U.S. Department of the Interior

U.S. Geological Survey

Circular 1260

Heat as a tool for studying the movement 

of ground water near streams
Confluence of Case Creek with Champoeg 

Creek in the Willamette lowland of Oregon. 

Temperatures in sediments beneath 

channels like these provide information on 

losses and gains of surface water to and 

from ground water. Case Creek is one of six 

study sites in the Willamette Basin where 

thermal techniques were used to produce 

estimates of seepage losses to ground 

water (see Chapter 5). 
Heat as a Tool for Studying the Movement 

of Ground Water Near Streams

EDITED BY 

David A. Stonestrom

Jim Constantz

U.S. Department of the Interior

U.S. Geological Survey

Circular 1260
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey,

Reston, Virginia: 2003

Available from U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

or

World Wide Web: http://pubs.water.usgs.gov/circ1260/

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

World Wide Web: http://www.usgs.gov/

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

SBN 0-607-94071-9
iii

Contents

Acknowledgements..................................................................................................................................... iv

Conversion factors and abbreviations ...................................................................................................... v

Chapter 1

Heat as a tracer of water movement near streams................................................................................ 1

Chapter 2

The Rio Grande—competing demands for a desert river...................................................................... 7

Chapter 3

Heat tracing in the streambed along the Russian River of northern California ............................... 17

Chapter 4

The Santa Clara River—the last natural river of Los Angeles ............................................................ 21

Chapter 5

Heat tracing in streams in the central Willamette Basin, Oregon...................................................... 29

Chapter 6

Trout Creek—evaluating ground-water and surface water exchange along an alpine stream,

Lake Tahoe, California................................................................................................................................ 35

Chapter 7

Combined use of heat and soil-water content to determine stream/ground-water exchanges,

Rillito Creek, Tucson, Arizona ................................................................................................................... 47

Chapter 8

Trout Creek—estimating flow duration and seepage losses along an intermittent stream tribtary to the Humboldt River, Lander and Humboldt Counties, Nevada................................................ 57

Appendix A

Determining temperature and thermal properties for heat-based studies of surface-water

ground-water interactions ........................................................................................................................ 73

Appendix B

Modeling heat as a tracer to estimate streambed seepage and hydraulic conductivity............... 81

References................................................................................................................................................... 91
iv 

Acknowledgments

The U.S. Geological Survey (USGS) Office of Ground Water and Water Resources Discipline’s National Research Program provided major funding for both the circular as well as the 

studies on which it is based. Studies also received matching support from state and local water 

agencies in Oregon, California, Nevada, Arizona, and New Mexico, and from the private sector. 

We especially thank Paul Pettit and Patricia Cannon of Newmont Mining (Carlin, Nevada), 

Douglas McGibbon and John Barber of Glamis Marigold Mining (Valmy, Nevada), and Karl 

Wozniak of Oregon Water Resources (Salem) for encouragement and support of specific studies 

within their purview. Many USGS colleagues contributed to this circular by providing technical assistance and critical reviews of draft chapters. They include John Callahan (Arizona), 

Fredrick Gebhardt (New Mexico), Stephanie Moore (New Mexico), Donita Parker (Oregon), 

Nye Pennington (Nevada), Russell Plume (Nevada), and John C. Stone (Nevada). David R. 

Jones (Menlo Park, California) designed the layout and provided graphical support. Keith G. 

Kirk (Menlo Park, California) provided overall editorial supervision, work-flow and production 

support.
v

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

meter (m) 1.094 yard (yd) 

Area

square meter (m2) 0.0002471 acre 

hectare (ha) 2.471 acre

square centimeter (cm2) 0.001076 square foot (ft2)

square meter (m2) 10.76 square foot (ft2) 

square centimeter (cm2) 0.1550 square inch (ft2)

hectare (ha) 0.003861 square mile (mi2) 

square kilometer (km2) 0.3861 square mile (mi2)

Volume

liter (L) 33.81 ounce, fluid (fl. oz)

liter (L) 2.113 pint (pt)

liter (L) 1.057 quart (qt)

liter (L) 0.2642 gallon (gal)

cubic meter (m3) 264.2 gallon (gal) 

cubic centimeter (cm3) 0.06102 cubic inch (in3) 

cubic decimeter (dm3) 61.02 cubic inch (in3) 

liter (L) 61.02 cubic inch (in3) 

cubic meter (m3) 35.31 cubic foot (ft3)

cubic meter (m3) 1.308 cubic yard (yd3) 

cubic kilometer (km3) 0.2399 cubic mile (mi3) 

cubic meter (m3) 0.0008107 acre-foot (acre-ft) 

Flow rate

cubic meter per second (m3/s) 70.21 acre-foot per day (acre-ft/d) 

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

liter per second (L/s) 15.85 gallon per minute (gal/min) 

Pressure

kilopascal (kPa) 0.009869 atmosphere, standard (atm)

kilopascal (kPa) 0.01 bar

Density

kilogram per cubic meter (kg/m3) 0.06242 pound per cubic foot (lb/ft3) 

Energy

joule (J) 0.2778 x 10-6 kilowatthour (kWh)

Hydraulic conductivity

meter per second (m/s) 3.281 foot per second (ft/s) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

 °F=(1.8×°C)+32

Conversion factors and abbreviations

Chapter 1

Heat as a tracer of water movement near streams

Jim Constantz and David A. Stonestrom

Introduction

Stream temperature has long been recognized as an important water quality parameter. Temperature plays a key role in 

the health of a stream’s aquatic life, both in the water column 

and in the benthic habitat of streambed sediments. Many fish 

are sensitive to temperature. For example, anadromous salmon 

require specific temperature ranges to successfully develop, 

migrate, and spawn [see Halupka and others, 2000]. Metabolic 

rates, oxygen requirements and availability, predation patterns, 

and susceptibility of organisms to contaminants are but a few of 

the many environmental responses regulated by temperature.

Hydrologists traditionally treated streams and ground 

water as distinct, independent resources to be utilized and 

managed separately. With increasing demands on water supplies, however, hydrologists realized that streams and ground 

water are parts of a single, interconnected resource [see Winter 

and others, 1998]. Attempts to distinguish these resources for 

analytical or regulatory purposes are fraught with difficulty 

because each domain can supply (or drain) the other, with 

attendant possibilities for contamination exchange. Sustained 

depletion of one resource usually results in depletion of the 

other, propagating adverse effects within the watershed.

An understanding of the interconnections between surface water and ground water is therefore essential. This understanding is still incomplete, but receiving growing attention 

from the research community. Exchanges between streams 

and shallow ground-water systems play a key role in controlling temperatures not only in streams, but also in their underlying sediments. As a result, analyses of subsurface temperature 

patterns provide information about surface-water/ground-water 

interactions.

Chemical tracers are commonly used for tracing flow 

between streams and ground water. Introduction of chemical 

tracers in near-stream environments is, however, limited by 

real and perceived issues regarding introduced contamination 

and practical constraints. As an alternative, naturally occurring variations in temperature can be used to track (or trace) 

the heat carried by flowing water. The hydraulic transport of 

heat enables its use as a tracer. 

Differences between temperatures in the stream and surrounding sediments are now being analyzed to trace the movement of ground water to and from streams. As shown in the subsequent chapters of this circular, tracing the transport of heat 

leads to a better understanding of the magnitudes and mechanisms of stream/ground-water exchanges, and helps quantify 

the resulting effects on stream and streambed temperatures. 

Chapter 1 describes the general principals and procedures 

by which the natural transport of heat can be utilized to infer 

the movement of subsurface water near streams. This information sets the foundation for understanding the advanced 

applications in chapters 2 through 8. Each of these chapters 

provides a case study, using heat tracing as a tool, of interactions between surface water and ground water for a different 

location in the western United States. Technical details of the 

use of heat as an environmental tracer appear in appendices.

What causes exchanges of water between 

streams and ground water?

Water in the subsurface flows from higher to lower total 

head, where total head is the sum of water elevation and water 

pressure (expressed as a head). The pressure head is zero (with 

respect to atmospheric pressure) at the stream surface and at 

all points on the water table. Therefore, the elevation of the 

water table relative to the stream surface indicates the direction of subsurface flow between streams and nearby ground 

water. The resistance to flow presented by sediments, as well 

as the gradient in head, governs the rate at which water moves 

between surface-water and ground-water systems [see Freeze 

and Cherry, 1979].

As water passes through streambed sediments, chemical 

reactions occur that change its composition and thus affect water 

quality. Dissolved materials increase due to mineral dissolution. 

Exchange and other reactions change the relative abundance of 

materials in solution. Changes in water chemistry can increase 

towards saturation as water continues to flow through geologic 

strata. If ground water enters the stream, the stream’s chemical 

composition is affected. Exchanges of water can sometimes be 

tracked by monitoring the chemistry of water along flow paths. 

Flow paths can be traced at watershed scales or at the smaller 

scales of stream banks, sand bars, and local reaches of a stream 

[see Bencala and others, 1984]. Local-scale exchanges may be 

separately inconsequential but collectively important. Multiple 

exchanges of surface and ground water can strongly influence 

the quality of surface-water resources. Heat is especially well 

suited for delineating these small-scale flow paths. Naturally 
2 Heat as a tool for studying the movement of ground water near streams 

occurring changes in temperature in the near-stream environment are often large and rapid, providing a clear thermal signal 

that is easy to identify and measure.

History of heat as a hydrological tracer

The concept of using heat as a tracer of ground-water 

movement is not new. By the early 1900s, researchers recognized that heat is transferred during the course of water 

movement through sediments and other porous materials 

[Bouyoucos, 1915]. In the middle of the last century, groundwater hydrologists explored the possibility of using temperature measurements to estimate the rate at which water travels 

from the surface to great depths [for example, see Rorabough, 

1954; and Stallman, 1963]. Since then, temperature patterns 

have been exploited to study subsurface flow systems ranging from irrigation water in rice paddies to geothermal water 

beneath volcanoes [Suzuki, 1960; Sorey, 1971]. Heat as a 

tracer of ground-water movement had many more theoretical 

than practical applications due to measurement and computational limitations. Recently, however, the measurement and 

modeling of heat and water transport have benefited from 

significant improvements in data-acquisition and computational 

techniques. These advances enable the economical and routine 

application of heat as a hydrologic tracer.

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For the case of a gaining stream (panel A), the hydraulic gradient 

is upward (higher total head beneath the stream than in the stream)

as indicated by the higher altitude of water in the piezometer (observation well) than in the stream stage (measured by the stream gage). 

The stream has a large diurnal variation in water temperature. The 

sediment beneath the streambed has only a slight diurnal variation, 

because water is flowing up from depths where temperatures are 

constant on diurnal time scales. The variation in sediment temperature beneath the streambed reflects the balance between the oscillating transport of heat via conduction (transfer of heat through a 

substance from warm areas to cool areas without movement of the 

substance) and upward transport of heat via advection (transport of 

heat by a moving fluid). At any given depth beneath the streambed, 

higher flows of ground water to the stream lead to smaller variations 

in sediment temperature while smaller flows lead to larger variations 

(which become increasingly damped with depth). Consequently, 

shallow installation of temperature equipment (inside the piezometer 

or directly in the streambed sediments) is necessary to characterize 

gaining stream reaches, in order to detect significant temperature 

variations. 

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For the case of a losing stream (panel B), the hydraulic 

gradient is downward (lower total head beneath the stream 

than in the stream). The downward flow of water transports 

heat from the stream into the sediments. The downward 

advection of heat results in large diurnal fluctuations in sediment temperature. In addition, since regional groundwater is 

not flowing into the stream, temperatures vary more in losing 

streams than in gaining streams [Constantz, 1998]. Consequently, deeper installation of temperature equipment (inside 

the piezometer or beneath the streambed) is necessary for 

characterizing losing streams.
Heat tracing as a hydrological tool near streams 3

Using heat to follow water flow near streams

Whenever a difference in temperature exists between 

two points along a flow path, heat will flow between them by 

transport in the flowing water (advective heat flow). This heat 

movement is in addition to thermal conduction through the 

non-moving solids and fluids (conductive heat flow). Typically, heat movement is traced by continuous monitoring of 

temperature patterns in the stream and streambed, followed by 

interpretation using numerical models. Even before modeling, temperature patterns can immediately indicate the general 

character of the flow regime. For example, reaches of the 

channel in which sediment-temperature fluctuations are highly 

damped relative to in-stream fluctuations indicate high rates 

of ground-water discharge to the stream (that is, ground-water 

discharge to a strongly gaining reach). Conversely, segments of the stream channel where fluctuations in streambed 

temperatures closely follow in-stream fluctuations indicate 

high rates of water loss through streambed sediments (that is, 

ground-water recharge from a losing reach). To quantify the 

rates, location, and timing of stream-flow gains and losses, 

an array of temperature sensors is deployed in the stream and 

adjacent sediments. 

The use of heat as a hydrologic tracer has several distinct 

advantages over applied chemical tracers. The signal arrives 

naturally. The primary measurement is of temperature, which 

is a robust and relatively inexpensive parameter to measure.

In contrast to chemical tracers, which often require laboratory 

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For the case of a dry streambed (panel C), pore-water pressures in channel sediments are negative relative to atmospheric, 

and not measurable with a piezometer. (Negative pore water 

pressures exist in materials that are not fully saturated, such as 

a damp sponge or towel. Significant amounts of water my be 

present but will not occupy a piezometer; instead, atmospheric 

air pressure pushes subatmospheric water from the tube.) The 

streambed has high diurnal variations in temperature from daytime heating and nighttime cooling. The ability of dry material to 

transport heat is lower than that of wet material, damping diurnal 

variations in sediment temperatures at relatively shallow depths. 

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For the case of a channel that conveys ephemeral stream 

flow (panel D), a distinct temperature signal almost always 

marks the initiation of flow. The piezometer will register only 

if the screened interval is below the water table (at which 

point it will register the water-table elevation). High rates 

of infiltration at the onset of ephemeral flow produce rapid 

thermal responses in the streambed, as seen in the abruptly 

arriving signal in the streambed thermograph. 

Figure 1. Idealized stream channel for four possible interactions with ground water—a perennial stream gaining 

water from the underlying sediments, a perennial stream losing water to the underlying sediments, an ephemeral 

stream without flow, and an ephemeral stream with flow. Inset graphs show stream-flow hydrographs and corresponding streambed thermographs in each case.
4 Heat as a tool for studying the movement of ground water near streams 

analyses before interpretation is possible, temperature data are 

immediately available for inspection and interpretation. 

Figure 1 provides a series of graphics portraying thermal 

and hydraulic responses to four possible streambed conditions. 

Panels A and B show gaining and losing perennial streams that 

are connected to the local ground-water system. Panels C and 

D show dry and flowing ephemeral streams that are separated 

from the local ground-water system by an intervening unsaturated zone. Ephemeral channels lose water when flowing. The 

panels provide graphical depictions relevant to installation 

of monitoring equipment by illustrating the unique thermal 

signature for each stream condition. The inset hydrograph 

(on the right of each panel) shows stream flow. The inset 

thermographs (on the left of each panel) show temperature 

histories corresponding to the hydrographs. The thermographs 

show diurnal (daily) patterns of temperature at the surface of 

the channel and beneath the channel. A piezometer (instrument for measuring pressure head) shows pressure within the 

streambed. As noted above, the thermographs by themselves 

(even without the pressure data) permit identification of 

strongly gaining or strongly losing conditions.

Computer simulations to estimate water movement below the streambed

Computer simulations are based on a set of mathematical 

expressions that represent the physical and chemical processes 

known to occur in the system. Computer simulations are useFigure 2. The hydraulic conductivity of saturated sediments (blue 

band) is strongly dependent on sediment texture (represented 

here by grain size), whereas the thermal conductivity (tan band) is 

almost independent of texture. The vertical width of the hydraulic 

and thermal-conductivity bands gives an approximate range of 

the respective parameter for a given texture. Arrows show the 

degree to which the two conductivities will vary for a given range 

in textures (stippled band).

Annual (or diurnal) streambed temperature profile

Stream

Downward flux

Upward flux

z = 10 m (or 0.5 m)

z

Increasing Temperature

January

(dawn)

July

(afternoon)

Uncertainty in the saturated conductivity

versus thermal conductivity

Hydraulic conductivity,

in cm/day

(Fourier) QT = KT�T Q = K�H (Darcy)

Thermal conductivity,

in W/m oC

Textural range

Increasing grain size

10-3

10-2

10-1

100

101

102

103

Increasing conductivity

Figure 3. Ranges of sediment temperatures versus depth, Z, for 

gaining conditions (green lines) compared with losing conditions (red lines), over daily or annual cycles. The depth at which 

the temperature becomes constant depends upon the upward 

or downward flow of water through the sediments. For annual 

profiles, this depth may be 10 meters or more for downward flow 

versus less than a few meters for upward flow. For diurnal cycles, 

the depths at which temperatures become constant are shallower 

by the square root of (365/1) for a neutral flux (see Appendix A).

ful for analyzing portions of the hydrological cycle that can be 

accurately described by algebraic and differential equations. 

Simulation of water exchange between streams and surrounding sediments requires knowledge of the thermal and hydraulic parameters used as input values. Hydraulic conductivity, 

which quantifies the resistance of a porous material to water 

flow, can vary by orders of magnitude from one streambed to 

another. In contrast, thermal conductivity, which quantifies the 

resistance of the material to heat flow, varies little from one 

streambed to another. Figure 2 shows the relative sensitivity 

of hydraulic and thermal conductivities to texture. Note that 

thermal conductivity is virtually independent of texture, while 

hydraulic conductivity is highly dependent on texture. This is 

because heat travels in a direct path through the entire crosssection of solids and pore-filling fluids, whereas fluid flow is 

confined to a tortuous path through interconnected pores. Fluid 

flow is the product of hydraulic conductivity and hydraulic 

gradient (Darcy’s law). Analogously, conductive heat flow is 

the product of thermal conductivity and temperature gradient

(Fourier’s law).

Continuous monitoring of streambed temperatures 

provide a time-series of profiles (temperature versus depth 

curves) that document changes in water flux into and out of 

the stream. Figure 3 shows hypothetical streambed temperature profiles for a losing stream (downward water flux) versus 

a gaining stream (upward water flux) over a natural thermal 
Heat tracing as a hydrological tool near streams 5

Figure 4. Measured and modelled temperatures in sediments 

beneath the Rio Grande. Observed temperature data (dots) are 

compared with results of computer simulations (lines) for different 

theoretical values of hydraulic conductivity (Khyd) and hydraulic 

gradient. These results show the large sensitivity of modeled sediment temperatures to hydraulic parameters.

cycle (either one day or one year). The penetration of cyclic 

temperature changes is greater for the case of downward water 

movement because the downward-moving water has been 

heated and cooled at the land surface. Conversely, the penetration of cyclic temperature changes is less for the case of 

upward water movement because the upward-moving ground 

water comes from depths that are buffered from temperature 

fluctuations at the land surface. This water has a relatively 

constant temperature close to the cyclical average. Maximum 

and minimum temperatures during a complete cycle (annual 

or daily) form a ‘temperature envelope’ for a particular site, 

within which all measured temperature profiles reside. For the 

annual cycle, January and July profiles typically approximate 

the bounds of the envelope. When ground water is flowing into 

a gaining stream, the annual envelope collapses toward the 

streambed surface. When the stream is losing water to underlying sediments, the envelope expands downward. The same 

thing happens on a smaller scale over the daily cycle, with 

dawn and afternoon profiles approximating the daily temperature envelope (in which all other, for example hourly, temperature profiles reside). 

Figure 4 depicts measured temperatures beneath the Rio 

Grande at Albuquerque, New Mexico together with simulated 

temperatures produced by various combinations of hydraulic 

conductivity and hydraulic gradient [Bartolino and Niswonger, 

1999]. The figure shows that a hydraulic conductivity of 

6.7 x 10-6 m/s (0.0000067 meters per second, or about 58 

centimeters per day) results in simulated temperatures that 

closely match the measured profile. From Darcy’s Law, the 

temperature-based estimate of hydraulic conductivity times 

the measured hydraulic gradient provides a robust estimate of 

the water flux. A typical hydraulic gradient is less than 10% 

(less than a 0.1-m decrease in head per meter of travel). Rates 

of ground-water movement are usually a small fraction of the 

hydraulic conductivity. Changing the hydraulic conductivity 

(or hydraulic gradient) results in significant changes to the 

predicted temperature profile (fig. 4). The large sensitivity 

of streambed temperatures to hydraulic conditions is readily 

apparent, and makes heat a versatile tracer of ground-water 

movement. The technical details of applying thermal tracing 

techniques are given in the appendices. Appendix A describes 

the procurement of data (temperature, heat capacity and thermal conductivity) required to measure and interpret dynamic 

thermal profiles. Appendix B describes how simulation models 

are constructed and applied to observed measurements, with 

specific attention on publicly available computer codes for 

simulating the coupled transport of heat and ground water near 

streams.

A preview

Protecting stream environments and water supplies 

requires an adequate understanding of the interactions between 

streams and their underlying ground water. The body of this 

circular comprises seven chapters describing the manner in 

which heat has been used to study these interactions in the 

western United States. 

As described in chapter 2, the Rio Grande is a narrow 

ribbon of water flowing through the parched New Mexico 

landscape. The prosperity of the region has depended on the 

Rio Grande since prehistoric times. Current demands on the 

river have become so severe that citizens of New Mexico are 

considering their long ignored rights to the Colorado River.

The alluvial aquifer beneath the Russian River in northern California is the primary source of water for residents of 

Sonoma and northern Marin Counties (chapter 3). Three fish 

species are currently listed as endangered, so impacts of waterresources utilization must be carefully monitored (see fig. 5). 

The Santa Clara River in southern California is the last 

natural stream in Los Angeles County (chapter 4). Maintenance of a healthy river depends intimately on the inter-connectivity of the stream with the adjacent flood plain, which 

broadens westward from the base of the San Gabriel Mountains towards the Pacific Ocean. 

Tributaries of the Willamette River south of Portland, 

Oregon, represent spawning habitats for a number of endangered and seagoing fish species. Agriculture in the Willamette 

Valley has shifted from non-irrigated grains to irrigated 

orchards, vineyards, and other crops (chapter 5). Changes 

in stream-water temperature and availability associated with 

3

5

7

9

11

13

15

TEMPERATURE, IN DEGREES CELESIUS

8 12 16 20 24

DEPTH, IN

METER

S

Data

Optimal fit

Khyd=1 order lower

Khyd=1 order higher

Reversed gradient
6 Heat as a tool for studying the movement of ground water near streams

ground-water extraction affect fish populations. Recognition 

of these effects has placed new emphasis on quantifying the 

impacts of irrigation withdrawals on fish habitats. 

 Trout Creek, California, flows into the southern end of 

Lake Tahoe, presenting the opportunity to study how stream 

interactions with ground water are affected by a lake (chapter 

6). The exchanges between Trout Creek and shallow ground 

water are strongly affected by lake level. Seasonally rising and 

falling lake levels create a drastic change in streambed thermal 

patterns that, in turn, affect stream ecology. 

Rillito Creek flows through Tucson, Arizona, providing a main source of recharge to the underlying ground-water 

system. Where and when recharge occurs beneath this rapidly 

growing city is an important uncertainty that affects the 

region’s urban planning (chapter 7). 

Trout Creek in central Nevada is a small stream that 

flows down the north side of Battle Mountain (chapter 8). The 

stream is typical of thousands of similar streams throughout 

the vast basin and range province. Trout Creek provides an 

excellent example for exploring the cumulative importance of 

mountain-front streams in providing recharge to regional aquifers. An understanding of mountain-front recharge is essential 

for managing water resources in rugged deserts throughout the 

world. 

As a set, these chapters provide a detailed assessment of 

interactions between surface water and ground water, using 

temperature patterns and their interpretation as a hydrologic 

tool. They also show the manner in which this information 

may be used to better understand and manage biological and 

water resources.

Figure 5. Pontoon rafts with fish counting wheels operating 

along the Russian River in coastal northern California. Particular attention to fishery habitat is needed when ground water is 

pumped near streams.
Introduction

The Middle Rio Grande Basin covers approximately 

7,900 square kilometers in central New Mexico, encompassing parts of Santa Fe, Sandoval, Bernalillo, Valencia, Socorro, 

Torrance, and Cibola Counties (“Middle Rio Grande Basin” 

here refers to the geologic basin defined by the extent of 

deposits of Cenozoic age along the Rio Grande from about 

Cochiti Dam to about San Acacia). The basin lies in an 

asymmetric elongated valley along the Rio Grande. The 

basin encompasses the inner valley, or floodplain, of the Rio 

Grande and the surrounding terrain that slopes from surfacedrainage divides toward the river. As in the rest of the Southwest, the area has grown rapidly since the Second World 

War; in 2000, the population of the Middle Rio Grande Basin 

was about 690,000, or about 38 percent of the population of 

New Mexico (Bartolino and Cole, 2002).

At the current time (2003), essentially the entire population of the basin depends on ground water from the Santa Fe 

Group aquifer system for their domestic-supply needs. This 

dependence on ground water, coupled with rapid growth, has 

led to ground-water-level declines of over 50 meters beneath 

parts of Albuquerque. Because the interaction between the 

Rio Grande and the aquifer system has long been recognized 

by the New Mexico Office of the State Engineer (NMOSE), 

regulations require major ground-water producers to obtain 

surface-water rights to compensate for streamflow depletion caused by ground-water pumping. The largest user of 

ground water in the Middle Rio Grande Basin is the City of 

Albuquerque and since the 1960s, its water plan has consisted 

of meeting water demand solely by production from ground 

water. The scientific understanding of the hydrogeology of 

the Middle Rio Grande Basin at that time suggested that 

seepage from the Rio Grande replenished the water in the 

aquifer withdrawn by pumping. Starting in 1995, a revised 

understanding of the hydrogeology of the basin suggested 

that the connection between the Rio Grande and Santa Fe 

Group aquifer system allowed less ground-water recharge 

than previously thought (Bartolino and Cole, 2002).

In 1995, the NMOSE declared the Middle Rio Grande 

Basin a “critical basin”; that is, a ground-water basin faced 

with rapid economic and population growth for which there 

is less than adequate technical information about the available water supply. Though the basin had been intensively 

studied for a number of years, important gaps remained in the 

understanding of the water resources of the basin. In an effort 

to fill some of these gaps, the U.S. Geological Survey (USGS) 

and other Federal, State, and local agencies conducted an 

intensive effort to improve the understanding of the hydrology, 

geology, and land-surface characteristics of the Middle Rio 

Grande Basin (Bartolino and Cole, 2002). 

Chapter 2

The Rio Grande—competing demands for a desert river

James R. Bartolino

200 MILES

0 100 200 300

0 100

400 KILOMETERS

38

36

34

32

108 106 104

UTA

H

COLO

R

A

D

O

COLORADO

NEW MEXICO O

K

NEW MEXICO

TEXAS

A

RIZO

N

A

NEW

MEXICO

NEW

MEXICO

TEX

AS

UNITED STATES

MEXICO

Middle Rio

Grande Basin

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Elephant Butte Reservoir

Heron Reservoir

El Vado Reservoir

Abiquiu Reservoir

Cochiti Lake

Elephant Butte Dam

Caballo Reservoir

Rio Grande

Grande Rio

Las Cruces

El Paso

Socorro

Albuquerque

Santa Fe

Santa Fe River

EXPLANATION

Rift basin

Figure 1. Location of the Middle Rio Grande Basin.
8 Heat as a tool for studying the movement of ground water near streams 

One of the most important gaps in the understanding 

of the hydrology of the Middle Rio Grande Basin is the rate 

at which water from the Rio Grande recharges the Santa Fe 

Group aquifer system. This question is important because 

ground-water pumping for municipal supplies depletes flow. 

In addition, the City of Albuquerque is pursuing plans for 

direct use of their San Juan Chama Project water (a transmountain diversion of Colorado River basin water into the Rio 

Grande basin upstream from the city) (City of Albuquerque 

Public Works Department, 1997). Currently (2003), competing 

demands for river water include agricultural irrigation, endangered species, Rio Grande Compact obligations, and planned 

direct use of surface water for municipal supplies. An understanding of the complex interactions between the surface- and 

ground-water systems is necessary for water-resource managers to make scientifically based management decisions.

The Middle Rio Grande Basin

The most prominent hydrologic feature in the Middle Rio 

Grande Basin is the Rio Grande, which flows through the entire 

length of the basin, generally from north to south. Though flow in 

the Rio Grande is currently (2003) regulated by a series of dams 

and storage reservoirs, the greatest flows tend to occur in late 

spring as a result of snow melt, and for shorter periods during the 

summer in response to rainfall. Historically, the Rio Grande has 

flowed year-round through much of the basin, “except for those 

periods of severe, extended drought” (Scurlock, 1998).

The inner valley of the Rio Grande contains a complex network of irrigation canals, ditches, and drains that has evolved 

from the original acequia system. The Middle Rio Grande 

Conservancy District administers this irrigation system and 

diverts Rio Grande water at four points in the basin: Cochiti 

Dam, Angostura (near Algodones), Isleta, and San Acacia 

(which serves an irrigation area downstream of the basin). During the irrigation season, water is diverted from the river and 

flows through the Rio Grande inner valley in a series of irrigation canals and smaller ditches for application to fields. This 

water either recharges to ground water, is lost to evaporation or 

evapotranspiration by plants, or is intercepted by interior drains 

and returned to the river (Bullard and Wells, 1992; Kernodle, 

McAda, and Thorn, 1995; Anderholm, 1997).

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Figure 2. Locations of study sites in the 

Middle Rio Grande Basin at which temperature methods have been used.
The Rio Grande—Competing demands for a desert river 9

The other main component of the inner-valley surfacewater system is a system of riverside drains, which are deep 

canals that parallel the river immediately outside the levees. 

They are designed to intercept lateral ground-water flow from 

the river, thus preventing waterlogged conditions in the inner 

valley. The riverside drains then carry this intercepted lateral 

ground-water flow back to the Rio Grande. Within the basin, 

riverside drains and levees are usually present on both banks 

of the river, except where bluffs adjoin the river.

The riparian vegetation of the bosque has evolved significantly in the last 100 years as a result of the introduction of 

exotic species and the construction of flood-control and bankstabilization projects. During the last 60 years, the bosque has 

developed in an area that was formerly semi-barren floodplain. 

It is probable that more water is required to maintain the dense 

vegetation of the bosque today than was required for the isolated stands of cottonwood and willow that existed in the past. 

Water movement between the river and aquifer

Several methodologies, including use of the GloverBalmer equation, flood pulses, and channel permeameters, 

have been used to quantify the amount and rate at which water 

moves between the Rio Grande and the Santa Fe Group aquifer system, with sometimes conflicting results. The reader is 

referred to Bartolino (2002) for a discussion of these studies.

 The work described in this chapter uses both groundand surface-water temperatures and water levels to quantify 

the direction and rate of ground-water flux between the river 

and underlying aquifer and to estimate the effective hydraulic 

conductivity values of the sediments underlying and adjoining 

the river. Data collected in the field will be interpreted with 

the use of numerical simulation in order to obtain flux and 

hydraulic conductivity values (see Appendix B).

Other temperature work in the Middle Rio Grande 

Temperature has been used by several authors to quantify 

the amount and direction of water moving between the surfaceand ground-water regimes in the Middle Rio Grande Basin 

along perennial reaches of the Santa Fe River, Tijeras Arroyo, 

and the Rio Grande (fig. 2) (Bartolino and Constantz, 2002). 

However, the use of water temperature as a tracer was expanded 

into the realm of ephemeral streams at both Bear Canyon and 

Abo Arroyo (fig. 2) in order to determine the downward movement of water and the downstream extent of flow in the arroyos 

(Bartolino and Constantz, 2002). (See Constantz and Thomas, 

1996; Thomas, Stewart, and Constantz, 2000; Niswonger and 

Constantz, 2001; Stewart and Constantz, 2001.)

One-dimensional approach

In the first phase of this study, as described in Bartolino 

and Niswonger (1999), seven sets of nested piezometers were 

installed during July and August 1996 at four sites along the 

Rio Grande in the Albuquerque area (fig. 2), though only four 

of the piezometer nests were simulated one-dimensionally. In 

downstream order, these four sites are (1) the Bernalillo site, 

upstream from the U.S. Highway 550 bridge in Bernalillo; (2) 

the Corrales site, upstream from the Rio Rancho sewage treatment plant in Rio Rancho; (3) the Paseo del Norte site, upstream 

from the Paseo del Norte bridge in Albuquerque; and (4) the 

Rio Bravo site, upstream from the Rio Bravo bridge in Albuquerque. All piezometers were completed in the inner-valley 

alluvium of the Santa Fe Group aquifer system. Ground-water 

levels and temperatures were measured a total of six times in 

the four piezometer nests from September 1996 through August 

1998. Ground-water temperatures from one of these phase one 

piezometers at the Paseo del Norte site are shown in figure 3.

A total of four one-dimensional numerical models of 

heat and water transport in the subsurface were constructed 

to simulate the field setting for each piezometer nest (see 

Appendix B). Comparison of the simulated vertical fluxes 

and estimated vertical hydraulic-conductivity values from 

this study with values from other investigations in the Middle 

Rio Grande Basin indicated broad agreement (Bartolino and 

Niswonger, 1999). 

Figure 3. Ground-water temperatures at selected times from 

September 1996 to August 1998 during the first phase of the 

study in the PDN01 piezometer. This piezometer is at the Paseo 

del Norte site and was used only during the first phase of the 

study.

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10 Heat as a tool for studying the movement of ground water near streams 

Table 1. Description of 

piezometers installed and 

monitored for this study 

[m, meters; S, shallow; M, 

medium; D, deep]

Two-dimensional approach

Despite the general success of the one-dimensional 

approach to simulate vertical flux and estimate hydraulic 

conductivity, it was hypothesized that the three sites near 

riverside drains (with the exception of the Corrales site) had 

a significant component of horizontal flow. In addition, if the 

drains intercepted a large proportion of the water infiltrated 

from the Rio Grande, the volume of ground-water recharge 

from the river to the Santa Fe Group aquifer system could be 

overestimated. With these limitations in mind, a second study 

phase was planned with three major differences: one site would 

be examined in much greater detail using a cross-sectional 

approach; temperature data would be collected at fewer depths 

in a selected well, but with much greater temporal resolution; 

and more data would be collected on boundary conditions, such 

as river stage and water temperature in the drains and river.

Piezometer

nest

 Location Altitude of land

surface (m

above sea level)

PiezometerPiezometer

depth (m)

Temperature

logger

Temperature

logger depth

(m)

P01 1,518.55 S 3.0 A 2

M 7.6 B 4

D 12.2 C 6

D 8

East bank of the

Corrales Riverside

Drain

E 12

P02 1,519.55 S 4.0 A 3

M 7.6 B 4.5

D 12.2 C 6

D 8

Midway between the

Corrales Riverside

Drain and west bank

of the Rio Grande

E 12

P03 1,518.93 S 2.1 A 1.5

M 6.7 B 3

D 12.2 C 5

D 8

West bank of the Rio

Grande at high flow

E 12

P04 1,518.77 S 2.1 A 1.5

M 6.7 B 3

D 11.3 C 4.5

D 7

Sandbar in the Rio

Grande

E 11

P05 1,518.41 S 2.1 A 1.5

M 7.6 B 3

D 11.3 C 4.5

D 7

Sandbar in the Rio

Grande, west bank of

the Rio Grande at low

flow

E 11

P06 1,519.43 S 2.4 A 2

M 6.1 B 4

D 12.2 C 6

D 8

East bank of the Rio

Grande

E 12

P07 1,519.32 S 4.9 A 3

M 6.7 B 4.5

D 12.2 C 6

D 8

Midway between the

the east bank of the

Rio Grande and the

Albuquerque

Riverside Drain

E 12

P08 1,518.39 S 4.0 A 3

M 6.7 B 4.5

D 12.2 C 6

D 8

West bank of the

Albuquerque

Riverside Drain

E 10

Site instrumentation and data collection

Eight sets of nested piezometers were installed from January-March 1999 on the north side of the Paseo del Norte bridge 
The Rio Grande—Competing demands for a desert river 11

Figure 4. The Paseo del Norte bridge study site.

over the Rio Grande in Albuquerque (fig. 4). The piezometer 

nests were installed from the east bank of the Corrales Riverside drain (P01), across the Rio Grande, to the west bank of the 

Albuquerque Riverside drain (P08). Three piezometers were 

installed in each nest at depths ranging from 2.1 to 12.2 m, and 

all piezometers were completed in the inner-valley alluvium of 

the Santa Fe Group aquifer system. Piezometer locations and 

depths are shown in table 1. A core was collected and piezometers were installed at each location using a Geoprobe soil-probing machine, model 8-MU, which is a truck-mounted hydraulic 

ram/percussion hammer that uses 2.5-cm diameter drill rod.

Ground-water temperatures were measured with singlechannel temperature loggers (as described in appendix A). These 

devices were suspended at five selected depths in the deep 

piezometer in each of the eight piezometer nests. Ground-water 

temperatures were measured and recorded at 1-hour intervals 

from March 1999 to July 2000. The reader is referred to Appendix A for additional information on temperature measurement.

Additional temperature loggers were installed at two 

locations in each of the surface water bodies at the site: the 

Corrales Riverside drain, the Rio Grande, and the Albuquerque 

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12 Heat as a tool for studying the movement of ground water near streams 

Figure 5. Thermographs showing water temperature in the Rio Grande and piezometer nests at the Paseo del Norte site. 

See figure 4 and table 1 for location and depth of the temperature measurements.

01 Mar 99 19 Apr 99 07 Jun 99 26 Jul 99 13 Sep 99 01 Nov 99 20 Dec 99 07 Feb 00 27 Mar 00 15 May 00 03 Jul 00

EXPLANATION

Surface water Piezometer nests

Rio Grande

Corrales Riverside Drain

Albuquerque Riverside Drain

Temperature logger A

Temperature logger B

Temperature logger C

Temperature logger D

Temperature logger E

Surface water

Water temperature, in degrees Celsius

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

P08

P07

P06

P05

P04

P03

P02

P01
The Rio Grande—Competing demands for a desert river 13

Field observations

Site characteristics

Conditions at the Paseo del Norte site are typical for 

much of the Rio Grande in the Middle Rio Grande Basin. The 

channel of the Rio Grande is braided, though the east bank has 

been stabilized by the installation of Kellner jetties. Levees are 

present on both sides of the river, with typical bosque vegetation (tamarisk, Russian olive, desert willow, and cottonwood) 

growing in the area between the river banks and levees. 

Outside the levees are riverside drains (Corrales on the west, 

Albuquerque on the east) installed to prevent waterlogging in 

the inner valley.

The closest long-term gaging station to the Paseo del 

Norte site is approximately 13 kilometers downstream at 

the Central Avenue bridge (Rio Grande at Albuquerque, 

08330000). From 1974 (when Cochiti Lake began filling) to 

2001, flow in the Rio Grande typically peaked in response to 

spring snowmelt and in response to summer thunderstorms.

During most of the year, Rio Grande flow at the Paseo del 

Norte site is confined to the main channel, defined as the area 

between piezometer nests P05 and P06. At river stages greater 

than approximately 1,520 m, there is also flow in the channel 

between P03 and P04. At stages greater than approximately 

1,521 m, the sandbar on which P04 and P05 are installed is 

completely submerged.

Temperature

Daily average water-temperature data for all measurement points are shown in figure 5. Several features of the data 

are readily apparent. First, there is typical large variability 

apparent in the surface-water temperature measurements ranging from 3°C in the winter to 26°C in the summer. Second, the 

maximum and minimum water-temperature measurements in 

each piezometer nest shift with increasing depth. Third, with 

increasing depth, the measurements in each piezometer nest 

have less range and variability in water-temperature than shallower measurements.

Water levels

Water-level data for the Paseo del Norte site are shown 

in figure 6. A good correlation exists between river stage 

and ground-water levels in the piezometer nests. In addition, 

ground-water levels decrease away from the river confirming that water flows away from the river toward the riverside 

drains. The hydrographs in figure 6 indicate there was little 

vertical movement of ground water during most measurement 

times at the eight nests.

Lithology

As mentioned previously, continuous core was collected at each piezometer nest. These cores were visually 

described and detailed lithologic descriptions were developed for each nest. However, for the purpose of developing 

a numerical ground-water model of the site, these detailed 

lithologic descriptions were grouped into one of the two main 

depositional/lithologic classes of the inner valley alluvium: 

poorly sorted, generally coarse-grained main channel deposits consisting primarily of sand and gravel, and well sorted, 

generally fine-grained overbank deposits consisting primarily 

of clay, silt, and fine sand.

Discussion

The riverside drains were constructed to intercept shallow 

ground-water flow originating in the river, a process confirmed by water-level data. Thus, water temperatures should 

reflect this movement of water from the river to the riverside 

drains—as is shown in a subset of the data showing water 

temperature in the Rio Grande and in ground water at the 6-

meter depth in the P06, P07, and P08 piezometer nests on the 

east side of the river (fig. 7). The P06 piezometer nest is on the 

east bank of the Rio Grande and consequently the approximate 

high and low temperatures in the piezometer (shown by red 

and blue arrows, respectively) occurred roughly at the same 

time as in the river. Approximately halfway between the river 

and Albuquerque riverside drain in piezometer nest P07 (146 

m from the river), the ground-water maximum and minimum 

temperatures lag approximately 10 weeks. In addition the temperatures show less short- and long-term variation than in the 

Rio Grande or P06. Finally, in piezometer nest P08 located on 

the west bank of the Albuquerque riverside drain (139 m from 

P07), ground-water maximum and minimum temperatures 

lag approximately 13 weeks from P07 and water temperature 

shows increased damping.

Due to the physical properties of heat, it is not possible to 

treat heat as a conservative tracer and simply estimate hydraulic-conductivity values using the Darcy equation because 

such properties as dispersivity, thermal conductivity, and heat 

capacity must be considered. 

Riverside drain. Surface-water temperatures were measured 

and recorded at 1-hour intervals from March 1999 to July 2000.

Ground-water levels were measured in each piezometer at 

approximately 2-week intervals from March 1999 to July 2000, 

with the exception of P04 and P05. Because of their location on 

a sandbar in the channel, these piezometer nests were submerged during high flows in the Rio Grande. Thus, water levels 

were not measured one time in P04, and five times in P05.

An inactive USGS streamflow-gaging station (Rio 

Grande near Alameda, New Mexico; 08329928) was reactivated for the study. River-stage data were collected at 15-

minute intervals from March 1999 to July 2000. Based on 

measurements conducted during the survey of the site and the 

difficulty and expense of instrumenting the drains to collect 

water levels, water levels in the Corrales and Albuquerque Riverside drains were assumed to be equal to the water levels in 

the shallow piezometers in the P01 and P08 nests, respectively. 
14 Heat as a tool for studying the movement of ground water near streams 

Figure 6. Hydrographs showing stage of the Rio Grande and water levels in the piezometer nests at the Paseo del Norte site.

Shallow peizometer, S

Medium piezometer, M

Deep piezometer, D

Water level, in meters above N

A

V

D 88 Stage 1,517

1,518

1,519

1,518

1,519

1,520

1,519

1,520

1,521

1,519

1,520

1,521

1,519

1,520

1,521

1,519

1,520

1,521

1,519

1,520

1,521

1,518

1,519

1,520

1,519

1,520

1,521

01 Mar 99 19 Apr 99 07 Jun 99 26 Jul 99 13 Sep 99 01 Nov 99 20 Dec 99 07 Feb 00 27 Mar 00 15 May 00 03 Jul 00

P08

P07

P06

P05

P04

P03

P02

P01

Rio Grande near Alameda gaging station (08329928)

EXPLANATION

Piezometers
The Rio Grande—Competing demands for a desert river 15

Figure 7. Thermographs showing water temperature in the Rio Grande and at 6 meter depth in the P06, P07, and P08 

piezometer nests.

P08C - 6meters

01 Mar 99 19 Apr 99 07 Jun 99 26 Jul 99 13 Sep 99 01 Nov 99 20 Dec 99 07 Feb 00 27 Mar 00 15 May 00 03 Jul 00

0

8

16

24

0

8

16

24

0

8

16

24

0

8

16

24

Water temperature, in degrees Celsius

Temperature

logger

EXPLANATION

Piezometers

Rio Grande

Surface water

Rio Grande

P06C - 6meters

P07C - 6meters

P08S - 4.0 meters

01 Mar 99 19 Apr 99 07 Jun 99 26 Jul 99 13 Sep 99 01 Nov 99 20 Dec 99 07 Feb 00 27 Mar 00 15 May 00 03 Jul 00

1,517

1,518

1,519

Water level, in meters above N

A

V

D 88 Stage

Rio Grande near Alameda gaging station (08329928)

P06S - 2.4 meters

P07S - 4.9 meters

1,518

1,519

1,520

1,519

1,520

1,521

1,519

1,520

1,521

Figure 8. Hydrographs showing stage of the Rio Grande and water levels in the shallow piezometer in the P06, P07, 

and P08 piezometer nests.
16 Heat as a tool for studying the movement of ground water near streams

Figure 9. The Rio Grande at Paseo del Norte in northern Albuquerque with three piezometers in the foreground used to monitor 

shallow, intermediate, and deeper water-levels and temperatures.

Figure 10. Riverside drains form part of a complex irrigation network that is intimately linked with the Rio Grande and underlying 

Santa Fe Group aquifer system.

Summary and Conclusions

One of the most important gaps in the understanding 

of the hydrology of the Middle Rio Grande Basin is the rate 

at which water from the Rio Grande recharges the Santa Fe 

Group aquifer system. This question is important because 

ground-water pumping for municipal supplies depletes flow in 

the river. Currently (2003), competing demands for river water 

include agricultural irrigation, endangered species, Rio Grande 

Compact obligations, and planned direct use of surface water 

for municipal supplies. An understanding of the complex 

interactions between the surface- and ground-water systems is 

necessary for water-resource managers to make scientifically 

based management decisions.

Several methodologies, including use of the GloverBalmer equation, flood pulses, and channel permeameters, 

have been applied to this problem in the Middle Rio Grande 

Basin. In this study, ground- and surface-water temperatures 

and water levels at a site at the Paseo del Norte bridge on 

the Rio Grande were measured (fig. 9). Initial analysis of the 

data indicates the conceptual validity of the water-temperature method. Further analysis will utilize a two-dimensional 

numerical ground-water model of the site and will yield the 

direction and rate of ground-water flux between the river, 

riverside drains (fig. 10), and underlying aquifer, as well as 

the effective hydraulic-conductivity values of the sediments 

underlying the river.

Water-level data for the Rio Grande and shallow piezometer in the P06, P07, and P08 piezometer nests are shown in 

figure 8. Correspondence between river stage and groundwater level is good in P06, in P07 the shape of the hydrograph 

is barely discernible, and there is no apparent correlation in 

P08. In addition, water-level changes in the piezometers do 

not appear to lag behind changes in the river stage as significantly as temperature, and water levels also decrease away 

from the river.

A similar analysis of ground-water temperatures on the 

west bank of the Rio Grande (piezometer nests P01-P05) 

shows a similar, though more complex pattern. The increased 

complexity is due to the more gradual slope of the west bank 

of the Rio Grande. As discussed previously, the west edge of 

water ranges between P03 and P05, depending on river stage. 

Thus, at low stages, P05 is at the west edge of water and 

its water temperatures mimic that of surface water. At high 

stages, water temperatures in P03, P04, and P05 all mimic 

surface-water temperature. Therefore, the thermographs for 

the west bank are more complex than those for the east bank, 

yet still indicate the seasonal movement of temperature. 
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Figure 1. Regional view of the Russian River as it flows south 

from Mendocino County to Sonoma County, with a box demarcating the river reach where the present study is located. [Note the 

location of the San Andreas Fault demarked by the long, narrow 

bay in western Marin County. Along the plate boundary, the flow of 

coastal streams have been sharply redirected by the northern slip 

of the Pacific Plate as it passed the North American Plate.]

Chapter 3

Heat tracing in the streambed along the Russian River of 

northern California

Jim Constantz, James Jasperse1, Donald Seymour1, and Grace W. Su2

Introduction

The Russian River flows south from headwaters in 

Northern California through Mendocino County into Sonoma 

County, as shown in figure 1. About 100 km north of the 

Golden Gate Bridge, active plate tectonics force the river 

to the west upon reaching the Santa Rosa Plain. The plain 

overlies a large alluvial ground-water basin, representing the 

primary source of water resources for Sonoma and northern Marin Counties. A variety of activities place increased 

demands on the water resources available beneath the Santa 

Rosa Plain. This landscape, which once featured oak studded hills with grazing cattle and vast apple orchards stretching across the lowlands, is rapidly following the course of 

neighboring Napa Valley to the east as an internationally 

renowned wine-producing region. Vineyard acreage is rapidly 

increasing in Sonoma and Mendocino Counties on either side 

of the Russian River. Vineyards require additional irrigation 

water compared with grazing land and apple orchards, and the 

attractiveness of both the river and burgeoning wineries have 

created rapid population growth and increased recreational 

activities during the long, hot, dry summer season. Concurrent 

with these activities, several seagoing fish species migrate up 

the Russian River toward the headwater in Mendocino County 

during the dry season. This complex environment mandates 

that regional water resources be managed to minimize the 

impacts of our activities on the fishery habitat as the river 

passes through the Santa Rosa Plain.

1

 Sonoma County Water Agency, Santa Rosa, CA 95406

2

 Lawrence Berkeley National Laboratory, Berkeley, CA 94720
Figure 2. A recharge pond constructed between the Russian 

River and Westside Road. Power poles extending from supply 

wells through the ponds toward the road provide scale. Each 

recharge pond is operated through a cycle in which river water is 

diverted to the pond for a week or so, then the pond is allowed to 

go dry for as long as a month to retard the buildup of a clogging 

algal mat on the pond bottom.

Figure 3. Inflatable dams are constructed of thick rubber for inflation with water for seasonal operation. This inflatable dam has 

fish ladders on either side to aid in fish migration that may occur 

during the seasonal operation of the dam. Portage for canoes and 

other small boats is initiated upstream of white float line.

18 Heat as a tool for studying the movement of ground water near streams 

Managing the river as a water resource

Water from the Russian River exchanges freely with 

the vast alluvial aquifer beneath the Santa Rosa Plain, due 

to coarse gravel deposits prevalent throughout the western 

portion of the basin. Since the middle of the last century, 

residents of Sonoma County have depended on water within 

these coarse sediments for municipal water supply, rather than 

diverting water directly from the river. This is because river 

water requires extensive treatment to remove dissolved materials and suspended sediments, while water extracted from the 

alluvial aquifer sediments is naturally filtered and requires no 

additional treatment beyond chlorination and possibly a pH 

adjustment prior to transmission to the distribution system. 

Traditionally, the water quality has been excellent though 

the water quantity is of periodic concern. The ability of the 

alluvial aquifer to produce water in necessary quantities is 

generally limited by the rate of recharge to the aquifer through 

the streambed. To augment this rate of recharge, infiltration 

ponds were developed along the river around 1960 to enhance 

recharge to the western edge of the Santa Rosa Plain (fig. 2). 

At a location in the river near the recharge ponds, an inflatable rubber dam was constructed to raise the river stage 3 m 

during the summer (fig. 3). The stage increase allows river 

water to be more readily diverted into the recharge ponds, and 

the resulting upstream backwater causes passive recharge of 

the alluvial sediments along the entire extent of the backwater. 

Thus, the water table is raised 3 m in several square kilometers 

of alluvial sediments on either side of the river. Typically, 

the dam is inflated in the spring as water demands increase 

and streamflows decline, then lowered in the late fall as water 

demands decrease and streamflows increase. Typically, water 

production from five supply wells located in the western portion of the Santa Rosa Plain is reduced by one-half when the 

dam and recharge ponds are taken out of operation in the late 

fall. Emerging water resources issues, including fish habitat 

concerns and optimization of water resources management, 

indicate that a quantitative model should be developed to 

accurately represent river exchanges with water in the alluvial 

aquifer in the region of the watershed encompassing the inflatable dam. Improved scheduling of dam and recharge pond 

operations, as well as supply well pumping patterns would be 

benefited by the development of a proven ground-water model 

for this region of the watershed. 

Successful development of a ground-water model 

requires that key hydraulic parameters are determined for 

the streambed materials along the reach of the river flowing 

through the Santa Rosa Plain. Of prime importance is the careful characterization of the spatial and temporal value of the 

streambed conductance, which is determined by knowing both 

the streambed conductivity at a location along the river and 

the thickness of the streambed at this same location. Several 

tools are available to estimate these two hydraulic parameters, 

such as pumping tests and chemical tracers. Some pumping 

tests have been performed for specific locations; however, 

introduced chemical tracers are not an option for the Russian 

River, due to environmental and esthetic concerns along this 

scenic reach of the river (fig. 4). Fortunately, naturally occurring 

variations in water temperatures in the Russian River provide 

the necessary boundary conditions to use heat as a natural tracer 

of stream exchanges with water in the alluvial aquifer.
Heat Tracing in the Streambed along the Russian River of Northern California 19

Figure 4. Looking upstream along the Russian River from the Wohler Bridge in April. The inflatable 

dam, 500 m downstream of the bridge, is usually inflated in May, so that the stage of the river is low 

in April with bare stream banks exposed on either side of the river. Two supply wells adjacent to 

the river are visible on the bank. These wells pump water from the alluvium at a depth of about 20 m 

below the bottom of the streambed.

Measuring hydraulic conductivities in the 

streambed

Research is ongoing along the Russian River to determine the streambed hydraulic parameters, with an array of 

promising results now available. For analysis of heat as an 

environmental tracer of ground-water movement, a series 

of observation wells were instrumented for water levels and 

ground-water temperatures for comparison with river stage 

and surface-water temperatures. Observed temperatures are 

being used to optimize simulated temperatures from VS2DH 

(Appendix B), for predicting the hydraulic conductivity at 

specific locations along this reach of the river. As an example, 

figure 5 portrays the cross-section of the Russian River at well 

location TW-01, along with the location of the temperature 

measurement in the screen interval of the observation well 

near the river. Figure 6 compares the ‘best-fitting’ simulated 

ground-water temperatures with observed temperatures. Based 

on similar fits, a narrow range of predicted hydraulic conductivities was derived from the different observation wells. 

Hydraulic conductivity values and hydraulic gradients based 

on stage differences between the river and the observation well 

provide estimates of fluxes through the sediments near the 

river. Figure 7 gives examples of poor fits, graphically demonstrating the sensitivity of sediment temperatures to changes in 

water flux through the sediments. This sensitivity is a primary 

reason why the use of heat as a tracer of stream exchanges 

with the underlying streambed is emerging as a powerful 

hydrological tool for better understanding water and nutrient 

movement in the streambed. Once a good fit is determined 

using VS2DH for each observed well, a hydraulic conductance 

value may be assigned for that streambed section of the study 

reach. All together this hydraulic information gives a quantitative representation of the variation in streambed conductance 

along the entire reach of the river flowing through the western 

portion of the Santa Rosa Plain.

Using knowledge to move forward

The water resource challenges in the Santa Rosa Plain are 

becoming common throughout coastal areas, where conjunctive use of streams and ground-water may conflict with the 

Figure 5. River cross-section used in the two-dimensional 

computer simulation model. The observation point where 

water-level and water temperature are monitored in the observation well is shown at the appropriate location in the river 

bank. (See Appendix A for a discussion of measurement methods.) Numerous observation wells are located along the river 

in the Santa Rosa Plain to measure differences in streambed 

hydraulic conductivity throughout the river reach.
Wohler Well TW-01: Best Fit

10

12

14

16

18

20

22

24

6/3/00 6/23/00 7/13/00 8/2/00 8/22/00 9/11/00 10/1/00 10/21/00 11/10/00

Date

Temperature (oC)

observed

predicted, K = 2.0 x 10-4 m/s

Wohler Well TW-01: Examples of Poor Fits

10

12

14

16

18

20

22

24

6/3/00 6/23/00 7/13/00 8/2/00 8/22/00 9/11/00 10/1/00 10/21/00 11/10/00

Date

Temperature (oC)

observed

predicted, K = 8.1 x 10-5 m/s

predicted, K = 1.2 x 10-3 m/s

20 Heat as a tool for studying the movement of ground water near streams

Figure 6. The observed sediment temperature over the season measured at the observation point in 

the well is compared with the ‘best-fit’ simulated sediment temperature, when a hydraulic conductivity value of 2.0 x 10-4 m/s (0.0002 m/s) was used in the simulation model. This hydraulic conductivity 

estimate can be multiplied by the known difference in water levels between the river and the well to 

determine the rate at which water moves through the alluvium from the river toward the observation 

well. (See Appendix B for a detailed discussion.)

Figure 7. The observed sediment temperature over the season measured at the observation point in 

the well is compared with poor-fits of simulated sediment temperature. The predicted sediment temperature at the observation well is strongly affected by computer-simulated estimates for the hydraulic 

conductivity. The fact that the sediment temperature is so sensitive to hydraulic parameters makes 

the use of heat as tracer a very visual and potentially useful tool for determining the rate of exchange 

of water between the river and the alluvium underlying the western region of the Santa Rosa Plain.

fishery habitat requirements. Thus, successful use of heat as 

tracer to aid in understanding movement of water between the 

Russian River and the alluvium underlying the Santa Rosa 

Plain may have great transfer value to other coastal watersheds. Along the Russian River, continuous monitoring of 

stream and streambed temperatures provide the opportunity 

to develop a detailed pattern of temporal and spatial variations in streambed conductance for the reach encompassed by 

the series of observation wells. Detailed hydraulic information acquired along the river provides input for constructing 

a physically-based, ground-water flow model. As shown in 

figures 6 and 7, predicted hydraulic conductivities can be order 

of magnitude different than the best estimates using heat as a 

tracer. Good estimates of streambed hydraulic conductivities 

are essential input into a simulation model used for representing physical flow processes between the river’s streambed. 

Computer simulation models with well characterized hydraulic 

parameters are useful in predicting the impacts of a range of 

possible scenarios, affording the opportunity to use these as a 

tool for improved management of water resources adjacent to 

the Russian River
Introduction

The West has gone through a period of rapid growth since 

the middle of the last century, and nowhere is this expansion 

more apparent than Southern California. Today, the Santa 

Clara River in northwest Los Angeles County is the only 

remaining natural river carrying water to the Pacific Ocean 

(fig. 1). Other major streams reaching the Pacific are extensively channelized and lined with impermeable material, such 

as concrete, along much of their lowland reaches, so that the 

opportunity for stream water exchanges with ground water are 

severely curtailed. As a consequence, the Santa Clara River 

represents a unique remnant of the natural coastal hydrological cycle in this vast epicenter of Southern California. As 

shown in figure 2, the river emanates from headwaters on the 

western flank of the San Gabriel Mountains near an elevation 

of 1,200 meters, then flows in a westerly direction for nearly 

50 km, before discharging into a coastal estuary in Ventura 

County. At the base of the San Gabriels, the river meanders 

through a gradually broadening valley at an elevation of 400 

meters. In this reach (or section) of the river, the youthful city 

of Santa Clarita spreads along both banks, where the Valencia 

and Saugus water reclamation plants discharge wastewaters to 

the river. Like most streams in the Southwest, without effluent 

from water reclamation plants, the river would be ephemeral 

(that is, rarely contains streamflow) in this reach in a similar fashion to the dry reach to the west. In eastern Ventura 

County, the Santa Clara River is joined by Piru Creek from the 

north, which is perennial as a result of an upstream reservoir. 

Downstream of the confluence the Santa Clara River is perennial as it meanders through the bountiful agricultural valley of 

southern Ventura County. 

The reach of the river between the treatment plants and 

the confluence winds through a broad valley with distinctive 

orange groves and other crops, which cover the flood plain 

of northwestern Los Angeles County and southern Ventura 

County. This reach gives one a glimpse back to more pastoral 

times in South California, as the Santa Clara River meanders 

over a sand-channel below cactus rimmed cliffs, giving way 

to green orchards, which radiate up toward arroyo scarred 

mountains. As growth continues, there has been increased 

environmental concerns that continued development may lead 

to increased discharge of effluent, which in turn may degrade 

the water quality not only of this pastoral reach, but of water 

flowing through Ventura County to the Pacific. 

1

 Now with URS Corporation, San Francisco, CA

Chapter 4

The Santa Clara River—the last natural river of Los Angeles

Jim Constantz, Marisa H. Cox, Lisa Sarma1, and Greg Mendez

Figure 1. The Santa Clara River meanders over gravel beds and 

sand bars in its middle reaches. This view is looking upstream.
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22 Heat as a tool for studying the movement of ground water near streams 

The county-line reach may be key to water quality

 As the Santa Clara meanders through the county-line 

reach, extensive opportunity exists for stream water to flow 

into the streambed sediments and adjacent sand bars, and 

either percolate down to the water table or emerge back into 

the river downstream. Figure 3 gives a bar graph of the relative 

gains and losses of water from or to the ground water as the 

river flows through the study reach. This significant exchange 

of stream and ground water results in changes in the downstream chemistry of both stream water and shallow ground 

water, which would not occur if the streambed were lined in a 

similar fashion to other rivers in Los Angeles County. West of 

the county-line reach, the present day river channel has a dry 

reach even with upstream effluent contributing to streamflow, 

and this dry gap flows only during heavy winter rains in the 

San Gabriels to the east. During most of the year, all stream 

water percolates into the streambed before the dry gap, and 

travels beneath the streambed as ground water. As mentioned 

before, the river becomes perennial again at the confluence 

with Piru Creek, and the ground water flowing beneath the 

dry gap is believed to discharge to the river downstream of the 

confluence. The revived river flows into the large agricultural 

valley in southern Ventura County, eventually discharging in 

the estuary near Oxnard. Thus, the amount of natural filtration 

of effluent-dominated stream water is affected by the volume 

of stream water exchanging with ground water upstream of the 

confluence. 

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Figure 2. Relief map of the areas 

of Los Angeles and Ventura Counties containing the Santa Clara River 

watershed. The section of the river 

with the study reach is shown in the 

overlay map, including the locations 

of the Valencia and Saugus water 

treatment plants and the three locations in the river where sampling 

cross-sections were located.

Figure 3. The plot of the change in 

streamflow compared to the immediate upstream location along the study 

reach. The blue bars indicate that the 

river gained streamflow compared with 

the upstream location, while a brown 

bar indicates that the river lost water 

compared with the upstream location.

Field Experiments along the county-line reach 

Direct measurements of the hydraulics controlling this 

interaction represent the first step in defining where, when, 

and under what hydrological conditions these exchanges occur 

along the county-line reach. During the fall of 1999 and the 

spring of 2000, heat was used as a tracer to determine the 

characteristics of stream/ground-water exchanges along the 

reach. The use of heat as a tracer is not intended to determine 

the water quality of ground water near the river, but rather heat 

tracing can determine where and when stream water transports 

chemicals into the ground (or when and where ground water 

transports chemicals into the river). As input data for using 

heat tracing techniques, temperature monitoring equipment 
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The Santa Clara River—The last natural river of Los Angeles 23

Figure 4. The streamflow hydrograph is shown for Water Year 1999 (Oct.98 through 

Sept. 99) at the USGS streamgage located downstream of Site 3 shown in figure 2.

Figure 5. The positioning of a 

series of 6 small piezometers 

and a large piezometer at the 

cross-section sites within the 

study reach.

was deployed in this reach of the Santa Clara River (SCR), 

through placement of equipment in the stream water, within 

underlying streambed sediments, and in nearby sandbars, at 

sites between the water reclamation plants and the terminus of 

streamflow at the upper end of the dry gap. 

The Santa Clara stream hydrograph for the Water Year 

2000 (October 1999 through September 2000) is shown in 

figure 4. The high streamflows of winter are bracketed by 

two extended low flow periods, typical for the Mediterranean 

climate of Central and Southern California. To use heat as a 

tracer of stream/ground-water exchanges, a series of piezometers, or observations wells (consisting of 0.10 meter internal 

diameter pipes) were installed beneath the stream and adjacent 

stream banks of this reach of the Santa Clara River. Figure 

5 gives a typical cross-section containing a set of 6 small 

piezometers and a single large piezometer. Temperature was 

continuously monitored in the stream and all piezometers, to 

examine the interaction of stream and ground water as heat 

was transported across the streambed throughout the reach. 

Figure 6 shows two views of site 5.

As discussed in the first chapter, computer simulation 

codes are essential to fully quantify the degree of exchange of 

stream water with shallow ground water. These heat and water 

transport codes simulate the expected sediment temperature 

resulting from a series of shallow ground-water flow scenarios. The scenario that best describes the observed (measured) 

sediment temperature over time is deemed to be the best representation of the actual shallow ground-water flow characteris-
Figure 6. The left photograph shows Site 5 from the north. The right 

photograph shows a close up of Site 5 with the six small piezometers 

along side the large piezometer, and the step ladder used to aid in 

installation.

24 Heat as a tool for studying the movement of ground water near streams 

tics at that stream site. Figure 7 provides the type of sediment 

temperature patterns that would be predicted from simulation 

codes. In this case, the USGS heat and ground-water transport simulation code, VS2DH, was used to generate thermal 

patterns shown in the figure. In this hypothetical example, 

one can see that cool ground water dominates in the gaining 

simulation of streambed temperature patterns. For the losing 

simulation, the cooler and warmer stream water is transported 

deeply into the underlying sediments during the night and day, 

respectively. Often hypothetical simulations like these are 

used to aid in determining where and how deeply piezometers 

should be installed at a site. In this study, both shallow and 

deeper piezometers where installed to examine the shallow 

and deeper, vertical and horizontal ground-water flow within 

the stream sediments. 

I. Deep streambed piezometers

 Piezometers were installed into the streambed to a depth 

of 2 to 3 meters at Site 3 and Site 5, to examine the deeper 

streambed hydraulics. A temperature-logging device (i.e., electronic equipment that measures temperature at specified time 

intervals and stores this information in memory) was installed 

in the stream around the base of the piezometer and inside the 

piezometer at 0.5, 1.0, and 2.0 meters below the streambed 

surface (see Appendix A for details on the measurement of 

temperatures near streams). Figure 8 provides a visual display 

of the observed transport of heat into the streambed for Site 3 

compared with Site 5. (Note the similarity with figure 7, 

except this figure displays the actual temperature pattern 

observed under the streambed during early October, 1999.) 

One can see that at the upstream site, Site 3, cool predawn 

water and warm afternoon water only slightly penetrated into 

the streambed, due to the low percolation rate of stream water. 

Downstream at Site 5, the rapid percolation of stream water 

carried both cool predawn stream water, and warm afternoon 

stream water below a depth of 2 meters. This thermal information not only helps hydrologists understand the patterns of 

stream exchanges with shallow ground water along the Santa 

Clara River, but is also useful to geochemists and microbiologists interested in the substream thermal environment along 

the river, for determining which microbes and chemical processes may be present in the near-stream ground water.

II. Shallow streambed piezometers

As depicted earlier in figure 5, a series of six shallow 

piezometers were installed at Sites 2, 3, and 5 to examine 

the stream interaction with the shallow streambed and adjacent streambank. Temperature was logged in a similar matter as described for the deeper piezometers, except only a 

single temperature logger was placed at the bottom of each 

small piezometer. Figure 9 shows thermographs (temperature patterns over time) for the piezometers at Sites 2, 3, and 

5. Based on field observations, Site 2 was expected to have 

less exchange between the stream and underlying streambed 

compared with the downstream sites. As shown in the figures, 

a clear difference in the sediment temperature patterns is 

detected for the three stream sites. Stream temperature patterns 

are mimicked more closely and extend to greater depths as 

water flows downstream from Site 2 to 3 to 5, which indicates greater interaction with the streambed as water flows 

downstream along the county line reach. Furthermore, the 

temperature pattern beneath the adjacent sandbar also suggests 

that water in the streambed flows horizontally to a greater 

and greater degree downstream. As discussed in Appendix B, 
Large piezometers

Site 3

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Figure 8. Observed streambed temperatures measured in 

large piezometers at Site 3 and Site 5, with the observed 

water temperature shown in the thin band at the top of each 

temperature contour.

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The Santa Clara River—The last natural river of Los Angeles 25

Figure 7. Computer simulation of the streambed 

temperature contours for cases in which a stream with 

the given water temperature (thin color ban at top) is 

gaining ground water, neutral, and losing ground water.
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Figure 9. The observed stream temperature, 

the observed streambed temperature in all 6 

small piezometers, and the simulated streambed temperatures for the 3 piezometers under 

the river for May 2-4, 2000 at Site 2, 3, and 5 

along the study reach.

26 Heat as a tool for studying the movement of ground water near streams 

streambed temperature data can be used as model input to 

predict both the vertical and horizontal movement of water in 

and out of the shallow streambed.

In conclusion, results from examining temperature patterns in stream sediments allows us to understand when and 

where stream water mixes with shallow ground water, and 

for how long this mixing takes place. This information then 

allows us to determine the amount of chemical exchange 

potentially occurring, which has a direct consequence on 

downstream water quality. Analysis of results aids hydrologists and civil engineers in predicting the impacts of future 

developments in the watershed on downstream water quality.
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The Santa Clara River—The last natural river of Los Angeles 27

Introduction

The Willamette Basin is located in northwestern Oregon 

(fig. 1), extending south from Portland approximately 160 km. 

It is home to approximately 70 percent of the State’s population and accounts for approximately 60 percent of gross crop 

sales in the State. The basin lowland is relatively flat, with 

fine-grained fertile soils. Annual rainfall is approximately 100 

cm in the lowland; about 70 percent of the annual rain falls 

from October through March. The summer growing season is 

warm and dry, in contrast to the cool, moist winter months.

In the Willamette lowland, early settlers grew crops, such 

as wheat, that required little, if any, irrigation. As markets and 

technology changed, irrigation of a diverse group of crops 

has evolved. The demand for irrigation water has grown as 

the number of acres cultivated 

for crops requiring irrigation, 

such as nursery stock and row 

crops, has increased. In the dry, 

summer months, when irrigation demand is high, agricultural 

fields are irrigated with ground 

water withdrawn from wells and 

surface water withdrawn from 

streams. Irrigation from surface 

water is generally restricted to 

land adjacent to large perennial 

streams, where water is directly 

pumped from the stream to the 

fields, because there are few irrigation canals in the basin. Additional 

withdrawals from many streams 

in the Willamette lowland are 

restricted during the summer to 

protect the water rights of existing users, and to provide summer 

flows for fish habitat and pollution 

abatement. Increasing demand for 

irrigation water supply will likely be satisfied from ground 

water. 

In the Willamette lowland, ground water naturally 

discharges to streams in many areas. Withdrawal of ground 

water from wells can capture ground water that naturally 

discharges to streams. In some cases, pumping ground water 

can lower water levels in aquifers near streams and reverse 

the flow of ground water so that stream water flows into the 

aquifer. These interactions between surface and ground waters 

are proportional to the head gradient between the stream and 

ground-water system, which may be related to the amount of 

water withdrawn from wells near the stream, and the hydraulic 

properties of the streambed. 

Chapter 5

Heat tracing in streams in the central Willamette Basin, Oregon

Terrence Conlon, Karl Lee, and John Risley

Willamette

River

Case Creek

Pudding

River

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WILLAMETTE

RIVER

RIVER

WILLAMETTE

Butte Creek

River

Molalla

Pudding R

Little

River

Yamhill

Case Cr

River River Pudding

Pudding

Butte Creek

Zollner Cr

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Figure 1. Location of seepage measurements and diagrammatic section, 

central Willamette Basin, Oregon
30 Heat as a tool for studying the movement of ground water near streams 

To better understand the interactions, it is necessary to 

quantify the amount of water that discharges, or seeps, from 

the aquifer to the stream, and the permeability of the streambed. This chapter discusses streambed seepage measurements 

made using heat as a tracer at six locations within the central 

part of the Willamette lowland and compares these measurements with measurements made using other techniques.

Streambed and streamflow characteristics

Most streams in the central Willamette Basin are perennial, or flow year round (fig. 2). Generally, the streambeds 

consist of fine-grained sediment, except in the Willamette 

River and the lower reaches of the Pudding and Molalla Rivers, which have gravel streambeds. The fine-grained sediment 

is mainly silt and clay (fig. 1) that was deposited as backwater deposits by repeated cataclysmic floods from breaching of ice-dammed lakes during the ice ages between 15,000 

and 13,000 years ago. The silt and clay form a relatively flat 

terrace with elevations ranging from 30 m in the north to 100 

m in the south. Thickness of the material ranges from 10 to 30 

m. Beneath the fine-grained sediments are permeable sand and 

gravel deposits, from which wells withdraw ground water. 

Streamflow in the smaller streams is greatest in the wet 

winter months and diminishes in the dry summer and fall 

months. Because the headwaters for these streams are either 

in the lowland or the foothills of the Cascades, snowmelt 

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Figure 2. Streamflow and 

precipitation in the central 

Willamette Basin, Oregon

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Figure 3. Diagram of installation to measure temperature and 

hydraulic gradient, Zollner Creek
Heat tracing in streams in the Central Willamette Basin, Oregon 31

does not contribute water directly to these streams in summer. 

Beneath the streams, ground water generally flows upward, 

discharges to streams in the lowland, and helps to maintain 

stream flow in the dry summer months. Using heat as a tracer 

along with other methods, the amount of ground water discharging to streams was estimated at locations along several 

streams of interest.

Techniques to measure stream seepage

Three methods were used to measure the flow of water 

between aquifers and streams during the dry period of August 

2000: heat as a tracer, seepage runs, and seepage meters. Six 

streams were instrumented with temperature sensors and 

seepage meters (fig. 1). The six streams can be classified by 

size and streambed material (table 1). Seepage runs were 

conducted on reaches of streams that included three of the six 

sites. 

Using heat as a tracer requires measuring temperature 

in the stream and streambed over an extended period of time. 

Piezometers were hand-driven into the streambed at six locations (fig. 1) to measure temperature at different depths within 

the streambed, and to measure hydraulic gradients between 

the stream and ground water. A diagram of an installation is 

shown in figure 3. Water levels in the piezometer represent the 

water pressure at the bottom of the open-ended piezometer. 

Because the streambed is always saturated and the steel 

piezometer readily conducts heat, the temperature of the water 

in the piezometer is assumed to be in thermal equilibrium 

with the streambed temperature; that is, the temperature of 

the water in the piezometer reflects the adjacent streambed 

temperature (see Appendix A). Temperature loggers were sus-

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Figure 4. Observed temperatures, Zollner Creek

Spring Fall

Stream Width flow flow Streambed Seepage

Name (m) m3/s m3/s Material Temperature Meter Run

LARGE STREAMS

Butte Creek 8 3 0.3 sandy silt x x x

Lower Pudding River 15 10 1 sandy silt x x x

Upper Pudding River 10 – 0.7 clayey silt x x x

SMALL STREAMS

Case Creek 3 0.1 0.05 clayey silt x x

Little Pudding River 3 – 0.1 clayey silt x x

Zollner Creek 3 0.06 0.02 clayey silt x x

Table 1. Characteristics 

of instrumented streams
32 Heat as a tool for studying the movement of ground water near streams 

pended within the piezometer to measure streambed temperatures at different depths below the stream. Streambed temperatures at shallow depths are similar to the stream temperature, 

while streambed temperatures at greater depths are generally 

colder and slowly increase with time during the summer (fig. 

4). At the bottom of the well, streambed temperatures fluctuate less over time and represent the ground-water temperature 

with little effect from fluctuating surface temperatures (see 

Chapter 1).

The streambed temperature patterns beneath the streams 

at the six sites were modeled using the simulation code 

VS2DH to estimate seepage by matching simulated temperatures to observed temperatures (see Appendix B). Observed 

temperatures from the middle sensor were used to calibrate 

VS2DH models because at this depth temperatures exhibit 

seasonal variation and possible heat conduction down the steel 

piezometer is minimized. 

During the summer of 2000, seepage was also estimated 

using seepage runs and seepage meters to compare with estimates from heat tracing. For seepage runs, streamflow is measured at two points along a stream reach, and after accounting for stream diversions and tributary inflow, the difference 

between the two measurements represents a seepage gain to 

or loss from the stream. If downstream flow is greater than 

upstream flow, the stream gains; if downstream flow is less 

than the upstream flow, the stream loses water to the aquifer 

(Riggs, 1972). Seepage run estimates where seepage is small 

relative to streamflow are often inconclusive or difficult to 

interpret because seepage is calculated from the difference of 

two streamflow measurements. The two streamflow measurements, in low seepage environments, are practically identical 

and the difference may be attributable to measurement error 

rather than seepage. Therefore, where seepage is relatively 

small, it is important to have other methods available, such as 

heat tracing and seepage meters, to estimate seepage. 

Seepage meters measure the amount of water that enters 

or leaves an open-ended drum that is open to the streambed 

(Lee and Cherry, 1978). The seepage is measured by comparing the initial and final volumes of water in a bag connected 

to the seepage meter (fig. 5). Flow into the drum represents a 

gain to the river; flow out of the drum represents a loss from 

the river. To compare seepage run and meter results to heat 

tracing, the amount of water entering the reach or drum per 

unit time is divided by the area so that the rate of inflow can 

be directly compared to heat tracing estimates.

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Figure 6. Simulated and observed temperatures, Zollner Creek

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Figure 5. Diagram of seepage meter
Heat tracing in streams in the Central Willamette Basin, Oregon 33

Figure 7. Seepage estimates using heat as a tracer

Figure 9. Temperature envelopes for two selected streams 

Seepage and streambed permeability from temperature measurements

The seepage values estimated using heat as a tracer in the 

central Willamette Basin are small compared to other seepage 

rates documented in this circular because of the relatively low 

permeability of the streambed material in the basin. The fit 

of simulated and observed values at most sites was similar to 

the close fit at Zollner Creek (fig. 6). Except for Case Creek, 

seepage was greatest in larger streams (lower Pudding River 

and Butte Creek) with some sandy material in the streambed 

(figure 7 and table 1). In smaller streams with fine-grained 

material in the streambed (Zollner Creek and Little Pudding 

River) and one large stream with a fine-grained streambed 

(upper Pudding River), seepage was less significant. 

The variation in seepage was a result of different hydraulic gradients and hydraulic conductivities at each site. Because 

the hydraulic gradient at some sites was measured, the hydraulic conductivity can be estimated (Chapter 1). The variation 

in hydraulic conductivity ranged from 1 x 10-7 to 2 x 10-6 m/s 

(fig. 8), which is similar to published values for silt (Freeze 

and Cherry, 1979). Seepage in Zollner Creek was low (fig. 7) 

because the hydraulic conductivity is relatively low (fig. 8) 

and the hydraulic gradient is average. Seepage in the lower 

Pudding River is relatively high, despite an average hydraulic 

conductivity, because the hydraulic gradient is relatively high.

Because seepage is the product of hydraulic conductivity 

and gradient, low seepage values may be the result of small 

values of hydraulic conductivity and/or gradient. As stated 

above, the streambed hydraulic conductivity is relatively low 

and reflects the fine-grained and compacted characteristics 

of the streambed at the six sites. The seepage values simulated using VS2DH for some locations are at the low end of 

sensitivity of the model; that is, simulating the streambed with 

a lower hydraulic conductivity will not change the simulated 

temperature significantly because the seepage was already 

very low. At low hydraulic conductivities (or hydraulic gradients), the model becomes increasingly sensitive to thermal 

properties, such as heat capacity and thermal conductivity. 

Thermal properties eventually become more important than 

hydraulic conductivity in simulating seepage.

Annual streambed temperature envelopes (Chapter 1) 

support the variability in estimated seepage. Because upward 

ground-water flow occurs at all six sites, a “collapsed” or shallow temperature envelope is expected at all sites. The greater 

the upward flow, the narrower and more collapsed the envelopes should be. This is evident for annual temperature envelopes for Butte Creek, a stream with relatively large upward 

flow, and the upper Pudding River, a stream with relatively 

low upward flow. Butte Creek’s envelope is narrower, suggesting a greater rate of upward flow of ground water.

 Comparison of seepage measurement methods

Seepage estimates using seepage runs and seepage meters 

were compared to heat tracing estimates. Generally, seepage 

estimates from the heat tracing method provided the highest 

estimate of seepage, except for Zollner Creek and Butte Creek, 

where seepage meter and seepage run measurements were 

greater (fig. 10). Generally, seepage estimates from the seepage meter method provided the lowest estimates. Estimates 

from seepage runs are difficult to compare with other methods 

because of measurement uncertainty and the assumptions 

used to convert volumetric seepage over a reach to a seepage 

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Figure 8. Vertical hydraulic conductivity estimates using heat as a tracer

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34 Heat as a tool for studying the movement of ground water near streams

Ground-water flow to streams in the central Willamette Basin

The results of this study show that heat tracing techniques 

are an excellent method to study the interaction of aquifers 

and streams in the Willamette Basin. The limited seepage from 

the aquifer to the stream and the low hydraulic conductivity estimated by the heat tracing technique indicate that the 

hydraulic connection between the stream and aquifer is limited 

by low hydraulic conductivities. Discharge of ground water to 

streams occurs, but at a rate that is small (sometimes less than 

5 percent) relative to streamflow, resulting in seepage estimates 

that were less than the uncertainty in seepage run measurements. Ground-water withdrawals from the underlying sand 

and gravel aquifer may capture water that would normally discharge to these streams; however, the amount of water is small 

relative to streamflow.

rate per area. Seepage estimated from seepage runs for Butte 

Creek compares well with the seepage estimated using heat as 

a tracer. Seepage was approximately 15 percent of streamflow 

in Butte Creek and was greater than the uncertainty in the 

measurements used in the seepage run. 

A loss of stream water was indicated by seepage runs 

along the upper and lower Pudding River, which contradicts 

the gains measured by seepage meters and heat as a tracer. 

There are two possible explanations: (1) if the selected reach 

includes both losing and gaining subreaches, the sum of the 

seepage may be a loss from the stream to the ground-water 

system, but a seepage estimate using a point measurement 

method may indicate a gain from aquifer to the stream, and 

(2) the stream losses may, in fact, not be losses because the 

losses were within the uncertainty of the seepage run measurement. Although the seepage estimates at a particular site vary 

more than one order of magnitude, they provide a range that 

constrains the magnitude of the interaction between surface 

and ground water and can be used in other applications, such 

as analytical and numerical models.

Studies using heat as a tracer in streams in Oregon have 

provided estimates of streambed hydraulic conductivity 

and seepage between streams and the ground-water system. 

Quantifying seepage rates and hydraulic properties of the 

streambed helps hydrologists and water-resource managers to 

understand the interaction of surface and ground waters. With 

an improved understanding of these interactions, managers can 

make informed decisions about the effect of future groundwater withdrawals on streamflow. 

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Figure 10. Comparison of seepage estimates using three methods
Introduction

Lake Tahoe is known as the “Jewel of the Sierra” mostly 

because of its deep, clear water and because it is surrounded 

by majestic snow capped peaks (fig. 1). Lake Tahoe straddles 

the Sierra Nevada about 300 km east of San Francisco, 

California (fig. 2), and is a favorite vacation spot to millions 

of tourists. Unfortunately, the beauty that attracts the tourists is being threatened because the lake has been losing its 

clarity at a rate of about 0.5 m/yr (Goldman and Byron, 1986, 

p. 7). Human activity in and around the lake has resulted in 

increased nutrients that support an increasing algae population, 

which reduces the clarity of the lake (Goldman, 1988). 

Nutrients enter the lake from streams, ground water, 

atmospheric deposition, overland runoff directly to the lake, 

and by shoreline erosion (Reuter and others, 1998; Reuter and 

Miller, 2000). Streams that discharge into Lake Tahoe may 

be contributing the greatest percentage of nutrients due to the 

relative ease with which urbanization can increase both flow 

and nutrients (Byron and Goldman, 1989).

Environmental improvement projects were implemented 

in the mid-1970s, shortly after the Tahoe Regional Planning 

Agency (TRPA) was created by the California and Nevada 

legislatures in 1969. TRPA’s mission is to lead the effort to 

preserve, restore, and enhance the unique natural and human 

environment of the Lake Tahoe region (Tahoe Regional Planning Agency, 2002). Since TRPA’s inception, efforts have 

increased by Federal, State, and regional agencies to construct 

Best Management Practices (BMPs) as well as other environmental improvement projects in an attempt to reduce the 

negative effects of human activity on Lake Tahoe and its contributing areas. One of the earliest efforts was the development 

of regional treatment plants that collect sewage from homes 

and cabins around the lake and then pump the wastewater out 

of the basin into neighboring valleys. More recently, increased 

efforts have focused on reducing sediments and nutrients that 

enter the lake from its many tributaries. 

Purpose and Scope

Water and nutrients in tributaries consist of a mixture of 

overland runoff, direct precipitation, and ground water. However, little information is available on the contribution of each 

source on flow and nutrients in each of the tributary streams 

that enter the lake. Knowing the contribution of each source 

is important to resource managers in developing an overall 

strategy in reducing nutrients in the streams. The purpose of 

the study along Trout Creek is to provide a better understanding of flow in Trout Creek in relation to ground water and 

the sources of nutrients in the stream. The study along Trout 

Creek is part of a larger effort by the U.S. Geological Survey 

and the TRPA to monitor and evaluate flow and nutrients in 

streams tributary to Lake Tahoe. Trout Creek was chosen for 

study because (1) it contributes the second greatest nutrient 

Chapter 6

Trout Creek—evaluating ground-water and surface water 

exchange along an alpine stream, Lake Tahoe, California

Kip K. Allander

Figure 1. Lake Tahoe, Nevada and California, looking south 

from the Mount Rose Highway (Hwy. 431). [P. A. Glancy, 

March 2000, U.S. Geological Survey]
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0 1 2 3 KILOMETERS

1 2 3 MILES

Nevada

California

Lake

Tahoe

South Lake

Tahoe

Tahoe Keys

Meyers

Stateline

Trout

C reek

Upper

Truckee

River

Nevada

California

Lake

Tahoe

South Lake

Tahoe

Tahoe Keys

Meyers

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C reek

Upper

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Pioneer TrailPioneer Trail

Heavenly Valle y

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Base from U.S. Geological Survey digital data, 1:24,000 and 1:100,000,

1969ñ85 Universal Transverse Mercator projection, Zone 10

Basin-fill deposits

Bedrock

Boundary of Lake Tahoe Basin

Boundary of Trout Creek watershed

Reach boundary

Site and river distance, in kilometers

Reach boundary and piezometer and

streambed temperature site

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EXPLANATION

Area

of map

Lake

Tahoe

Fallen

Leaf Lake

CALIFORNIA

NEVADA

San Francisco

Reno

San Francisco

Reno

Sierra NevadaSierra Nevada

Carson RangeCarson Range

36 Heat as a tool for studying the movement of ground water near streams 

Figure 2. Location of study area
R. Whitney, January 1993, U.S. Geological Survey

T. G. Rowe, April 1993, U.S. Geological Survey

K. K. Allander, October 1999, U.S. Geological Survey

K. K. Allander, September 1996, U.S. Geological Survey

Trout Creek at river distance 14.2 km above Lake Tahoe under

typical mid-winter conditions; upper part of watershed is

characterized by steep topography, steep stream-channel gradient,

heavy forest and riparian vegetation, and deep snow pack in the

winter. View is to the west looking mostly downstream.

Trout Creek at river distance 6.9 km above Lake Tahoe under

typical mid-spring conditions; middle part of watershed is

characterized by gentle rolling topography, moderate to mild

stream-channel gradient with meandering channel pattern, narrow

flood plain with meadow being encroached by heavy forest and

remnants of large winter snow pack. View is to the south looking

upstream.

Trout Creek at river distance 4.5 km above Lake Tahoe under

typical early fall conditions; lower-middle part of watershed is

characterized by mostly flat with occasional low hill topography,

mild stream-channel gradient with a mostly meandering streamchannel pattern, a moderately wide flood plain that is mostly

meadow but with frequent riparian vegetation. View is to the

south looking downstream from the Martin Avenue Bridge.

Picture also shows in-channel instrumentation used to monitor

stream stage, shallow ground-water levels, and streambed

temperatures.

Trout Creek at river distance 1.1 km above Lake Tahoe under

typical early fall conditions; lower part of watershed is

characterized by nearly flat topography, very mild channel

gradient with poorly defined channel geometry with frequent

divergence of flow, large meadow that transitions into marsh

before entering into Lake Tahoe. View is to the east looking

upstream.

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Trout Creek—Evaluating ground-water and surface water exchange along an alpine stream, Lake Tahoe, California 37

and suspended-sediment load to Lake Tahoe (Rowe and others, 2002), (2) it has been urbanized along most of its lower 

reach, (3) it has extensive ongoing monitoring of surface and 

ground water, and (4) it is being restored by channel reconstruction throughout the developed urban area. 

This chapter describes how streamflow, water-level, and 

temperature measurements were used to evaluate changes in 

ground-water contributions to Trout Creek. Recently, studies 

demonstrated that the combined analysis of streamflow and 

temperature aids in the delineation of losing versus gaining 

reaches along alpine streams (Constantz, 1998). For Trout 

Creek, the temperature measurements along with differences 

in water levels between the stream and the shallow ground 

water were designed to evaluate periods when ground water 

is contributing flow to the stream at two sites along the lower 

reach of the stream.

Description of Study Area

Although Trout Creek has the same name as the Trout 

Creek near Battle Mountain, Nevada, which is described in 

Chapter 8 of this report, the streams are distinctly different. 

This creek drains the west side of the Carson Range south 

of South Lake Tahoe (fig. 2) and has many small mountain 

tributaries. Trout Creek is perennial along much of its course 

and flows through large meadows and a marsh (fig. 3) before 

discharging to the south end of Lake Tahoe. Bedrock is 

composed mostly of Cretaceous age granodiorite of the Sierra 

Figure 3. Photographs showing variability of Trout Creek watershed and stream characteristics.
O N D J F M A M J J A S

1995 1996

STREA

MFLO

W, IN CUBIC METERS PER SECOND

O N D J F M A M J J A S

1995 1996

0

10

2

4

6

8

PRECIPITATION,

IN CENTIMETERS

Trout Creek at Martin Avenue (river distance 4.5 kilometers)

Fallen Leaf SNOTEL site

0

1

2

3

4

5

6

7

8

38 Heat as a tool for studying the movement of ground water near streams 

Nevada batholith (Tahoe Regional Planning Agency and 

U.S. Forest Service, 1971). The basin fill near the base of the 

mountains is mostly fluvial sand and gravel mixed with glacial 

deposits. The basin-fill sediments become finer near Lake 

Tahoe and grade mostly into sand with layers of silt and clay. 

Major tributaries to Trout Creek are Saxon Creek, Cold Creek 

and Heavenly Valley Creek (fig. 2). Annual precipitation in the 

Trout Creek watershed ranges from about 50 to 100 cm and 

occurs mostly as snow during the winter. However, significant 

precipitation may occur in the spring and fall as rainstorms or 

during the summer as thunderstorms. Hydrographs (fig. 4) for 

Trout Creek for water year 1996 reflect the seasonal climate 

patterns by exhibiting higher prolonged flows during spring 

snowmelt runoff as well as smaller duration peaks from rain 

events that can occur anytime of the year.

Methods Used to Evaluate Ground-Water 

Exchange Along Trout Creek

Streamflow measurements were made in the headwaters 

and along the main channel of Trout Creek, and at all the 

tributaries that were contributing flow to the main channel to 

estimate ground-water exchange along Trout Creek. Because 

streamflow measurements only provide an estimate of gains 

and losses during a specific time, two sites on Trout Creek 

were selected for continuous monitoring of seepage characteristics. Stream stage, ground-water levels, and subsurface 

temperatures were monitored at these two sites to evaluate if 

ground-water exchange varied during the year.

Streamflow Measurements

A series of streamflow measurements along Trout Creek 

and its tributaries were initially made on September 26, 1996, 

to identify reaches of Trout Creek that were gaining or losing 

flow from or to ground water. The measurements were made 

in the fall to minimize the influences of evapotranspiration 

and seasonal storms. Streamflow gains and losses from ground 

water along selected reaches of Trout Creek were estimated 

by subtracting all tributary flows along a reach and flow at the 

beginning of a reach from flow at the end of a reach. Cumulative gains from ground water were calculated by adding the 

Figure 4. Hydrographs showing streamflow for Trout Creek near Tahoe Valley and daily precipitation below Fallen Leaf Lake, 

1996 water year (precipitation data courtesy of USDA National Resource Conservation Service).
Right bank piezometer

Streambed piezometer,

Streamgage

Left bank

piezometer

Right bank piezometer

Streambed piezometer,

Streamgage

Left bank

piezometer

0 30 METERS

0 100 FEET

0 30 METERS

0 100 FEET

Trail Pioneer

Golden Bear Trail

N

�

Trout

Creek

Trout Creek

Trout Creek

Trout Creek

Black Bart Road

Martin Ave

N

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Figure 5. Site map sketch of Trout Creek at Pioneer Trail (A), and 

Trout Creek at Martin Avenue, near Tahoe Valley (B), California.

Trout Creek—Evaluating ground-water and surface water exchange along an alpine stream, Lake Tahoe, California 39

gains and losses from each reach in the downstream direction 

starting with zero gain at the most upstream measurement. 

Seepage rates per unit stream width were estimated for each 

reach by dividing the overall gain or loss between measurements by the length of the stream between measurement 

locations. The streamflow measurements were repeated each 

October from 1997 through 2001.

Water-Level Measurements

The two sites used are Trout Creek at Pioneer Trail near 

South Lake Tahoe and Trout Creek at Martin Avenue near 

Tahoe Valley (sites 4.5 and 6.9, respectively, fig. 2). During 

late-September 1999, two shallow monitoring wells were 

installed at each site about 7.5 m out from the edge of each 

stream bank (figs. 5A and 5B). Each well was placed between 

2.1 and 3.0 m below land surface. A third monitoring well was 

installed near the thalweg of the main channel at each site and 

was 2.1 m below the streambed. Stream stage and the water 

level in the well beneath the streambed were monitored every 

30 minutes using pressure transducers. Wells on the stream 

banks were monitored approximately once every 2 weeks 

using a standard engineers steel tape. Reference measurements were made for stream stage and in the well beneath the 

streambed to verify the pressure transducer measurements. 

Elevation of the tops of all wells were determined by running 

levels from known reference marks after initial installation 

then remeasured once each summer through the period of study.

Temperature Measurements

During September 1999, five thermocouple sensors were 

installed at the two sites at depths of 0.15, 0.6, 0.9, 1.5, and 2.1 

m below the streambed and were located next to the streambed 

piezometer. The thermocouple sensors were logged at halfhour intervals. A description on thermocouple temperature sensors and their theory of operation is described in appendix A. 

Ground-water exchange along Trout Creek

Streamflow measurements in Trout Creek were used 

to characterize flow, and to measure cumulative exchange 

between the ground water and stream during the fall periods. 

Water-level and streambed temperature measurements were 

used to monitor the directions of exchange between the shallow 

ground water and stream throughout the year.

Streamflow

Streamflow measurements in Trout Creek generally 

increased downstream (fig. 6A). Flow in Trout Creek each fall 

generally reflected the amount of precipitation that fell during 

the previous winter. Flows were greatest for measurements in 

September 1996 and October 1997-99. These flows correspond 

to previous winters in which precipitation was above normal. 

Flows during October 2000 and 2001 were much less than the 

above periods and reflect much lower precipitation during the 

previous winters. Following wet years, flow in Trout Creek 

between measurement sites at 4.5 and 1.1 km upstream of 

Lake Tahoe (fig. 2) would remain steady or increase slightly, 

however, following dry years, flow decreased (fig. 6A). Heavenly Valley Creek enters Trout Creek just below the site at 4.5 

km upstream of the lake but its contribution generally is negligible during the fall. Similarly, Saxon Creek adds some flow 

to Trout Creek between measurement sites at 10.8 and 6.9 km 

upstream of the lake, but the majority of tributary inflow to 

Trout Creek is from Cold Creek between measurement sites at 

6.9 and 4.5 km upstream of the lake. Inflow from Cold Creek 

about doubles the streamflow in Trout Creek. The elevation 

of Lake Tahoe ranged from 1902.8 m on October 19, 2000, to 

1903.5 m above sea level on October 15, 1998, then dropped 3 

m to an elevation of 1899.8 on October 17, 2001 (fig. 6A). 
40 Heat as a tool for studying the movement of ground water near streams 

�

�

-0.10

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14 12 10 8 6 4 2 0

RIVER DISTANCE FROM LAKE TAHOE, IN KILOMETERS

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RIVER DISTANCE FROM LAKE TAHOE, IN KILOMETERS

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10/08/97

10/15/98

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10/19/00

10/17/01

09/26/96

10/08/97

10/15/98

10/14/99

10/19/00

10/17/01

09/26/96

Figure 6. Instantaneous streamflow (A) and cumulative gains (B) along Trout Creek.

Water Levels 

Measurements of ground-water levels adjacent to and 

beneath Trout Creek at Pioneer Trail and at Martin Avenue 

sites show patterns of ground-water exchange that vary 

through time (fig. 7). At the Pioneer Trail site, ground-water 

levels generally were above the stream from October 1999 

through April 2000, from late-January 2001 through mid-May 

2001, and again from mid-December 2001 through mid-JanuThe cumulative gain from ground water along Trout 

Creek for each measurement beginning in September 1996 

and continuing each October through 2001 showed a mixed 

pattern of gains and losses along the stream (fig. 6B), which 

indicates ground-water exchange along the stream is dynamic 

from year to year. Generally, however, Trout Creek gained 

flow between the uppermost and lowermost measurement sites 

following winters of above normal precipitation (September 

1996 through October 1998) and lost flow following winters 

of below normal precipitation (October 2000 and 2001). On 

October 17, 2001, following two consecutive winters of below 

normal precipitation, Trout Creek was consistently losing 

between measurement sites 6.9 and 1.1 km above the lake and 

showed no gain upstream.
� Trout Creek at Martin Avenue near Tahoe Valley

1903.6

1903.7

1903.8

1903.9

1904.0

1904.1

1904.2

1904.3

10/1/1999 1/31/2000 6/1/2000 10/1/2000 1/31/2001 6/2/2001 10/2/2001 2/1/2002

DATE

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Left bank piezometer

Streambed piezometer

Stream stage

Right bank piezometer

� Trout Creek at Pioneer Trail near South Lake Tahoe

1911.4

1911.5

1911.6

1911.7

1911.8

1911.9

10/1/1999 1/31/2000 6/1/2000 10/1/2000 1/31/2001 6/2/2001 10/2/2001 2/1/2002

DATE

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Left bank piezometer

Streambed piezometer

Stream stage

Right bank piezometer

M

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stly

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ainin

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sin

g

Figure 7. Water-level hydrographs of Trout Creek piezometers and stream stage.

Trout Creek—Evaluating ground-water and surface water exchange along an alpine stream, Lake Tahoe, California 41

ary 2002, which indicates ground-water flow was to Trout 

Creek. Ground-water levels were below the stream from midJuly 2000 to mid-October 2000 and again from late-May 2001 

to December 2001, which indicates the stream was losing flow 

to ground water. Exchange during the remaining intervals is 

mixed because water levels were above the water level of the 

stream on one side of the stream and below on the other side.

At the Martin Avenue site, ground-water levels generally 

were above the water level of the stream from mid-October 

1999 through March 2000, for a brief period during April 

2001, and again from mid-February 2002 through early March 

2002, which indicates ground-water flow was to Trout Creek. 

Ground-water levels generally were below the level of the 

stream from mid-June 2000 through mid-March 2001 and 

again from mid-May 2001 through December 2001 indicating 

the stream was losing flow to ground water. Exchange during 

the remaining intervals is mixed because water levels were 

above the stream on one side of the stream and below on the 

other side. Trout Creek at Martin Avenue generally had shorter 

periods when the stream was gaining flow from ground water 
-0.01

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JANUARY 2000

14 15 16 17 18 19 20 21 22 23 24

JANUARY 2000

0

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Depth = 0 meter

Depth = 0.15 meter

Depth = 0.61 meter

Depth = 0.91 meter

Depth = 2.13 meters

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42 Heat as a tool for studying the movement of ground water near streams 

Figure 8. (A) Streambed temperature profile and difference in water level between stream and shallow groundwater (positive difference in water level indicates upward gradient) for Trout Creek at Pioneer Trail during a gaining period.

Temperature

Streambed-temperature profiles in conjunction with 

differences between stream and ground-water levels also can 

illustrate the dynamic nature of ground water exchanged at the 

Pioneer Trail and Martin Avenue sites (figs. 8 and 9, respectively) during the study period. An increase in the hydraulic 

gradient between the ground water beneath Trout Creek and 

the stream at Pioneer Trail on January 18, 2000 (fig. 8A, bottom graph), is reflected initially by an increase in temperature 

at a depth of 0.91 m with a subsequent increase in temperature 

at a depth of 0.61 m and then by an increase in the stream 

temperature (fig. 8A, top graph). Below a depth of 0.61 m, 

the higher temperatures and the lack of a diurnal temperature 

signal contrast with the diurnal temperature of the stream 

indicating that movement of heat is upward from below. The 

and longer periods when it was losing flow to ground water 

than at the Pioneer Trail site (fig. 7). 

The Trout Creek at Pioneer Trail and at Martin Avenue 

sites exhibited a similar seasonal pattern of directions of 

ground-water exchange with the stream during the 2000 water 

year (fig. 7). Both sites were mostly gaining flow from ground 

water in winter and early spring periods during increasing 

snowmelt conditions. Both sites became a mix of groundwater exchange conditions during peak snowmelt conditions 

and were mostly losing flow during the end of snowmelt conditions. In water year 2001, the sites had similar patterns but 

with some differences in timing and duration. Trout Creek at 

Pioneer Trail followed a pattern similar to the previous water 

year, but Trout Creek at Martin Avenue had a much smaller 

mixed flow period and almost a non-existent period of mostly 

gaining conditions.
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Depth = 0 meter

Depth = 0.91 meter

Depth = 2.13 meters

Depth = 0.15

meter

Depth = 0.61

meter

Trout Creek—Evaluating ground-water and surface water exchange along an alpine stream, Lake Tahoe, California 43

increase in stream temperature prior to the increase in temperature at depth 0.15 m indicates that ground water is entering 

the stream above the sensors. The presence of a diurnal signal 

at a depth of 0.15 m indicates considerable mixing of stream 

water. In contrast, during August 2000, the difference between 

ground-water and stream levels becomes more negative, which 

indicates that the stream is losing flow to ground water (fig. 

8B) and is reflected by the diurnal stream temperature signal 

being propagated to a depth of 0.91 m below the streambed. 

A similar pattern in temperature was recorded at the 

Martin Avenue site for periods when the ground-water level 

was above the stage in the stream (fig. 9A) in February 2000. 

A rapid increase in the gradient between the ground water 

and the stream on February 14 resulted in a rapid increase in 

temperature at depths of 0.61 and 0.15 m below the streambed 

as well as in the stream. During the rapid increase in temperature, there were no diurnal fluctuations in stream or groundwater temperature. The diurnal signal returned in the stream 

once the gradient declined, however, the higher temperatures 

at the 0.15 m depth indicates ground water is maintaining a 

higher temperature immediately beneath the stream, which in 

turn indicates that ground water is discharging to the stream. 

These temperature data are consistent with the gaining period 

observed through the water levels of the wells adjacent to 

and beneath the stream during mid-October through March 

2000 (fig. 7B). With the exception of December 24-25, 2001, 

the water-level gradient between the ground water and the 

stream was slightly greater than zero during the last week in 

December 2001 and stream temperature was near freezing 

(fig. 9B). Temperatures at depths of 0.61 and 0.15 m were 

slightly greater than the stream temperature indicating that 

heat was being transferred to the stream, which is consistent 

Figure 8. (B) Streambed temperature profile and difference in water level between stream and shallow groundwater (positive difference in water level indicates upward gradient) for Trout Creek at Pioneer Trail during a losing period.
Depth = 0 meter

Depth = 0.15 meter

Depth = 0.61 meter

Depth = 1.52 meters

Depth = 2.13 meters

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44 Heat as a tool for studying the movement of ground water near streams 

Figure 9. (A) Streambed temperature profile and difference in water level between stream and shallow groundwater (positive difference in water level indicates upward gradient) for Trout Creek at Martin Avenue near Tahoe Valley during a gaining period.

Summary

In summary, measurements of flow along Trout Creek 

during the fall and detailed measurements of stream stage, 

ground-water levels, and temperature at two sites on Trout 

with the slight upward gradient observed between the ground 

water and the stream. Beginning December 23, the gradient 

changed such that the stream stage was higher than the water 

level in the well beneath the streambed before returning to a 

slightly upward gradient during the evening of December 25. 

During this brief period, the temperature at a depth of 0.15 m 

dropped briefly to that of the stream and the temperature at a 

depth of 0.61 m dropped 0.8°C before slowly increasing to the 

temperature prior to December 23. However, the most noticeable change is the drop in streambed temperature of more than 

2°C at a depth of 1.52 m, which indicates water influenced by 

stream temperature was briefly flowing downward into the 

underlying ground water. As the hydraulic gradient returned 

to near zero, the temperature at this depth began to rise slowly 

(fig. 9B). 
Depth = 0 meter

Depth = 0.15 meter

Depth = 0.61 meter

Depth = 1.52 meters

Depth = 2.13 meters

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20 21 22 23 24 25 26 27 28 29 30

DECEMBER 2001

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Trout Creek—Evaluating ground-water and surface water exchange along an alpine stream, Lake Tahoe, California 45

Creek show a dynamic ground-water exchange that varies seasonally and spatially. Detailed measurements at the two sites 

indicate that ground water is contributing flow to Trout Creek 

during the winter and early spring and losing flow during the 

summer and fall. Analyses of the data are ongoing. Purpose of 

the analyses is to determine the extent and duration of ground 

water contribution to Trout Creek. Knowing this contribution 

and the nutrient concentrations in ground water are important 

in designing environmental improvement projects that are 

effective in reducing nutrients to Trout Creek and to Lake 

Tahoe.

Figure 9. (B) Streambed temperature profile and difference in water level between stream and shallow groundwater (positive difference in water level indicates upward gradient) for Trout Creek at Martin Avenue near Tahoe Valley during a losing period.

Introduction

The city of Tucson and surrounding communities obtain 

virtually all their municipal, agricultural, and industrial water 

from ground water that is withdrawn from thick alluvial 

aquifers underlying the desert basins. A large fraction of this 

ground water entered the aquifers as recharge after percolating 

through channel deposits along ephemeral streams (Matlock 

and Davis, 1972; Davidson, 1973; Hanson and Benedict, 

1994). Most of the ground water in the underlying aquifers is 

thousands of years old (Kalin, 1994), and the amount of water 

that recharges the aquifers is insufficient to meet current and 

future demands. The resultant ground-water deficit, which will 

grow as the population increases, is manifested in water-level 

declines of more than 60 meters since the middle of the 20th 

century. To help mitigate the deficit, an in-stream recharge 

facility has been proposed in the Rillito Creek channel on the 

north side of Tucson. The source of water for the recharge 

facility is likely to be Colorado River water, transported from 

Lake Havasu and delivered to the Tucson area through the 

Central Arizona Project aqueduct. 

Infiltration of streamflow is known to occur in ephemeral streams in the Southwestern United States; however, a 

better understanding of the infiltration processes can improve 

the effectiveness of in-stream recharge facilities. This chapter describes one component of an investigation designed to 

improve our understanding of infiltration processes in ephemeral-stream alluvium. In particular, we discuss the variability 

of infiltration rates during a streamflow event and show how 

temperature methods in conjunction with soil-water content 

measurements can be used to evaluate potential sites for 

recharge facilities. 

In this chapter, we show examples of how numerical 

simulations using temperature methods are used to estimate 

rates of infiltration in the shallow Rillito Creek stream-channel 

deposits during an ephemeral streamflow event. Water-content 

changes measured at several depths are used to estimate the 

rapid infiltration rate at the onset of streamflow. The variation 

in infiltration rates during a streamflow event is examined. 

Drainage rates at the cessation of streamflow, determined on 

the basis of soil-water content measurements, are compared to 

estimated infiltration rates near the end of streamflow for each 

profile. These estimated infiltration rates and drainage rates 

are compared with previous estimates of these rates obtained 

by other techniques.

Rillito Creek 

Rillito Creek has a drainage area of 2,256 square kilometers at the streamflow-gaging station Rillito Creek at Dodge 

Boulevard (09485700) and has two major tributaries: Tanque 

Verde Creek and Pantano Wash (fig. 1). The creek is typical 

of ephemeral streams in the arid and semiarid Southwestern United States. During most of the year, the creek is dry; 

however, after prolonged or intense periods of rainfall and 

(or) snowmelt, it has flowed for several hours to several days 

along its 20-kilometer length. Precipitation runoff and snowmelt from the Santa Catalina Mountains to the north and the 

Rincon Mountains to the east, as well as urban runoff from the 

northeastern suburbs of Tucson, contribute most of the flow to 

Rillito Creek. Rillito Creek is a losing stream along its westward course toward its confluence with the Santa Cruz River.

Rillito Creek is underlain by recent stream-channel deposits and Pleistocene or older basin-fill deposits (Anderson, 1987). 

The channel deposits, which were derived from the surrounding 

mountain ranges, comprise fine- to coarse-grained alluvium and 

are about 10 meters thick. They predominantly are sand and 

gravel and contain less than 10 percent clay and silt, indicating 

that streambed infiltration is rapid. The underlying basin-fill 

deposits generally are finer grained and extend to depths of 

several hundreds of meters. Both deposits generally are loosely 

compacted but the basin fill is moderately compacted in places. 

Depth to ground water beneath Rillito Creek typically ranges 

from less than 3 meters in the upper reach near the confluence 

of Tanque Verde Creek and Pantano Wash to about 45 meters 

near the confluence with the Santa Cruz River to the west.

Chapter 7

Combined use of heat and soil-water content to determine stream/ground-water exchanges, Rillito Creek, 

Tucson, Arizona

John P. Hoffmann, Kyle W. Blasch, and Ty P. Ferre ́1

1

 Department of Hydrology and Water Resources, University of Arizona, 

Tucson, AZ 85721
48 Heat as a tool for studying the movement of ground water near streams 

Figure 1. Location of study area showing position of instrumentation relative to left streambank.

6.1 Meters from left bank

Combined time-domain reflectometry

and temperature-sensors

3.0 Meters 3.0 Meters 3.0 Meters

4.0 Meters

from left bank

1 2 KILOMETERS

0 1 2 MILES

0

Base from U.S. Geological Survey

digital data, 1:100,000, 1982

Universal Transverse Mercator

projection, Zone 12

R

Road

iver

Dodge

Boulevard

111� 110�55'

U.S. Geological Survey

streamflow-gaging station

Dodge Boulevard Bridge

10

32�20'

32�15'

Study

area

A R I Z O N A

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Column 1 Column 2 Column 3 Column 4

Flow direction

0.05 Meter temperature sensor

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Combined use of heat and soil-water content to determine stream/ground-water exchanges, Rillito Creek, Tucson, Arizona 49

Field instrumentation

The streambed was instrumented with a two-dimensional 

vertical array of 28 paired thermocouple temperature probes 

and time-domain reflectometry (TDR) moisture probes placed 

perpendicular to flow (fig. 2). The thermocouples used measure temperature with a precision of about 0.1 degree Celsius; 

TDR probes measure volumetric water content with a precision of about 3 percent (see Appendix A for discussion of thermocouple accuracy). The paired probes were arranged in four 

columns (profiles C1, C2, C3, and C4 in figure 2) spaced 3 

meters apart. There are seven rows (depths) within the array at 

depths of about 0.50, 0.75, 1.0, 1.25, 1.50, 2.0, and 2.5 meters 

below the stream-channel surface. Depths of the probes varied 

by as much as 0.25 meters owing to deposition and erosion 

during flow events. A near-surface temperature sensor also 

was placed adjacent to the paired two-dimensional array at a 

depth of 0.05 meter. Depth to the regional water table is about 

42 meters at the site. The U.S. Geological Survey (USGS) 

streamflow-gaging station Rillito Creek at Dodge Boulevard is 

45 meters downstream from the site.

Temperature data

As discussed in chapter one, heat can be transferred 

through sediments by advection and conduction. Although 

both advective- and conductive-heat transport occur during 

infiltration, advective-heat transport is more prevalent in high 

water flux settings, whereas conductive-heat transport is more 

prevalent in static or very low water flux conditions. For most 

hydrologic applications related to infiltration through alluvial 

sediments, advection is the primary mechanism for the transport of heat by flowing water and conductive heat transport is 

regarded as a negligible component of heat transfer. 

Subsurface temperatures change rapidly at the onset of 

streamflow (fig. 3) because heat transport is coupled directly 

with water flow through advection. The temperature changes 

are reduced in amplitude and show an increasing lag time with 

depth. Temperature changes occur in both the horizontal and 

vertical dimensions (fig. 4).

Soil-water content data

The highly transient conditions that exist at the onset of 

streamflow are difficult to simulate numerically; therefore, a 

direct analysis of water-content measurements probably is the 

most accurate method of estimating initial infiltration rates. 

Infiltration rates at the onset of streamflow can be estimated 

using wetting-front arrival times at successive TDR probes. 

Once streamflow ends, the water that has infiltrated into the 

subsurface continues to redistribute vertically and horizontally. The rate of drainage depends on the distribution of water 

Figure 2. Photograph and schematic of the two-dimensional array of sensors within the stream-channel deposits. Each black circle 

represents a temperature and time-domain reflectometry sensor. Refer to figure 6-1 for location of array within Rillito Creek.
50 Heat as a tool for studying the movement of ground water near streams 

Figure 3. Thermograph of Rillito Creek sediments at depths of 0.05, 0.5, and 1.0 meter. Solid bars above thermographs show periods of streamflow.

One-dimensional simulation results

As discussed in chapter one, temperature and water-content measurements are interpreted using numerical models that 

describe water flow and heat transport. Multidimensional flow 

simulations are required to accurately represent infiltration into a 

heterogeneous medium, such as layered stream-channel deposits, 

and near the margins of the wetted perimeter of the advancing 

wetting front where capillary flow dominates. However, infiltration is predominantly vertical near the center of streamflow 

in a homogeneous medium after a period of sustained flow. 

Infiltration was assumed to be predominantly vertical within the 

relatively homogeneous stream-channel deposits of Rillito Creek; 

therefore, simplified one-dimensional model simulations were 

used. The time from the onset of flow required for predominantly 

vertical infiltration to occur varies depending on streamflow 

conditions and the texture of the streambed material. For instance, 

small braided ribbon flows over fine-grained material may never 

result in predominantly vertical infiltration, whereas large bankto-bank flows of coarse-grained material may produce predominantly vertical infiltration beneath the streambed within minutes.

Thermographs predicted by numerical simulations are 

fitted to measured thermographs from the field by adjusting 

model parameters within appropriate ranges until the best 

match is found between simulated and measured thermographs 

(see Appendix B for details). A typical set of measured Rillito 

Creek thermographs and the best-fit numerically simulated 

thermographs are shown in figure 7. Numerical simulations 

throughout the subsurface at the end of streamflow. Drainage 

rates, similar to infiltration rates, are determined from the 

elapsed time between sharp decreases in water content at each 

depth (fig. 5). Drainage rates through the Rillito Creek streamchannel deposits typically are between 0.5 and 1.0 meters per 

day (Blasch and others, 2000).

Water-content data show rapid changes at the onset of 

streamflow (fig. 5). Volumetric water content increases from 

about 20 percent to 40 percent within minutes of the onset 

of streamflow. These initial infiltration rates were as high 

as 3.5 millimeters per second, which if sustained would be 

equivalent to 300 meters per day. The high rates are likely to 

include vertical and lateral flow components. Similar to the 

temperature data, the water-content data indicate that infiltration occurs in both the horizontal and vertical directions at the 

onset of streamflow (fig. 6). Drainage rates determined from 

water-content measurements after the cessation of flow for the 

same event for which modeled simulations are presented in 

this chapter were about 0.46 meter per day.

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Combined use of heat and soil-water content to determine stream/ground-water exchanges, Rillito Creek, Tucson, Arizona 51

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Figure 4. Two-dimensional temperature distribution within shallow stream-channel deposits. 

(A) Thermal transport through conduction before the onset of a streamflow event. (B) Thermal 

transport through a combination of advection and conduction at the onset of a streamflow 

event. Multidimensional percolation through the sediments. (C) Combined advection and conduction thermal transport to the deeper sediments several hours into a flow event.
52 Heat as a tool for studying the movement of ground water near streams 

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Figure 5. Water-content data showing rapid increases at the onset of streamflow; a stabilization of 

water content during the streamflow event; and subsequent drainage after the streamflow is over.
Combined use of heat and soil-water content to determine stream/ground-water exchanges, Rillito Creek, Tucson, Arizona 53

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Figure 6. Two-dimensional water-content distribution in sediments beneath Rillito Creek. (A) Soil-water content before the onset of 

streamflow. (B) Soil-water content 5 minutes after the onset of streamflow. (C) One-dimensional dewatering immediately after the cessation of flow. (D) One-dimensional dewatering approximately 2 days after the cessation of flow.
54 Heat as a tool for studying the movement of ground water near streams 

Discussion

Ground-water recharge is a critical component of the 

hydrologic cycle. Currently, many areas in the Southwestern United States pump more ground water than is naturally 

recharged. Current and future artificial recharge sites will 

shown in this chapter are for a bank-to-bank flow event 

in April 2001. Vertical flow is assumed since temperature 

changes were measured predominantly in the vertical direction. Although the simulated and measured thermographs are 

in general agreement, significant departures exist. Simulated 

temperatures can differ from measured temperatures for several reasons, such as incorrectly defined boundary conditions, 

incorrect hydraulic and thermal property assignments, or an 

inability for a one-dimensional model to represent multidimensional infiltration. In the case of the latter, multidimensional simulations might yield thermographs that are in closer 

agreement to field data than those shown in figure 7.

An example of simulated thermographs that best match 

the measured thermographs at 0.75 meter depth in two profiles 

is shown in figure 8. There is general agreement between 

simulated and measured thermographs. The predicted infiltration rates vary from less than about 0.35 to about 0.39 

meter per day throughout the 2-day flow period (fig. 9). This 

represents a variation in predicted infiltration rates of less than 

10 percent among the four columns, indicating that infiltration 

was uniform and predominantly vertical. The infiltration rate 

generally declines as the streamflow events proceed.

Figure 9. Simulated infiltration rates at columns 1, 2, 3, and 4 during a streamflow event.

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Figure 7. Measured and simulated thermographs at a depth of 

0.75 meter, column 3.

Figure 8. Set of measured and simulated thermographs for two 

adjacent columns.
Combined use of heat and soil-water content to determine stream/ground-water exchanges, Rillito Creek, Tucson, Arizona 55

become increasingly important in achieving sustainable water 

supplies. The potential exists to use water-content measurements and temperature measurements to evaluate the potential 

suitability of in-stream recharge facilities and to provide guidance on citing such facilities.

Infiltration rates can be estimated from temperature measurements; these estimates may be complimented by initial 

infiltration and drainage-rate estimates from water-content 

measurements. The water-content measurements enable better 

estimates of rapid infiltration rates associated with the onset 

of streamflow. In Rillito Creek, initial instantaneous rates 

were estimated to be as high as 3.5 millimeters per second, 

which included both vertical and lateral flow components that 

occurred only during the onset of streamflow. 

Within several minutes after streamflow has been established, the stream-channel deposits become fully saturated and 

remain so during subsequent flow. For this reason, temperature 

measurements are more useful for estimating infiltration rates 

during streamflow than are water-content measurements. Onedimensional analyses of temperature measurements collected 

during a streamflow period in April 2001 show that infiltration rates through the Rillito Creek stream deposits were 

sustained at about 0.37 meter per day; however, there was a 

general decline in infiltration rates over time during a flow. A 

decline in infiltration during streamflow events in the Rillito 

has been recognized using temperature methods by other 

investigators (Bailey and others, 2000a, b). They attributed 

this decline to the accumulation of a fine-grained surface layer 

that effectively clogged the streambed. One of their simulations required a change in the hydraulic conductivity of the 

shallow streambed sediments during streamflow to reproduce 

the observed subsurface thermographs. Another set of simulations showed that the hydraulic conductivity of this shallow 

streambed material changed four orders of magnitude between 

two sequential streamflow events.

An estimated sustained infiltration rate of about 0.37 

meter per day during streamflow agrees well with the estimated post-streamflow drainage rate of 0.46 meter per day. 

These rates show general agreement with estimates ranging 

from 0.41 to 0.50 meter per day made by other investigators 

along Rillito Creek (Burkham, 1970; Lane, 1983; Katz, 1987). 

The good agreement among these independent measures provides confidence that the temperature method enables accurate 

estimates of infiltration. As such, vertical arrays of temperature probes can be located along stream reaches to estimate 

the potential for in-stream recharge and to provide guidance 

on citing recharge facilities. However, high infiltration rates 

at shallow depths are not sufficient to ensure that water can be 

recharged at a high rate. Generally, the primary constraints on 

recharge rates are the total amount of water that infiltrates into 

the subsurface over time and the rate at which that water can 

move down through the entire subsurface into an aquifer. To 

estimate potential recharge rates, long-term vertical infiltration 

rates need to be estimated. Infiltration rates determined from 

shallow measurements should be considered an upper limit of 

the potential recharge rate for a particular site.

Introduction

Water in the Great Basin of Nevada is used by a variety of competing interests, including irrigation, mining, and 

municipal. A rapidly increasing population and expansion of 

large gold-mining operations are placing additional demands 

on the region’s limited water resources. Several deep open-pit 

mines in the Humboldt River basin of north-central Nevada 

require dewatering (fig. 1), which has nearly doubled groundwater withdrawals in the Humboldt River basin. Ground water 

pumped from the mines is being used to irrigate crops, to generate power, to recharge ground water, and to augment flow in 

the Humboldt River. Although mine dewatering has increased 

flow in the Humboldt River, which is used for irrigation, the 

long-term effects of this dewatering on the ground-water 

resources and flows in the Humboldt River are not completely 

understood. Studies in cooperation with the Nevada Department of Conservation and Natural Resources are designed to 

gain a better understanding on how ground-water withdrawals 

in the basin affect flow in the Humboldt River, an important 

agricultural water supply in northern Nevada. 

Ground water pumped for agriculture in the Humboldt 

River basin is from alluvial aquifers beneath the valleys, 

whereas most of the open pits being dewatered are in consolidated-rock aquifers at the base of or in the adjacent mountains. 

Average annual precipitation is less than 250 mm/yr on the 

valley floors and ranges from about 300 mm/yr on the lower 

parts of mountains to more than 1,000 mm/yr on some of the 

highest peaks. Water entering the basin-fill aquifers is mostly 

from (1) infiltration along intermittent channels on alluvial 

fans where streams exit the mountains; (2) infiltration along 

through-flowing streams such as the Humboldt River; and 

(3) subsurface flow from consolidated rocks in the adjacent 

mountains. Infiltration of precipitation on alluvial fans and 

valley floors is usually insufficient to supply large quantities 

of recharge to the basin-fill aquifers. Infiltration beneath the 

intermittent channels on the alluvial fans and streams that 

cross the valley floors is limited generally to snowmelt runoff, 

which occurs from late winter to early summer.

Purpose for study on Trout Creek

The purpose of the study on Trout Creek is to determine 

the frequency, duration and quantity of water that exits the 

mountains and enters the basin fill as seepage losses on the 

alluvial fan from snowmelt runoff and as subsurface flow from 

the consolidated rocks in the mountains to the basin-fill aquifer along the Humboldt River. Trout Creek, a tributary to the 

Humboldt River (fig. 2), was chosen as one of seven sites in 

the desert Southwest to study the distribution and frequency of 

recharge beneath intermittent streams that flow across alluvial 

fans as part of the Southwest Ground-Water Resources Project 

of the USGS. Trout Creek was chosen because it is within 

the area of a larger regional study and because it is typical 

of small intermittent mountain streams in the northern Great 

Basin where flow in the channel is dependent primarily on 

snowmelt runoff and on an occasional intense thunderstorm of 

short duration. Initial work on Trout Creek began in spring of 

1999 and will be completed in 2003.

Description of Trout Creek drainage

Trout Creek drains the northwest flank of Battle Mountain near the town of Valmy, and is about 25 km west of the 

town of Battle Mountain in north-central Nevada (figs. 1 and 

2). Trout Creek is perennial only for short reaches upstream 

of a northeast-southwest trending normal fault where flow is 

supported by small springs discharging from quartzite, chert, 

siliceous shale and greenstone of Ordovician Age (Willden, 

1964). Near the fault, the stream is confined to a narrow steep 

channel (figure 3A). Downstream of the fault, the channel 

has cut into older alluvium that covers greenstone, chert, 

and argillite of Pennsylvanian Age and rhyolitic flows and 

pyroclastics of Tertiary Age (Willden, 1964). Near the base of 

the volcanic rocks, seasonal springs and seeps discharge water 

into the stream during snowmelt (fig. 3B). At Marigold mine, 

the channel was moved westward to accommodate expansion 

of the mine (fig. 2). The stream reenters its original channel 

about 2 km below Marigold mine (fig. 2). After leaving the 

Chapter 8

Trout Creek—estimating flow duration and seepage 

losses along an intermittent stream tributary to the 

Humboldt River, Lander and Humboldt Counties, Nevada

David E. Prudic, Richard G. Niswonger, James L. Wood, and Katherine K. Henkelman
FRANCIS DEBOIS, FALLON, NEVADA, 1994 116�

115�

39�

40�

119�

41�

118�

117�

River

Rye Patch

Reservoir

Humboldt

Humboldt

River

Ruby Mountains

LANDER COUNTY

NYE COUNTY

ELKO COUNTY

WHITE PINE COUNTY

PERSHING COUNTY

CHURCHILL COUNTY

Winnemucca

Elko

Lovelock

HUMBOLDT COUNTY

PERSHING COUNTY

EUREKA COUNTY

LANDER COUNTY

Golconda

Battle

Mountain

Humboldt

Sink

CHURCHILL

LANDER

River

Humboldt

Battle

Mountain

WHITE PINE

EUREK A

Location of

Figure 2

Location of

Figure 2

Direction of

Photo

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0 10 30 50 KILOMETERS

20 50 MILES

20

10 30 40

40

EXPLANATION

Hydrographic-area boundary

Active mine--Circled symbol indicates mine

was being dewatered in 1998

Reno

Carson City N E V A D A

Area of

figure

(Humboldt E River Basin) ly

Tonopah

Las

Vegas

Base from U.S. Geological Survey digital data,

1:100,000, 1977-88; Universal Transverse

Mercator projection, Zone 11

58 Heat as a tool for studying the movement of ground water near streams 

Figure 1. (A) Map showing gold mines in the Humboldt River basin of Nevada that were being dewatered in 1996; and (B) oblique aerial 

photograph of one of the active mines being dewatered. 
0 5 MILES

0 5 KILOMETERS

40�37'30"

40�45'

117�15' 117�00'

EXPLANATION

Weather station

Modeled reach

Channel measurement site and identification—G is stream gage, T is surface

temperature recorder, and S is subsurface

temperature recorder

Stream cross section used in model

Model node

Mine

Fault—D is downthrown side,

U is upthrown side

Off-channel measurement site and identification—T is surface temperature recorder

D

U

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Valmy

Marigold

Mine

Lone Tree

Mine

Abandoned

channel

Base prepared by U.S. Geological Survey from digital data, 1:100,000 and 1:250,000

Universal Transverse Mercator projection, Zone 11

Battle

Mountain

Battle

Mountain

Humboldt

River

Trout

Creek

Middle

fan reach

Lower

fan reach

Upper

fan reach

Marigold

Mine reach

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North Fork

Trout

Creek

North Fork

1

2

3

4

5

6

7

Elko

Winnemucca

Battle

Mountain

NEVADA

Humboldt

River

Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 59

Figure 2. Location of Trout Creek in the Humboldt River basin, north central Nevada showing types of data collected along channel and 

extent of surface-flow routing model. Location of figure 2 is shown on figure 1.
D.E. PRUDIC, U.S. GEOLOGICAL SURVEY

D.E. PRUDIC, U.S. GEOLOGICAL SURVEY

J.L. WOOD, U.S. GEOLOGICAL SURVEY

J.L. WOOD, U.S. GEOLOGICAL SURVEY

Trout Creek where it crosses normal fault and emerges from

canyon; North Fork Trout Creek enters from left; view is to south.

Trout Creek downstream of North Fork; springs discharge along

creek near intersection of roads; temperature logger at site 2 is

downstream of road; view is to north.

Trout Creek on alluvial fan below Marigold mine; subsurface

temperature datalogger at site 4 is in orange box, view is to north.

Trout Creek at base of fan near Humboldt River floodplain; weir

and gage at site 7 is in foreground; view is to south.

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60 Heat as a tool for studying the movement of ground water near streams 

mountains, the stream flows north in a channel incised into a 

broad alluvial fan (figs. 3C and 3D) to the flood plain of the 

Humboldt River where the channel is no longer identifiable. 

Sediments of the alluvial fan are composed of sand and gravel 

mixed with clay and silt. Since 1999, flow reached the Humboldt River flood plain only for a few weeks during the spring 

of 1999 following a winter of above normal snowpack in the 

mountains. 

Above Marigold mine, the regional water table is within 

the pre Cenozoic-Age rocks (fig. 4) and is more than 150 m 

below the stream. The seasonal springs just downstream of the 

fault likely form as a result of perched water in the volcanic 

rocks during spring snowmelt. Depth to ground water gradually 

decreases to less than 10 meters next to the Humboldt River. 

Dewatering of the Lone Tree mine northwest of Trout Creek 

(fig. 2) began in 1992 and has caused the water table beneath 

Trout Creek to decline about 20 meters at Marigold Mine.

Figure 3. Photographs of Trout Creek (A) where it emerges across normal fault; (B) downstream of North Fork tributary; (C) 

on alluvial fan below Marigold mine; and (D) at base of alluvial fan near Humboldt River floodplain. Location of sites on Trout 

Creek is shown on figure 2.

Duration of flow estimated from temperature 

and stream stage 

Streams flowing onto alluvial fans likely are an important 

source of recharge to the alluvial aquifer in the Great Basin 

region. Yet the extent and duration of flow, and seepage loss 

rates along small mountain streams are often unknown. A 

series of recording temperature sensors were placed in Trout 

Creek (sites 2, 3, 4, 5, 6, and 7; fig. 2) and off channel (OC1; 

fig. 2) in April 1999 in an attempt to monitor the duration of 

runoff at different locations along the channel as described in 

Appendix A. Initially, the temperature sensors were placed on 

the streambed but this resulted in excessive heating of the sensors during the summer. Subsequently, the sensors were buried 

about 7 cm below the streambed in the channel and beneath 

land surface off channel. Additional temperature sensors were 

installed on the bank adjacent to sites 3, and 4 in March 2000 
1,100

1,200

1,300

1,400

1,500

1,600

ALTIT

U

D

E, IN

M

E

T

E

R

S

A

B

O

V

E

S

E

A LE

V

EL 1, 700

1,800

1,900

0 3 6 9 KILOMETERS

Vertical exaggeration x 21

EXPLANATION

Active mine area

Interstate 80

Valmy

1-G

2-T

3-GT

4-ST

5-ST

7-GST

?

7-GST

Well

Test hole

S N

Cenozoic basin-fill sediments

Cenozoic rhyolitic flows and pyroclastics

Pre-Cenozoic rock—Queried where uncertain

Fault—Arrows show relative vertical

movement.

Water table in 2000

Estimated water table in 1990

Measurement site on Trout Creek, location shown on figure 2

G — Stream-stage recorder

T — Stream channel temperature

S — Subsurface temperature

Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 61

Figure 4. Profile along Trout Creek from upper stream gage to Humboldt River floodplain showing thickness of Cenozoic sediments 

and volcanic rocks beneath the stream channel. Geologic information is from test holes and wells drilled near Trout Creek (Glamis Gold 

Mining Company, Valmy, Nev., written commun., 2002 and Nevada State Engineers Office, Carson City, Nev., written commun., 2002). 

Water-level data from Glamis Gold Mining Company, Nevada State Engineers Office, Newmont Mining Corporation (Winnemucca, Nev., 

written commun., 1999), and U.S. Geological Survey. Location of sites is shown on figure 2.

because initial evaluation of temperature data indicated that 

changing weather conditions complicated the interpretation of 

flow and no flow with stream temperature. 

Subsurface temperature measurements were made at 

three locations along the channel (sites 4, 5, and 7; fig. 2). 

Temperature measurements were made by attaching thermocouples placed at depths of 10, 20, 50, 100 and about 150 

centimeters beneath the channel to dataloggers (small computers) that routinely collected temperature at 30-minute intervals. The subsurface temperature measurements were designed 

to estimate seepage loss rates using the approach described in 

Appendix B, and also were useful in identifying the duration 

of flow. 

In addition to temperature measurements along and 

beneath the channel, three automated stream stage (waterlevel) recorders (pressure transducers) were installed along 

the channel to monitor flow. Newmont Mining Corporation installed the first stage recorder upstream of the fault 
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62 Heat as a tool for studying the movement of ground water near streams 

Figure 5. Daily mean discharge at two sites along Trout Creek during water year 2000. Daily mean discharge estimated from water 

levels (stream stage) recorded every 15 minutes at site 1 and every 30 minutes at site 3. No flow was recorded at site 7 since water-level 

recorder installed in March 2000. Data at site 1 is from Newmont Mining Corporation (Winnemucca, Nev., written commun., 2002). Location of sites is shown on figure 1.

(site1; fig. 2) in October 1999. Two additional recorders were 

installed by the USGS in March 2000 just upstream from 

Marigold mine (site 3; fig. 2) and at the base of the alluvial 

fan (site 7; fig. 2). Stage in the stream is recorded every 15 

minutes at site 1 and every 30 minutes at sites 3 and 7. Relationships between stage and discharge at sites 1 and 3 were 

determined from repeated flow measurements made with a 

pygmy meter over the range of observed flow. A rectangular-notch weir was installed during November 1999 at site 7; 

however, no flow has been recorded at this site since the weir 

was installed. 

Flow in Trout Creek upstream of the fault (site 1 on fig. 

2) was observed from October 1999 through early July 2000 

before becoming intermittent during July through September 

2000 (fig. 5). Spring snowmelt began near the end of February 

at site 1 and peaked in April. The daily mean discharges at 

sites 1 and 3 from the end of March to early June 2000 show 

good correlation, with less flow and a slight delay in peak 

discharge at site 3 (fig. 5). The gage at site 3 (6.2 km downstream from site 1) was not installed until March 29, 2000 and 

flow extended about 1 km downstream of this site on that date. 

Flow at site 3 ceased in June 2000 and the channel remained 

dry through September 2000. No flow was measured at site 7, 

at the base of the fan, from mid-March to September 2000 and 

there was no evidence of flow from November 1999 when a 

weir was installed to mid-March 2000. 

The duration of flow at selected locations on Trout Creek 

was estimated from streambed temperatures. Considerable 

interpretation, which may vary depending on the character of 

runoff in an intermittent channel, was needed to estimate the 

duration of flow from streambed temperatures. Flow at site 3, 

above Marigold mine, commenced on March 22, 2000, a week 

before the automated water recorder was installed at the site 

(fig. 6). Prior to March 22, the minimum streambed temperature each day was routinely below freezing. In contrast, the 

minimum temperatures at site 2, where flow was continuous, 

remained above freezing. Once flow commenced at site 3, 

the minimum temperatures corresponded more closely to the 
-10

0

10

20

30

MAR 15 MAR 18 MAR 21 MAR 24 MAR 27 MAR 30 APR 2 APR 5 APR 8

2000

T

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A

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D

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S

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0

10

20

30

S

T

R

E

A

M

S

T

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C

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TIM

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T

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S

A

B

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T

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Site 2-T, Surface temperature below North Fork D

Site 3-T, Surface temperature above Marigold mine

Site 3-G, Stream stage above Marigold mine

Flow commenced at site 3-T?

Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 63

Figure 6. Estimate of when flow began in March 2000 at site 3 from streambed temperatures. Location of site 3 is shown on figure 2.

minimum temperatures at site 2, except during some nights 

when water at the temperature sensor froze (temperatures 

slightly less than 0o C). Flow at site 3 was continuous until 

June 5, when flow ceased in the late afternoon and became 

intermittent until mid June (fig. 7A). The stage recorder was in 

operation during the first three days of the period of intermittent flow at site 3. Temperature of the streambed shows a 

deflection when flow ceased each afternoon and when it began 

in the morning. Apparently, sufficient moisture was left in 

the channel during each night that the minimum temperature 

remained similar to that at site 2, even though there was no 

flow in the channel. Although there is no record of stage from 

June 7 to June 28, 2000, temperatures at site 3 from June 7 to 

June 17 (fig. 7B) suggest that flow continued to be intermittent 

until June 14; afterwards the streambed dried sufficiently and 

the minimum temperature was higher than at site 2. 

Flow at site 4 (below Marigold mine) did not commence 

until April 9, 2000. On that date, the daily minimum temperature at site 4 began to correspond to that at site 3 (fig. 8). Prior 

to flow at site 4, the daily minimum and maximum temperatures were warmer than those at site 3 because site 4 is at a 

lower altitude (fig. 2) and because air temperatures had begun 

to warm rapidly. Once flow began at site 4, the minimum 

temperatures were similar to that at sites 2 and 3. However, the 

maximum temperature in the channel increased downstream 

(from site 2 to site 4) in response to heating of water during 

daylight hours and the maximum temperature at site 4 was 

similar to that at the off channel site OC1-T (fig. 2). Flow at 

site 4 may not have been continuous throughout the period of 

flow because temperature deflections similar to those during 

intermittent flow at site 3 were observed as noted on figure 8. 

Higher minimum temperatures after flow ceased in the 

channel at sites 3 and 4 suggest that the total period of flow 

(neglecting brief periods of intermittent flow) along the channel could be simply evaluated by comparing the streambed 

temperatures along the channel to a temperature recorder buried at a similar depth away from the channel. Such a method 

may not be usable everywhere, particularly if the minimum 

temperature at the off-channel site is similar to the minimum 

temperature of water in the channel.

The duration of flow down Trout Creek during snowmelt 

runoff in 2000 was estimated by subtracting the daily minimum temperatures at an off-channel site (OC1-T, fig. 2) from 

the daily minimum temperatures at sites 2, 3, 4, and 5 in Trout 

Creek (fig. 9) starting March 29, 2000 when the temperature 

sensors were all placed 7 cm below either the land surface or 

the streambed. The difference in the daily minimum temperature between site 4 and OC1 was near 0o

 C except during flow 

in the channel. The generally close agreement in minimum 

temperature between site 4 and OC1 during periods of no flow 
0

10

20

30

40

June 7 June 8 June 9 June 10 June 11 June 12 June 13 June 14 June 15 June 16 June 17

2000

T

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D

E

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No FlowNo FlowNo FlowNo FlowNo FlowNo FlowNo Flow

No Flow

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-10

0

10

20

30

May 28 May 29 May 30 May 31 June 1 June 2 June 3 June 4 June 5 June 6 June 7

2000

T

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D

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-10

0

10

20

30

S

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Site 2-T, Surface temperature below North Fork

Site 3-T, Surface temperature above Marigold mine

Site 3-G, Stream stage above Marigold mine

No FlowNo FlowNo Flow

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Figure 7. (A) Changes in streambed temperature compared with water level in stream (stream stage) during first week of June 2000. 

(B) Estimates of no flow determined from streambed temperature only during second week of June 2000. Location of site 3 is shown 

on figure 2.

64 Heat as a tool for studying the movement of ground water near streams 
Figure 8. Estimate of when flow began and period of intermittent flow (gray shaded area) in April 2000 at site 4 from streambed temperatures. Location of site 4 is shown on figure 2.

-10

APR 1 APR 3 APR 5 APR 7 APR 9 APR 11 APR 13 APR 15 APR 17 APR 17 APR 21

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Site 3-T, Surface temperature above Marigold mine

Site 4-T, Surface temperature below Marigold mine

Flow commenced at site 4-T

Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 65

is because site 4 is close to OC1 and because it is in a wide 

and shallow section of channel used to divert Trout Creek 

around Marigold mine. Minimum temperatures at the other 

sites (sites 2, 3, and 5) were generally less than the minimum 

temperature at OC1 even during periods of no flow because 

the channel is more incised at these locations and the steeper 

banks provide shade. Differences in daily minimum temperature during flow at sites 2, 3, and 4 (April 9–May 15) were 

similar except at site 4, where flow may have been discontinuous starting April 21 and continuing into May. Periods of no 

flow at site 4 were marked by a rapid increase in the minimum 

temperature relative to OC1 (difference is less negative) followed by rapid decrease in daily minimum temperature when 

flow recommenced. From field observations, snowmelt runoff 

during 2000 did not reach site 5 and the difference in daily 

minimum temperatures between site 5 and OC1 were consistently less than differences at sites 2, 3, and 4 during periods 

of flow (fig. 9). 

The end of snowmelt runoff at site 4 likely occurred on or 

near May 15 when the difference in daily minimum temperature at site 4 became less than at sites 2 and 3 (fig. 9). The end 

of snowmelt runoff at site 3 likely occurred near June 14 when 

the difference in daily minimum temperature became less than 

at site 2. Lastly, the generally increasing difference in daily 

minimum temperature between site 2 and OC1 (differences 

generally became more negative between the two sites from 

May to July) ceased on July 19 and the difference in daily 

minimum temperatures became less (fig. 9). This change suggests that flow ceased on or before that date at site 2, although 

there may have been periods of intermittent flow beginning 

at the end of June. The decrease in the temperature difference 

between site 2 and OC1 on July 19 also corresponds to the 

beginning of no flow at site 1 less than 1 km upstream (fig. 5). 

Subsurface temperatures beneath the streambed at sites 

4, 5, and 7 (fig. 2) were also used to estimate the duration of 

flow. During flow, heat in the stream is transmitted down as 

water infiltrates through the streambed. A marked changed in 

subsurface temperatures at depths greater than 50 cm beneath 

the streambed were observed beginning on April 9 (fig. 10A). 

The marked change in subsurface temperatures corresponds 

to a sudden change in temperature of the streambed (fig. 8) 

and provides additional evidence that flow began on April 9 at 

site 4. Estimating brief periods of discontinuous flow or when 
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Figure 9. Flow in stream determined from difference in daily minimum temperature at channel sites 2, 3, 4, and 5, and off-channel site 

OC1. Recording temperature sensors in Trout Creek were buried 7 centimeters beneath the streambed and off channel sensor was 

buried at a similar depth in soil. Location of sites is shown on figure 2. 

66 Heat as a tool for studying the movement of ground water near streams 

Streambed hydraulic conductivity and seepage 

loss rate estimated from subsurface temperature profile at site 4

During infiltration into the sediments beneath a stream, 

heat in the stream can be used as a tracer to estimate the ability 

of the sediments to transmit water (the property known as the 

hydraulic conductivity), which is important for estimating the 

rate of water flow (or seepage) through the sediments (Chapter 1 explains why heat can be used to estimate the seepage 

loss rate through a streambed). Consequently, temperature 

changes in sediments beneath the stream were used to estimate 

the hydraulic conductivity and seepage losses along a stream 

as described in Appendix B. During the spring of 2000, flow 

only reached site 4, the uppermost site, where thermocouples 

had been placed beneath the streambed. Thus, site 4 was the 

only place where an estimate of streambed hydraulic conductivity and seepage loss rates could be determined from a 

subsurface temperature profile. The inverse-simulation method 

described in Appendix B was used in the analysis. The period 

of flow from April 13 through April 19, 2000 was used for 

the analysis. Stream-water temperatures were used for the 

upper boundary and subsurface temperatures at 20, 50, and 

100 cm below the streambed were used as observations for 

model calibration. The model extended laterally on each side 

of the stream 15 m so that lateral flow would not be inhibited 

by no-flow boundaries on the sides. The best-fit simulation 

to the measured temperatures at depths of 20 and 50 (fig. 11) 

resulted in an estimate of the saturated streambed hydraulic 

conductivity of 0.56 m/d and a downward seepage loss rate of 

0.46 m/d (Appendix B; and Niswonger, 2001).

Uncertainty in the inversely predicted streambed seepage loss rate at Trout Creek was analyzed using Monte Carlo 

techniques (Niswonger and Rupp, 2000). The standard deviaflow in the channel ceases entirely is difficult to evaluate using 

the subsurface temperature profile because drainage through 

the sediments beneath the streambed continues for some time 

after flow in the channel has ceased. However, fluctuations 

at depths of 100 and 138 cm decreased after April 27, suggesting flow in the channel may have ceased on or before that 

date. Fluctuations in temperature also were observed at depths 

of 100 and 138 cm on May 1 and could have been caused by 

brief flow in the channel. The subsurface temperature profile 

at site 5 does not indicate flow because there were no temperature perturbations below a depth of 50 centimeters similar to 

those observed at site 4 (fig. 10), which is consistent with field 

observations.
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Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 67

Figure 10. Temperature in sediments beneath Trout Creek from March 28, 2000 to May 5, 2000 at (A) site 4 on alluvial fan below Marigold Mine and (B) site 5 at Interstate 80. Location of sites 4 and 5 is shown on figure 2. 
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Stream, measured

20 centimeters, measured

20 centimeters, simulated

50 centimeters, measured

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APR 13 APR 14 APR 15 APR 16 APR 17 APR 18 APR 19 APR 20

Figure 11. Comparison of simulated to measured temperatures for depths 20 and 50 centimeters beneath Trout Creek at site 4 from April 

13 to April 20, 2000. Estimated seepage rate into the streambed is 52 centimeters per day. Location of site 4 is shown on figure 2.

68 Heat as a tool for studying the movement of ground water near streams 

tion in the predicted seepage loss rate converged to a value of 

0.11 m/d for an average seepage loss rate of 0.52 m/d after 450 

realizations. This uncertainty suggests the ninety-five percent 

confidence interval in the predicted seepage loss rate was 

±0.22 m/d and was due to errors in representing stream sediment thermal parameters in the model. A similar uncertainty 

analysis was performed testing the effects of temperature 

measurement error on the predicted seepage loss rate (Niswonger and Rupp, 2000). The mean and standard deviations 

for the temperature measurement error were estimated based 

on manufacturer recommendations and other sources of error 

due to instrument installation. Ninety-five percent confidence 

in the predicted seepage loss rate due to temperature measurement error was much smaller than for thermal parameter 

uncertainty and was about ±0.05 m/d. 

Estimates of flow and seepage losses incorporated into a model of Trout Creek

Seepage loss rates as a function of stream stage were 

estimated for eight channel cross sections along Trout Creek 

in a manner similar to estimating the hydraulic conductivity 

and seepage loss rate from the subsurface temperature profile

at site 4, except the hydraulic properties determined at site 4 

were held constant and stream stage was allowed to vary over 

the vertical range of each channel cross section. The estimates 

of seepage loss rates as a function of stage were then incorporated into a one-dimensional surface flow model (Niswonger, 

2001). The model was formulated specifically for the case 

when there is an unsaturated zone separating the stream 

from the underlying aquifer, which is typical for intermittent 

streams that flow across alluvial fans in the Humboldt River 

Basin. The surface water model was used to evaluate the 

duration and quantity of seepage loss along the channel during 

differing flows from snowmelt runoff. Because there is little 

vegetation in or adjacent to the channel, much of the seepage 

loss along Trout Creek eventually recharges the underlying 

basin-fill aquifers.

Due to the intermittent nature of Trout Creek, an important aspect of the simulation model was the ability to simulate reaches of no flow. The modeled reach was divided into 

sections delineated by measured cross sections (fig. 2). The 

modeled reach began at site 3 where detailed stage and flow 

estimates were available. 

Discharge was measured at sites 2, 3, 4, 5, and 7 on May 

12, 1999 and at sites 2, 3 and 4 on April 13, 2000 (fig. 12). 

No flow was observed at sites 5 and 7 on April 13, 2000. The 
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DISTANCE DOWNSTREAM FROM SITE 1, IN KILOMETERS

Discharge measured

May 12, 1999

Simulated flow for

May 12, 1999

Discharge measured

April 13, 2000

Simulated flow for

April 13, 2000

Site 2

Site 3

Site 4

Site 5

Site 7

Model node 3

Model node 7

Model node 5

Model node 1

Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 69

Figure 12. Modeled flows compared with measured discharge along Trout Creek for May 12, 1999 and April 13, 2000. Discharge 

measurements were made between 7:30 am and noon Pacific Standard Time on May 12, 1999 and between 7:00 am and 9:00 am Pacific 

Standard Time on April 13, 2000 starting at furthest upstream site on both dates and working downstream. Model simulations are for the 

same time periods on each date. Location of sites and model nodes are shown on figure 2. 

average seepage loss between sites 3 and 4 was about 6 L/s 

per km over the 7.3 km reach of the stream on both dates. The 

seepage loss downstream of Interstate 80 (sites 5 and 7) on 

May 12, 1999 was about 20 L/s per km; or more than 3 times 

as much as that estimated between sites 3 and 4. Although, the 

channel becomes wider downstream of Interstate 80, the slight 

increase in area determined from measured channel cross sections was insufficient to produce the observed loss indicating 

that the streambed is more permeable downstream of Interstate 

80. 

The model was initially calibrated to the discharge 

measurements on May 12, 1999 using the measured flow 

and stream stage at site 3 as the upper boundary. The streambed hydraulic conductivity determined from the subsurface 

temperature profile was used over the modeled reach between 

sites 3 and 5 and resulted in a reasonable match of the measured seepage loss rate on both dates (as determined by the 

slope of the measured and simulated flows). The change in 

the modeled seepage loss rate does not correspond entirely 

to that measured between sites 5 and 7 because the model 

computed flows at the midpoint between cross sections, thus 

an increased seepage loss rate was simulated slightly upstream 

of where flow measurements indicate a change. More importantly, the dramatic increase in the seepage loss rate between 

sites 5 and 7 on May 12, 1999 could only be simulated when 

the hydraulic conductivity of the streambed was increased to 

1.2 m/d. 

Slight variations in the simulated channel seepage losses 

between sites 3 and 5 on both dates result from variations in 

the channel’s wetted perimeter at a particular stage from one 

channel cross section to the next. Slight changes in the slope 

of the measured discharge along the channel profile are consistent with variations in the simulated flow. The model was able 

to mimic variations in seepage losses according to differences 

in channel dimensions along the stream profile. This suggests 

that variations in seepage loss rates between sites 3 and 5 are 

due to variations in channel dimensions and not as much to 

variations in the hydraulic conductivity of the streambed sediments. 

After establishing that the model was calibrated with 

respect to seepage loss rates and discharge, the model was 

used to simulate snowmelt runoff from March 29, 2000 to 

April 27, 2000. During the modeled period, flow at site 3 

(fig. 5) was used as the upper-modeled boundary (fig. 13). 
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70 Heat as a tool for studying the movement of ground water near streams 

Figure 13. Simulated flow at selected distances along Trout Creek during April 2000. Flow at upper model boundary is estimated discharge at site 3. Locations of site 3 and modeled nodes are shown on figure 2.

Simulated flow during the morning of April 13, 2000 was 

compared with measured discharges (fig. 12). Simulated flow 

reasonably matched the measured discharge, indicating that 

the seepage loss rates determined from stream stage and model 

calibration at much higher flows worked well at the lower 

measured discharges during the spring of 2000. The measured 

discharges in April 13, 2000 are much less than those of May 

12, 1999 and result from less accumulation of snow during 

the winter of 2000 compared with the winter of 1999. The 

diurnal variation in flow shown in figure 13 is due to increased 

snowmelt as ambient temperatures increased until mid-day 

and then decreased as the temperature cooled into the night. 

The diurnal variation in snowmelt results in a diurnal variation in the point downstream where all the flow seeps into the 

underlying sediments. Simulated discharges at different places 

along the channel profile show this diurnal migration of where 

the flow ceases in the channel. The simulated duration of flow 

at model node 5 (a distance of 1.1 km downstream of site 4; 

fig. 2) shows duration of flow similar to that estimated from 

the surface and subsurface temperatures at site 4 (figs. 8,9 

and 10). The simulated flow begins on April 7, slightly earlier 

than temperature data indicates at site 4 and has brief periods 

of no flow for several days, consistent with changes in the 

diurnal surface temperature pattern (fig. 8). The modeled flow 

is continuous from April 12 through April 19, and becomes 

discontinuous afterwards. This is also consistent with observations at site 4. In the model simulation, flow does not reach as 

far as Interstate 80 (site 5), again consistent with surface and 

subsurface temperature measurements at that site (figs. 9 and 

10). 

Much of the seepage loss along Trout Creek during 

the first part of spring runoff in early April was upstream or 

adjacent to Marigold mine (fig. 14; site 2 to model node 2 on 

fig. 2). As snowmelt runoff in Trout Creek reached its peak in 

mid April, a greater percentage of the cumulative seepage loss 

was transferred downstream. By mid April, about 50 percent 

of the total loss was on the upper alluvial fan (between model 

nodes 2 and 4) and about 10 percent was on the middle fan 

(between model nodes 4 and 6) downstream of Marigold mine 

even though the duration of flow on the middle fan was only 

a couple of weeks. Snowmelt runoff during the spring of 2000 

was near or below normal on the basis of precipitation records 

during the fall of 1999 and winter of 2000. This suggests that 

during years of near normal to above normal precipitation, a 

substantial part of the seepage loss along Trout Creek is on the 

alluvial fan below Marigold mine. 
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Seasonal streamflow losses along Trout Creek near Battle Mountain, Nevada 71

Figure 14. Percentage of cumulative seepage for selected reaches along Trout Creek during April 2000. Locations of site 3 and modeled 

nodes along stream channel are shown on figure 2.

In summary, estimates of the duration of flow from 

stream temperature and subsurface temperature profiles were 

useful in understanding the variability of flow and seepage 

losses along Trout Creek. However, changing weather conditions, which can create considerable uncertainty, complicates 

the analyses of stream temperatures to ascertain periods 

of flow and no flow along the stream channel. Subsurface 

temperature profiles are useful at detecting when flow starts 

following extended periods of no flow and also can be used 

to provide reliable estimates of the seepage loss rates. However, the profiles are questionable in determining a precise 

time when flow stops because continued drainage through the 

streambed masks this event. Although not perfect, a simple 

analysis of comparing differences in daily minimum stream 

temperatures in the stream to an off-channel temperature 

sensor provides a reasonable estimate of the total duration of 

flow along Trout Creek. The method, however, is insensitive 

to brief periods of no flow during the night as the stream channel remains damp and has a minimum temperature similar to 

when flow is in the channel. A detailed analysis of the stream 

temperature along with additional field observations are 

necessary to determine the brief periods of no flow that occur 

as a result of decreased snowmelt at night. A channel routing 

model that incorporates channel seepage losses provided a 

means for estimating the cumulative volumes of seepage loss 

along Trout Creek as well as insight to the diurnal variability 

of flow and seepage losses along the channel.

Appendix A 

Determining temperature and thermal 

properties for heat-based studies of 

surface-water ground-water interactions

David A. Stonestrom and Kyle W. Blasch

Introduction

Advances in electronics leading to improved sensor 

technologies, large-scale circuit integration, and attendant 

miniaturization have created new opportunities to use heat as 

a tracer of subsurface flow. Because nature provides abundant 

thermal forcing at the land surface, heat is particularly useful 

in studying stream-groundwater interactions. This appendix 

describes methods for obtaining the thermal data needed in 

heat-based investigations of shallow subsurface flow.

Techniques for measuring temperature have evolved 

considerably since 1714, when German physicist Gabriel 

Daniel Fahrenheit introduced the sealed mercury-in-glass thermometer as an improvement over Galileo’s alcohol-in-glass 

thermometer (Star, 1983). The Galilean thermometer, being 

open to air, also responded to barometric fluctuations. The 

temperature scale that bears Fahrenheit’s name pays tribute 

to the significance of solving the long-standing problem of 

creating an accurate, readily transferable unit of temperature. 

Swedish astronomer Anders Celsius introduced a water-based, 

power-of-ten scale shortly thereafter that was later adopted by 

the Swedish Academy of Sciences as the basis of the metric 

temperature scale (Kant, 1984). On adoption, the Academy 

wisely reversed Celsius’ original assignments of 0 oC and 100 

oC, respectively, to the boiling and freezing points of water. 

Development and linkage of the Celsius scale to the thermodynamically based Kelvin scale paved the way for quantitative 

theories of heat flow and transformation during the 1800’s 

that formalized the concepts of heat capacity and thermal 

conductivity. Mathematicians, physicists, and engineers who 

developed the conceptual framework included such notables as 

Jean Baptiste Joseph Fourier, James Prescott Joule, and William Thompson (Lord Kelvin). Their work spurred scientific 

investigations into the thermal behavior of matter that continue 

today (Lienhard and Layton, 1988).

Industry, government, and other technical organizations 

provide periodic compendia of temperature-measurement 

techniques (for example, Herzfeld, 1962; Schooley, 1982; 

ASTM, 1993; CSIRO, 1998). These works include elaborate, 

special-purpose techniques for specific applications. The 

focus herein is on practical methods employed in hydrologic 

investigations. These methods are relatively inexpensive and 

accurate, and comprise the thermal measurement techniques 

used in the case studies of this circular. 

Types and characteristics of temperature sensors

Applications that use heat as a tracer of subsurface flow 

usually require multiple measurements of temperature through 

time at relatively inaccessible locations. This requirement 

generally limits suitable sensors to those that convert temperature to some form of electronic signal. The sensors most 

often employed are thermocouples (Constantz and Thomas, 

1996) and thermistors (LeCain, Lu, and Kurzmack, 2002). 

Resistance temperature devices (RTDs) and integrated-circuit 

(IC) sensors can also be used (Paluch, 2002). Figure 1 shows 

characteristic responses of these sensors together with advantages and disadvantages of each. Due to their small thermal 

masses, all of the sensors depicted in Figure 1 respond quickly 

to changes in temperature.

Thermocouples are the least expensive and most easily 

deployed sensor (fig. 1A). They can be fabricated as needed 

from thermocouple cable with little more than a soldering tool 

and a wire stripper. Thermocouples operate on the principle, 

discovered by Thomas Seebeck in 1821, that dissimilar metals 

in a circuit develop a voltage proportional to the temperature 

difference between their junctions (Finch, 1962). Thermocouples are more stable than thermistors but less stable than 

RTDs. Being self-powered, they are not subject to self-heating 

effects like thermistors, RTDs, and IC sensors. Of common 

thermocouple pairs, type T (copper-Constantan) is well suited 

for hydrologic applications due to its high sensitivity (relative to other thermocouple types) and corrosion resistance. 

Thermocouples require linearization and measurement of 

reference-junction temperatures. Linearization and reference 

circuitry is often integrated into data-acquisition systems, 

making thermocouples suitable for multi-point sampling 

arrays. An important consideration with thermocouples is that 

their output voltages are small, placing stringent demands on 

signal-conditioning equipment. A type T thermocouple generates only 0.04 millivolt per oC temperature difference between 

reference and measuring junctions, requiring the data-acquisition system to resolve four millionths of a volt (0.000,004 

V) to detect a 0.1-oC change in temperature. Stray currents in 

poorly configured systems can cause common-mode (error) 

voltages much larger than this (Horowitz and Hill, 1989; 

Morrison, 1998). Another consideration stems from the fact 

that any errors in reference-junction temperatures produce 

equal errors in indicated subsurface temperatures. Such errors 

may represent a time-invariant bias common to all measured 

temperatures, with perhaps little consequence on inferred 

transport. But if the reference junction is even a few millimeters from the reference-temperature-measurement point, 
74 Heat as a tool for studying the movement of ground water near streams 

Figure 1. Common electronic temperature sensors with schematic symbols, response characteristics, and 

advantages and disadvantages of each type (adapted from Hewlett Packard, 1983). RTD and IC are industry 

acronyms for resistance temperature device and integrated circuit, respectively. 

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Appendix A—Determining temperature and thermal properties for heat-based studies of surface-water ground-water interactions 75

thermal transients in the data-acquisition system can produce 

time-varying errors that are on the same order of magnitude as 

the signal of interest. Isolation of the data-acquisition system 

from thermal transients, usually by insulating and burying it, is 

essential for avoiding these errors.

The other commonly deployed sensor is the thermistor. 

Thermistors are temperature-dependent resistors made from 

transition-metal oxides (Hewlett-Packard, 1983). They have 

a large base resistance, typically on the order of 2000 ohms 

at 20 oC, and a nonlinear sensitivity in the range of -10 to -20 

ohms oC-1. Thermistors are usually embedded in glass or other 

material for chemical protection (fig. 1B). Thermistors can be 

made to microscopic dimensions, trading off calibration stability 

for thermal mass. But all thermistors drift with time, requiring 

periodic calibration (CSIRO, 1998). This becomes a consideration for long-term deployments in inaccessible locations.

Resistance temperature devices (RTDs) have highly 

stable calibrations even in harsh environments. Figure 1C 

shows a platinum RTD embedded in a ceramic body. Platinum 

RTDs are sufficiently stable to serve as calibration-transfer 

standards in metrology laboratories (Klock and Sullivan, 1962; 

Morris, 2002). The temperature sensitivity of RTDs is positive, 

slightly nonlinear, and small relative to thermistors (fig. 1). 

The relative insensitivity of RTDs, typically 0.04 ohms oC-1 for 

platinum, limits their use to settings with relatively large thermal gradients. Because of their low base resistance (typically 

100 ohms at 0 oC), RTDs require redundant leads and active 

compensation for lead-wire resistance. RTDs are also the most 

expensive of the common sensor types.

IC sensors are based on a semiconductor resistor embedded in an integrated circuit for conversion to a linear electrical 

output (fig. 1D). Current-output IC sensors require only two 

wires for connection to data-logging equipment, making them 

relatively easy to deploy (Sheingold, 1980). Unfortunately, 

most IC sensors are designed for dry environments and have 

relatively short times-to failure in moist environments. IC sensors are actively being developed, and may soon emerge as an 

advantageous choice for field deployments.

Single-channel temperature loggers offer an alternative to 

multiplexed sensor installations. Available from various manufacturers, these devices contain a thermistor or thermocouple 

integrated with signal-conditioning circuitry, a real-time clock, 

a memory unit, and an optical or infrared interface to provide 

access by computer or portable data shuttle. Figure 2A shows 

an example of one such device. Response times are slower 

than the sensors in Figure 1, but fast enough to track most 

hydrologic signals of interest (fig. 2B). Self-contained devices 

have the advantage of not needing an external data logger or 

connecting wires. The user retrieves the devices to acquire 

collected data.

Specific heat capacity, thermal conductivity, 

and thermal diffusivity

The thermal properties of soils and sediments can be 

obtained either from literature values, laboratory analyses of 

field samples, or field measurements. As explained in Chapter 1, 

Figure 2. (A) Self-contained temperature logger is about 3 cm in diameter. Note thermistor in mounting eyelet. (B) Dynamic response of 

four self-contained temperature loggers during calibration tests. Loggers, initially at room temperature, were immersed in a 0-oC bath, 

followed by a 32oC bath. The average 95% response time of the loggers was about 5 minutes. Data sets are color coded. To avoid clutter, 

individual data points are shown for only one of the loggers.

Thermistor

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76 Heat as a tool for studying the movement of ground water near streams 

thermal properties vary over a much narrower range than do 

analogous hydraulic properties. Because of this, estimates 

of water flux are insensitive to errors in thermal properties 

relative to errors in hydraulic properties. Thermal properties are difficult to measure outside of the laboratory. Thus, 

temperature is usually the only thermal parameter measured 

in the field.

Specific heat capacity is the amount of heat absorbed or 

released per mass of material when the material’s temperature 

increases or decreases by a small increment, operationally 

defined as one degree Celsius (oC). Multiplying specific heat 

capacity by density (mass per unit volume) gives volumetric heat capacity, which is the change in heat per volume of 

material per change in temperature. Units of volumetric heat 

capacity are joules per cubic meter per degree Celsius (J m-3

o

C-1). Heat capacities of relevant phases rank in the order: [liquid water] > [organic solids] > [mineral solids] >> [soil gases] 

(table 1A). Heat capacities of porous materials depend on their 

composition and bulk density, and vary linearly with water 

content (table 1B, fig. 3).

Heat capacities of unconsolidated materials can be determined in the laboratory with a calorimeter, which is an insulated chamber equipped with a stirrer and precision thermometer. The method of Taylor and Jackson (1986) determines heat 

capacity by mixing a slurry made from the porous medium 

with water at a different temperature. The heat capacity of the 

sediment is calculated from the masses and temperatures of 

initial slurry, added water, and final slurry. In practice, heat 

capacities are often calculated from the volume-weighted sum 

of heat capacities of constituents making up the material, using 

literature values (de Vries, 1966). Denoting volume fractions 

as x and heat capacities as c, the volumetric heat capacity of 

the bulk material Cb is approximately

Cb = xwcw + xoco + xmcm+ xaca,

where subscripts w, o, m, and a denote water, organic 

solids, mineral solids, and air, respectively. 

Thermal conductivity, κ, is a measure of a material’s ability to conduct heat. It is defined as the amount of heat transTable 1A. Thermal properties of selected materials -- Individual phases

Individual phase

Density

(106 g/m3)

Volumetric

heat capacity

(106 J/m3 °C)

Thermal

conductivity

(W/m °C)

Thermal

diffusivity

(10-6 m2/s)

Air1 0.001 0.001 0.024 19.

Liquid water1 1.0 4.2 0.60 0.14

Ice2 0.9 1.9 2.2 1.2

Quartz3 2.7 1.9 8.4 4.3

Average, soil minerals3 2.7 1.9 2.9 1.5

Average, clay minerals4 2.7 2.0 2.9 1.5

Average, soil organic matter3 1.3 2.5 0.25 0.10

Table 1B. Thermal properties of selected materials -- Porous media

Porous medium

Bulk

Density

(106 g/m3)

Porosity

(Vpores/Vbulk)

(Liquid)

Water

content

Volumetric

heat capacity

(106 J/m3 °C)

Thermal

conductivity

(W/m °C)

Thermal

diffusivity

(10-6 m2/s)

Tottori sand5 1.83 0.31 saturated 2.6 2.2 0.85

Clarion sandy loam6 1.38 0.48 saturated 3.2 1.8 0.55

Harps clay loam6 1.21 0.54 saturated 3.2 1.4 0.42

Sandfly Creek sand7 1.50 0.43 dry 1.3 0.25 0.18

Yolo silt loam8 1.30 0.51 dry 1.1 0.26 0.23

Clarinda clay7 1.16 0.56 dry 1.2 0.18 0.15

Snow9 0.46 0.50 dry 1.0 0.71 0.68

Snow9 0.18 0.80 dry 0.4 0.13 0.36

Snow9 0.05 0.95 dry 0.1 0.06 0.60

1

Carslaw and Jaegger (1959, p. 497); 2van Wijk and de Vries (1966a, p. 40); 3van Wijk and de Vries (1966b, p. 105); 4de Vries (1966, p. 210); 5Hopmans, 

Simunek, and Bristow (2002); 6Ren, Kluitenberg, and Horton (2000); 7Bristow, Kluitenberg, and Horton (1994); 8Wierenga, Nielsen, and Hagan (1969); 9

van Wijk and de Vries (1966b, p. 110).
Appendix A—Determining temperature and thermal properties for heat-based studies of surface-water ground-water interactions 77

mitted per unit time per unit area per unit temperature gradient. Units of thermal conductivity are watts (joules per second) 

per square meter per degree Celsius per meter (W m-1 oC-1). 

The thermal conductivity of porous materials depends upon 

the composition and arrangement of the solid phase. Coarsegrained materials generally have higher thermal conductivities 

than fine-grained materials. Also, because water conducts heat 

much better than air, thermal conductivity depends strongly on 

water content (table 1A and B; fig. 3). Due to the complexities 

of pore geometry, this dependence is non-linear and difficult 

to predict (Wierenga, Nielsen, and Hagan, 1969). In practice 

empirical equations are used to fit measured thermal-conductivity data over limited ranges of water content (Hopmans, 

Simunek, and Bristow, 2002). 

Thermal conductivities of porous media can be measured 

using steady-state or transient-state methods (Jackson and Taylor, 1986). Steady-state methods facilitate testing of Fourier’s 

law, which is almost universally assumed to govern heat 

conduction (Carslaw and Jaeger, 1959). Maintaining a thermal 

gradient in moist materials, however, induces fluid flow along 

temperature and density gradients. Fluid flow complicates the 

measurement of thermal conductivity because advection (as 

well as conduction) transfers heat. In partly saturated media, 

latent heat transfer (that is, heat associated with transitions 

from vapor to liquid and liquid to vapor) become important. 

Additionally, water contents in partly saturated media become 

non-uniform when temperature gradients are maintained. To 

avoid complications associated with these processes, rapid 

transient-state methods have been developed for measuring 

thermal conductivities in moist materials. The pulsed cylindrical-heat-source method (also known as the pulsed thermalprobe method; described below), is the most commonly used 

transient method for measuring thermal conductivities in both 

field and laboratory applications (de Vries, 1952; Wierenga, 

Nielsen, and Hagan, 1969; Jackson and Taylor, 1986; Shiozwa 

and Campbell, 1990).

Thermal diffusivity is the ratio of thermal conductivity 

to volumetric heat capacity. The units of thermal diffusivity 

are meters squared per second (m2 s-1). Thermal diffusivity is 

a measure of how quickly an imposed change in temperature 

is transmitted through the material. Air has a large thermal 

diffusivity, despite having a low thermal conductivity, because 

its volumetric heat capacity is small (table 1A). With almost 

no capacity for storing or releasing heat, temperature signals 

travel quickly through air.

Jackson and Taylor (1986) described a method for the 

direct determination of thermal diffusivities of soils and sediments. The method analyzes transient temperatures within 

a sample as heat is applied to its surface through a copper 

plate. The method, while relatively simple, is difficult to apply 

outside the laboratory. Recent advances in the pulsed thermalprobe method have produced field-deployable probes that 

simultaneously determine various combinations of heat capacity, thermal conductivity, and thermal diffusivity (Campbell, 

Calissendorff, and Williams, 1991; Bristow, Kluitenberg, and 

Horton, 1994; Kluitenberg, Bristow, and Das, 1995; Hopmans, 

Simunek, and Bristow, 2002). These techniques apply heatpulse theory to cylindrical probes made from hypodermic-needle tubing. One probe contains a heater. Parallel to this probe 

are one or more auxiliary probes for measuring temperature 

responses. Pulses of heat induce changes in surrounding temperatures measured by auxiliary probes. Analytical or numerical analyses of temperature histories produce estimates of 

thermal properties. Pulsed thermal probes have been combined 

with time-domain-reflectrometry probes for simultaneously 

measuring thermal properties, water content, and bulk electrical conductivity (Noborio, McInnes, and Heilman, 1996; Ren, 

Noborio, and Horton, 1999).

Figure 3. Dependence of volumetric heat capacity and thermal 

conduction on water-content for selected materials. Dashed lines 

are volumetric heat capacities calculated as described in the text, 

using data from table 1A. Points are experimentally determined 

thermal conductivities, from deVries (1966). Solid curves are 

empirical fits to the thermal-conductivity data.

Sensor deployment and data acquisition

A pipe driven into loose sediments can provide a temporary casing while sensors are deployed to desired depths. The 

sediments collapse around the wires as the pipe is withdrawn 

(fig. 4A, B, and C). To avoid induced preferential flow, 

intervals between sensors can be grouted with swelling clay 

(Nielsen and Sara, 1992) or expanding foam (Faybishenko, 

2000). These materials are emplaced through the temporary 

casing as the casing is withdrawn. Proper grouting is required 

in cohesive soils and sediments. To minimize disruption of 

sedimentary layers and soil structures, sensors can be installed 

through holes that slant diagonally beneath the study area or 

extend horizontally from an adjacent access point (Faybishenko, 2000). Wires connecting streambed sensors to remote 

data loggers need to be deeper than the maximum depth of 

scour. Conduit anchored to the streambed can help protect 

the wires. Deploying a precision temperature reference on the 

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78 Heat as a tool for studying the movement of ground water near streams 

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Appendix A—Determining temperature and thermal properties for heat-based studies of surface-water ground-water interactions 79

Figure 4. Field deployment of temperature-measuring equipment. (A,B,C) Installation of thermocouple sensors in a stream channel. 

(D,E) Data logger for thermocouple installation. (F) Installation of stream-bed sensor. (G) Swing-out thermocouple arm on access tube. 

(H) Top of access tube prior to grouting. (I) Grouting access tube with two-component foam. (J,K) Access-tube enclosure at channel 

surface. (L) Single-channel temperature logger on cable for suspension in access tube. Foam baffles on either side of logger prevent 

advection. See text for additional explanation.

Design of temperature-measurement arrays

Success of thermal methods for quantifying surface-water 

ground-water exchange is dependent on appropriate placement 

of temperature sensors. Appropriate placement depends on (1) 

hydraulic and thermal properties of the sediments, (2) climatic 

conditions, which determine the nature of thermal forcing, (3) 

anticipated pore-water velocities, and (4) practical considerations, such as depth of scour. Experimental design includes 

selecting the frequency of data collection. While the overall 

strategy will be dictated by the purpose of the study, standard 

principles of experimental design should be incorporated at 

every stage of planning (Garcia-Diaz and Phillips, 1995). In 

large-scale projects, formalized data-quality objectives can 

help produce efficient measurement networks (USEPA, 2000).

Preliminary modeling is useful for selecting measurement 

locations and frequencies (Constantz, Stonestrom, and others, 2001). Fluid flow modulates the transmission of thermal 

signals into the profile (van der Kamp and Bachu, 1989; 

Silliman, Ramirez, and McCabe, 1995). Fluid flow can thus 

be determined by the departure of temperatures from a purely 

conductive pattern (Silliman and Booth, 1993; Constantz and 

Thomas, 1996). To guide sensor placement, theoretical temperature patterns can be calculated from numerical solutions 

of the coupled transport equations (Appendix B). For simple 

cases, theoretical temperature patterns can be predicted from 

analytical solutions. The analytical solution for pure thermal 

conduction in a deep, uniform profile with sinusoidal heating 

at the land surface is (Carslaw and Jaeger, 1959)

∆T(z,t) = A · e-z/D · sin[(2π/P)(t-t0)-(z/D)],

where ∆T is the departure of temperature from the average value, z is depth, t is time, A is the amplitude of temperature at the surface, D is the damping depth, P is the period 

of surface temperature, and t0 is the time at which ∆T equals 

zero. The damping depth D is equal to (Pα/ π)

-1⁄2, where α is 

the thermal diffusivity.

Daily and annual temperature fluctuations imposed at 

the land surface are quasi-periodic. As periodic thermal waves 

move into a profile, the storage and release of energy by the 

conducting medium attenuates the signal as it propagates 

away from the thermally forced boundary. In consequence, 

the magnitude of periodic temperature perturbations decreases 

with depth. The depth below which cyclic surface fluctuations 

wiring panel reduces reference-junction errors. A thermally 

conductive strip on the wiring panel minimizes temperature 

offsets between the reference junction and reference-junctiontemperature measurement point. Burial of loggers in watertight containers that are packed in thermal insulation further 

reduces errors from temperature transients (fig. 4D and E).

Self-contained temperature loggers can be buried directly 

in the ground with or without protective housings, or deployed 

in access tubes. Loggers directly buried in stream channels 

usually have housings that are tethered to anchors driven into 

the channel upstream of the measurement point (fig. 4F). 

Access tubes need to be grouted to prevent preferential flow 

down the annular space around the tube (figs. 4H-J). Baffles 

inhibit thermally induced advection (fig. 4L). In addition to 

the self-contained temperature loggers, figures 4G-L also 

show external thermocouples on moveable arms that press 

against surrounding sediments after the access tube is in position. A two-component expanding foam grouts the annular 

space, locking the arms into position as it hardens (fig. G-J).
80 Heat as a tool for studying the movement of ground water near streams

of a given magnitude have no measurable effect depends on 

the period of the fluctuations, the precision and accuracy of 

the temperature measurements, and the velocity of subsurface 

fluid flow. For the purely conductive case, the depth D at which 

daily temperature fluctuations are damped 63% (= 1 – e-1) is 

approximately 0.08 m in dry sand and 0.14 m in wet sand (van 

Wijk and de Vries, 1966b). Damping depths change in direct 

proportion to the square root of the period of fluctuations. 

Annual fluctuations thus have damping depths that are roughly 

19 times (= 365-1⁄2) greater than their diurnal equivalents. 

Damping depths for annual fluctuations (in the absence of 

fluid flow) are about 1.5 m in dry sand and 2.7 m in wet sand. 

Downward movement of water increases the apparent damping depth; similarly, upward movement decreases it. Instruments used for recording temperatures in field installations 

typically have resolutions ≥0.01 oC and accuracies ≥0.1oC. 

The maximum depth to which annual temperature cycles are 

resolvable is thus usually about 10-15 meters.

Temperature sensors need to be located within the thermally active zone for studies of surface water-ground water 

interactions. Depending on the requirements of the study, sensors can be placed at uniform-depth increments, exponentially 

increasing increments, or according to stratigraphy or other 

hydrogeologic feature. Multi-dimensional arrays of sensors 

allow assessment of heterogeneity and lateral flow. Multiple 

sensors at the same location, possibly of different types, 

reduce (or expose) uncertainty and provide insurance against 

sensor failure. 

An increasing number of techniques can measure temperature and even thermal properties in field settings. These 

techniques facilitate the use of heat as a tracer of exchanges 

between surface water and ground water. As new sensors and 

data-acquisition systems come onto the market, costs should 

decrease further while accuracy improves and the variety of 

instrumental options expands. Thermal techniques will continue to improve understanding of surface water-ground water 

interactions and other hydrologic processes as well.
Appendix B

Modeling heat as a tracer to estimate 

streambed seepage and hydraulic conductivity

Richard G. Niswonger and David E. Prudic

Introduction 

This appendix focuses on estimating streambed seepage 

and hydraulic conductivity using numerical model techniques 

and presents the steps that are normally used in making the 

estimates. The first part describes several conceptual frameworks for which heat as a tracer has been used to estimate 

streambed seepage and hydraulic conductivity; the second 

discusses published U.S. Geological Survey (USGS) numerical models commonly used to model heat as a tracer; the third 

outlines several approaches for modeling; the fourth describes 

the importance of observational data in assessing model 

results; the fifth presents guidelines for model calibration; and 

the last discusses methods for performing sensitivity analyses 

and estimating uncertainty. 

Numerical models (for example models by Voss, 1984, 

Kipp, 1987, and Healy and Ronan, 1996) have been developed 

that solve the equations governing the flow of water and heat 

through sediments (Stallman, 1965). These models can be 

used for both gaining and losing streams to estimate streambed 

seepage and hydraulic conductivity. 

Conceptual framework

A conceptual framework is necessary to construct 

a model for estimating streambed seepage and hydraulic 

conductivity using temperature data in the stream and in the 

sediments surrounding the stream. Streambed refers to the 

sediments that exhibit changes in temperature due to variations in the thermal energy in the stream and the streambed 

thickness will differ among streams. The application of heat as 

a tracer provides estimates over a finite volume of space. In all 

cases, simplifications and assumptions will be made in order 

to estimate seepage and hydraulic conductivity from temperature measurements. The conceptual framework of water 

exchange through the streambed will differ depending on the 

direction of ground-water flow. Surface water usually has 

greater variations in temperature compared with water in the 

underlying sediments and consequently, changes in temperature in the streambed are greater for losing streams (Lapham, 

1989). Using streambed temperatures beneath gaining streams 

may require an analysis of other thermal inputs to the stream 

in addition to the contribution from ground water. Three 

examples are presented to illustrate common water exchange 

through the streambed. These examples are differentiated by 

the dominant direction of flow through the streambed.

Development of a conceptual framework requires a combination of hydrologic intuition and data interpretation. The 

application of heat as a tracer begins with an initial assessment 

of the stream and its relation to ground water. A relation can 

be determined by comparing the elevation of water levels in 

nearby wells with the elevation of the stream surface (stream 

stage) and the relation between stream temperatures with 

temperatures in the streambed. Shallow wells can be installed 

into or near the streambed to estimate the direction of water 

exchange across the streambed. Because the stream surface 

and ground-water elevations may change over short periods 

of time, measurements of stream surface and ground-water 

elevations are important during the period when temperatures 

are being measured.

The first example considers one-dimensional (1d) downward flow through the streambed (fig. 1). Downward flow (or 

nearly downward flow) through the streambed occurs when 

the water table is well below the stream and the streambed 

sediments are not completely saturated or the sediments are 

saturated but water pressures in the sediments are at or near 

zero. For streambed sediments that are unsaturated, a downward hydraulic gradient of one can be assumed. However, 

measuring the water content of the streambed is important. If 

the ground-water elevation is near the streambed elevation, 

Figure 1. Conceptual framework when flow through streambed is 

downward.

Streambed

sediments

Heat and

water flow

are strictly

vertical

Temperaturemeasurement

point

Stream stage

Ground-water level

Well with screen

Heat and

water flow

are vertical
82 Heat as a tool for studying the movement of ground water near streams 

seepage across the streambed may be mostly downward but 

the downward hydraulic gradient will need to be determined 

by measuring the water-level difference between the stream 

and a well installed beneath the stream.

A numerical model can be used with measured streambed temperatures to test the assumption of downward seepage 

beneath streams. If the streambed seepage is not downward, 

then a simple model that assumes only downward flow will 

not be able to match the measured streambed temperatures and 

a more complicated conceptual framework will be required. 

The second example considers two-dimensional (2d) 

flow through the streambed that is both outward and downward (fig. 2). This example is used when ground-water levels 

are near the top of the streambed and hydraulic gradients 

have both a downward and outward component. Water-level 

measurements made in shallow wells beneath the stream and 

along the stream banks can be used to determine the direction 

of the hydraulic gradient. Seepage may occur in 2d for unsaturated streambeds that have a variety of sediments, which have 

different water and heat transmitting properties. For this case, 

it is usually necessary to measure streambed sediment water 

content or water pressure (negative when unsaturated) to estimate the streambed seepage and hydraulic conductivity. 

The third example considers 2d flow through the streambed that is both parallel to the stream and vertically downward 

(fig. 3). This conceptual framework is used when groundwater levels are near the top of the streambed and the stream 

is losing flow along its upper reach while gaining flow along 

its lower reach. This situation occurs commonly in streams 

from scales of a few meters (for example—between pools and 

riffles) to many kilometers (for example—where changes in 

sediment properties or stream gradients force ground water to 

discharge into the stream).

Streambed seepage and hydraulic conductivity normally 

are not estimated with three-dimensional (3d) models because 

available data are not sufficient to refine estimates beyond 

what can be determined from 1d or 2d models. Public-domain 

models such as HST3D (Kipp, 1987) are readily available for 

simulating 3d systems. Three-dimensional flow and transport models have not been used because data collection costs 

increase exponentially and conceptualization of the flow system becomes much more difficult. 

Possible line of symmetry

Ground-water

level

Stream

stage

Possible line of symmetry

Temperaturemeasurement

point

Well with

screen

Figure 2. Conceptual framework when flow through streambed is downward and outward.
Appendix B—Modeling heat as a tracer to estimate streambed seepage and hydraulic conductivity 83

Model descriptions

Common to all models used for applying heat as a tracer 

are the governing equations that are solved. These equations 

include some form of the variably saturated or strictly saturated ground-water flow equation coupled with an energy 

and/or solute transport equation. Short descriptions of the 

USGS models VS2DH (Healy and Ronan, 1996) and SUTRA 

(Voss, 1984), which have been used to estimate streambed 

seepage and hydraulic conductivity with temperature data, are 

presented in this section. Each model has detailed documentation that explains how the model can be used to simulate the 

transport of heat through ground water. All of the models are 

available free and can be downloaded from the USGS website (http://water.usgs/nrp/gwsoftware/). When using heat as 

a tracer, the most commonly used model within the USGS 

is VS2DH. Examples of how heat as a tracer was used with 

VS2DH are presented by Ronan and others (1998) and Bartolino and Niswonger (2000). 

Other ground-water flow and heat transport models may 

be useful, and warrant consideration, as well. Model selection 

is based on the desired criteria of interest. For example, if the 

influence of temperature on streambed biologic activity were 

a criterion of interest, then an alternative model that has the 

necessary equations embedded into it would be preferred.

VS2DH

VS2DH is a 2d variably saturated ground-water flow 

model that was modified to simulate heat transport by advection and conduction (Healy and Ronan, 1996). VS2DH uses an 

energy transport approach via the advective-dispersion equation (Healy 1990) for simulating heat transport. A Windowsbased graphical user interface was developed for VS2DH, 

called VS2DI (Hsieh and others, 2000). This interface allows 

the user to quickly develop a model using dialogue boxes and 

a point and click approach for creating all the needed input 

information for VS2DH. The post-processing component of 

VS2DI allows the user to visualize model output for evaluating results. The process of adjusting the hydraulic conductivity 

until measured and simulated temperatures are in close agreement requires the post processing of model results outside of 

the VS2DHI environment. 

SUTRA

SUTRA is a 2d model that solves the variably saturated 

fluid density-dependent ground-water flow equation (Voss, 

1984). In addition, SUTRA simulates either heat or single 

species chemically reactive transport. Because of its finite-element construction, SUTRA offers more flexibility than finite 

difference models. This may be a useful attribute for incorporating variability in streambed surfaces as well as heterogeneity in hydraulic parameters of the subsurface. SUTRA’s ability 

to simulate density-dependent flow makes it a useful model 

when simulating systems where buoyancy effects are important, such as for large solute or heat gradients. SUTRA, along 

with a Windows-based graphical user interface and post-processor, can be downloaded from the USGS website. 

Building the model

Creating a numerical model of a stream and its streambed 

involves converting the conceptual framework into input that 

can be used by the selected model. The input requirement for 

each model is specific and only general details are provided 

in this section. The model domain and boundaries for the 

conceptual frameworks described in figures 1 and 2 are shown 

in figure 4. The model domain and boundary conditions corresponding to the conceptual framework presented in figure 3 

are shown in figure 5. 

Upstream

ground-water

level

Downstream

ground-water

level

Temperaturemeasurement

point

Well with

screen

Stream stage

 Figure 3. Conceptual framework when seepage through the streambed parallels stream profile.
84 Heat as a tool for studying the movement of ground water near streams 

Figure 4. Model domain showing boundary conditions generalized for models of downward and outward flow through the streambed.

Surface boundary

Surface boundary conditions account for heat and water 

exchange between the stream and streambed. The hydrostatic 

pressure exerted by the stream on the streambed is represented 

by a total or pressure head boundary condition. Heat exchange 

into and out of the stream is modeled by setting the temperature boundary equal to the measured stream-water temperature. In general, surface boundary conditions of the stream will 

be time varying because both stream temperature and stream 

stage often vary on an hourly basis.

Surface boundary conditions depend on the dimensionality of the conceptual framework. A 1d model will have only 

one node that represents the stream boundary condition; 

however, a 2d model that is perpendicular to the stream (fig. 4) 

will have several nodes that represent the stream and several 

nodes that represent the stream bank above the stream stage. 

Ephemeral streams that lose all their water to the streambed 

may be dry for part of the simulation period. For sections of 

the stream that are dry, only a conductive temperature boundary condition is defined equal to the measured temperatures of 

the dry streambed.

When performing 2d modeling of a stream with fluctuating stream stage, all model nodes that lie below the highest 

stream stage should be set as a time-dependent total head 

boundary. This approach avoids activating and deactivating 

stream boundary nodes every time the water level rises and 

falls. If the total head applied to a node is less than the elevation of the node, the node will have a negative water pressure, 

as would be the case for a draining stream bank. Stream bank 

temperature measurements are used to define the boundary 

condition along the surface of the model above the stream 

stage.

Finally, a 2d model that is parallel to the stream (fig. 5) 

will have several nodes that represent the stream in profile. 

Each node along the stream profile is represented by a stream 

stage and temperature boundary. Normally, measured stream 

stage and water temperature are used to define the boundary 

conditions at all nodes. 

Subsurface boundary conditions

Subsurface boundary conditions also vary depending on 

the dimensionality of the conceptual framework. A 1d model 

will have a single node to represent water and heat exchange 

across the bottom of the model, whereas a 2d model will have 

a series of nodes (figs. 4 and 5). For the case when the water 

Possible line

of symmetry

Time-variable head

and temperature boundary

No flow and time-variable

temperature boundary

Specified head and constant

temperature boundary

Constant or time-variable boundary

when horizontal flow dominates

Temperature

measurement

point

No-flow boundary

when vertical flow

dominates
Appendix B—Modeling heat as a tracer to estimate streambed seepage and hydraulic conductivity 85

Figure 5. Model domain showing boundary conditions generalized for models of flow through streambeds along a stream profile.

table is below the top of the streambed, the bottom of the 

model can be represented by a zero pressure head boundary 

and specified temperature equal to the measured temperature 

at the water table. For the case when the water table is at or 

near the top of the streambed, the bottom boundary can be set 

equal to the measured water levels and temperatures in wells. 

If water flow through the streambed in both 2d models is horizontal, then the bottom boundary can be assigned as no water 

and heat flow. 

The sides of a 1d model are always set for no water or 

heat flow (fig. 4). Side boundaries of a 2d model are dependent on the hydraulic gradient through the streambed. When 

the water table is below the top of the streambed, the lateral 

boundaries for a 2d model perpendicular to the stream (fig. 4) 

are placed far enough away from the stream so they have no 

influence on the infiltrating water. The lateral boundaries for 

a 2d model parallel to the stream are set equal as either water 

and heat flow or as a specified head and temperature, provided 

pressure and temperature data are available in the streambed 

above the water table. When the water table is at or near the 

top of the streambed, the side boundaries for both 2d models 

(fig. 4 and 5) are assigned measured water levels and temperatures from wells placed at different depths. 

Initial conditions

Initial estimates of head and temperature are needed for 

every active node inside of the model boundaries. There are 

two common ways of defining heads and temperatures at all 

the active nodes: spatial interpolation and simulation.

 Point measurements of head and temperature are interpolated to all the nodes in the model spatially. This approach 

works relatively well if there are enough measurements to 

define the temperature distribution throughout the model 

domain. However, this approach can introduce bias into the 

model results, particularly early in the simulation period. 

The bias can be explained by comparing the elapsed simulation time to rates of change in simulated temperatures. If the 

simulation begins with a temperature distribution that matches 

measured data, then as time passes, the simulated temperatures will continue to be similar to the initial temperatures 

(called an initial value problem) until the effects of heads and 

temperatures along the boundaries have propagated throughout the model domain (called a boundary value problem). 

Consequently, a sufficient time period (a few days for small 

models and longer for larger models) is needed to estimate the 

streambed seepage and hydraulic conductivity.

A second approach uses simulated heads and temperatures for defining initial conditions. This approach uses 

heads and temperatures generated from a model whereby the 

distribution of heads and temperatures are allowed to come 

to equilibrium with the model boundaries. The time needed 

to establish the initial distribution of heads and temperature 

within the model domain is on the order of the residence time 

of a packet of water to move through the model. Similar to the 

first approach, this approach amounts to matching observation 

data with the model corresponding to times later in the simulation period.

Model parameter data

Modeling water and heat movement through a streambed 

requires several model parameter values that are specific to 

the site being analyzed. These parameters are listed in table 1 

along with an expected range for stream sediments based on 

available literature. The most important parameters to estimate 

accurately before model calibration are the heat capacity and 

thermal conductivity of the stream sediments. Both of these 

parameters are a function of the sediment water content.

Specified head

and temperature

boundary

No-flow and specified

temperature boundary

Temperature

measurement point

Stream flow
86 Heat as a tool for studying the movement of ground water near streams 

Parameter Sensitivity Range in values

Parameters for saturated flow through fluvial sediments

Saturated hydraulic conductivity1 (m/s) High 10-7 to 100

Horizontal and vertical hydraulic conductivity ratio1 High 3 to 100

Porosity1 (m3/m3) Moderate 0.25 to 0.5

Dispersivity2 (m) Moderate 0.01 to 1

Heat capacity of dry sediments3 (J/m3 oC) Moderate 1.1x106 to 1.3x106

Thermal conductivity of saturated sediments (W/moC)3 Moderate 1.4 to 2.2

Heat capacity of water at 20 oC 4 (J/m3 oC) Low 4.2x106

Additional parameters for variably saturated flow through fluvial sediments

Unsaturated hydraulic conductivity parameters in van 

Genuchten retention model5

 α (per meter) Moderate 1 to 500

 n (dimensionless exponent) Moderate 1.1 to 2.8

Thermal conductivity at residual water content3 (W/moC) Moderate 0.18 to 0.26 

Residual water content5 (m3/m3) Low 0.00 to 0.10 

1

 Values are from Freeze and Cherry (1979, p. 29, 32-34, and 37) for silty sand, clean sand and gravel.

2

 Thermal dispersivity is assumed analagous to solute dispersivity. Solute dispersities are from Fetter (1993, p. 71-77) for

 observation scales between 1 and 10 m.

3 Values are for sandy, loamy, and clayey soils - see Appendix A, table 1B.

4 See Appendix A, table 1A.

5

 Values are from Kosugi and others (2002, p. 743) for soils, and from Fayer and others (1992, p. 693) for gravel.

Table 1. Parameters used in VS2DH to model heat as a tracer through fluvial sediments

The function that relates the heat capacity to water content can be established using a volume-weighted sum of the 

heat capacity of water and the dry sediments. Heat capacity 

of water is a well-known quantity and heat capacity of the 

dry sediments can be determined based on bulk density and 

texture of the sediment. 

Thermal conductivity is a linear function of water content 

when sediments are near saturation; however, thermal conductivity is not linear at low water content. Because streambeds 

often are near saturation for flowing streams, VS2DH assumes 

a linear relation and requires values for sediment thermal conductivity at residual and saturated water content only. These 

values can be estimated from the literature based on sediment bulk density and texture. When modeling flow through 

streambeds with low water content, the thermal conductivity 

for a range in water content may be determined in the laboratory using core samples. 

When monitoring ephemeral streams, temperature 

measurements often are collected when stream flow is absent. 

In this case, heat conduction is the dominant process and the 

sediment thermal parameters can be estimated using automated inverse procedures of conduction only. The automated 

inverse procedure requires knowledge of the sediment moisture content at the time the temperature measurements were 

made and only provides a value of the thermal properties of 

the streambed sediments at the observed water content.
Appendix B—Modeling heat as a tracer to estimate streambed seepage and hydraulic conductivity 87

Min � = � �Ym – Yo�

2

i i i

Model calibration

The first calibration method is based on trial and error 

and is most appropriate for simple problems such as homogeneous and isotropic 1d or 2d models. The second method 

utilizes an automated inverse procedure and is most useful 

for complex anisotropic and heterogeneous 2d or 3d models. 

Model calibration in the context of using heat as a tracer usually requires the adjustment of the hydraulic conductivity in 

such a manner that simulated temperatures in the model match 

corresponding measured temperatures. Modeling saturated 

streambeds with fluctuating stream stage and heads may 

require adjustment of the aquifer specific storage to get a better match between simulated and measured heads. 

Obtaining a good match to both the measured head and 

temperature data (water content for unsaturated streambeds) 

is necessary for obtaining a reliable estimate of streambed 

seepage and hydraulic conductivity. Even if the simulated and 

measured temperatures agree well, any disagreement between 

the simulated and measured heads (water content) will be 

compensated by errors in the hydraulic conductivity. 

Trial and error modeling

Trial and error calibration consists of making repeated 

simulations while adjusting the hydraulic conductivity until 

simulated heads (water content) and temperature match 

measured heads (water content) and temperatures. An initial 

streambed hydraulic conductivity is assigned. Following the 

initial guess, the hydraulic conductivity is adjusted higher 

or lower depending on the difference between simulated 

and measured temperatures. If the hydraulic conductivity is 

too high, the simulated temperature signal will have higher 

amplitude and a phase that is shifted back in time as compared to the measured temperatures (fig. 6A). If the hydraulic 

conductivity is too low, the simulated amplitude will be too 

small and the phase will be shifted forward in time as compared to the measured temperatures (fig. 6B). Figure 6 is for 

a simple conceptualization of vertical downward flow through 

homogeneous and isotropic sediments beneath an ephemeral 

stream (Trout Creek, Nevada; Chapter 8). The best-fit estimate 

of streambed hydraulic conductivity is 0.42 m/d (fig. 6C) 

and the good agreement between the measured and simulated 

temperatures supports the concept of dominantly vertical flow 

beneath the channel. However, even the best-fit simulation is 

not perfect as indicated by the less than perfect match in the 

amplitude and phase of the temperature variations at the 50 cm 

depth beneath the stream. This error likely results from sediments beneath the channel not being completely homogeneous 

and isotropic.

Automated inverse procedure

Complex systems require an automated approach because 

of the large number of different combinations of parameters 

that could be used to calibrate the model to measured heads 

(water content) and temperatures. For such systems, a trial and 

error approach is impractical. The automated inverse procedure adjusts the different parameters through repeated simulations until the process finds the best solution to the observation 

data. Several computer programs are available that can be used 

with any models that simulate flow and heat transport. The 

concepts associated with using automated inverse procedures 

are basically the same for all programs. The USGS offers 

a free model independent inverse program called UCODE 

(Poeter and Hill, 1998) and it can be downloaded from the 

USGS web page (http://water.usgs/nrp/gwsoftware/). Another 

commonly used inverse program is called PEST (Doherty, 

2002). Both of these inverse programs use an objective function to find the best combination of model parameters by minimizing the sum of the squared deviations between simulated 

and measured observations as follows:

 

where φ is the value of the objective function; Ym is the 

measured temperatures or heads; Yo is the simulated temperatures or heads; and i is a subscript designating the observation 

number.

Model uncertainty

After streambed seepage and hydraulic conductivity 

have been estimated, the final step is determining how much 

uncertainty exists in the estimates. Uncertainty results from all 

All other model parameters required for using heat as a 

tracer usually can be estimated based on available literature 

values such as those listed in table 1 and information on sediment texture. The hydraulic conductivity does not need to be 

estimated accurately before modeling because it is estimated 

in the modeling procedure. The modeler needs only to provide 

the model with an initial guess of the hydraulic conductivity 

that will be refined in the modeling process based on observation data.

Observation data

For observation data to be used for estimating streambed 

seepage and hydraulic conductivity, three requirements must 

be met. First, the observation data (head for saturated streambeds, water content for unsaturated streambeds and streambed temperature) should have small uncertainty. Second, the 

coordinates of the observation data relative to the stream and 

other observations and the time of the observations should 

be known accurately. Third, temperature data should exhibit 

some spectrum of variation. For the solution to be unique, 

two aspects of temperature variation need to be simulated, the 

attenuation of the temperature signal’s amplitude and the shift 

in the temperature signal’s phase in the direction of groundwater movement.
88 Heat as a tool for studying the movement of ground water near streams 

Figure 6. Comparisons of simulated and measured temperatures assuming flow through streambed 

is downward and the streambed consists of uniform sediments (example is from Trout Creek, Nevada 

described in Chapter 8). Comparison when: (A) hydraulic conductivity is too high; (B) hydraulic conductivity is too low; and (C) hydraulic conductivity is the best fit to measured data.

Stream, measured

50 centimeters, simulated

50 centimeters, measured

0

5

10

15

20

25

2000

� Streambed hydraulic conductivity of 0.42 meter per day

0

5

10

15

20

25

TEMPER

AT

U

RE, IN

DEG

REES

CELSIU

S

� Streambed hydraulic conductivity of 0.042 meters per day

0

5

10

15

20

25

Apr-13 Apr-14 Apr-15 Apr-16 Apr-17 Apr-18 Apr-19 Apr-20

Apr-13 Apr-14 Apr-15 Apr-16 Apr-17 Apr-18 Apr-19 Apr-20

Apr-13 Apr-14 Apr-15 Apr-16 Apr-17 Apr-18 Apr-19 Apr-20

� Streambed hydraulic conductivity of 4.2 meter per day
Appendix B—Modeling heat as a tracer to estimate streambed seepage and hydraulic conductivity 89

the various sources of error that arise in the model formulation of the system being analyzed. The error that is addressed 

here comes from the uncertainty in all other model parameters 

other than the parameters being estimated in the model inversion. 

The uncertainty that arises due to model input parameters 

varies depending on the parameter and the system under investigation. Uncertainty in some parameters will have a negligible 

effect on the solution, whereas others will have a significant 

effect. Table 1 provides a list of the required parameters for 

modeling heat as a tracer along with a qualitative description 

of the impact (low, moderate, or high) each parameter has on 

modeling results. In general, the most important parameters 

with respect to uncertainty are the sediment hydraulic parameters. However, the parameters providing the most uncertainty 

and the magnitude of the uncertainty depend on the system 

being analyzed and the dynamics of this system. Consequentially, an uncertainty analysis is desirable when using heat as a 

tracer. 

A sensitivity analysis is the simplest method for estimating uncertainty. Model simulations using the maximum and 

minimum values for each of the input model parameters provide a range in the estimated streambed seepage and hydraulic 

conductivity. If the range in the hydraulic conductivity and 

seepage resulting from this exercise is too high, more accurate 

estimates of, for example, the thermal parameters are required. 

This type of sensitivity analysis provides a rough estimate 

of uncertainty and considers uncertainty for each parameter 

independently. 

For complex problems that require more accurate predictions of model uncertainty, a Monte Carlo approach can be 

used. This approach requires a detailed explanation that is 

beyond the scope of this paper. A good explanation of the 

Monte Carlo method is described by de Marsily (1986) and 

an example of this method being applied to determine uncertainty in inverse solutions using heat as a tracer is presented by 

Niswonger and Rupp (2000). A list of available documentation 

for USGS ground-water models, along with compiled models, 

may be retrieved from http://water.usgs.gov/nrp/gwsoftware.

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