would occur by evaporation from the capillary fringe, and subsequent “wicking” of water upward from the water table), the upward flux (loss) of water from unconfined aquifers to the atmosphere is dominated by a family of plants known as phreatophytes, characterized by deep roots that extend to and below the water table.
• Water withdrawal by pumping from wells. As discussed in the previous section, pumping at wells induces radial flow toward the well. As the cone of depression grows, the well accesses water over a larger region of the aquifer. In some cases, as the cone of depression grows it may intercept water that would otherwise exit the aquifer via natural seeps or springs (e.g., Figure 37 on the next page), thus “redirecting” a flux that would have been an outflow somewhere else.
• Natural groundwater flow or discharge at springs or seeps, or to surface water bodies.

Surface Water-Groundwater Interaction

One specific class of inflow or outflow from groundwater systems results from surface water–groundwater interaction, water flows from aquifers into surface water bodies at seeps or springs, or infiltrates from rivers or lakes into aquifers (Figure 39; also note the dual-sided arrow between the aquifer and stream in Figure 37 indicating that the flux may be either to or from groundwater to surface water). If there is a net groundwater flux to surface water, the surface water body is said to be gaining (for example, a gaining stream is one that is fed by groundwater). As you may recall from Module 4, the component of streamflow derived from groundwater influx is termed baseflow. Alternatively, if the water table lies below the surface water body, the potential energy (hydraulic head) in the surface water body will be higher than in the groundwater system and water will percolate downward to the aquifer. In this configuration, the surface water body is said to be losing (i.e. a losing stream), because the stream or river discharge decreases downstream. While the land surface and stream channel generally remain at the same elevation, the water table commonly fluctuates over time (see Figures 32-33). As a result, it is common for streams to alternate between gaining to losing due to major recharge events, seasonality in precipitation and recharge, and variations in pumping rates.

Although water rights and policies are sometimes constructed with the implicit assumption that surface water and groundwater systems act independently, this is clearly not the case. A number of interesting situations arise from their interaction. As noted above in the Effects of Pumping Wells section, pumping at wells can reverse groundwater flow, and change a gaining stream to a losing one. In such a scenario, it isn’t always clear whether surface water rights are violated by groundwater pumping – even though groundwater extraction directly causes a reduction in surface water discharge, the water is withdrawn from the groundwater system, not the river. In large aquifer systems, the intercepted baseflow may impact users far downstream, across county and state borders. In other cases, also as noted earlier in this module, substantial or rapid influxes of surface water to groundwater systems, for example through fractures or sinkholes, can lead to groundwater contamination. If a direct connection between surface water and groundwater is demonstrated by the presence of microorganisms or increased water turbidity (cloudiness indicating suspended particles) in well water, additional treatment of groundwater is required before it is considered suitable for domestic or municipal use.

Figure 37. Schematic diagram showing examples of inflows and outflows from aquifer (blue, as labeled) and surface water system.

Source: Colorado State Division of Water Resources [7]

Figure 38. A series of induced recharge pits near Orlando, FL.

Source: USGS [8]

Figure 39. Diagrams illustrating surface water-groundwater interaction, including (A) a gaining stream, (B) a losing stream in which surface water percolates downward and laterally to the water table, and (C) a losing stream that is “disconnected” or “detached” from the underlying aquifer; this scenario typically occurs only in arid environments.

Source: USGS Circular 1186

Water Budgets

The balance of water inflows and outflows, or water budget, for a groundwater system, is described by a simple equation:

$$I-O=\Delta S$$

where I is the total of the inflows to the system, O the total outflows and ΔS is the change in storage. The water balance equation is no different than a bank statement: the difference between deposits (inflows) and withdrawals (outflows) is equal to the change in the account balance (storage). In the case of groundwater systems, changes in storage are manifested as changes in the potentiometric surface, either due to drop in the water table (in unconfined aquifers) or reduction in elastic storage as aquifer is depressurized (in confined aquifers).

In a steady state, or equilibrium condition, inflows and outflows are perfectly balanced (i.e. I = O in the budget equation above), and ΔS is zero. In other words, the potentiometric surface is steady. Often, groundwater systems are considered to be at steady state if inflows and outflows balance over a yearly or decadal timescale. This is because, in many aquifers, both recharge and extraction may be strongly seasonal. For example, recharge in many aquifers in the western US is mostly restricted to the winter months when precipitation is highest, and withdrawal rates are highest in the summer and early fall dry season. As a result, the potentiometric surface may fluctuate over the course of the year but is more-or-less constant over the long-term.

A variety of processes can lead to non-steady state conditions. Most notably in aquifers that are used heavily for irrigation, industry, or municipal supply, pumping may significantly exceed recharge, leading to net decreases in storage. In other cases, reduced recharge – for example due to urbanization and construction of impervious surfaces that do not allow infiltration, removal of leach fields upon installation of sewers (Figure 30), or long-term climate trends that drive changes in the amount or timing of precipitation – also results in negative changes in storage. Reductions in groundwater extraction, or periods of increased precipitation, will have the opposite effect and lead to increases in storage.

Figure 40. Hydrograph from monitoring well in Long Island, illustrating steady-state conditions from about 1940 to about 1960, and a new steady state after the system equilibrated to the construction of a sewer system and concomitant reduction in recharge by about 1975. The perturbation (change in infiltration and recharge) led to non-steady conditions from around 1960-1973, manifested in a clear decrease in water level.

Source: U.S. Geological Survey circular 1186

Overdraft

Groundwater overdraft is a specific condition in which extraction greatly exceeds the influxes of water (mainly recharge). This produces an unsustainable condition characterized by sustained declining water levels. Much like overdraft of a bank account, groundwater overdraft is not a desirable state of affairs. Not only is it unsustainable in terms of management of the groundwater resource, but it also leads to long-lasting damages (a lot like what happens to your credit rating if your bank account is overdrafted!).

Depressurization of the aquifer, if large enough, may cause irreversible collapse and compaction. This reduces both storage (porosity) .and hydraulic conductivity. It can also lead to land subsidence, especially in cases where the magnitude of overdraft is large and the aquifer units are thick and highly compressible, as is common for unconsolidated or uncemented sedimentary aquifers. One well-known example of groundwater overdraft is the Central Valley of California (Figure 41). Another is the Ogallala aquifer, a major groundwater system spanning across eight states in the American Midwest (Figure 43; see The High Plains Aquifer section). Substantial overdraft and subsidence also occur in widespread areas of the southeastern U.S., the Gulf Coast, and parts of Arizona and Las Vegas (Figure 44).

Figure 41. (Top) image showing satellite-based observations of changes in the Earth’s gravitational field that reflect a reduction in water storage in California, from June 2002 to June 2008, to June 2014. Colors progressing from green to red indicate increasing water loss. Most of the reduction is focused in the Central Valley, due to increased groundwater extraction for agricultural use. Over the period from 2011-2014, the change in water storage in the Central Valley equates to a loss of about 4 trillion gallons, or 12 million acre-feet of water each year – almost the entire flow of the Colorado River.

Source: NASA/JPL-Caltech/University of California, Irvine

Figure 42. Photo from the region of maximum land subsidence in the Central Valley. The utility pole is marked to show the elevation of the land surface in 1925, 1955, and 1975. The total subsidence at this location exceeds 9 m.

Source: Image on bottom from USGS Multimedia Gallery

Figure 43. Diagram summarizing the water budget of the southern High Plains aquifer (of which the Ogallala is a major part). Pre-development influxes and outflows were balanced. Development of the central part of the aquifer, primarily for irrigation, has slightly reduced natural seeps and springs along its eastern edge (A). Total withdrawals grossly exceed natural recharge (by about 35 times); a large fraction re-infiltrates as irrigation return flow, but the deficit is over ten times the recharge (B). All units are million cubic feet per day.

Source: U.S. Geological Survey Circular 1186

Figure 44. (Top) Areas of land subsidence in the U.S. associated with groundwater overdraft (from USGS Fact Sheet-165-00). (Bottom) Satellite-based estimates of groundwater stored in the subsurface on July 7, 2014, relative to the average from 1948 to 2009. Blue regions have more groundwater for this time of year than the average for this time of year, whereas red areas have less than the average. Note the correlation between areas of groundwater deficit and land subsidence.

Source: Map from NASA Earth Observatory [9]