Introduction to Hydrogeology

William K. S. Pao

P/E18, Pariser Building, School of MACE,The University of Manchester, Manchester M60 1QD, United Kingdom

1 The Properties of Water

Pure water (H2O) is:

• Clear, colorless• No discernable taste or smell• At 1 atmosphere - Melting point: 0oC; Boiling point, 100oC• Density at 4oC: 1.00 g/cc

Water is present throughout the Earth. It is an essential ingredient for life.There are a couple of things that makes water unique:

• Water is a polar molecule (Fig. 1)• Water is highly cohesive (Fig. 1)

The polarity of the water molecules results in:

• High surface tension• High solvent ability (water is the ’universal solvent’)

Fig. 1. Model of water molecules showing a) molecule polarity, and b) attractionbetween water molecules responsible for cohesiveness and surface tension.

Preprint for Applied Hydrogeology Lecture 1 Ver 1.0 16 January 2007

2 Distribution of Water on the Earth

Over 75% of the Earth’s surface is covered by water. The vast majority of thatis unfit for human consumption. Most of the freshwater is locked up in the icecaps and glaciers. Usable, available freshwater, in the lakes and rives on thesurface and in the underground reservoirs, is less than one percent of the totalwater in the world. The distribution of the world’s water is presented in Table1.

Salt water in oceans 97.2%

Ice caps & glaciers: 2.14%

Groundwater: 0.61%

Soil moisture: 0.005%

Atmosphere: 0.001%

Fresh surface water: 0.0009%Table 1The distribution of the world’s water

3 The Hydrologic Cycle Systems

A cycle is defined as a dynamic system that contains the following four com-ponents:

• An element or set of elements that are in flux (not necessarily a chemicalelement), e.g., water

• A set of reservoirs in which the element resides, e.g., the oceans, the ice caps• A set of fluxes, or processes that are moving the elements within reservoirs

and from one reservoir to another e.g., rivers, precipitation• And some source of energy that is driving the cycle

Water occurs throughout the Earth, from the outer reaches of the atmosphereto deep in the mantle (and possibly as deep as the core). Early in the historyof the Earth’s formation, around the time that the Earth’s crust began toform, volcanic activity released lots of volatile gasses, including water, fromthe underlying mantle. These volatile gasses made up the early atmosphereand oceans. It is thought that almost all of the water that we find in theoceans, lakes, streams, atmosphere, and the subsurface today was outgassedat this time, and that volume of water has been cycling around ever since.

2

Fig. 2. A generalized and simplified diagram of the hydrologic cycle.

The hydrologic cycle is defined as the set of reservoirs and fluxes which holdand move water through the atmosphere, on the surface, and in the subsurfaceof the Earth, Fig. 2.

With the exception of minor amounts of extraterrestrial water brought inby comets, and small amounts of water vapor that is lost to outer space atthe upper reaches of the atmosphere, there is a set volume of water in thewater cycle. Within the cycle, there are various reservoirs holding water andvarious processes that move water within reservoirs and from one reservoir tothe next. Figure 2 shows the main reservoirs and fluxes, as well as the twoenergy sources that drive the cycle. Reservoirs in the water cycle include theoceans, atmosphere, rivers, freshwater lakes, the unsaturated soil moisture, thesaturated groundwater, connate water in deep sedimentary rocks, magmaticwater from the mantle, water in the ice caps and glaciers (the cryosphere), andwater in plants and animals (the biosphere). The fluxes are all the processesthat move water from one reservoir to the next (e.g., evaporation, infiltration)or within a reservoir (e.g. groundwater flow, ocean currents).

We treat the hydrologic cycle like a closed system – the cycle has a fixedamount of water that does not change; however, energy does enter the systemin the form of sunlight. The amount of water gained from (or lost to) outerspace is so small that we can consider it negligible. Within the hydrologic cycle,we can identify and delineate a number of open systems. The oceans are anexample – water enters the oceans from rain, surface runoff, and groundwaterdischarge, and water leaves the oceans through evaporation, through mineralreactions, and at subduction zones. A lake is another example of an open

3

Fig. 3. The hydrologic cycle.

system.

The science of hydrogeology deals with a specific part of the hydrologiccycle – the part that is underground. The primary focus of this course is onthe saturated groundwater flow systems near the surface of the Earth – i.e.within the first 1 or 2 kilometers below the surface.

Note: Because of the nature of this lecture, we will use a mixture of Imperialand SI units throughout this course. As an Engineer, you should be able towork in multiple unit systems. So do not complaint but get use to it.

4 Basics of Surface Water

Groundwater is directly linked to the surface water as part of the hydro-logic cycle, and the freshwater runoff system (including evaporation, precipi-tation, infiltration, runoff, and accumulation in lakes) is the primary avenueof recharge to and discharge from the groundwater. In addition to the linksbetween groundwater and surface water, the surface runoff network (Figure3) is a primary source of water for people, agriculture, and industry, and it isimportant to have a basic understanding of the system and how we study it.This chapter will deal with surface water and the interactions between surfacewater and groundwater. When rain hits the Earth, some of it soaks into theground, some is taken up by plants and animals, and some evaporates into the

4

Fig. 4. Schematic diagram of a watershed.

Fig. 5. 3-D image of a watershed.

air. The rest of the water – the part that drains to the nearest creek or riverand flows towards the ocean – makes up the part of the hydrologic cycle thatwe call surface water.

A stream is the general term that we use for any body of flowing water on theEarth’s surface that is contained within a channel. Streams receive their waterfrom a surrounding area called a drainage basin or a watershed. Watershedsare defined by the topography surrounding the stream, and watersheds aredetermined by arbitrarily selecting a point on a stream and delineating thearea that drains to that point, as shown in figures 4 and 5.

5

Some definitions:

a. The topographic high that separates one watershed from the next is calleda drainage divide.

b. The place where the stream begins, up in the watershed, is called the head-waters or the end of the stream.

c. The point where the stream finally flows into the ocean (or a lake, or anotherriver) is called the mouth of the stream.

d. The primary channel in the stream is called the mainstem; smaller streamsthat flow into the mainstem are called tributaries.

5 Evaporation, Transpiration, and Precipitation

5.1 Evaporation

Evaporation occurs when the number of water molecules passing to the vaporstate exceeds the number forming the liquid state. The rate of evaporationdepends upon the water temperature and the temperature and humidity ofthe air above the water. Humidity refers to the amount of moisture in theair; more specifically:

– Absolute humidity – mass of water per unit volume of air (usually gramswater per cubic meter of air)

– Saturation humidity – maximum amount of moisture the air can hold at agiven temperature

– Relative humidity – the absolute humidity over the saturation humidity(i.e., the percent ratio of the amount of moisture in the air to the totalamount it could possibly hold)

Evaporation from lakes and river, and even directly from the groundwater, isa significant flux in the water cycle and must be considered in water-budgetstudies. Evaporation rates from a lake or a reservoir can be determined indi-rectly by measuring the inflows, outflows, and changes in storage in the lake,and using the hydrologic equation to fill in the evaporation part. This can bedifficult, because it is hard to measure how much water is entering or leavingthe groundwater

Evaporation can be measured directly using shallow pans of water. Pans aremaintained throughout the country by the Meteological Office for constantmonitoring of evaporation rates. Water is maintained in these pans at a fairlyconstant depth, and the amount of water added to the pan (by the operatorsas well as by precipitation) is used to calculate evaporation rates.

6

One of the complications of using pans to estimate the amount of water thatwould evaporate from a nearby reservoir is that the pan absorbs heat fromthe sun much more readily than the reservoir, and the pan can also lose heat(through the sides and bottom) much more easily than the reservoir. There-fore, the pans always overestimate the rate of evaporation. Pan evaporationrates must be multiplied by a pan coefficient, which is a number less than1 (usually somewhere between 0.5 and 0.8).

5.2 Transpiration

Plants are constantly pumping water from the ground into the atmospherethrough a process called transpiration. Plants take up water for their ownuse (i.e., for building plant tissue), but only about 1% of what they suck upgets used; the rest is released to the atmosphere through leaves. Transpirationis a difficult thing to quantify; it varies with the time of the day (most dur-ing daylight hours, when photosynthesis is occurring) and time of year, andindividual types of plants will take up water at different rates. Transpirationis significant anywhere there are plants, but in some cases it can drasticallyreduce the amount of water in streams.

5.3 Evapotranspiration

When studying water in the field, one cannot separate water lost to evapo-ration from transpiration losses; therefore it is typical to lump them togetheras evapotranspiration (E-T. To understand this we need to distinguish be-tween potential evapotranspiration and actual evapotranspiration).

Potential evapotranspiration is the water loss that would occur if there is anunlimited supply of water available for transpiration and evaporation.

In reality, the amount of water that transpires or evaporates is limited bythe amount of water that is available. If the amount of water available is lessthan the potential, then the actual evapotranspiration will be lower than thepotential.

Figure 6 shows the relationship between precipitation and potential/actualE-T in an area with a warm, dry summer and a cool, wet fall/winter/spring.In the summer months, when precipitation is low, there is not enough waterto satisfy the potential; therefore the actual E-T is less than the potential.

Actual E-T cannot exceed the potential, but if precipitation and the capacityof the soil to store water are both low, then actual can be much less than

7

Fig. 6. Graph of potential evapotranspiration, actual evapotranspiration and pre-cipitation.

potential. In areas where precipitation is more evenly distributed throughoutthe year, actual E-T will be close to potential E-T. This is important becausewe can measure potential evaporation (i.e. pan evaporation) and determinepotential transpiration for specific plants, but we have to take into accountthat the potential will not be reached if there is not enough water available.

5.4 Precipitation

As masses of air cool, the saturation humidity decreases, and the relativehumidity, in turn, increases. When the relative humidity approaches 100%condensation begins to occur. Condensation forms on particles of dust or icecrystals suspended in the air to form clouds. When air masses rise, they ex-pand, and as they expand they cool and water condenses. If enough watercondenses, it will exceed the air’s capacity to hold it and water will fall outas precipitation. The amount of rain that falls during a storm is usually mea-sured in terms of a depth. This depth refers to the depth of water that is leftin a rain gauge after the storm. If we know the depth at any given point, andthe area of our watershed, we can determine the volume of water that fell inthe drainage basin during the storm. However, the rate and the total depth ofprecipitation will vary from place to place in an area during a storm. Whenattempting to determine the amount of rain that falls in a watershed, we needto calculate some sort of average precipitation, or effective uniform depth(EUD) of precipitation for the watershed. If our rain gauge stations are dis-

8

Fig. 7. Isohyetal contour on the map.

tributed evenly throughout the area, each gauge will represent an equal areaof the watershed. In that case, we can take a simple average of all the rainfallvalues at each station will give you an effective uniform depth. Unfortunately,rain gauges are almost never evenly distributed throughout the watershed,and we will need to adjust the values so that an EUD can be determined.There are two basic ways of doing this.

Isohyet method: Isohyetal lines are lines of equal rainfall. These are drawnon a map of the watershed just like any contour map. The area bounded byadjacent isohyets is measured, and the average depth of the two isohyets isapplied to that area. The areas are then weighted and averaged based on therelative size of each isohyetal area. Figure 7 shows an isohyetal map.

The drawback of this method is that, since the distribution of rain is neverthe same, a new map must be redrawn with each rain event.

Thiessen method: This is similar to the previous method, except that itweights the areas around each gauge. Adjacent stations in the watershed are

9

Fig. 8. Development of a Thiessen polygon map of the rain gauge network a) Linesare drawn connecting the gauge location and b) The perpendicular lines are con-nected to form the polygons.

connected with a network of lines. A perpendicular line is drawn at the mid-point between each line. These are then extended until they intersect with thenearest line, to create a series of polygons covering the area. The area of eachpolygon is measured, and the percentage of the total area is determined. Therainfall depths at each station are then Image not available for this publica-tion; an alternate image will be provided in class weighted based on the areaof the polygon, and these are averaged to determine the EUD. Figure 8 showsa Thiessen polygon map.

The advantage of the Thiessen polygon method is that one only needs tocalculate the weighting factors for the gauge stations once.

These methods have limitations in mountainous areas, where orographic effectscan create vastly different microclimates over short distances. In such areas,detailed studies of vegetation or more detailed rain gauge coverage is neededto properly distribute the rainfall values.

6 Infiltration

When precipitation falls from the sky, several things can happen to it. Somewill be intercepted by plants before it reaches the ground; this water canevaporate or can eventually fall to the ground or move down the stems ofplants or trees to the ground. Some of the rainfall that reaches the ground caninfiltrate into the soil.

The infiltration capacity of the soil refers to the rate at which the soil canabsorb water. For dry soils, the infiltration capacity is high due to capillaryaction pulling the water into the soil. As the soil becomes wetter, the infil-

10

Fig. 9. Infiltration capacity versus time.

tration capacity diminishes, and less water can infiltrate. Infiltration capacitychanges as a function of time throughout a rain event and follows an expo-nential decay curve (Figure 9). The horizontal line on the curve (fc) is theequilibrium infiltration capacity, and represents the lowest point that theinfiltration capacity will reach.

If the precipitation rate does not exceed the equilibrium infiltration capacity,all the precipitation reaching the land surface will infiltrate and there willbe no runoff. If the precipitation rate is greater that equilibrium infiltrationcapacity, but less than the initial capacity (fo), initial infiltration will acceptall of the precipitation followed by runoff or formation of puddles of water onthe surface (called depression storage). If the precipitation rate exceeds theequilibrium infiltration capacity and the initial infiltration capacity, runoff ordepression storage will commence immediately.

Water that infiltrates into the subsurface will percolate vertically unless itencounters the water table or some variation in permeability that causes it tomove laterally. Layers of low-permeability material in the subsurface can slowdown the vertical percolation of groundwater and cause it to move horizontallytowards a stream. This flow of water is called interflow.

11

Fig. 10. Relationship between infiltration, depression storage and overland flow.

7 Streams

Streams are generally hydraulically connected to the underlying groundwater.When groundwater is discharging into the stream, we call the stream a gain-ing stream (see Figure 11). The amount of water that flows into the streamfrom the groundwater is called baseflow.

If infiltration causes the water table to rise, the hydraulic gradient in thegroundwater will increase and the amount of baseflow will also increase. Formany streams, baseflow is the source of water to the stream except duringstorms, when precipitation in the watershed exceeds the infiltration capacityand the depression storage is filled. In this case, runoff or overland flow willoccur, and this runoff will flow into the stream. Natural runoff is usually asmall component of the total volume of water flowing through a watershed;only in arid regions where the streams are losing streams and are not receivingbaseflow, is natural runoff a significant contributor. In heavily urbanized areas,with a lot of impervious cover (parking lots, roads, buildings), runoff is a much

12

Fig. 11. A generalized and simplified diagram of the hydrologic cycle.

Fig. 12. Cross-section of stream showing velocity profile.

more significant contribution to the surface water system.

7.1 Discharge

Discharge is defined as the volume of water moving past a point on a streamin a given period of time. In the simplest terms, stream discharge (Q) is equalto the velocity of the water (v) times the cross sectional area of the stream(A), or

Q = vA. (7.1)

The complication is that water in the stream is flowing fastest in the middleof the stream and is slowest at the edges and along the bed of the stream.Figure 12A shows a cross section of a stream flowing out of the page. Figure2B shows contours indicating the changes in velocity (in units of, say, cm/sec)throughout the stream. The line a-a shows the velocity profile – the arrowsrepresent velocity vectors. Image not available for this publication; an alternate

13

Fig. 13. Cross section of stream showing stream gaging stations.

Fig. 14. Stage-discharge rating curve.

image will be provided in class

To measure discharge, we have to determine the average velocity of the waterin the stream. We can measure velocity using a current meter. Experience hasshown that, in water greater than 2.5 feet deep, velocity measured at 0.2 and0.8 of the total depth and averaged together will give a good average for thewater velocity. If the stream is less than 2.5 feet deep, one measurement at0.6 of total depth will give an average velocity (Figure 13). Measurements aremade at regular intervals (e.g., 0.5 foot) across the stream. The velocity is thenmultiplied by the interval and the depth of the stream in that interval to get adischarge for that 0.5 foot-wide strip of the stream. These individual dischargemeasurements are added up to get the overall discharge of the stream.

If a lot of stream gage measurements are made at different times of the yearunder different flow conditions (i.e., low flow, high flow), a relationship betweenstream stage (i.e., water surface elevation) and discharge can be developed.This is done by measuring the stage height each time the discharge is measureduntil you have a lot of measurements, then plotting the values on a graph andconnecting them with a curve. This curve is called a stage-discharge ratingcurve. The utility of this is that it is much easier to measure river stage, soonce a stage-discharge curve is developed, you can use it to convert stage todischarge.

14

Fig. 15. Different types of weirs.

Stage-discharge rating curves are not linear (Figure 14). This is because thecross-sectional area in the stream increases a lot faster than the elevation does.So, as the water level gets higher, the overall area available for water to flowthrough increases much more dramatically and the discharge will thereforeincrease faster. We can also measure stream discharge in small streams usinga weir. A weir is basically a dam with a small opening of a pre-determined sizeand geometry that allows water to flow through. The most common shapesfor weirs are the rectangular weir, trapezoidal (or Cipolletti) weir, and the 90o

V-notch weir (Figure 15).

The equations for the rectangular and V-notch weirs are:

Rectangular weir Q = 1.84(L− 0.2H)H23 (7.2)

90o V-notch weir Q = 1.379H52 (7.3)

where

Q discharge in (m3/s)

L Length of weir crest (m)

H height of backwater above weir crest (m)

These equations are empirically derived, so the numbers do not have any realmeaning. They are simply coefficients relating water elevation to discharge.

15

7.2 Manning Equation

The average velocity of flow in an open channel can be calculated using theManning equation:

V =1

nR

23 S

12 , (7.4)

where

v velocity in (m/s)

R the ratio of the cross-sectional area of flow to the wetted perimeter (m)

S energy gradient (or the slope of the water surface)

n Manning roughness coefficient.

The wetted perimeter refers to the length of the channel that is in contact withthe water. The Manning roughness coefficient is an empirically-derived numberthat basically describes how the roughness of the channel creates friction thatslows down the water in the channel.

This equation is simply a way of determining flow velocity, or indirectly dis-charge. It can be used to model streams that don’t exist; for example, ifsomeone wants to put a drainage ditch on their property, they can use theequation to estimate how fast the water will flow in the ditch. Or, if there isa storm and water velocities are changing too fast to measure discharge, andyou know something about the slope and dimensions of the channel, you canuse this equation to calculate flow.

7.3 Stream Hydrograph

A stream hydrograph is a graph that represents river discharge at a sin-gle point on a river as a function of time. A stream hydrograph shows howdischarge in the stream changes with time and, if plotted with precipitation,also shows how discharge responds to storms. A specific hydrograph for astorm event is called a storm hydrograph. Figure 16 shows a typical stormhydrograph.

The columns represent daily precipitation. The flood peak, or point whereflow is highest, occurs at some time after the precipitation peak. This differencein time is called the lag time. The lag time is due to the fact that it takes timefor water to flow overland or through the subsurface as interflow. The lag time

16

Fig. 16. Hypothetical storm hydrograph showing response to a 4-day storm event.

Fig. 17. Storm hydrograph showing the specific parts of the curve.

is different for different watersheds, and is a function of the size and geometryof the watershed as well as the geologic materials in the watershed. The partof the curve that is increasing is the rising limb of the curve; the part thatis decreasing as storm water drains out of the watershed is the falling limb.

The hydrograph can be broken up into specific components (Fig. 17). Theflow in the stream is a combination of baseflow from the groundwater andsurface runoff from the storm event. The baseflow increases throughout thestorm event in response to higher water levels in the groundwater around thestream. At the point where the runoff from the watershed is exhausted andthe stream goes back to being only baseflow, the stream is in recession.

In the absence of precipitation, the recession part of the hydrograph continuesto follow a decreasing curve similar to an exponential decay curve. Eventually,as the groundwater continues to drain and groundwater levels drop further, thestream stops receiving baseflow from the groundwater, and stream dischargewould be zero. The shape and slope of the baseflow recession hydrographis a function of the geometry of the basin as well as the geology and soils

17

characteristics, and is unique to each stream.

8 Terminologies for Hydrology

The strict technical definition of groundwater is any water that is foundbeneath the surface of the Earth. This definition includes

(1) The moisture that is found in the pores between soil grains(2) The fresh to slightly saline water, found in saturated geologic units near

the surface, which is used for drinking and irrigation(3) The extremely salty brines associated with petroleum deposits and deep

sedimentary units(4) The water found in the lower lithosphere and in the mantle.

In this lesson, we are primarily concerned with item (2), the fresh to slightlysaline water found near the surface that is frequently used for domestic, agri-cultural, and industrial purposes.

No branch of science is without its terminology. Before going further, we mustdefine the terms used to discuss subsurface waters. The traditional categoriza-tion of subsurface waters, and the one adopted here, is shown in Fig. 18.

Fig. 18. Cross-section showing the distribution of water in the shallow subsurface.

Subsurface waters are divided into two main categories: the near-surface unsat-urated or vadose zone and the deeper saturated or phreatic zone. The bound-ary between these two zones is the water table, which is technically definedas the surface on which the pore water pressure equals atmospheric pressure.In cross-section drawings like Fig. 18, the water table and other water surfacesare typically marked with the symbol ∇. The terms phreatic surface and freesurface are synonymous with water table. Measuring the water table is easy.

18

If a shallow well is installed so it is open just below the water table, the waterlevel in the well will stabilize at the level of the water table.

The unsaturated or vadose zone is defined as the zone above the watertable where the pore water pressure is less than atmospheric. In most of theunsaturated zone, the pore spaces contain some air and some water. Capillaryforces attract water to the mineral surfaces, causing water pressures to beless than atmospheric. The term vadose water applies to all water in theunsaturated zone. The terms soil water and soil moisture are also applied towaters in the unsaturated zone, usually in reference to water in the shallowpart where plant roots are active.

Below the water table is the saturated or phreatic zone, where water pres-sures are greater than atmospheric and the pores are saturated with water.Groundwater is the term for water in the saturated zone. Aquifer is a fa-miliar term, meaning a permeable region or layer in the saturated zone. Thisbook deals with both vadose water and groundwater, but most of the emphasisis on groundwater, since it is the main reservoir of subsurface water.

The capillary fringe is a zone that is saturated with water, but above thewater table. It has traditionally been assigned to the unsaturated zone, eventhough it is physically continuous with and similar to the saturated zone.The thickness of the capillary fringe varies depending on the pore sizes in themedium. Media with small pore sizes have thicker capillary fringes than mediawith larger pore sizes. In a silt or clay, the capillary fringe can be more thana meter thick, while the capillary fringe in a coarse gravel would be less thana millimeter.

9 Fluxes Affecting Groundwater

Groundwater is a part of the dynamic hydrologic cycle, and water must some-how enter as well as leave the subsurface. Water entering the subsurface iscalled recharge. Recharge to the subsurface is generally through infiltra-tion – percolation of surface water (from rain, perennial streams, meltingsnow etc.) downward into the soil. As the water percolates down through thesoil, sediment, and rock, the percentage of the pore space that is filled withwater (or the degree of saturation) increases until it reaches 100% (i.e.complete saturation).

Just as water enters the saturated zone, it must eventually leave it. Movementof water out of the saturated zone is called discharge. Natural discharge canbe through a spring, into the bed of a stream, lake or ocean, or via evaporationdirectly from the water table. Pumping of groundwater through wells, holes

19

drilled into the ground for the purpose of accessing subsurface fluids, is anotherway that water discharges from the saturated zone. Figure 19 summarises allthe possible components that could affect the dynamics of groundwater.

Fig. 19. Reservoirs and water fluxes affecting groundwater dynamics.

10 Hydrologic Balance

Groundwater is always flowing and it flows from higher hydraulic heads (orhigher water elevation) to lower hydraulic heads. The distribution of hydraulicheads in the saturated zone determines the direction in which the water willflow.

The speed with which groundwater flows, also called the velocity or flux,is determined by the difference in hydraulic head and the permeability ofthe sediment or rock through which it flows. Permeability is a number whichdescribes the ease with which a fluid (like water) will move through a porousmedium (i.e. a rock, soil, or sediment which has enough pore space to allowwater to move through it).

Hydrologic balance is the basic concept of conservation of mass with respectto water fluxes. Take any region in space, and examine the water fluxes intoand out of that region. Because water cannot be created or destroyed in thatregion, hydrologic balance requires

flux in− flux out = rate of change (10.1)

20

The units of each term in this equation are those of discharge [L3/T]. Thisis a volume balance, but because water is so incompressible, it is essentiallya mass balance as well. Hydrologic balance is useful for estimating unknownfluxes in many different hydrologic systems.

Example 10.1. Consider a reservoir with one inlet stream, one outlet at adam and a surface area of 2.5 km2. There hasn’t been any rain for weeks, andthe reservoir level is falling at a rate of 3.0 mm/day. The average evaporationrate from the reservoir surface is 1.2 mm/day, the inlet discharge is 10,000m3/day, and the outlet discharge is 16,000 m3/day. Assuming that the onlyother important fluxes are the groundwater discharges in and out of the reser-voir, what is the total net rate of groundwater discharge into the reservoir?

Solution

21

Fluxes in and out of the saturated zone of an aquifer in a stream basin areillustrated in Figure 20). Using symbols defined in the figure’s caption, the

Fig. 20. Water fluxes in and out of the saturated zone of an aquifer under a streambasin. R is recharge, Gi and Go are groundwater inflows and outflows throughthe lateral boundaries and bottom of the aquifer, Gs is groundwater discharge tostreams, ETd is deep evapotranspiration extracted from the saturated zone, and Qw

is well discharge.

general equation for hydrologic balance in this piece of aquifer is as follows:

R + Gi −Go −Gs − ETd −Qw =dV

dt(10.2)

where dV/dt is rate of change in the volume of water stored in the region.If, over a long time span, there is an approximate steady-state balance whereflow in equals flow out, then the transient term disappears and the balanceequation becomes

R + Gi −Go −Gs − ETd −Qw = 0 (10.3)

Imagine that the basin has been operating in a rough steady state for manyyears without any pumping wells. At this time, the above equation with Qw =0 describes the balance. Later a well is installed and begins pumping at asteady rate Qw > 0. Immediately, the system is thrown into imbalance; Eq.(10.2) applies and the volume stored in the aquifer declines (dV/dt < 0). Infact, at the start of pumping, all the water pumped comes from a correspondingdecline in the volume of water stored (Qw = −dV/dt). The decline in volumestored causes a declining water table. If the well discharge is held constant fora long time, a new long-term equilibrium will be established, the water tablewill stabilize, and Eq. (10.3) will apply once again, this time with Qw > 0. Toachieve this new long-term balance, other fluxes must adjust: R and Gi mayincrease, while Go, Gs, and ETd may decrease.

22

Increasing the discharge of pumping wells in a groundwater basin always hassome long-term effects on other fluxes and/or the volume stored in the basin.In many cases, the rate of pumping is so high that a new steady state cannotdevelop: the flows out of the system are greater than the flows in. In such cases,the pumping could be viewed as ”mining”, simply pulling water out of storage.This has been the case in the High Plains Aquifer in the south-central U.S.,where there is widespread irrigation and a dry climate. The water table hasdropped more than 30 m in parts of this aquifer in Texas, where the averagerate of pumpage far exceeds the average recharge rate, which is estimated tobe less than 5 mm/year. By 1980, pumping had removed about 140 km3 ofstored water from the aquifer in Texas.

Long-term changes caused by pumping can affect large areas, far beyond thewell owner’s property lines. Groundwater basins often transgress property linesand political boundaries, so most countries have regulations governing ground-water use. Regulation of well discharges and groundwater resources is complexbecause of interaction between different aquifers, surface water bodies, andwells.

Often pumping wells located near streams cause a noticeable reduction ingroundwater discharge to the stream. In other words, the wells steal somebaseflow from the stream. The interaction between well discharge and ground-water discharge to a nearby stream was a key technical issue in A Civil Action,a popular nonfiction book and movie about a trial involving contaminated wa-ter supply wells. The defendants in the lawsuit were major corporations thatowned polluted sites near the water supply wells. If the supply wells pulledmost of their water from the nearby stream, then a significant fraction of thepollutants in the well water could have come from distant sites upstream alongthe stream, and the owners of local sites would have been less culpable.

11 Tutorial

(1) A cistern collects rainfall from the roof of a 7.62 m × 13.72 m building.The cistern holds 1000 gallons. During one particular storm, the rainfallamounts were as shown in Table 2. At about what time did the cisternoverflow?

[Ans:5:27pm]

(2) The cistern of the previous problem is used to water a garden. It takes 80min for the full cistern to drain through a hose that has a 3.175 cm insidediameter. Calculate the average discharge rate of the hose in gallons/min,ft3/sec, and m3/sec. Calculate the average velocity of water in the hoseduring drainage, reporting your answer in ft/sec and m/sec units.

23

Time Period (pm) Rainfall (in)

1:00-2:00 0.12

2:00-3:00 0.24

3:00-4:00 0.53

4:00-5:00 0.32

5:00-6:00 0.49

6:00-7:00 0.28

7:00-8:00 0.14

8:00-9:00 0.06Table 2Data for Problem 1.

[Ans: 3.26 ft/sec or 0.99 m/sec]

(3) The drainage area of the Colorado River is about 653,000 km2 and itsaverage annual discharge is about 15 million acre-feet. The average pre-cipitation rate in the basin is about 12 inches/year. Calculate the riverdischarge divided by the drainage basin area in inches/year. What frac-tion of the annual precipitation rate is this? What fates, other than endingup in the Colorado River, can precipitated water have in this basin?

[Ans: 1.1 in/yr or 9%]

(4) Refer to Figure 21 showing stream discharges at two streams in Indi-ana. October 1 was preceded by a long period without precipitationin both basins, so stream flow at that time was predominantly base-flow. The discharge at the Tippecanoe River gage on October 1 was 22ft3/sec, and at the Wildcat Creek gage the discharge was 6.4 ft3/sec.Take these discharges and divide them by the stream’s drainage area toget baseflow/area for each stream on October 1, and report your answerin inches/year. Discuss the result for each stream in light of the drainagebasin geology and the average annual rainfall rate, which is about 40inches per year.

[Ans: Tippecanoe River: 2.6 in/yr; Wildcat Creek:0.59 in/yr.]

(5) A groundwater and river basin has an area of 340 mi2. Estimates havebeen made of the average annual rates of precipitation (28 inches/year),stream flow (13 inches/year), baseflow (6 inches/year). The amount ofgroundwater that is pumped for irrigation (which ultimately evaporatesor transpires) is 1.8 × 109 ft3/year. Assume that there is zero net fluxof groundwater through the basin boundaries. Create a chart like Fig. 5illustrating fluxes in the basin. Estimate the average annual rates of thefollowing items:

24

Fig. 21. Hydrographs for two nearby streams in northern Indiana during 1988. Thebasin upstream of the gage on the Tippecanoe River is 113 mi2, and the basinupstream of the Wildcat Creek is 146 mi2.

(a) Overland flow + interflow (lump these two)(b) Recharge(c) Evapotranspiration.Report your answers in inches/year (think of it as volume/time/basinarea).

[Ans: 7 in/yr; 8.3 in/yr; 12.7 in/yr]

12 Assignments

(1) Every summer you visit the same lake in Maine, and every summer theneighbor goes on and on about how the lake is ”spring-fed” (groundwa-ter discharges up into the lake bottom). You got to wondering if thatwas true, so you collected all the information you could from the localgeological survey office about the lake hydrology for the month of June:• The surface area of the lake is 285 acres.• There is one inlet stream. For the month of June, the total discharge

measured at a stream gage at the lake inlet was 2.77 × 107 ft3.• There is one outlet stream. For the month of June, the total discharge

measured at a stream gage at the lake outlet was 3.12 × 107 ft3.• During the month of June, the total precipitation measured in a rain

25

gage at the lakeshore was 1.63 inches.• Direct evaporation off the lake surface totaled 3.47 inches during the

month of June.• The lake level dropped 4.30 inches during the month of June.(a) List the items that contribute flow into the lake, and items that con-

tribute flow out of the lake (there may be unknown items which arenot listed above). Write a hydrologic equation for the water balanceof the lake in June.

(b) Quantify each of the terms in the hydrologic equation in units of ft3

for the month of June, and solve for unknowns in the equation.(c) What, if anything, can you conclude about the notion that the lake

is ”spring-fed”?(d) What measurements would you make to prove whether or not ground-

water is discharging up into the lake bottom? (Assume someone iswilling to pay for it.)

(2) The discharge of a stream and the concentration of a trace element instream water has been monitored through the course of a single storm.The concentration in precipitation is 2.5 µg/L (10−6 grams/liter) andthe concentration in groundwater is 55 µg/L. Use the chemical baseflowseparation technique to create a graph showing stream discharge andestimated baseflow vs. time. Get the stream discharge and concentrationvs. time data from a tab-delimited text file available on website. Usespreadsheet software to open this file and to do the computations andgraphing. In this file, discharges (Q) are in m3/sec, time t is in hours,and concentrations (c) are in µg/L.(a) Derive a mathematical formula Qb = ... that expresses baseflow in

terms of other parameters that are known in this problem. Label allunits in this equation, and show how the units of Qb are consistentwith the units of quantities on the other side of the equation.

(b) Create a scaled graph showing stream flow, quickflow, and baseflowvs. time. Clearly annotate the graph with axis labels and a legendfor the three curves.

(3) Consider the water balance for a reservoir with a surface area of 2.3 km2.A tab-delimited text file on the internet contains measurements of thefollowing fluxes over the course of a year:• Discharge of the inlet stream (m3/month).• Discharge of the outlet stream (m3/month).• Precipitation rate on the reservoir surface (cm/month).• Evaporation rate off the reservoir surface (cm/month).• Reservoir elevation above sea level at the beginning of the month (m).Other than the net groundwater discharge into the reservoir, the abovefluxes are the only significant ones.(a) Write out the equation for hydrologic balance for the case of this

26

reservoir.(b) Download the tab-delimited data file for this problem, open it with

a spreadsheet program and use the program to do all computationsand graphing. Determine the average net groundwater discharge eachmonth of the year, and create a graph of net groundwater dischargevs. time through the year. In your computations, make sure to con-vert all fluxes to a common set of units such as m3/month.

References

[1] Fetter CW (2001) Applied Hydrogeology. 2nd ed. Upper Saddle, NJ: PrenticeHall.

[2] Fitts CR (2002) Groundwater Science. Academic Press Inc., US: Elservier.

27