IV    Report Title

Scientific Investigations Report 2010–5200

U.S. Department of the Interior

U.S. Geological Survey

Quantity and Sources of Base Flow in the

San Pedro River near Tombstone, Arizona
COVER: The start of winter base flow in the San Pedro River near Tombstone (station number 09471550) on December 29, 2009. Photo is looking downstream. 

On this day, all discharge had infiltrated into the stream channel about 100 m downstream of the gage (Photograph by J.R. Kennedy.) 
Quantity and Sources of Base Flow in the 

San Pedro River near Tombstone, Arizona

By Jeffrey R. Kennedy and Bruce Gungle

Scientific Investigations Report 2010–5200

U.S. Department of the Interior

U.S. Geological Survey
Cataloging-in-publication data are on file with the Library of Congress (URL http://www.loc.gov/).

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia 2010

This report and any updates to it are available online at:

http://pubs.usgs.gov/sir/2010/5200

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copyright owners to reproduce any copyrighted material contained within this report.

Suggested citation:

Kennedy, J.R., and Gungle, Bruce, 2010, Quantity and Sources of Base Flow in the San Pedro River near Tombstone, 

Arizona: U.S. Geological Survey Scientific Investigations Report 2010–5200, 43 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Acknowledgments................................................................................................................................2

Description of the Study Area ............................................................................................................4

Previous Studies ...................................................................................................................................5

Description of Base Flow ...........................................................................................................5

Previous Base-Flow Estimates for the San Pedro River.......................................................7

Definitions ..............................................................................................................................................7

Groundwater and Surface-Water Hydrology............................................................................................9

Base Flow in the San Pedro River near Tombstone.................................................................................9

Temporal Pattern...................................................................................................................................9

Base-flow Volume...............................................................................................................................10

Methods to Identify Sources of Base Flow ....................................................................................13

Hydrograph Characteristics.....................................................................................................13

Environmental Isotopes ............................................................................................................17

Trend in Base Flow .............................................................................................................................21

Variation in Base Flow Caused by Precipitation...................................................................21

Change in Base Flow from Reduced Inflow from the Regional Aquifer...........................28

Spatial Pattern of the Change in Base Flow..........................................................................30

Discussion.....................................................................................................................................................34

Summary and Conclusion...........................................................................................................................35

References Cited..........................................................................................................................................37

Appendix 1.....................................................................................................................................................40

Figures

1. Map of the upper San Pedro River basin showing the location of stream-flow gaging 

stations, piezometer well pairs, and geographic features. ...................................................3

2. Graph showing streamflow at San Pedro River near Tombstone, Arizona (station number 09471550), June 2000 to June 2003....................................................................................10

3. Graph showing seasonal distribution of streamflow at San Pedro River near Tombstone, Arizona (station number 09471550). .............................................................................11

4. Graph showing comparison of four base-flow separation methods applied to the 

streamflow record at San Pedro River near Tombstone gage (station number 

09471550). The start of winter base flow is identified as the local minimum in the fall, 

shown as the vertical dashed line. ..........................................................................................12

5. Flow duration curves and stream hydrographs at San Pedro River near Tombstone 

(station number 09471550) for 1968–1986 and 1997–2009. Blue points indicate streamflow during the months of November through June; red points are July through October. Vertical dotted line shows the 25th percentile...............................................................15

6. Scatter plot of winter base-flow volume vs. flow percentile. .............................................16
iv

7. Streamflow at San Pedro River near Tombstone (station number 09471550) September 

2002 to May 2005. Blue dots indicate average base flow 

 contribution to streamflow. .......................................................................................................16

8. Streamflow at San Pedro River near Tombstone (station number 09471550) for 1980 to 

1981, and 1998 to 1999, showing comparison of the average base flow contribution to 

streamflow, based on the 2003 to 2005 record.......................................................................17

9. Graph showing mean hydrogen and oxygen ratios at selected sites along and near the 

San Pedro River. Winter base flow is the average of samples collected from December 

to March at discharge rates less than 20 cfs. Summer flow is the discharge-weighted 

average of samples collected from July to September. Horizontal and vertical error 

bars show ± one standard deviation of the mean.................................................................18

10. Graph showing hydrogen isotope samples collected during winter at the Charleston, 

Tombstone, and Babocomari River gages..............................................................................19

11. Map showing δH2 concentrations at regional and alluvial groundwater sampling sites. 

Shaded region shows the region for which the Sierra Vista-area isotopic composition 

is calculated. ...............................................................................................................................20

12. Graph showing average monthly precipitation measured at Tombstone (NWS Coop ID 

028619) from 1931 to 2009, and for data subsets from 

 1968 to 1986 and 1997 to 2009....................................................................................................23

13. Graph showing monthly precipitation measured at Tombstone from October through 

March for each year from 1967 to 2009. Each month is plotted according to the calendar year, not water year.............................................................................................................23

14. Scatter plot matrices of winter base flow (mean monthly flow after hydrograph separation) and monthly 3-day low flow vs. summer streamflow and winter precipitation. Red 

points represent the early period of record at the gaging station near Tombstone, from 

1968 to 1986, and blue points represent the later period, from 1997 to 2009. Values are 

the Pearson correlation coefficient.........................................................................................25

15. Scatter plot matrices of four different base-flow metrics vs. summer streamflow and 

winter precipitation. Red points represent the early period of record at the gaging 

station near Tombstone, from 1968 to 1986, and blue points represent the later period, 

from 1997 to 2009. Values are the Pearson correlation coefficient....................................26

16. Graph of response surface showing the coefficient of determination (R2) for the summer streamflow vs. winter base-flow linear regression. Summer streamflow is calculated as the average mean daily flow over a time span of n days, shown on the y-axis, 

centered on the date on the x-axis..........................................................................................27

17. Graph showing the response surface of the LOWESS multiple-regression model for 

varying values of the independent variables of December to January rainfall and 

cube-root of October mean daily flow. Red points are the measured base flow used to 

construct the model. ..................................................................................................................28

18. Graphs showing LOWESS regression diagnostic characteristics: A, scatter plot of 

measured vs. predicted base flow, B, regression residuals vs. predicted base flow, C, 

regression residuals vs. standard normal quantiles.............................................................28

19. Graph showing measured and adjusted base-flow volume. Adjusted values are based 

on the LOWESS regression shown in figure 17. ....................................................................29

20. Graphs showing vertical gradient and water-level elevation at eight paired wells near 

the San Pedro River. Wells are in order from north at the top to south at the bottom. 

Locations of wells are shown in figure 1. Solid lines are pressure transducer measurements and triangles are tape-down measurements.............................................................31
v

21. Box plots showing January and February 3-day low flow at San Pedro River at 

Palominas (station number 09470500), San Pedro River at Charleston (station number 

09471000), and San Pedro River near Tombstone (station number 0471550). The early 

period of record is 1968 to 1981, and the late period of record is 1997 to 2009. ...............33

Tables

1. Water recharged to and withdrawn/discharged from the regional aquifer underlying 

the Sierra Vista Subwatershed in 2006. ....................................................................................6

2. Base-flow discharge estimates at the Tombstone gaging station. Values are volume of 

base flow in acre-ft. .....................................................................................................................8

3. Base flow statistics for San Pedro River near Tombstone (USGS station number 

09471550) ......................................................................................................................................14

4. Median of the mean daily flow by month for the period from 1968 to 1986 and from 1997 

to 2009 for the San Pedro River near Tombstone. .................................................................22

5. Data for wells used in vertical gradient analysis. .................................................................30

Appendix

1. Annual hydrographs showing measured flow (black) and output from base-flow 

separation (measured flow with storm runoff removed) .....................................................40
vi

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Volume

acre-foot (acre-ft) 1,233 cubic meter (m3)

acre-foot (acre-ft) 0.001233 cubic hectometer (hm3

) 

Flow rate

acre-foot per year (acre-ft/yr) 1,233 cubic meter per year (m3

/yr)

acre-foot per year (acre-ft/yr) 0.001233 cubic hectometer per year (hm3

/

yr)

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

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

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Altitude, as used in this report, refers to distance above the vertical datum.

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

kilometer (km) 0.5400 mile, nautical (nmi) 

meter (m) 1.094 yard (yd) 

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

°F=(1.8×°C)+32
Quantity and Sources of Base Flow in the San Pedro River 

near Tombstone, Arizona

By Jeffrey R. Kennedy and Bruce Gungle

Abstract

Base flow in the upper San Pedro River at the gaging 

station (USGS station 09471550) near Tombstone, Arizona, 

is an important factor in the long-term sustainability of the 

river’s riparian ecosystem. Most base flow occurs during the 

non-summer months (typically, from November to May), 

because evapotranspiration (ET) is greater than groundwater 

discharge to the riparian zone during the growing season 

and typically causes periods of zero flow in the spring and 

fall. Streamflow during the summer months occurs only as a 

result of rainfall and runoff. Using a hydrograph separation 

technique that partitions streamflow into stormflow and base 

flow, based on the change in runoff from the previous day, 

median base flow at the Tombstone gage from 1968 to 2009 

(1987 to 1996 data absent) is 4,890 acre-ft/yr. Median base 

flow for the earlier period of record, 1968 to 1986, is 5,830 

acre-ft/yr and for the later period, 1997 to 2009, is 2,880 

acre-ft/yr. 

Base flow in the upper San Pedro River is derived from 

groundwater discharge to the river from the regional and 

alluvial aquifer. The regional aquifer is defined as having 

recharge zones away from the river, primarily at mountain 

fronts and along ephemeral channels. The alluvial aquifer is 

recharged mainly from stormflow. Based on environmental 

isotope data, the composition of base flow in the upper San 

Pedro River at the gaging station near Tombstone is 74±10 

percent regional groundwater and 26±10 percent summer 

storm runoff stored as alluvial groundwater for the 2000 to 

2009 period. 

The volume of base flow in a given year is well 

explained, using multiple regression, by mean daily flow during the previous October and by rainfall during the months of 

December and January (R2

 = 0.9). This does not suggest that 

streamflow is composed only of these two sources; rather, 

these two sources control the degree of saturation of the nearstream alluvial aquifer and, therefore, the amount of winter 

base-flow infiltration that is possible upstream of the Tombstone gaging station. Because of losing conditions upstream 

of the Tombstone gage, there is no minimum amount of base 

flow that would be expected in any given year. 

The regression equation was used to adjust the measured base flow to account for year-to-year variation in 

precipitation. Adjusted base flows decreased, independent 

of climate, from the early period of record to the late period 

of record. In addition to total base flow, other metrics were 

considered, including the start and end dates of base flow, 

the number of days of base flow, the 25th percentile mean 

daily flow, and the number of days of zero flow. Each of 

these showed a decline in base flow between the early 

period of record and the late period. The available evidence 

to evaluate this decrease—hydraulic gradients in the alluvial and regional aquifers and a 10-yr record of streamflow 

environmental isotope samples—indicates that no reduction in groundwater discharge has occurred over this period 

of record. Continued regional groundwater pumping will, 

however, eventually lead to a decline in the contribution of 

regional groundwater to base flow. 

Introduction

Riparian ecosystems depend on perennial streamflow 

to sustain plant and animal communities. Between rainfall 

events, the source of this streamflow is groundwater discharge, or base flow. In arid and semiarid environments, 

the presence or absence of base flow controls the extent of 

riparian ecosystems. In these environments, dry periods may 

last several months, and base flow becomes an increasingly 

important resource as other ecosystem water sources disappear. Because of this, knowledge of the sources and quantity 

of base flow is important to understanding these ecosystems 

and, in particular, their response to historical and future 

groundwater pumping. This report describes groundwater 

sources and quantity of base flow to the upper San Pedro 

River in southeastern Arizona.

The San Pedro River (fig. 1) is the last remaining stream 

in southern Arizona that has long perennial reaches. The riparian ecosystem that parallels the stream bed provides habitat 

for over 350 species of birds, 80 species of mammals, and 40 

species of reptiles and amphibians. Several of these plants and 

animals are listed as federally endangered species (Bureau 
2 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

of Land Management, 1989; Rojo and others, unpub. data, 

19991). The biological importance of the San Pedro River’s 

riparian ecosystem was formally recognized in 1988 by an act 

of Congress that created the San Pedro Riparian National Conservation Area (SPRNCA), the first of its kind. The SPRNCA 

stretches along the river from the international boundary with 

Mexico to a point north of the ghost town of Fairbank and 

south of St. David. The Bureau of Land Management (BLM) 

is responsible for managing and protecting the SPRNCA.

A regional groundwater budget is a tool used to evaluate 

the relative magnitude of inflows to and outflows from a given 

aquifer. The groundwater budget of the Sierra Vista Subwatershed (Subwatershed) of the Upper San Pedro Basin has been 

a topic of intense scrutiny for over two decades, principally 

because outflows from the regional aquifer—primarily groundwater pumping, evapotranspiration (ET), and streamflow—are 

greater than the rate of recharge. As a result, the annual groundwater deficit was about 5,200 acre-ft in 2006 (Department of the 

Interior, 2008). If total withdrawals from the regional aquifer 

continue at the present rate, reduction in groundwater discharge 

to the San Pedro River will lead to the eventual loss of perennial 

reaches and degradation of the riparian ecosystem.

Groundwater budgets are developed using the most precise estimates of inflows and outflows available. In the Subwatershed, inflows considered are recharge from mountain-block, 

mountain-front, ephemeral channel, and artificial infiltration 

and groundwater subflow. Outflows considered are streamflow, 

groundwater subflow, pumping, and ET. While exact measurement of each of these processes is not possible, the addition of extensive instrumentation over the past 10 years has 

greatly increased the amount of data available to make these 

estimates. As new data become available and are analyzed, 

groundwater budget components may be revised. For example, 

Scott and others (2006) published a comprehensive study of 

groundwater discharge from the SPRNCA via ET. Their work 

increased this value by 3,100 acre-ft over the previous best 

estimate, an amount equal to over 50 percent of the annual 

groundwater deficit in 2006, which was the first reporting year 

that the revised ET number was incorporated into Congressional reporting in compliance with P.L. 108-136, Section 321 

(table 1) (Department of the Interior, 2008). Other sources of 

uncertainty in the regional water budget include the amount of 

pumping from wells of less than 35 gal/min pumping capacity. 

Such pumping is exempt from reporting requirements under 

Arizona law. Natural recharge along the Subwatershed mountain fronts and in the ephemeral stream beds is also extremely 

difficult to measure directly. Most studies have used estimates 

of groundwater discharge to the river, or “base flow,” that then 

1

 Internal report available from Commisssion for Environmental Cooperation: Rojo, H.A., Bredehoft, John, Lacwell, Ronald, Price, Jeff, Stromberg, 

Julie, and Thomas, G.A., 1999, Sustaining and enhancing riparian migratory 

bird habitat on the upper San Pedro River, final draft: Montreal, Commission 

for Environmental Cooperation, 123 p.

discharges from the Subwatershed to estimate this value. Base 

flow itself is another component of the water budget for which 

a wide range of values have been calculated over the years. 

Estimated base-flow discharge from the Subwatershed ranges 

from 2,800 to 7,400 acre-ft/yr and is dependent upon the 

period of record evaluated (table 2).

Interest in this latter groundwater-budget component, 

base-flow discharge from the Subwatershed as measured at 

the streamflow-gaging station named “San Pedro River near 

Tombstone,” herein referred to as the “Tombstone gage” 

(station number 09471550), has sharpened in recent years. 

In physical terms, an actual increase in the long-term, mean 

base-flow discharge at the Tombstone gage could indicate 

progress toward sustainability—more water is available from 

the regional aquifer to enter the river and is exiting the Subwatershed as surface flow. In terms of the water budget alone 

(with all other terms held constant—no change in the physical 

system), however, a larger outflow number means not only 

that there is more surface flow in the system than previously 

estimated but also that there is a larger annual deficit in the 

Subwatershed water budget. As a result, any refinement to this 

value will reflect an improved understanding of the physical 

system but may also have management implications. 

As part of its continuous effort to improve the Subwatershed water budget, the Upper San Pedro Partnership 

has charged the U.S. Geological Survey (USGS) to conduct 

an analysis of base-flow discharge at the Tombstone gaging station to reduce the uncertainty currently found in the 

Tombstone gage base-flow estimates and to inform decision 

makers regarding the likely causes of changes over the period 

of record. The results of this analysis will be available to the 

Upper San Pedro Partnership for incorporation into future 

reports and to inform its discussion of the Tombstone gagingstation record. The current report fulfills these responsibilities. 

Purpose and Scope

This report was prepared to define the volume of winter 

base flow at the streamflow-gaging station on the San Pedro 

River near Tombstone, Arizona, USGS station number 

09471550, in support of the reporting requirements of the 

Upper San Pedro Partnership under P.L. 108-136, Section 

321. The entire period of streamflow record, from 1968 

to 1986 and from 1997 to 2009, is considered. Other data 

presented are streamflow isotope samples from two sites on 

the San Pedro River and one site on the Babocomari River, 

precipitation measured at the City of Tombstone, Arizona, and 

water-level measurements at eight paired piezometers along 

the San Pedro River. 

Acknowledgments

The analyses found here resulted from numerous discussions with persons interested in the science of the upper San 
Introduction 3

Figure 1. Map of the upper San Pedro River basin showing the location of streamflow-gaging stations, piezometer well pairs, and 

geographic features.

110o

31o30’

31o40’

31o50’

31o20’

ARIZONA

SONORA

UNITED STATES

MEXICO

Palominas

Bisbee

P

de ro

i

R

Babocomari

iver

92

90

90

82

TOMBSTONE

HILLS

WHETSTONE

HUACHUCA

MOUNTAINS

MOUNTAINS

MULE

MOUNTAINS

80

Tombstone

SIERRA VISTA

SUBWATERSHED

SUBWATERSHED

BENSON

R

ver

Huachuca City

Tucson

A R I Z O N A

Upper San Pedro

Basin

Sierra Vista subwatershed

study area

San

UNITED STATES

MEXICO

Fort Huachuca

0 5 MILES

0 5 KILOMETERS

Sierra Vista

SANTA CRUZ 

COUNTY

PIMA

COUNTY

COCHISE

COUNTY

110o20’ 110o10’ 109o50’

Base from U.S. Geological Survey

digital data, 1:100,000, 1982

Universal Transverse Mercator

projection, Zone 12

EXPLANATION

U.S. GEOLOGICAL SURVEY STREAMFLOW-

 GAGING STATION AND ISOTOPE SAMPLING

 SITE

ALLUVIAL AQUIFER WELL

SPRING WITHIN THE SAN PEDRO

 RIPARIAN NATIONAL CONSERVATION

 AREA

San Pedro

Riparian

National

Conservation

Area

BABOCOMARI HILLS

BRONCO HILLS

San Pedro River

at Charleston

Babocomari

River

San Pedro River

near Tombstone

Lewis Springs

FBK-LO/LI

CONSUD/CONSUS

BOQSUD/BOQSUS

MOSLND/MOSLNS

CLRSUD/CLRSUS

LSP5/LSP1

COTUCD/COTBLM

HERSUD/HERSUS

Fairbank

San Pedro River

at Palominas
4 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Pedro River and its attendant riparian system. These include 

Jim Leenhouts of the USGS; Russ Scott of the Agricultural 

Research Service; Nate Dieterich, Paul Brown, and Tom 

Dabbs of the Bureau of Land Management; Tricia Gerrodette 

of Audubon Arizona; Tom Runyon of Fort Huachuca’s Environment and Natural Resources division; and Holly Richter 

of The Nature Conservancy, among others. None of the current upper San Pedro research would be possible without the 

comprehensive work and thought of Don Pool of the USGS 

in Tucson. He is responsible for the original monitoring 

network across the Sierra Vista Subwatershed, not to mention 

the development of the conceptual framework, groundwater 

model, and related estimates of water budget components 

and hydrologic properties for the Subwatershed. Finally, the 

support and interest of the Upper San Pedro Partnership collectively and each of its 21 member jurisdictions, agencies, 

and organizations individually continue to support collection 

of data and drive the high quality of scientific research in the 

Sierra Vista Subwatershed.

Description of the Study Area

The Upper San Pedro Basin is a groundwater management unit that extends from the international boundary with 

Mexico to a bedrock constriction north of Benson, Arizona, 

called The Narrows. The San Pedro River runs south to north 

through the center of this basin. The surface watershed extends 

from the city of Cananea in the state of Sonora, Mexico, to the 

confluence with the Gila River at Winkelman, Arizona. The 

2,460 km2 Sierra Vista Subwatershed is the southern subunit of 

the Upper San Pedro Basin; its northern boundary is located in 

the vicinity of the volcanic rocks of the Tombstone Hills near 

Fairbank that form a partial barrier to groundwater movement 

(Freethey, 1982). 

The USGS gaging station near Tombstone (station 

number 09471550; Tombstone) is about 3 km north of the 

historic settlement of Fairbank along State Highway 82 and 

defines the north boundary of the Sierra Vista Subwatershed 

(fig. 1) (Department of the Interior, 2008). The Tombstone 

streamflow-gaging station was first installed by the USGS in 

1967 and was used continuously through the end of September 1986, when the station was discontinued due to lack of 

funding and the recorder was removed from the gage house. 

In September of 1996, the gage datum was checked and, 

on October 1, 1996, the gaging station was reactivated with 

updated measuring equipment. Since 1996, the Tombstone 

gaging station has been in continuous operation, including 

basic maintenance and updates to the measurement equipment and reference marks. Additional upstream streamflowgaging stations on the San Pedro River are at Charleston, 14 

km upstream (station number 09471000; Charleston), and 

Palominas, 41.5 km upstream and 6 km downstream from 

the international boundary with Mexico (station number 

09470500; Palominas).

The Sierra Vista Subwatershed is part of a broad alluvial valley located in the southern part of the Basin and 

Range physiographic province and is bounded by fault-block 

mountains. To the east are the Mule Mountains (2,250 m elev) 

and the Tombstone Hills (1,620 m elev); to the west are the 

Huachuca Mountains (2,890 m elev) and the smaller Mustang 

Mountains (2,000 m elev) are in the northwest corner of the 

Subwatershed (fig. 1). The north flank of the Sierra San Jose 

(2,500 m elev), south of the Subwatershed in Mexico, drains 

into Greenbush Draw, a major ephemeral tributary that joins 

the San Pedro River from the east about 8 km north of the 

international boundary with Mexico.

The primary tributary to the San Pedro River in the 

Sierra Vista Subwatershed is the interrupted-perennial Babocomari River that enters the San Pedro River about 3.5 km 

south of the Tombstone gaging station. Opposite the Babocomari River, Walnut Gulch joins the river. Walnut Gulch and 

Greenbush Draw are the two major ephemeral tributaries that 

enter the river in the Subwatershed. Numerous other ephemeral tributaries empty into the river, with about twice as many 

on the west side of the Subwatershed as on the east side 

(Coes and Pool, 2005).

Precipitation falls preferentially on the mountains around 

the perimeter of the Sierra Vista Subwatershed and is temporally bimodal. About half falls during the summer convective season and about another third falls during the winter 

months. There is a distinct pre-summer drought from late 

April through June in most years. Tropical systems occasionally cause significant precipitation events during the fall (for 

example, 1972, 1977, 1983, 2000), and moderate to strong 

El Niño events can result in wet winters, with January and 

February typically receiving most of the precipitation (for 

example, 1978, 1984, 2010).

The major population centers in the Subwatershed (fig. 

1) include Sierra Vista (population 46,597 in 2009, including 

Fort Huachuca), Bisbee (population 6,423), Huachuca City 

(population 1,955), and Tombstone (population 1,720) (Arizona Department of Commerce, 2010). Annual groundwater 

pumping and natural discharge in the Subwatershed exceeded 

natural and artificial recharge in 2006 by about 5,200 acre-ft; 

the majority of the groundwater pumping occurs between the 

Huachuca Mountains and the San Pedro River, in the vicinity 

of Fort Huachuca and Sierra Vista (table 1) (Department of 

the Interior, 2008).

Numerous studies have described in some detail the 

geology (Bryan and others, 1934; Brown and others, 1966; 

Hereford, 1993; Pool and Coes, 1999; Arizona Department 

of Water Resources, 2005a; Coes and Pool, 2005; Pool and 

Dickinson, 2007), biological resources (Hereford, 1993; Rojo 

and others, unpub. data, 1999; Leenhouts and others, 2005), 

climate (Arizona Department of Water Resources, 2005a; 

Leenhouts and others, 2005; Gungle, 2005; Thomas and 

Pool, 2006; Department of the Interior, 2008), and historical, cultural, and socioeconomic setting (Bryan and others, 

1934; Hereford, 1993; Rojo and others, unpub. data, 1999; 

Arizona Department of Water Resources, 2005b; Department 
Introduction 5

of the Interior, 2008) of the Upper San Pedro Basin. Please 

refer to these publications for more detail on specific basin 

characteristics.

Previous Studies

Description of Base Flow

Base flow in a natural channel is commonly defined as 

that contribution to streamflow composed solely of groundwater (Meyboom, 1961; Todd, 1980; Bedient and Huber, 1992). 

Whereas rainfall-induced stormflow is quickly delivered to 

the stream by overland and shallow subsurface flow, base flow 

represents the much slower transmission of water delivered to 

the stream via deeper groundwater flow (Freeze and Cherry, 

1979). Once overland flow and near-surface flow have ceased, 

base flow in a perennial stream can be identified on the stream 

hydrograph as the subsequent period of quasi-exponential 

decay. This base-flow recession typically is consistent for each 

watershed and independent of such things as the magnitude 

of precipitation events or peak flows (U.S. Army Corps of 

Engineers, 1999). Separation of the stream hydrograph into 

stormflow and base-flow components is necessary to determine rainfall-runoff relations and related flood forecasting and 

can provide information about the nature of the groundwater 

regime in a given watershed. In particular, estimates of steadystate groundwater recharge and discharge are typically derived 

from annual base-flow volumes. 

An exact definition of base flow varies depending on the 

author and focus of the study. Thomas and Pool (2006) caution 

that base flow should not be confused with all of the groundwater that moves toward a stream. In arid regions particularly, 

water removed by ET can represent a significant portion of all 

groundwater discharging to the riparian zone. If sufficiently 

high, ET demand can cause a negative hydraulic gradient 

and losing conditions in the immediate vicinity of the river, 

causing it to decline to zero flow, even though the hydraulic 

gradient in the regional aquifer may still force water into the 

near-stream zone. The quantity of base flow in an intermittent 

stream like the San Pedro River is thus strongly influenced by 

ET and may change over time due to both changes in ET and 

changes in regional hydraulic gradients, such as those caused 

by groundwater pumping.

Base-flow-separation techniques are intended to remove 

the high-frequency, short duration stormflow peaks seen on 

a stream hydrograph. The remaining streamflow is typically 

deemed “base flow,” which can be derived both from mediumterm storage of stormflow in the near-stream aquifer (“bank 

storage”) and from long-term storage in the regional aquifer, 

which is recharged primarily at the basin-bounding mountain 

fronts. The term “bank storage” implies storage in the shallow 

subsurface laterally away from the river, although storage may 

be primarily below the stream channel. Some authors use the 

term “base flow” as essentially synonymous with low flow, 

with sources including groundwater, bank storage, and other 

delayed discharge sources (Hall, 1968). Others more narrowly 

define base flow to mean only that part of streamflow derived 

from long-term, regional aquifer storage (Todd, 1980; Bedient and Huber, 1992; Thomas and Pool, 2006). Most authors 

consider bank storage a significant source of discharge immediately following high-flow events (for example, S.G. Brown 

and B.N. Aldridge, unpub. USGS administrative report, 1973; 

Freeze and Cherry, 1979; Todd, 1980), and Meyboom’s 

(1961) discussion of bank-storage contributions to flood 

flows implies that bank storage and regional aquifer groundwater contributions together form base flow during floods. 

In intermittent streams, however, bank storage can also be 

an important source of water to streams long after a highflow event has passed. Kondolf and others (1987) indicate, 

for example, that bank storage along the Carmel River in 

California continued to provide surface flow to the river for 

two months after the last high-flow event of the wet season. 

Squillace (1996) made a similar observation about bank storage along the Cedar River in Iowa using a groundwater flow 

simulation. He found that a 2-m rise in river stage caused 

bank-storage water to move horizontally and vertically into 

the alluvial aquifer—70 percent of the total bank-storage 

water moved vertically down through the river bed. Bank 

storage supplied base flow to the stream for 5 weeks following peak river stage. Whiting and Pomeranets’ (1997) 

subsequent modeling work indicates that banks are capable 

of storing and slowly releasing such volumes of water, wider 

valleys sustain greater bank discharges longer than narrow 

ones, and sand and gravels store and discharge greater volumes faster than silt and clay. The authors note that a balance 

between yield and discharge duration is critical to maintaining base flow during periods of drought.

Hall (1968) defines base flow as deriving from not just 

a regional groundwater source, but also from the “portion of 

flow that comes from groundwater storage or other delayed 

sources” (p. 973; emphasis added), which would include 

bank storage that discharges over time. In other words, once 

enough time has passed, the water in the stream is considered 

base flow regardless of its source. Base flow may or may not 

include contributions from bank storage during and immediately following high flows, but it does include contributions 

from bank storage at some point adequately distant in time 

from the end of the last high-flow event.

Thomas and Pool (2006) initially distinguish between 

bank storage and short-term alluvial-aquifer storage in their 

statistical assessment of flow in the San Pedro River at the 

Palominas and Charleston gaging stations. They subsequently 

note, however, that the boundary between bank storage and 

short-term alluvial-aquifer storage is unclear and, thus, they 

consider the two as a single kind of bank storage, although 

separate from base flow as previously mentioned. Based on 

their observations at Palominas and Charleston, they determine that streamflow persistence in the San Pedro River is 

primarily a function of bank storage unrelated to monthly 

precipitation. Apparently they agree with the observations of 

Kondolf and others’ (1987) and Squillace’s (1996) observations noted above in everything except terminology.
6 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Table 1. Water recharged to and withdrawn/discharged from the regional aquifer underlying the Sierra Vista Subwatershed in 2006.

[+, inflows; –, outflows]

Component Estimated volume

(acre-ft/yr) Description

Natural aspects of system

Natural recharge1 15,000 Inflow largely from percolating waters on and around mountains and 

through ephemeral channels

Groundwater inflow1 3,000 Subsurface inflow from Mexico

Groundwater outflow1 -440 Subsurface outflow at USGS San Pedro River near Tombstone streamflow-gaging station (09471550)

Stream base flow1 -3,250 Groundwater discharge to the river that flows out of the subwatershed

Evaporation and plant transpiration2 -10,800 Groundwater consumed in the riparian system exclusive of evapotranspiration supplied by near-riparian recharge from precipitation or flood runoff

Pumping

Pumping. water companies and public 

supply – gross -10,610 Groundwater extractions by water companies and municipalities

Pumping, rural/exempt well – gross3 -4,390 Groundwater extractions by private wells

Pumping, industrial (turf, sand, and 

gravel, stock tanks) – gross -1,490 Groundwater extractions for industrial and golf course uses

Pumping, irrigation – net4 -430 Groundwater extractions for agricultural use

Active management measures

Reduction of riparian evapotranspiration 475 Management of invasive mesquite

Municipal effluent recharge5 3,030

Detention basin recharge6 310

Passive recharge resulting from human activities

Incidental recharge7 2,090

Urban-enhanced recharge8 2,300

Aquifer storage change9 -5,200 Additions or reductions in stored aquifer water

1

Flow volume estimated by the Arizona Department of Water Resources (2005b). 

2

Value of evapotranspiration (ET) is the average of the high and low estimates of Scott and others (2006). This value replaces the 7,700 acre-ft/year estimate 

used in previous Section 321 reports (derived from Arizona Department of Water Resources, 2005b). The increase of 3,100 acre-ft annually does not necessarily 

suggest that actual ET has increased, but rather that the estimate of ET has increased. 

3

Value is lower than in previous Section 321 report owing to use of a revised calculation technique consistent with that of the Arizona Department of Water 

Resources (2005a). Exempt-well population derived from Arizona Department of Economic Security 2006 data. Earlier reports calculated population as number of exempt wells times 4.72 people per well (from Arizona Department of Water Resources, 2005a). 

4

Pumping for irrigation is consumptive use only. Area considered is the groundwater basin portion of the Sierra Vista Subwatershed only. The area within 

the boundaries of the Sierra Vista Subwatershed includes more agricultural lands than the area within the groundwater basin portion of the Subwatershed. These 

agricultural lands are primarily located in the head waters of the Babocomari River. 

5

Municipal effluent recharge is water returned to the aquifer through recharge facilities as reported by Sierra Vista (M. Hemesath, City of Sierra Vista Public 

Works, written commun., 2007), Fort Huachuca ( Fort Huachuca, 2007, Biological opinion annual report for 2006, 12 p.), City of Tombstone (Arizona Department of Water Resources, 2005a), and City of Bisbee (Russ McConnell, City of Bisbee Public Works, written commun., 2007)

6

Recharge of stormwater within basins that have been installed to mitigate increased flood peaks in ephemeral-stream channels resulting from urbanization.

7

Incidental recharge is an estimate of water returned to the aquifer from septic tanks and turf watering. Value reduced from prior Section 321 report owing to 

revised technique for calculating exempt-well pumping. 

8

Urbanization causes enhanced recharge by concentrating storm runoff in ephemeral-stream channels. Recharge in arid and semiarid environments is more 

likely to occur if runoff from precipitation reaches permeable stream-channel sediments. Recharge caused by urbanization only partially mitigates the increased 

pumping that accompanies increased urbanization. 

9

Value rounded to nearest 100 acre-ft/yr.
Introduction 7

Previous Base-Flow Estimates for the San Pedro 

River

Bryan and others (1934) wrote the first comprehensive 

review of the water resources of the San Pedro River valley and likely were first to make observations related to the 

base flow of the San Pedro. They noted that nearly all of the 

low-water discharge of both the Babocomari and San Pedro 

Rivers was being diverted for irrigation. Perhaps the earliest estimate of base flow on the San Pedro River came from 

Brown and Aldridge (S.G. Brown and B.N. Aldridge, unpub. 

USGS administrative report, 1973). Based on estimates of 

mountain-front recharge and underflow at the international 

boundary, base-flow discharge at Charleston was estimated to 

be 4,800 acre-ft/yr. No estimate was made for discharge at the 

Tombstone gaging station, which had begun operation in 1967. 

(This and other estimates of base flow discharge on the San 

Pedro River at Charleston and (or) at or near the Tombstone 

gage are compiled in table 2.)

A number of subsequent base-flow estimates for the San 

Pedro River occurred in concert with the development of 

groundwater models for the area. Freethey (1982) modeled 

pre-development (circa 1940) base flow near Tombstone to be 

about 7,500 acre-ft/yr. Modeled base flow for 1968 was about 

4,300 acre-ft/yr and for 1977, 4,500 acre-ft/yr. Vionnet and 

Maddock (1992) updated Freethey’s (1982) model and estimated base-flow values for Charleston; they did not include 

base-flow values for discharge from the Subwatershed at the 

Tombstone gage, however. Corell and others (1996) estimated 

pre-development base flow at the Tombstone gage to be about 

9,500 acre-ft/yr and base flow in 1990 to be about 6,450 

acre-ft/yr. Their subsequent modeled results were lower: about 

5,700 acre-ft/yr of base flow was simulated at the Tombstone 

gage for 1990. Goode and Maddock (2000) constructed a 

new groundwater model but, similar to Vionnet and Maddock 

(1992), did not look at the Tombstone gage base-flow discharge. Most recently, Pool and Dickinson (2007) developed 

a 5-layer Subwatershed model, including a 2-layer component 

for the Mexican part of the basin. Pre-development baseflow discharge at the Tombstone gage was estimated at 8,500 

acre-ft/yr, while simulated pre-development base flow was 

higher, about 9,150 acre-ft/yr. Simulated base-flow discharge 

from March 2002 to March 2003 was about 2,800 acre-ft/yr. 

An important factor to note is that all of these groundwater 

models simulate only regional groundwater discharge to the 

river and disregard contributions from storage in the alluvial 

aquifer. The calibration process of each model is unique; 

however, where models are calibrated to measured streamflow, 

no efforts were made to separate alluvial aquifer and regional 

aquifer components of streamflow.

Other publications have also included estimates of and 

(or) observations about San Pedro River base flow. Rojo 

and others (unpub. data, 1999) used previous models and an 

analysis of 10-yr flow-duration curves to arrive at a Tombstone 

gage base-flow value of 7,400 acre-ft/yr in 1990. Pool and 

Coes (1999) found a declining trend in summer (June) base 

flow at the Charleston gage over the period 1936 to 1997 and 

observed that the long-term trend of decreasing wet-season 

(June–October) runoff is similar to the declining trend in summer base flow. They found no trend in winter base flow for the 

same period. 

Whitaker (2000) estimated that bank-storage effects 

(both release of water from storage and the effect of bank 

storage on regional groundwater discharge) contributed about 

8.5 percent of the total flow to the San Pedro River near 

Charleston from August to December, 1997. Using a 7-day 

low-flow analysis and the entire period of record, USGS 

estimated a value of 4,230 acre-ft/yr for the Tombstone gage 

base flow in 2002 (Department of the Interior, 2005). That 

analysis calculated base flow using the difference between 

annualized winter base flow and ET of 7,070 acre-ft/yr. If 

the more recent ET figure of Scott and others (2006) were 

used instead, the estimated base flow value would decrease 

greatly, to about 500 acre-ft/yr. The Arizona Department of 

Water Resources (Arizona Department of Water Resources, 

2005a,b) determined a Tombstone gage base-flow value 

of 3,250 acre-ft/yr based on non-flood-influenced months 

between September and May during the period 1997–2003. 

This value is also used by the Upper San Pedro Partnership 

(2008) in the Subwatershed water budget as part of its reporting requirements under P.L. 108-136, Section 321. An extensive study by Thomas and Pool (2006) analyzed trends in 

the flow of the San Pedro River at Charleston. Using median 

monthly 3-day low flows, total base flow at Charleston was 

estimated to be 4,300 acre-ft for the period 1991–2002. 

Unlike Tombstone, where ET is in excess of available nearstream groundwater, a summer base-flow contribution of 900 

acre-ft was assumed for Charleston. Dieterich calculated a 

base flow value of 5,850 acre-ft/yr at the Tombstone gaging 

station based on median flow data from 1968–85 (Nathan 

Dieterich, Bureau of Land Management, written commun., 

2009; Jim Kenna, Arizona BLM State Director, written commun., 2009).

Isotopic analysis can also be used to assist in separating 

groundwater from surface-water runoff in streamflow. Baillie 

and others (2007) present analysis of stable isotope and other 

geochemical tracers from the San Pedro River reach beginning 

at Palominas and ending at Charleston. A simple two-endmember mixing model of deuterium and hydrogen isotopes 

was evaluated, using the average δH/δO isotope ratio of eight 

basin wells as one end member and the average δH/δO ratio 

of summer precipitation as the other. Using this model, the 

authors found an increasing proportion of groundwater in base 

flow downstream, varying from 20±28 percent at Palominas to 

45±19 percent at Charleston.

Definitions

The present study concerns specifically the groundwater 

discharge component of the water budget. Given the lack of 

consensus in the literature about what, specifically, composes 
8 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Table 2. Base-flow discharge estimates at the Tombstone gaging station. 

[-, no data]

Source

Last time period 

used in analysis

Method of estimating base 

flow

Charleston gage

flow volume (acre-ft)

Tombstone gage

flow volume (acre-ft)

PredevelopmentLast time 

period

PredevelopmentLast time 

period

S.G. Brown and 

B.N. Aldridge (unpublished USGS administrative report, 1973)

1970

estimate of mountain

front recharge and 

underflow

- 4,800 - -

Freethey (1982) 1977 model - - 7,500 4,500

Vionnet and Maddock 

(1992) 1988 model 8,300 2,900 - -

Corell and others (1996) 1985–1991 analysis of streamflow data 9,500 4,800 - -

Corell and others (1996) 1990 model (final year) - - 9,500 5,700

Corell and others (1996) 1941–1990 model (total average) - - 9,500 6,290

Rojo and others (unpublished data, 1999) 1990

10-yr flow duration 

curves in combination 

with earlier models

- - 9,500 7,400

Goode and Maddock 

(2000) 1997 model 9,600 6,400 - -

Arizona Department of 

Water Resources (2005a, 

2005b)

1997–2003 NA - - - 3,250

USGS/Upper San Pedro 

Partnership (2005)

1967–1986; 

1996–2002

7-day winter low flow

and evapotranspiration - - - 4,230

Thomas and Pool (2006) 1991–2002 3-day monthly low flows 7,900 4,300 - -

Pool and Dickinson (2007) pre-development earlier estimates with

recent evapotranspiration - - 8,500 -

Pool and Dickinson (2007) 03/2002–03/2003 model - - 9,150 2,800

Nathan Dieterich, written 

commun., 2009 1968–85 median total discharge - - - 5,850

Current study (2010)

1968–1986

1997–2009

1968–1986 and

1996–2009

delta filter

delta filter

delta filter

- - - 2,880

5,830

4,890

base flow, we will use the following terminology to ensure 

conceptual clarity. 

“Stormflow” refers to direct runoff from rainfall and also 

to the rapid release of water stored in the shallow subsurface 

immediately following a rainfall event. The period of stormflow following rainfall is on the order of days.

“Base flow” refers to water that flows in the river channel 

in the absence of any immediate influence from storm runoff; base flow is composed of regional groundwater, alluvial 

groundwater, or both. At the Tombstone gaging station, 

upstream groundwater flow to the vicinity of the stream is less 

than the volume of water removed by ET during the growing 

season; therefore, during the summer there is no base flow at 

the Tombstone gage.

In the context of streamflow, “regional groundwater” 

refers to groundwater from the regional aquifer that has discharged to the surface stream and is flowing between its banks. 

Regional groundwater is that portion of base flow composed 

entirely of groundwater discharged from the regional aquifer. 

It is water that has recharged away from the river. 

“Alluvial groundwater” refers to water stored temporarily 

in the near-stream alluvium as distinct from “regional groundwater,” which is sourced from the regional aquifer. In this context, alluvial groundwater is synonymous with bank storage 
Base Flow in the San Pedro River near Tombstone 9

but is used, instead, to clearly denote that storage occurs in a 

large zone surrounding the stream channel rather than strictly 

at the sides of the channel. Storage is typically on the order 

of days to months but may persist for a year or longer following very large runoff events. Alluvial groundwater does not 

include short-term storage during and immediately following 

storm runoff. While recognizing that, in many parts of the 

Subwatershed, the regional aquifer is well connected to the 

alluvial aquifer and that there may be little difference between 

the two, the concept of alluvial groundwater distinct from 

regional groundwater is important in the water-budget context. 

Alluvial groundwater is recharged by flood flows due to an 

increase in head and subsequent or increased negative hydraulic gradient (Whitaker, 2000). Most alluvial groundwater, in 

other words, has previously flowed in the stream channel of 

the San Pedro River (or Babocomari River); regional groundwater has not.

Groundwater and Surface-Water 

Hydrology

Between the Charleston gage and the Tombstone gage, 

the San Pedro River flows across the western portion of the 

Upper Cretaceous Tombstone volcanic-plutonic complex 

(Shipman and Ferguson, 2006). Low-lying, southwest-striking 

horst lie on either side of the river, separated by a southwestnortheast striking normal fault (Ferguson and others, 2006). 

The gaging station at Charleston lies on the southwest margin 

of this volcanic complex at a location where groundwater 

subflow is forced to the surface, resulting in perennial streamflow. This bedrock high is nearly continuous to the northeast 

towards the city of Tombstone and is assumed to be continuous with the Tombstone Hills volcanic complex (Shipman and 

Ferguson, 2006). The magnitude of groundwater flow through 

fractures and faults in the volcanic material is unknown but 

probably small relative to flow through the basin-fill aquifer 

to the west. As a result, the groundwater contribution to base 

flow east of the San Pedro River between the Charleston and 

Tombstone gages is expected to be minimal, although some 

amount likely occurs as subflow near Walnut Gulch, just 

upstream of the Tombstone gage. To the west of the river, 

surficial material is largely alluvium with the exception of an 

exposed elongate 3 km by 6 km horst of Cretaceous sedimentary rock capped by Uncle Sam Tuff (Ferguson and others, 

2006). This block forms a subsurface barrier to flow near the 

confluence of the Babocomari River and the San Pedro River, 

which likely forces subflow near to or north of the gaging station near Tombstone. A groundwater channel that would direct 

flow from the north end of the Huachuca Mountains to the 

river has been postulated between the Babocomari Hills and 

the Bronco Hills (Corell and others, 1996) (fig. 1). Upstream 

from Charleston, the river flows across sedimentary material 

as much as 1.5 km thick (Gettings and Houser, 2000) and has 

no significant interaction with bedrock material.

Primary surface-water tributaries between Charleston and 

the Tombstone gage are the Babocomari River to the west, 

which drains about 800 km2

 at the north end of the Huachuca 

Mountains and the Mustang Mountains, and Walnut Gulch to 

the east, which drains about 160 km2 starting at the southern 

end of the Dragoon Mountains. These tributaries join the San 

Pedro River nearly opposite one another at a point about 3 

km upstream from the Tombstone gage, just south of Arizona 

Route 82. The Babocomari contains some sections of perennial flow but is intermittent at the confluence with the San 

Pedro River. Walnut Gulch is entirely ephemeral.

Both gaining and losing reaches exist upstream from 

the gaging station near Tombstone. The reach between the 

Charleston gage and the Tombstone gage is primarily losing, 

although water levels in co-located piezometers and in one 

horizontal transect indicate that, respectively, a consistent 

upward gradient exists in some locations and that at least one 

reach will shift from losing to gaining and back during the 

year (Leenhouts and others, 2005, appendix 3). Following 

the summer monsoon, near-stream sediments in this reach 

must remain saturated for perennial flow to exist at the gaging 

station near Tombstone. If summer streamflow is insufficient 

to maintain flow in the fall, upstream inflow must resaturate 

these sediments until seepage becomes sufficiently small and 

streamflow resumes. Gaining reaches are concentrated primarily between Arizona Route 90 and Charleston (Pool and Coes, 

1999). Inflow to the stream channel in this area is derived from 

storage in both the alluvial and regional aquifers. 

Groundwater discharged as base flow can be evaluated 

two ways. First, the total amount of groundwater discharge 

can be determined by taking the base-flow discharge rate for 

the period when vegetation is dormant and ET is minimal and 

integrating over every day of the year. The amount of ET, 

determined independently, can be subtracted from this yearround groundwater discharge to determine the amount of base 

flow. This method ignores ET-induced changes in hydraulic 

gradients and, therefore, changes in groundwater discharge 

rates. Second, base flow may be determined directly from the 

streamflow record using a hydrograph-separation method to 

remove stormflow peaks and integrating the actual amount of 

measured discharge. We focus on the second method.

Base Flow in the San Pedro River near 

Tombstone

Temporal Pattern

Streamflow at the San Pedro River near the Tombstone 

gage has a distinct seasonal pattern. Peak streamflow occurs in 

the summer during the North American monsoon, as convective thunderstorms produce infiltration-excess overland flow. 

Streamflow declines following the monsoon and typically 

reaches a minimum in October or November. In wetter years, 

such as 2001, stored alluvial groundwater sustains streamflow 
10 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

throughout the fall (fig. 2) (all dates refer to water years, October 1 through September 30). In drier years, such as 2002 and 

2003, streamflow declines to zero following the summer monsoon. Following the first freezing temperatures in the fall, ET 

demands decrease dramatically (Goodrich and others, 2000) 

and streamflow returns, reaching a steady flow rate in midwinter in most years. In the driest years, such as 2003, base-flow 

discharge increases slowly in the fall, reaches a maximum for 

a short time in midwinter, and declines quickly in the spring 

with the onset of ET (fig. 2). In all but the wettest years, the 

river becomes dry in late spring or early summer, when ET 

demand is high and before the onset of the summer monsoon. 

The only exception during the period of record is 1979, when 

the river flowed continuously at the Tombstone gage from summer 1978 through spring 1980. The earliest date of zero flow in 

spring is May 2 (1996), and the latest date is July 8 (1972, when 

runoff-producing rainfall occurred in late May and June). The 

median first date of zero flow for the period of record is May 30, 

for the period 1968–1985 is June 13, and for the period 1996–

2009 is May 16. In the 12 years that the San Pedro River near 

Tombstone declined to zero flow in the fall, the earliest date for 

the onset of winter base flow is October 21, and the latest date 

is December 16 (table 3). Eight of these twelve years occurred 

during the latter period of record, 1996 to 2009. 

Base-flow Volume 

Mean annual discharge of the San Pedro River at the 

gaging station near Tombstone varies widely, from 7,310 

acre-ft/yr in 1997 to 113,300 acre-ft/yr in 1984. Average 

mean annual discharge for the period of record is 35,100 

0.1

1

10

100

1,000

10,000

JUN 00 SEP 00 DEC 00 MAR 01 JUN 01 SEP 01 DEC 01 MAR 02 JUN 02 SEP 02 DEC 02 MAR 03

MEAN DAILY FLOW, 

CUBIC FEET PER SECOND

Figure 2. Graph showing streamflow at San Pedro River near Tombstone, Arizona (station number 09471550), June 2000 to June 2003.

acre-ft/yr, and the median mean annual discharge is 29,500 

acre-ft/yr. Twenty-seven percent of mean annual flow occurs 

during the month of August, and 53 percent of mean annual 

flow, or 18,600 acre-ft, occurs during the monsoon runoffdominated months of July, August, and September (fig. 3). 

October has the third-highest mean monthly flow of 5,160 

acre-ft. Streamflow in October may be from remnant tropical storms, midlatitude fronts, base flow, or a combination 

of these. Total discharge from November through June is on 

average 32 percent of the total annual discharge, or 11,200 

acre-ft. This amount primarily reflects discharge from both 

regional groundwater and alluvial groundwater but may also 

include a small component of direct storm runoff during certain years. 

To determine mean annual base-flow volume, a baseflow-separation method can be used. Methods to quantify 

base flow include (1) low-flow indexes, in which some 

criteria, such as monthly 3-day low-flow discharge, is assumed 

to represent base flow for a given period, (2) flow-duration 

curve percentiles, for example, streamflow on all days when 

discharge is below the median (50th percentile) is considered 

base flow, and (3) hydrograph-separation methods. Low-flow 

indexes—typically the lowest mean daily flow averaged over a 

3- or 7-day period in a given month—are problematic considering the temporal pattern of streamflow at the Tombstone 

gage. If calculated on a monthly basis in those months when 

base flow is increasing to or decreasing from the midwinter 

maximum (fig. 2, 2003), the minimum value at the start of 

the month (in fall) or end of the month (in spring) would not 

be representative of the monthly discharge. As a result, base 

flow would be underestimated. Nonetheless, low flow indexes 

provide a useful measure of base flow requiring minimal 
Base Flow in the San Pedro River near Tombstone 11

0

5

10

15

20

25

30

0

29

58

87

116

145

174

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

MEAN MONTHLY FLOWS,

CUBIC FEET PER SECOND

PERCENT OF TOTAL ANNUAL FLOW

Figure 3. Graph showing seasonal distribution of streamflow at San Pedro River near Tombstone, Arizona (station number 09471550).

assumptions. Flow-duration-curve percentiles are widely used 

to delineate base flow, with the 50th percentile (the flow that is 

exceeded 50 percent of the time) being one of several possible 

base-flow metrics (Smakhtin, 2001). Flow duration curves 

for the San Pedro River near Tombstone, however, indicate 

that the winter base-flow discharge is somewhat higher than 

the 50th percentile flow. A hydrograph separation method and 

a flow-duration-curve metric are both used in this report to 

evaluate base flow at the gaging station near Tombstone. 

Common hydrograph separation methods currently used 

are (1) streamflow partitioning into periods of either exclusively base-flow runoff or stormflow-influenced runoff, based 

on antecedent/concurrent precipitation or hydrograph characteristics (Shirmohammadi and others, 1984; Rutledge, 1998; 

Sloto and Crouse, 1996) and (2) low-pass filters that separate 

the high frequency stormflow signal from the low frequency 

base-flow signal (Boughton, 1993; Chapman, 1999; Eckhardt, 

2005). Five hydrograph separation methods—four streamflow 

partitioning methods and one low-pass filter—were tested on 

the entire streamflow record at the Tombstone gage (fig. 4). 

The USGS computer program PART (Rutledge, 1998) 

uses daily change in streamflow to partition streamflow. 

Intended primarily for periods of continuous flow, the PART 

algorithm requires that daily streamflow be less than streamflow the previous day to qualify as exclusively base flow. 

Because of this, it was unable to account for gradually increasing base flow in fall due to diminishing ET and it truncated the 

beginning part of the hydrograph (fig. 4). Another commonly 

used USGS program, HYSEP (Sloto and Crouse, 1996), 

also produced unacceptable results. The HYSEP algorithm 

identifies low points in the stream hydrograph in one of three 

ways: as the lowest daily streamflow in an n day period, as 

the lowest daily streamflow in a sliding interval, or as local 

minima. As with PART, each of these underestimated streamflow during the fall when the river first begins to flow and 

in the spring when streamflow declines to zero (fig. 4). The 

method also tends to partition small day-to-day fluctuations 

in streamflow as stormflow. The “one-parameter” digital filter 

method (Eckhardt, 2005) was also found to be unsatisfactory. 

Parameters a, the base flow recession constant, and BFImax, 

the maximum base flow index that can be modeled by the 

algorithm, were varied across a reasonable range (0.85 to 

0.99 and 0.01 to 0.99, respectively). BFImax primarily controls 

the minimum streamflow value, but no reasonable parameter 

value was found that was satisfactory for both dry base-flow 

periods, with streamflow about 10 cfs, and wetter periods, 

with sustained base flow of 20 cfs or more. 

Because methods examined above were found to have 

limitations, we derived a new technique called the “delta 

filter” due to its reliance on a day-to-day discharge difference 

threshold. Similar to PART, the delta filter uses an increase or 

decrease in mean daily flow less than 2 cfs from the previous day to indicate base flow on that day (PART uses any 

decrease in streamflow from the previous day). If the increase 

or decrease in mean daily flow is 2 cfs or greater than the 

day before, that day is considered stormflow-influenced, 

and a base-flow rate is linearly interpolated between the two 

nearest days of base-flow discharge. Through visual analysis 

of base-flow-separated hydrographs, we determined that a 

2 cfs threshold performed better—that is, neither too much 

stormflow nor too little was removed—than thresholds of 1, 

3, 5, or 10 cfs. Using the daily change in streamflow proved 

to be more successful than using a precipitation threshold to 

indicate base flow (a method not shown in fig. 4), due largely 
12 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

to the lack of spatially extensive historical precipitation data 

in the large contributing area upstream of the Tombstone gage. 

Annual base-flow-separated hydrographs are presented in 

Appendix 1. 

To determine the volume of winter base flow, criteria 

are needed for selecting start dates and end dates (“winter” is 

used to denote the seasonality of streamflow and not calendar dates). Selection of the end date is straightforward—it is 

identified as the last day of non-zero mean daily flow, when 

ET withdrawals equal or exceed base flow. Springtime zero 

flow occurs every year except 1979. Likewise, the start date 

for base-flow calculations in years when the San Pedro River 

near Tombstone is dry in the fall can be easily determined 

as the first day of non-zero mean daily flow. For other years, 

when streamflow is continuous from the summer monsoon 

through the winter base-flow season, the start date for baseflow calculations requires interpretation. One method is to 

Figure 4. Graph showing comparison of four base-flow separation methods applied to the streamflow record at San 

Pedro River near Tombstone gage (station number 09471550). The start of winter base flow is identified as the local minimum 

in the fall, shown as the vertical dashed line.

identify the first date of steadily increasing groundwater 

discharge in the fall (fig. 4). This represents the date when the 

average upstream hydraulic gradient reverses from a negative to a positive hydraulic gradient, allowing groundwater to 

flow into the channel. Storm runoff in October or November 

obscured this point of minimum streamflow in 1972, 1978, 

1979, 1982, 1984, 1986, and 2001, and for those years no 

estimate of start date has been made. Instead, base flow for 

these years was estimated using a linear regression between 

base flow and 25th-percentile flow (presented below).

Using the start and end date criteria outlined above, and 

the delta-filter hydrograph separation method, base flow in 

the San Pedro River near Tombstone varies from 1,220 acre-ft 

in 1999 to 20,600 acre-ft in 1985 (table 3). Two years, 1979 

and 1985, have anomalously high values. Winter precipitation 

was above average for both of these years, and the base-flow 

volume probably reflects a significant amount of short-term 

0.1

1

10

100

1,000

JUL 82 AUG 82

DISCHARGE

DELTA - FILTER

ONE PARAMETER

START OF WINTER

BASE FLOW

OCT 82 DEC 82 JAN 82 MAR 82 MAY 82

MEAN DAILY FLOW,

CUBIC FEET PER SECOND

EXPLANATION

PART

HYSEP
Base Flow in the San Pedro River near Tombstone 13

storage even after application of the hydrograph separation 

method. The proportion of base flow to total flow between the 

annual start date and end date varies from 23 percent in 1979, 

an El Niño period with associated heavy rainfall, to 100 percent in 2002, 2006, and 2009. In general, winters with greater 

rainfall are associated with a lower proportion of base flow to 

total flow. Eighteen of 25 years have a base flow of 94 percent 

or greater of total winter-flow volume, showing that winter 

storm runoff is typically a relatively small proportion of total 

winter streamflow. 

Using a different method in which base flow was identified as the ratio of monthly 3-day low flow to total flow, 

Thomas and Pool (2006) found that base flow at the Charleston gage is on average 82 percent of total flow in winter 

(November to March), 72 percent in early spring (April to 

May), 55 percent in late spring (June), and 67 percent in late 

fall (October) for the period 1931 to 2002. These average values, while in the same range as those calculated for our study, 

mask the large year-to-year variation in the ratio of base flow 

to total flow.

To extend the base-flow analysis to years when a start date 

is not readily obtained or where winter precipitation obscures 

the base-flow record, flow-duration curves (FDCs) are used. 

FDCs for the streamflow record at the gaging station near 

Tombstone typically show a distinct flat profile for percentiles 

higher than about the 25th percentile, which represents the 

midwinter steady flow rate (fig. 5). A slope breakpoint is clearly 

visible at about the 25th percentile in most years, after which 

lower-percentile mean daily flows increase rapidly. Plotting 

the FDC mean daily flow values by group—flow during the 

summer monsoon and flow during the rest of the year—clearly 

shows that this breakpoint is the division between summer and 

winter flow and that flow at percentiles higher than the 25th are 

generally winter/nonmonsoon-influenced flow.

Because the 25th percentile is closely related to winter mean daily flow, it can be used as a surrogate for winter 

base-flow volume. Use of the 25th percentile contrasts with 

the more commonly used 75th or 90th percentiles (Smakhtin, 

2001) but is necessary given the periods of zero flow at the 

gaging station near Tombstone—the 90th percentile is nearly 

always zero and the 75th percentile is often so. A linear regression model, calculated using ordinary least squares, is used to 

estimate base flow in years when hydrograph separation is not 

feasible (fig. 6). These base-flow values are denoted by italics 

in table 3.

If the 25th percentile mean daily flow represents groundwater discharge to the river, integrating this value over an 

entire year provides the total volume of groundwater that contributes to both streamflow and riparian ET. Using the values 

from table 3, this volume is 11,580, 7,090, and 10,860 acre-ft 

annually for the early, late, and combined period of record, 

respectively. These values are about the same magnitude as the 

range of annual ET, 9,600 to 12,055 acre-ft, estimated by Scott 

and others (2006). This suggests that, in the absence of summer storm runoff, it is possible that all groundwater discharging as streamflow could instead be removed as ET. 

Methods to Identify Sources of Base Flow

Base flow in the San Pedro River is a combination of 

regional groundwater and storm runoff that is stored in the 

near-stream alluvial aquifer as “alluvial groundwater”. Alluvial 

groundwater has residence times in the subsurface from days to 

months, whereas regional groundwater has residence times on 

the order of decades, centuries, or longer. The relative contributions of each of these to base flow and changes in each over 

time, are evaluated through further inspection of the stream 

hydrograph and analysis of environmental isotope tracers. 

Hydrograph Characteristics

Drier-than-average summer monsoons and low winter 

rainfall in 2002, 2003, and 2004 provide an opportunity to 

look at the regional groundwater contribution to streamflow 

independently from alluvial groundwater. Streamflow at the 

Tombstone gage goes to zero quickly at the end of the monsoon (September) in each of these years and does not return 

until December (fig. 7). We can assume that alluvial-groundwater contributions to streamflow are minimal during these 

years and that the source of winter streamflow is primarily 

regional groundwater. Average base flow is about 1,680 acre-ft 

during this period (the area under the dotted line curve in fig. 

7). If this value is assumed to represent regional groundwater 

contributions to base flow for the period 1996 to 2009, alluvial 

groundwater contributions to base flow are the difference 

between this value and the total winter base flow and range 

from 0 acre-ft (in 1999 and 2004) to 2,730 acre-ft (in 1998) or 

from 0 to 62 percent of total base flow. 

Comparing this same average base-flow value, 1,680 

acre-ft, to measured base flow in 1999 (fig. 8), however, shows 

that the minimum regional groundwater contribution may be 

somewhat less—total base flow in 1999 is just 1,220 acre-ft, 

even though the total summer monsoon flow was 6,530 acre-ft 

(compared to 4,070, 6,910, and 7,710 acre-ft of monsoon 

flow in 2003, 2004, and 2005, respectively). The difference 

between 1999 and the 2002 to 2004 period is likely because 

of small variations in the timing of summer runoff and winter 

rainfall—in 1999, monsoon runoff stopped earlier in the summer and winter rainfall was less than the other years. This suggests that, even following the relatively dry summers of 2002 

through 2004, some component of alluvial groundwater may 

be present in base flow.

The average 1,680 acre-ft of base flow from regional 

groundwater observed for the 2003 to 2005 period occurs 

later than base flow in a dry year, 1981, during the early 

period of the record (fig. 8), in agreement with the results of 

Thomas and Pool (2006), who found that 60 percent of the 

decrease in annual base flow from 1931 to 2002 was from 

September to November. Streamflow in 1981 begins a full 

month earlier, in late October, than it does in 2003 to 2005, 

when it does not begin until late November. The rate of 
14 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Water year Base flow 

start date

Base flow 

end date

Days of 

base flow

25th percentile flow 

(cfs)

Percent 

dry

Base flow

(acre-ft)

Base flow as a 

percent of total flow 

between start and 

end dates

1968 10/27 6/16 233 32.5 7.6 10120 41.1

1969 9/30 6/9 252 16.0 9.6 5000 98.4

1970 10/11 6/15 247 16.0 7.1 5160 94.9

1971 10/8 6/15 250 24.0 7.9 5950 95.2

1972 NA 7/8 21.0 1.9 5830 94.3

1973 11/9 6/4 207 30.0 16.7 8930 67.9

1974 11/6 5/13 188 15.0 23.2 3540 95.7

1975 10/19 6/16 240 13.5 4.6 4830 96.6

1976 10/9 5/30 234 16.0 7.9 5020 98.9

1977 10/20 6/14 237 18.5 5.2 5400 98.8

1978 NA 6/20 38.0 8.7 10300 77.6

1979 NA -- 71.0 5.5 19000 23.0

1980 10/7 6/11 248 14.0 17.2 4940 99.5

1981 10/28 5/20 204 9.7 19.4 2790 99.7

1982 NA 5/21 12.0 15.0 3460 77.7

1983 10/26 6/5 222 28.0 14.2 8140 28.4

1984 NA 5/31 53.5 8.7 14400 61.4

1985 11/9 6/25 228 79.5 3.6 20600 46.7

1986 NA 6/20 34.0 4.9 9260 98.0

1997 11/5 5/21 197 9.6 31.7 2910 98.3

1998 10/31 5/30 211 15.0 15.3 4400 79.6

1999 12/7 5/7 151 6.7 33.6 1220 99.6

2000 10/15 5/9 207 9.6 2.5 2710 97.7

2001 NA 6/11 43.5 8.2 11800 55.6

2002 11/13 5/19 187 13.0 35.5 3860 100.0

2003 12/2 5/17 166 7.0 41.5 1790 99.7

2004 12/16 5/10 146 6.3 46.2 1530 84.3

2005 11/26 5/15 170 9.1 33.1 1910 79.2

2006 11/23 5/2 160 10.0 32.8 2270 100.0

2007 11/5 5/18 194 13.0 15.8 3990 99.9

2008 11/27 5/17 172 13.0 29.8 2880 97.9

2009 10/30 5/14 196 14 29.5 4620 100.0

Median

Median, 1967–1986 10/20 6/10 234 16.0 7.9 5830, 5000<C50<9260 95

Median, 1997–2009 11/18 5/16 180 9.8 29.8 2880, 1910<C50<3990 99

Median, 1967–2009 10/31 5/30 207 15.0 14.6 4890, 3860<C50<5400 96

Table 3. Base-flow statistics for San Pedro River near Tombstone (USGS station number 09471550). 

[cfs, cubic feet per second; C50, median value. Bold, Continuous flow through fall months; date estimated as first date of continuously increasing streamflow. Italic, Base flow could not be estimated from hydrograph; a linear regression model between 25th percentile and mean daily flow was used (fig. 6). 

NA, Start date could not be estimated, because storm runoff events obscured start of base flow. 1979 and 1982, flow begins on 10/21 with a storm event in 

both years, not used. --, Flow was continuous through spring 1979; base flow as a percent of total flow between start and end dates is calculated assuming 

an end date of 7/1]
Base Flow in the San Pedro River near Tombstone 15

0.1

1

10

100

1,000

1

10

100

1,000

1

10

100

1,000

1

10

100

1,000

1

10

100

1,000

1

10

100

1,000

1

10

100

1,000

0 50

1

10

100

1,000

100/ 0 50 100/ 0 50 100/ 0 50 100

Percent of year since October 1 (gray line)/Percent of time that a given flow is exceeded (red/blue dots)

1968 1969 1970 1971

1972 1973 1974 1975

1976 1977 1978 1979

1980 1981 1982 1983

1984 1985 1986 1997

1998 1999 2000 2001

2002 2003 2004 2005

2006 2007 2008 2009

0.1

0.1

0.1

0.1

0.1

0.1

0.1

DAILY FLOW, CUBIC FEET PER SECOND

Figure 5. Flow duration curves and stream hydrographs at San Pedro River near Tombstone (station number 09471550) for 

1968–1986 and 1997–2009. Blue points indicate streamflow during the months of November through June; red points are July 

through October. Vertical dotted line shows the 25th percentile. 
16 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Figure 6. Scatter plot of winter base-flow volume vs. flow percentile. 

y = 263.86x + 292.77

R2 = 0.9755

0

5,000

10,000

15,000

20,000

25,000

0 10 20 30 40 50 60 70 80 90

25TH PERCENTILE MEAN DAILY FLOW,

CUBIC FEET PER SECOND

WINTER BASE FLOW, ACRE-FEET

Figure 7. Streamflow at San Pedro River near Tombstone (station number 09471550) September 2002 to May 2005. Blue 

dots indicate average base flow contribution to streamflow.

increase in discharge is also higher during the earlier period, 

reaching the midwinter steady flow rate by early January and 

lasting until mid-March. In contrast, the increase in discharge 

during the latter period (shown by the dotted line in fig. 8) 

is more gradual, and the midwinter steady flow rate is much 

shorter (~two weeks) in duration. Following the midwinter 

steady flow rate, both the early record and the late record 

show discharge declining at a similar rate as ET withdrawals 

increase and cause losing conditions. 

One possible explanation for the later start date of 

flow during the later period of record and, in particular, the 

difference between the 1981 and 2002 to 2004 hydrographs, 

is the date of the first freezing temperature in the fall. The first 

hard freeze (below about –5°C) along the river causes leaf 

mortality and a large reduction in ET almost immediately and 

allows gaining conditions to be established in the stream channel (Goodrich and others, 2000). Records from the National 

Weather Service cooperative observer station (NWS station 

028619) in the city of Tombstone, AZ, indicate that the first 

low temperature in fall 1980 occurred on October 16, and flow 

resumed soon afterwards (fig. 8). In fall 2002, 2003, and 2004, 

the first low temperatures occurred on December 4, November 

0.1

1

10

100

1,000

10,000

JUL 02 OCT 02 JAN 03 APR 03 JUL 03 OCT 03 JAN 04 APR 04 JUL 04 OCT 04 JAN 05 APR 05

Mean daily flow, cfs MEAN DAILY FLOW,

CUBIC FEET PER SECOND

DISCHARGE AVERAGE BASE FLOW, 2003 TO 2005
Base Flow in the San Pedro River near Tombstone 17

Figure 8. Streamflow at San Pedro River near Tombstone (station number 09471550) for 1980 to 1981, and 1998 to 1999, showing 

comparison of the average base flow contribution to streamflow, based on the 2003 to 2005 record. 

25, and November 2, respectively, and flow resumed later in 

these years. Lack of a clear relation between recorded temperature at Tombstone and temperature along the river corridor 

and absence of long-term records of temperature along the 

river corridor, however, preclude definitive conclusions about 

the effect of temperature on winter base flow. 

Environmental Isotopes

Environmental isotope ratios such as hydrogen (δ2H/δ1H) 

and oxygen (δ18O/δ16O) provide a further means to evaluate 

regional and alluvial groundwater sources. The isotopic composition of rainfall is influenced by the temperature at which 

it forms; higher altitude rainfall is generally more depleted 

in heavier isotopes than lower altitude rainfall. Because of 

this, orographic uplift of rain-forming clouds causes isotopic 

fractionation, and higher elevations generally receive more 

isotopically depleted rainfall. This effect occurs even where 

topographic relief is minor (Clark and Fritz, 1997) and results 

in variations in groundwater isotopic composition in the San 

Pedro Basin that correlate with recharge source-area elevation (Pool and Coes, 1999). Once precipitation leaves the 

atmosphere and becomes runoff and (or) recharge, the isotopic 

signature generally does not change. The isotopic composition 

of streamflow reflects its source waters and, if two or more 

sources have sufficiently different signatures, the amount of 

each in a composite sample may be estimated.

In this report, we use the mass-balance method to evaluate the relative contribution of regional groundwater and 

alluvial groundwater to base flow. A simple linear relation 

describes the conservative mixing of two end members,

 (1)

where Q refers to discharge, δ is isotope composition, and the 

subscripts t, agw, and rgw refer to total flow, alluvial groundwater, and regional groundwater, respectively. This relation 

is used with a single constituent isotope, either hydrogen or 

oxygen, and may be calculated independently for each (for end 

members that fall on the meteoric water line (MWL), however, the two isotopes will provide the same result). The end 

members for the mixing model are regional groundwater and 

alluvial groundwater.

Beginning fall 1999, water samples of in-stream flow 

have been collected at approximately monthly intervals at 

five sampling sites on the San Pedro River and one site on 

the Babocomari River. These samples are analyzed for stable 

hydrogen and oxygen isotope ratios at the USGS Reston 

Stable Isotope Laboratory. Hydrogen (deuterium) activity is 

measured using a hydrogen equilibration technique (Révész 

and others, 2008a). Oxygen activity is measured using an 

automated CO2

 equilibration technique (Révész and others, 

2008b). Values are reported in per mill units (‰) relative to 

Vienna Standard Mean Ocean Water. Measurement uncertainties (2 standard deviations) for oxygen and hydrogen are 0.2‰ 

and 2‰ , respectively.

Thirty-six streamflow samples collected at the Tombstone 

gage plot along a line in a δ18O-δ2H graph (fig. 9) and have a 

slope that departs from the meteoric water line, which indicates evaporative enrichment (Gat, 1996). Evaporative fractionation causes the isotopic composition of water to become 

enriched as lighter isotopes preferentially evaporate. The most 

depleted streamflow at the Charleston gage, the Tombstone 

gage, and the Babocomari gage occurs at the beginning of 

most winters (fig. 10). The composition of Tombstone gage 

samples is either between the Charleston and Babocomari 

River gage samples or more enriched than both. Over the 

course of a winter, samples at all sites become more enriched, 

but the rate of change is greatest at the Tombstone gage. The 

most enriched samples are collected at the end of the winter 

auses isotopic fractionation, and higher elevations generally receive more isotopically 

 This effect occurs even where topographic relief is minor (Clark and Fritz, 1997) and 

ns in groundwater isotopic composition in the San Pedro Basin that correlate with 

area elevation (Pool and Coes, 1999). Once precipitation leaves the atmosphere and 

nd (or) recharge, the isotopic signature generally does not change. The isotopic 

reamflow reflects its source waters and, if two or more sources have sufficiently 

es, the amount of each in a composite sample may be estimated. 

port, we use the mass-balance method to evaluate the relative contribution of regional 

alluvial groundwater to base flow. A simple linear relation describes the conservative 

d members, 

����

��

� �������

���������

, (1) 

 discharge, δ is isotope composition, and the subscripts t, agw, and rgw refer to total 

undwater, and regional groundwater, respectively. This relation is used with a single 

pe, either hydrogen or oxygen, and may be calculated independently for each (for end 

 on the meteoric water line (MWL), however, the two isotopes will provide the same 

members for the mixing model are regional groundwater and alluvial groundwater. 

g fall 1999, water samples of in-stream flow have been collected at approximately 

 at five sampling sites on the San Pedro River and one site on the Babocomari River. 

e analyzed for stable hydrogen and oxygen isotope ratios at the USGS Reston Stable 

ry. Hydrogen (deuterium) activity is measured using a hydrogen equilibration 

DISCHARGE AVERAGE BASE FLOW, 2003 TO 2005

0.1

1

10

100

1,000 MONSOON FLOW: 4,185 ACRE - FEET

WINTER RAINFALL: 89 mm

MONSOON FLOW: 6,530 ACRE - FEET

WINTER RAINFALL: 27 mm

JUN 80 AUG 80 OCT 80 DEC 80 FEB 81 APR 81 JUN 98 AUG 98 OCT 98 DEC 98 FEB 99 APR 99

DISCHARGE,

CUBIC FEET PER SECOND
18 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Figure 9. Graph showing mean hydrogen and oxygen ratios at selected sites along and near the San Pedro River. Winter base flow is 

the average of samples collected from December to March at discharge rates less than 20 cfs. Summer flow is the discharge-weighted 

average of samples collected from July to September. Horizontal and vertical error bars show ± 1 standard deviation of the mean.

-60.00

-58.00

-56.00

-54.00

-52.00

-50.00

-48.00

-46.00

-44.00

-42.00

-40.00

-7.50 -7.00 -6.50 -6.00

del D

del 18O

an isotopes for selected conditions

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

-10 -9.5 -9 -8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5

OXYGEN ISOTOPE RATIO, PER MILL

HYDROGEN ISOTOPE RATIO, PER MILL

SUMMER STORMFLOW, 

 SCALED BY DISCHARGE

METEORIC WATER LINE

SIERRA VISTA 

 GROUNDWATER AVERAGE

SUMMER PRECIPATION

TOMBSTONE WINTER BASE FLOW

BASIN GROUNDWATER AVERAGE

FLOW-WEIGHTED SUMMER 

 PRECIPATION AVERAGE

PRE-EVAPORATIVE 

 ENRICHMENT

base-flow season. Although the evaporative enrichment process applies only to water evaporated from the river and from 

soil water directly and does not occur through transpiration 

(Gat, 1996), the rate of evaporation and therefore fractionation 

likely increases with the onset of ET in spring as discharge 

decreases and air and water temperatures rise. By projecting 

the best-fit line of the enriched samples to the intersection with 

the meteoric water line, the original pre-evaporative composition of Tombstone winter base flow may be estimated as 

–56.75‰ δ18O and –8.1‰ δ2H (fig. 9). 

This isotopic composition of pre-evaporative Tombstone base flow is more enriched than most regional groundwater west of the San Pedro River and similar to regional 

groundwater east of the river (fig. 11). Regional groundwater 

composition is spatially well defined at 106 locations by 

samples collected at wells and springs during previous studies (Pool and Coes, 1999; Wahi, 2005; Goodrich and others, 

2004). Groundwater recharged at high elevations in the 

Huachuca Mountains has the most depleted isotopic composition in the basin. The average isotopic composition of this 

Sierra Vista-area groundwater (gray-shaded area in fig. 11) is 

–65.5±3.2‰ δ18O and –9.31±0.4‰ δ2H, whereas the average 

composition of all sites west of the river (excluding alluvial 

aquifer wells) is –59.8±5.6‰ δ18O and –8.5±0.82‰ δ2H. 

This isotopically depleted region corresponds with the steepest hydraulic gradients in the basin (Schmerge, 2009) and is 

generally believed to contribute a substantial proportion of 

the regional groundwater contribution of winter base flow 

(Pool and Coes, 1999; Baillie and others, 2007). To account 

for the isotopic signature of winter base flow at Tombstone, 

however, one or more other, more enriched groundwater 

sources must also contribute.

Potential isotopically enriched regional groundwater 

sources of Tombstone winter base flow are subflow from the 
Base Flow in the San Pedro River near Tombstone 19

Figure 10. Graph showing hydrogen isotope samples collected during winter at the Charleston, Tombstone, and Babocomari River gages. 

Dashed boundary denotes continuous data.

-9

-7

-5

-5

-7

-9

AUG-99NOV-99

FEB -00

MAY -00

AUG-00

NOV-00

FEB -01

MAY -01

AUG-01NOV-01

FEB -02

MAY -02

AUG-02NOV-02

FEB -03

MAY -03

AUG-03NOV-03

FEB -04

MAY -04

AUG-04NOV-04

FEB -05

MAY -05

AUG-05

NOV-05

FEB -06

MAY -06

AUG-06NOV-06

FEB -07

MAY -07

AUG-07NOV-07

FEB -08

MAY -08

AUG-08NOV-08

FEB -09

MAY -09

CHARLESTON TOMBSTONE BABOCOMARI

OXYGEN ISOTOPE RATIO, PER MILL OXYGEN ISOTOPE RATIO, PER MILL

south and groundwater recharged in the lower-elevation Mule 

Mountains east of the river, subflow channeled between the 

Bronco and Babocomari Hills west of the river, and subflow 

from the Walnut Gulch watershed east of the river (fig. 1). 

Regional groundwater samples collected at 12 sites east of 

the river (excluding alluvial aquifer wells) have an average 

composition of −55.5±3.2‰ δ18O and −7.90±.46‰ δ2H. In the 

lower part of the basin, samples collected at Monitor Well 7, 

representative of subflow between the Bronco and Babocomari 

Hills west of the river, and at four sites in Walnut Gulch, east 

of the river, all have compositions similar to or more enriched 

than Tombstone base flow. Because these values, together with 

the isotopic composition of Sierra Vista-area groundwater, 

bracket the composition of Tombstone base flow, a significant 

amount of inflow of groundwater from the south, east, and 

north could account for the isotopic signature at Tombstone.

A second potential contributor of isotopically enriched 

groundwater to Tombstone base flow is summer stormflow 

that is stored as alluvial groundwater when elevated river stage 

causes infiltration into stream channel alluvium. It typically is 

more enriched than winter base flow, but storms may also produce lighter-composition streamflow, as well. In some years, 

such as 2000, both isotopically light and heavy precipitation 

(and therefore streamflow) occur during the same summer 

(fig. 10). Similar to regional groundwater, this inconsistent 

signature makes identification of an average precipitation and 
20 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Figure 11. Map showing δ 2H concentrations at regional and alluvial groundwater sampling sites. Shaded region shows the 

region for which the Sierra Vista-area isotopic composition is calculated. 

110o

31o30’

31o40’

31o50’

31o20’

ARIZONA

SONORA

UNITED STATES

MEXICO

Bisbee

i

R

Babocomari

iver

92

90

90

82

HILLS

WHETSTONE

HUACHUCA

MOUNTAINS

MOUNTAINS

MULE

MOUNTAINS

80

Tombstone

SIERRA VISTA

SUBWATERSHED

SUBWATERSHED

BENSON

R

ver

Huachuca City

San

Fort Huachuca

0 5 MILES

0 5 KILOMETERS

Sierra Vista

SANTA CRUZ 

COUNTY

PIMA

COUNTY

COCHISE

COUNTY

110o20’ 110o10’ 109o50’

Base from U.S. Geological Survey

digital data, 1:100,000, 1982

Universal Transverse Mercator

projection, Zone 12

BABOCOM

RI HILLS

BRONCO HI

Pedro

TOMBSTONE

"

##

#

#

##

#

#

#

#

# #

"

"

"

" "

"

"

"

"

" "

"

"

"

"

"

"

"

"

" " " " " " "

"

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" "

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"

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"

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Value High : -49.6 Low : -71.0

Regional Aquifer

Alluvial Aquifer

Spring

Explanation

A

LLS

San Pedro

Riparian

National

Conservation

Area

Fairbank

San Pedro River

near Tombstone
Base Flow in the San Pedro River near Tombstone 21

stormflow signature difficult. Samples collected during periods 

of high flow, when storage of runoff in the alluvial aquifer 

is highest, have a greater impact on the average stormflow 

composition than samples collected at lower discharge rates. 

Therefore, a discharge-weighted average value is more representative than a simple average. The average composition of 

alluvial groundwater from eight streamflow samples, collected 

at the Charleston gage during runoff events (discharge greater 

than 25 cfs) in July, August, and September, and four summer 

rainfall samples is –41.7±6.3‰ δ18O and –7.30±0.89‰ δ2H 

(fig. 9). Discharge at the Charleston gage while samples were 

collected varied from 25 to 404 cfs. Although a number of 

samples have been analyzed from wells located in the alluvial 

aquifer, these are excluded from the average value because 

they represent an unknown mixture of regional and alluvial 

groundwater, whereas the stormflow and precipitation samples 

represent only water derived from summer stormflow.

Because of the uncertainty in determining the isotopic 

composition of regional groundwater that contributes to base 

flow, described above, a simple average of all regional groundwater samples is used in the mixing model analysis. Otherwise, detailed knowledge of the isotopic composition and 

discharge rates of specific zones of groundwater discharge to 

the river would be needed to fully define this end member. The 

average value is believed to be representative because hydraulic gradients indicate that groundwater flow throughout the 

basin is toward the river (Schmerge, 2009), and sampling bias 

has resulted in more samples collected west of the river, where 

hydraulic gradient is highest. This results in the region west of 

the river having a greater influence on the average value of the 

isotopic composition of regional groundwater.

Using the isotopic compositions for the groundwater end 

members and winter base flow described above, the average 

proportion of regional groundwater to total winter base flow 

at the Tombstone gage is 74 percent. Alluvial groundwater 

supplies the other 26 percent. Considering uncertainty in the 

average values used for the source groundwater and the mixed 

water at the Tombstone gage (Phillips and Gregg, 2001), the 

95 percent confidence interval is 64 percent to 84 percent. 

Applying this average composition of winter base flow at 

the Tombstone gage to the median value of winter base flow 

calculated during the later period of record (2,880 acre-ft, 

table 3), the median amount of annual regional groundwater 

discharged as base flow from 2000 to 2009 is 2,130 acre-ft. 

Identifying a single value of regional groundwater 

contribution to base flow at the Tombstone gage oversimplifies the complexity of a large, dynamic, natural system. The 

large year-to-year variation in winter base-flow volume makes 

identification of an average composition difficult, and any 

given year may have winter base flow that differs significantly 

from that average. Reasonable estimates of the groundwater 

contribution to base flow can be made only because a large 

number of samples have been collected over a 10-yr period, 

and these estimates apply only to the period for which isotope 

data are available. Changes in infiltration rates (such as those 

caused by channel incision), seasonality of rainfall, and ET 

would all potentially cause regional and alluvial groundwater 

proportions to be different in the past. 

Trend in Base Flow

Summary statistics of the different base-flow metrics 

show differences between the early period of record, 1967 to 

1986, and the late period, 1996 to 2009 (table 3). The median 

is a more useful indicator of central tendency in this case, 

because it is not skewed by the anomalously wet winters in 

1979 and 1985. Base flow during the late period of record 

is shorter in duration and at a lower discharge than the early 

period. The median number of days of winter base flow 

has decreased from 234 to 180, and the period of zero flow 

during the calendar year has increased from 7.9 percent to 

29.8 percent. Total base-flow volume has decreased about 51 

percent, from a median value of 5,830 acre-ft/yr for the early 

period to 2,880 acre-ft/yr for the later period. Average base 

flow for the entire period of record is 4,890 acre-ft/yr. 

The decrease in base flow is most pronounced during late 

fall/early winter and is apparent whether using the delta-filter 

method described above to separate base flow from total flow 

or the 3-day monthly low-flow method (table 4). The largest 

decreases, 80 percent and 51 percent (calculated from base 

flow-separated streamflow), are in November and December, 

respectively. Somewhat smaller decreases of about 40 percent 

are observed in January through April. Possible causes for 

this decrease in base flow are a decrease in precipitation and, 

therefore, reduced runoff and storage in the alluvial aquifer, 

reduced inflow of regional groundwater, or increased ET.

Variation in Base Flow Caused by Precipitation

One apparent reason for the decline in streamflow from 

the early period of record to the late period is a decline in 

precipitation. While the average annual rainfall does not differ 

significantly—from 348 mm for the early period to 330 mm 

for the late period—the decline occurs in the months most 

likely to influence winter base flow, September and October 

(fig. 12). These two months exhibit the largest decrease from 

the early period to the late period. This lack of late- and postsummer rainfall has a direct effect on the amount of desaturation of the alluvial aquifer caused by ET and, therefore, 

on the date that flow resumes at the Tombstone gage in late 

fall/early winter, which directly influences winter base-flow 

volume. Rainfall amounts in September and October for the 

late period are close to the long-term average (1931 to 2009), 

while winter precipitation is lower than average (fig. 12). 

Rainfall during the early period of record in the months from 

September to November and from January to March are higher 

than the long-term average, and this is likely reflected in the 

streamflow record at the San Pedro River near Tombstone. A 

comparison of monthly rainfall for each year shows that for 
22 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

the early period of record significant winter rainfall occurred 

primarily in the months of October, December, and January 

(fig. 13). This figure also highlights the lack of winter precipitation during the late period. Between 1968 and 1986, rainfall 

of 40 mm or greater was recorded in a total of 20 months 

between October and March. Between 1997 and 2009, only 

5 months have had 40 mm of rainfall, and none of these have 

occurred since 2001.

To evaluate the importance of factors other than rainfall on the volume of annual winter base flow, the relation 

between rainfall and streamflow must be quantified. Linear 

regression using ordinary least squares is a commonly used 

technique that assumes that the residuals (measured value 

minus predicted value) are homoscedastic (have constant 

variance), independent, and normally distributed. These 

assumptions, while not prohibitive, often do not hold true for 

streamflow data (Helsel and Hirsch, 2002). A nonparametric 

alternative to linear regression that makes no assumptions 

about the underlying distribution is Locally Weighted Scatterplot Smoothing, or LOWESS, which will be used here. This 

smoothing algorithm involves fitting a weighted least-squares 

regression to subsets of the data. Within each subset, points 

that are farther from the center in either the x or y direction 

receive less weight. In contrast, ordinary least squares places 

greater emphasis on minimizing large residuals, caused by 

points that plot away from the center of the data. LOWESS 

regression results in a non-linear line that more closely fits the 

central tendency of the data and is less influenced by outlying 

data, compared to linear regression. A LOWESS regression 

may be implemented either as a simple regression, with a 

single explanatory variable, or as a multiple regression, with 

two or more explanatory variables.

Ideally, the explanatory variables in the regression 

analysis are independent of the dependent variable. Because 

the streamflow record exhibits autocorrelation (that is, 

streamflow on a given day can be at least partially predicted 

by streamflow on previous days), it cannot be an independent predictive variable for itself. Because of this, rainfall 

depth is a better independent variable. During the summer 

months, however, rainfall is highly variable in space, and 

the record from a single gage, or even several gages, does 

not adequately represent the watershed. Therefore, summer 

streamflow is used as a surrogate for effective summer rainfall across the Subwatershed. Because ET withdraws more 

water than is supplied by base flow in summer, all summer 

streamflow at the Tombstone gaging station is the result of 

summer rainfall only.

Winter rainfall is a second explanatory variable for winter 

base flow. Direct runoff from winter storms is usually small, 

but several large storms in the early 1980s are an exception. 

Although the delta-filter base-flow-separation method removes 

small stormflow peaks from the base-flow record, long duration, widespread storms are more difficult to separate from 

groundwater contributions to base flow. During these periods, 

Table 4. Median of the mean daily flow by month for the periods from 1968 to 1986 and from 1997 to 2009 for the San Pedro River 

near Tombstone. 

[Base flow, measured streamflow with stormflow removed, as described in discussion; low flow, lowest 3-day average of mean daily flow in a given month; C50, 

median value for which half of the data points are above and half are below; C.I., confidence interval]

Period

(water year) Method

November December January

Median C.I.1 Median C.I.1 Median C.I.1

1968 to 1986

Base flow 10.6 7.8 ≤ C50 ≤18.5 14.2 12.6 ≤ C50 ≤19.5 16.8 14.4 ≤ C50 ≤26.4

Low flow 14.0 12.6 ≤ C50 ≤19.6 15.8 13.5 ≤ C50 ≤33.5 2.5 0.8 ≤ C50 ≤5.8

1997 to 2009

Base flow 2.2 0.1 ≤ C50 ≤4.2 6.9 1.9 ≤ C50 ≤12.6 10.1 6.5 ≤ C50 ≤12.8

Low flow 7.0 0.7 ≤ C50 ≤12.6 9.9 9.2 ≤ C50 ≤13.9 0.0 0.0 ≤ C50 ≤0.1

Period

(water year) Method February March April

Median C.I.1 Median C.I.1 Median C.I.1

1968 to 1986

Base flow 17.7 16.0 ≤ C50 ≤30.9 15.8 13.6 ≤ C50 ≤31.1 10.8 9.5 ≤ C50 ≤18.7

Low flow 6.2 4.1 ≤ C50 ≤16.0 10.0 8.7 ≤ C50 ≤14.0 15.0 12.0 ≤ C50 ≤20.0

1997 to 2009

Base flow 10.0 9.1 ≤ C50 ≤13.5 9.9 9.2 ≤ C50 ≤13.9 6.5 5.1 ≤ C50 ≤8.7

Low flow 0.0 0.0 ≤ C50 ≤1.9 5.2 0.8 ≤ C50 ≤6.1 7.7 2.8 ≤ C50 ≤11.0

1

 Confidence interval is a nonparametric estimate calculated using a binomial distribution table, after Helsel and Hirsch (2002). For the period 1968 to 1986, it is 

the 93.6 percent confidence interval (n = 19); for the period 1997 to 2009, it is the 90.8 percent confidence interval (n = 13).
Base Flow in the San Pedro River near Tombstone 23

0

10

20

30

40

50

60

70

80

90

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

1931 to 2009

1968 to 1986

1997 to 2009

MONTHLY RAINFALL, MILLIMETERS

0

20

40

60

80

100

120

140

160

1967 1972 1977 1982 1987 1992 1997 2002 2007

MONTHLY RAINFALL, MILLIMETERS

(NO STREAMFLOW DATA

AT SAN PEDRO RIVER

NEAR TOMBSTONE) 

OCT.

NOV.

DEC.

JAN.

FEB.

MAR.

Figure 12. Graph showing average monthly precipitation measured at Tombstone (NWS Coop ID 028619) 

from 1931 to 2009, and for data subsets from 1968 to 1986 and 1997 to 2009. 

Figure 13. Graph showing monthly precipitation measured at Tombstone from October through March for 

each year from 1967 to 2009. Each month is plotted according to the calendar year, not water year. 
24 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

some correlation between precipitation and base flow would 

be expected. In addition, prior to the onset of flow in late fall/

early winter, direct infiltration of winter rainfall on the (dry) 

stream channel between the Charleston and Tombstone gages 

reduces seepage losses and serves to increase the volume of 

base flow. Occasional snowfall is generally insignificant at 

the low-elevation precipitation stations used in this study, and 

any snowpack at higher elevations does not contribute direct 

surface runoff to winter base flow in the San Pedro River. 

Several dependent variables representative of winter 

base flow are possible, including (1) mean monthly flow after 

hydrograph separation using the delta filter outlined above, 

(2) monthly 3-day low flow, (3) the 25th percentile mean 

daily flow, (4) total flow volume from the base-flow-separated 

hydrograph, (5) the start date of winter base flow, and (6) the 

midwinter steady-state mean daily flow. The total flow volume 

from table 4 incorporates the effects of the start date of base 

flow, the midwinter steady-state mean daily flow, and the 

effect of any rainfall or stormflow that was not removed from 

the streamflow record by hydrograph separation. The start 

date of winter base flow is only identifiable in years when the 

river is dry or when there is a distinct minimum flow in the 

fall. In years when the river is dry in the fall, this value varies 

based on the particular stream channel configuration. As the 

wetting front advances downstream, it starts and stops based 

on the local bed composition and thickness. Because of the 

sand composition of the stream channel in the vicinity of the 

Tombstone gage, local channel shape changes from year to 

year. Streamflow may pool behind a small obstruction or dip 

in the channel and then advance rapidly once that section is 

saturated and (or) overtopped. The midwinter steady-state flow 

is reached when the stream channel is largely saturated, losses 

between the Charleston and Tombstone gages are minimal and 

steady, streamflow at the Tombstone gage is no longer increasing, and before ET causes a decrease in streamflow. In years 

with little winter precipitation, the midwinter steady-state flow 

can be identified manually as a plateau in the stream hydrograph or as a wide flat region in the center of the flow-duration 

curve (fig. 5). As with the start date, it cannot be identified 

every year. 

Data transformations, such as the log transform, are often 

used with streamflow data to improve statistical analyses 

(Helsel and Hirsch, 2002). Tests of different transformations 

on discharge at the Tombstone gage show that a cube-root 

transform on the mean daily flow variables was useful to 

make the relation between them and base flow more linear. A 

cube-root transform was more satisfactory than a log, natural 

log, or square-root transform. In addition, it has the advantage 

over log transforms that zero values in the data, as occasionally occur in the streamflow data, are preserved. Therefore, 

mean daily base flow, monthly 3-day low flow, and midwinter 

steady state flow were cube-root transformed before plotting 

and further analysis.

A scatter-plot matrix provides an efficient way to analyze 

the effect of several independent variables on several dependent variables. Many possible combinations were considered; 

only the most relevant are presented here. Plots of mean daily 

base flow, calculated for each month from the base flow-separated hydrographs, show a greater dependence on mean daily 

flow in September and October than on mean daily flow over 

the entire summer (fig. 14, left two columns), even though 

the greatest amount of rainfall is in July and August (fig. 12). 

Monthly 3-day low flow follows a similar pattern. The relation 

between summer streamflow (either July to October or September to October) and either January or February winter flow 

is nearly identical, indicating that the choice of time period 

of winter flow for regression analysis is relatively unimportant. A relation between winter flow and winter rainfall is also 

apparent (fig. 14, right two columns). This indicates that the 

base-flow separation process removes only the short-duration 

effect of rainfall and some longer-term effects remain. January 

rainfall has a higher correlation with winter base flow than 

December rainfall, and both of these months have higher correlations than October, November, or February (not shown). 

This is most likely because these two months have the highest 

amount of rainfall (fig. 13) and also because rainfall that 

occurs later during the winter cannot affect streamflow during 

the early winter.

Similar to winter base-flow rate, winter base-flow volume 

and 25th-percentile flow show a higher correlation with late 

summer streamflow than total summer streamflow (fig. 15). 

The other two metrics—start date of winter base flow and 

midwinter maximum—show little correlation with either summer streamflow or winter rainfall. Large scatter and generally 

low correlation coefficients for all of the scatter plots shown in 

figures 14 and 15 suggest that multiple independent variables 

influence base flow. For instance, high base flow could be 

caused either by a large amount of streamflow (and therefore 

storage in the near-stream aquifer) during the summer or by a 

large amount of rainfall during the winter. 

Having determined that winter base flow is correlated 

to summer streamflow, it is helpful to find the period of time 

in the summer to which base flow is most closely related. To 

avoid using arbitrary month-long divisions or arbitrary start 

and end dates over which to average summer streamflow, a 

response surface of the R2

 statistic for different summer time 

frames is used (fig. 16) to identify the period in summer with 

the highest correlation to winter base flow. A moving window 

with a variable span from 5 to 45 days and with a midpoint 

varying from July 1 to October 20 was identified, and the 

average mean daily flow during that window was calculated 

for each year. Later midpoints were not considered to be 

representative of summer rainfall. Next, the R2 statistic (also 

known as the coefficient of determination) between summer 

streamflow and winter base flow for a LOWESS regression is 

calculated as

(2)

where yi

 is the observed winter base flow (either total volume 

or 3-day low flow), f

i

 is the predicted winter base flow for a 

month-long divisions or arbitrary start and end dates over which to average summer stre

response surface of the R2

 statistic for different summer time frames is used (figure 16) 

period in summer with the highest correlation to winter base flow. A moving window w

span from 5 to 45 days and with a midpoint varying from July 1 to October 20, was ide

average mean daily flow during that window was calculated for each year. Later midpoi

considered to be representative of summer rainfall. Next, the R2

 statistic (also known as 

of determination) between summer streamflow and winter base flow for a LOWESS reg

calculated as 

�� � � � � �������� �

� �������� �

, 

where yi is the observed winter base flow (either total volume or 3-day low flow), fi is th

winter base flow for a given summer streamflow, and �� is the mean observed winter bas

x,y pair in the R2

 calculation is the mean daily summer flow within a given window and 
Base Flow in the San Pedro River near Tombstone 25

Figure 14. Scatter plot matrices of winter base flow (mean monthly flow after hydrograph separation) and monthly 3-day low flow vs. 

summer streamflow and winter precipitation. Red points represent the early period of record at the gaging station near Tombstone, from 

1968 to 1986, and blue points represent the later period, from 1997 to 2009. Values are the Pearson correlation coefficient.

given summer streamflow, and ȳ is the mean observed winter 

base flow. Each x,y pair in the R2 calculation is the mean daily 

summer flow within a given window and the base flow for the 

following winter, respectively. Thirty-one years were considered. Finally, a contour plot is constructed from the R2

 values 

for each window span and midpoint, using warmer colors for 

stronger correlations. 

The response surface shows that streamflow early in the 

summer has little effect on winter base flow (fig. 16). Not 

surprisingly, streamflow in late summer has the greatest influence on winter base flow. The highest R2

, 0.7, occurs when a 

window from 25 to 55 days and a midpoint between October 5 

and October 20 is used. To simplify further regression analysis, 

October mean daily flow is used as an independent variable. In 

essence, this is the same as using a window with a span of 30 

days and a midpoint of October 15.

A multiple LOWESS-regression model was constructed 

using S-Plus statistical software (Insightful, 2001) that uses 

the cube-root of October mean daily flow and the combined 

December and January precipitation as explanatory/independent variables and winter base-flow volume as the dependent variable. Other models were considered and rejected 

because of low R2

 values or over-parameterization. Given 

the limited time span and sample size of the analysis, overparameterization would allow too many degrees of freedom 

in the regression model and misleading uncertainty estimates. The span parameter of the LOWESS regression model 

controls the window size considered in the local regression 

0.49 0.58 0.14 0.57

0.37 0.48 0.34 0.59

0.40 0.47 0.19 0.58

0.40 0.46 0.26 0.63

0

0

0

0

2

4

2

4

2

4

2

4

6

0 5 10 0 5 10 0 25 50 75 25 50 75 0

CUBE-ROOT OF MEAN DAILY BASE FLOW 

CUBIC FEET PER SECOND 

B

CUBE-ROOT OF MEAN DAILY BASE FLOW 

CUBIC FEET PER SECOND 

B

CUBE-ROOT OF MEAN DAILY BASE FLOW 

CUBIC FEET PER SECOND B

JUL TO OCT SEPT TO OCT DEC. JAN.

RAINFALL, MILLIMETERS

FEB. JAN. FEB. JAN.
26 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Figure 15. Scatter plot matrices of four different base-flow metrics vs. summer streamflow and winter precipitation. Red points 

represent the early period of record at the gaging station near Tombstone, from 1968 to 1986, and blue points represent the later 

period, from 1997 to 2009. Values are the Pearson correlation coefficient.

and, therefore, the degree of smoothing. A value of 0.75 was 

found to work well. A locally linear model was used because 

the equivalent number of parameters, 5.4, was nearly half that 

of a locally quadratic model. Because of the non-parametric 

nature of LOWESS, no intercepts are calculated to directly 

examine the effect of multiple explanatory variables. Instead, a 

response surface can be used to graphically show the interaction of variables.

The LOWESS response surface is constructed by evaluating the model over a range of input parameters (independent 

variables) and plotting the predicted dependent variable at 

that location. This surface shows a strong dependence on both 

winter rainfall and the cube-root of October mean daily flow 

(MDF) (fig. 17). Care must be taken in evaluating the response 

surface; the model results outside of the domain of the input 

data should be treated as suspect. In particular, the region 

of the response surface that curves upward at low values of 

winter rainfall and high values of October MDF is an artifact 

of the model and not representative of how the system would 

respond to these conditions. The model is most realistic for 

values that fall in the low rainfall/low October MDF quadrant.

As expected, the highest base-flow volume is predicted 

for the combination of high October MDF and high winter 

rainfall, and the lowest base-flow volume is predicted for low 

values of each. A comparison of the data used to construct 

the LOWESS model (red dots) with the model itself (fig. 17) 

0 5 10 0 5 10 0 0

6

10

14

18

280

300

320

340

20

40

60

80

5,000

10,000

15,000

20,000

25,000

0.41 0.50 0.21 0.64

0.40 0.48 0.19 0.65

-0.18 -0.19 -0.04 0.02

0.04 0.28 0.36 0.00

25 50 75 25 50 75

CUBE-ROOT OF MEAN DAILY BASE FLOW 

CUBIC FEET PER SECOND B

RAINFALL, MILLIMETERS

JUL TO OCT SEPT TO OCT DEC. JAN.

MIDWINTER MAXIMUM,

CUBIC FEET PER SECOND

START DATE,

DAY OF YEAR

25TH PERCENTILE,

CUBIC FEET PER SECOND

BASE FLOW VOLUME,

ACRE-FEET
Base Flow in the San Pedro River near Tombstone 27

Figure 16. Graph of response 

surface showing the coefficient of 

determination (R2

) for the summer 

streamflow vs. winter baseflow linear regression. Summer 

streamflow is calculated as the 

average mean daily flow over a time 

span of n days, shown on the y-axis, 

centered on the date on the x-axis. 

0

0

0

0

0.10.2

0.3

0.4

0.5

0.5

0.6

0.6

0.6

0.6

0.7

AUG 20

10

20

30

40

50

60

70

80

90

MIDPOINT OF WINDOW

NUMBER OF DAYS IN WINDOW

SEP 1 SEP 10 SEP 20 OCT 1 OCT 10

shows that nearly all years lie in the low October MDF/low 

winter rainfall quadrant. Here the model is more sensitive to 

October MDF than rainfall, suggesting that there may be a 

minimum threshold for winter rainfall, and rainfall amounts 

below this threshold have little effect. Outside of this quadrant, 

the model is defined by fewer points. The largest amount of 

base flow occurs in years that have high rainfall amounts and 

moderate October MDF; during years that have only moderate 

winter rainfall but high October MDF, base flow is somewhat 

less. R2 for the LOWESS regression is 0.90, indicating that 90 

percent of the variation in winter base flow can be explained 

by the variation in October MDF and combined December and 

January precipitation. This value may be somewhat misleading, however, because it is determined largely by outlying data 

in two clusters: two closely spaced points with high rainfall 

and moderate October MDF and three closely spaced points 

with high October MDF and moderate rainfall.

Model residuals—the measured value minus the value 

predicted by October MDF and winter rainfall—provide further diagnostics of the LOWESS regression model. The residual interquartile range, between the 25th and 75th percentiles, 

is –783 acre-ft to 872 acre-ft. In other words, the model would 

be able to predict the measured base flow within about 800 

acre-ft for 50 percent of the time. Considering that many of 

the base-flow values are 4,000 acre-ft or less, these residuals 

are relatively large. A plot of the residuals versus the base-flow 

value predicted by LOWESS regression shows near-constant 

variance for smaller volumes of predicted base flow; a lack of 

samples at larger volumes of base flow precludes estimation 

of residual variance for the entire range of model predictions 

(fig. 18B). Significant year-to-year variation remains in the 

predicted values, but the model is able to estimate the mean 

value. Further evidence for normally distributed residuals 

with constant variance are shown by plots of measured vs. 

predicted base flow, and the residuals vs. standard normal 

quantiles (fig. 18A, C).

The residuals from the LOWESS regression represent 

values from which the effect of year-to-year climate variation 

has largely been removed. Statistical tests on the residuals 

can be used to determine whether the streamflow record at 

the gaging station near Tombstone during the later period is 

significantly different than the earlier period. If so, such differences would be due to factors other than rainfall. Common 

trend tests, such as the non-parametric Kendall tau test, are not 

applicable in this instance because of the missing data in the 

record between 1986 and 1996. Instead, a test comparing two 

samples is used. The Wilcoxon rank-sum test (equivalent to 

the Mann-Whitney test) compares the median of two samples 

for significant differences, making no assumptions about the 

underlying distribution of the data (Helsel and Hirsch, 2002). 

The null hypothesis, that the two groups are from the same 

population (in this case, that winter base flow, when adjusted 

for annual rainfall, is the same for the earlier period as for the 

later period), is tested by comparing the test statistic to a table 

of values. Like most statistical tests, the rank-sum test is only 

capable of rejecting a null hypothesis; this does not necessarily 
28 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Figure 17. Graph showing the response surface of the LOWESS multiple-regression model 

for varying values of the independent variables of December to January rainfall and cuberoot of October mean daily flow. Red points are the measured base flow used to construct 

the model.

Figure 18. Graphs showing LOWESS regression diagnostic characteristics: A, scatter plot of measured vs. predicted base 

flow, B, regression residuals vs. predicted base flow, C, regression residuals vs. standard normal quantiles. -2,000 0 2,000 -2,000 0 2,000

A B C

PREDICTED BASE FLOW (ACRE-FEET) PREDICTED BASE FLOW (ACRE-FEET) QUANTILES OF STANDARD NORMAL

MEASURED BASE FLOW 

(ACRE-FEET)

RESIDUALS (ACRE-FEET)RESIDUALS (ACRE-FEET)

5,000 10,000 15,000 5,000 10,000 15,000 -2 -1 0 1 2

5,000 10,000 15,000 20,000

indicate acceptance of an alternate hypothesis. For this study, 

the level of significance—that is, the probability of rejecting 

the null hypothesis when it is in fact true—is set at 5 percent. 

Annual adjusted base flow, corrected for year-to-year climate variability using the LOWESS regression, is calculated 

as mean base flow for all years plus the regression residual. 

Adjusted base flow is lower than measured base flow in wetter years and higher than measured base flow in drier years 

(fig. 19). Adjusted base flow during the later period of record 

appears to be lower than the earlier period. The rank-sum 

test applied to the adjusted base flow indicates that the null 

hypothesis (that there is no difference between the early period 

and late period) should be rejected. The p-value for this test is 

0.0033, indicating that the probability of a Type I error—when 

the null hypothesis is rejected but is in fact true—is less than 1 

percent, which supports the hypothesis that some factor other 

than climate is responsible for the decline in base flow at the 

gaging station near Tombstone.

3000

4000

5000

6000

7000

8000

9000

10000

15000

15000

20000

20 40 60 80 100 120 140

1

2

3

4

5

6

7

8

9

DECEMBER AND JANUARY RAINFALL, MILLIMETERS

1/3

OCTOBER MEAN DAILY FLOW,

CUBIC FEET PER SECOND
Base Flow in the San Pedro River near Tombstone 29

Figure 19. Graph showing measured and adjusted base-flow volume. Adjusted values are based 

on the LOWESS regression shown in figure 17.

Change in Base Flow from Reduced Inflow from 

the Regional Aquifer

Exchange of water between the regional aquifer and 

alluvial aquifer is driven by hydraulic gradients, measured by 

comparing piezometer water levels at two different horizontal 

and (or) vertical locations. Positive vertical gradients indicate 

upward movement of water; negative gradients are the reverse. 

A zero hydraulic gradient indicates hydrostatic equilibrium 

and no movement of groundwater. A decrease in groundwater 

movement towards the river, caused by groundwater pumping 

between the mountains and the river, would be reflected by a 

decrease in the measured hydraulic gradient. Gradients may 

also be influenced by withdrawal of water from the alluvial 

aquifer by ET. As this water is removed, the water-table elevation in the near-stream aquifer lowers. Because the root zone 

of riparian vegetation does not extend to the deeper aquifer, 

water-table elevation there is unaffected by ET. Therefore 

the gradient becomes more positive, because the difference 

between the water-level elevations increases. 

Vertical gradient measurements have been made at a 

number of locations near the San Pedro River beginning 

around year 2000 (table 5). Piezometer pairs are typically deep 

and more representative of the regional aquifer (well names 

beginning with BOQ, CLR, LSP, HER) or shallow and representative of the alluvial aquifer (well names beginning with 

CON, FBK, MOS, COT). Gradients are generally positive 

at all locations, except at constantly negative HER wells and 

at FBK and MOS wells that alternate between positive and 

negative gradients as a result of seasonal ET withdrawals 

(fig. 20). Data from seven of the eight piezometer pairs show 

essentially no trends over time, either in water level or gradient. An exception to this lack of trend is seen at Lewis Springs 

where water levels have risen in both the deep and shallow 

piezometers. Water level has risen faster in the shallow well, 

resulting in a decrease in the vertical gradient. This decrease in 

gradient is not attributable to a decrease in water level, such as 

would be caused by pumping. Most piezometer locations show 

fluctuations in water level during the summer monsoon, but 

these do not persist as longer-term trends.

Despite variation in climate, water levels and gradients 

in wells located near the San Pedro River show little interannual variability. The period from 2000 to 2010 has exhibited 

both wet periods (October 2000, summer 2006 and 2008) and 

extreme dry periods (summer 2002 to 2004, summer 2010, 

winter 2002 and 2006). The lack of decline in water levels 

and gradients during this period is evidence that the cone of 

depression caused by groundwater pumping in the Sierra Vista 

area has not significantly affected vertical gradients in and 

near the alluvial aquifer during the period and in the locations 

for which water level data exist. If groundwater pumping was 

affecting conditions in the alluvial aquifer, a continual and 

increasing decline in gradients would be expected. Apart from 

small fluctuations during the summer monsoon, neither wet 

1 965 1 9 7 0 1 9 7 5 1 980 1 985 1 990 1 995 2 000 2 005 2 0 1 0

0

5

10

15

20

25

BASE FLOW (THOUSANDS OF ACRE-FEET)

MEASURED BASE FLOW

ADJUSTED BASE FLOW
30 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Table 5. Description of wells used in vertical gradient analysis. 

[UTM N, Universal Transverse Mercator Zone 12 N northing; UTM E, Universal Transverse Mercator Zone 12 N easting]

Well name USGS site ID UTM N UTM E Cadastral ID Well depth

(m)

Distance 

upstream 

from Tomb- stone gage

(km)

HER-SUS 312642110063701 3479288 584481 D-23-22 09ACD1 25.5 35.0

HER-SUD 312642110063702 3479284 584481 D-23-22 09ACD2 37.6 35.0

COT-BLM 313105110074501 3487517 582637 D-22-22 17ACC3 8.2 26.5

COT-UCD 313105110074502 3487519 582641 D-22-22 17ACC4 16.2 26.5

LSP-1 313312110082302 3491201 581654 D-22-22 06AAA1 10.5 22.5

LSP-5 313312110082303 3491200 581648 D-22-22 06AAA5 54.9 22.5

CLR-SUS 313508110085701 3494840 580667 D-21-22 19CDB1 19.3 19.0

CLR-SUD 313508110085702 3494838 580671 D-21-22 19CDB2 52.9 19.0

MOS-LNS 313643110100101 3497725 578961 D-21-21 13BAB1 3.7 15.5

MOS-LND 313643110100102 3497723 578963 D-21-21 13BAB2 6.1 15.5

BOQ-SUS 314144110104701 3506985 577665 D-20-21 14BCC1 14.0 6.5

BOQ-SUD 314144110104702 3506985 577665 D-20-21 14BCC2 51.4 6.5

FBK-LI 314318110113101 3509846 576427 D-20-21 3CBA 4.9 2.8

FBK-LO 314317110113401 3509871 576504 D-20-21 3CAB 6.2 2.8

CON-SUS 314558110121601 3514779 575268 D-19-21 21DBB2 8.2 -2.0

CON-SUD 314558110121602 3514780 575265 D-19-21 21DBB1 16.2 -2.0

nor dry periods appear to have much lasting effect on vertical 

gradients. In contrast, water levels at a majority of wells in the 

greater Sierra Vista area to the west of the river show consistent declines between 2001 and 2006, with a decrease of as 

much as 9 m at some wells (Schmerge and others, 2009). This 

leads to the conclusion that, to date, conditions in the deeper 

alluvial aquifer are largely independent of both annual variation in rainfall and groundwater withdrawals. Of course, basic 

hydrologic understanding indicates that, with continued pumping, the cone of depression will eventually affect the alluvial 

aquifer and capture streamflow (Leake and others, 2008). 

Change over time in the isotopic composition of base flow 

could also be an indicator of reduced inflow from the regional 

aquifer. If the isotopically depleted water in the Sierra Vista 

area contributes to base flow, as the mixing analysis suggests, 

a decrease in base-flow contribution from this source due to 

groundwater pumping would cause base flow to become more 

isotopically enriched. A Mann-Kendall trend test (Helsel and 

Hirsch, 2002) is used to evaluate trends in isotopic composition. A single δ18O value is selected for each year; in this case 

the most depleted value from the winter base-flow season is 

used to minimize any isotopic enrichment effect. Although this 

δ18O value is correlated somewhat with annual precipitation—

drier years have a more depleted isotopic composition, representing an increased proportion of regional groundwater—this 

effect was not sufficiently significant to be accounted for using 

regression analysis (R2 = 0.14 using the same independent variables used in the LOWESS regression). The trend test indicates 

that the null hypothesis—that there is no trend—should not be 

rejected (p = 0.37). Therefore, similar to the hydraulic gradient data, isotope concentrations do not indicate a decline in the 

regional groundwater contribution to base flow. 

Spatial Pattern of the Change in Base Flow

An additional method used to evaluate trend in base 

flow in the San Pedro River, and the difference between the 

early and late period of record at the Tombstone gage, is to 

compare winter base flow at different locations along the 

river. Three-day low flow in January and in February is used, 

because it was shown to be very similar to the base flowseparated mean daily flow and is a more consistent measure 

than using the hydrograph separation method at different 

stations. Discharge records are available at San Pedro River 
Base Flow in the San Pedro River near Tombstone 31

1140

1142

1144

1146

1148

1150

1152

-0.02

0.03

0.08

0.13

0.18

1204

1206

1208

1210

1212

1214

1216

-0.2

0

0.2

0.4

0.6

0.8

1

1170

1172

1174

1176

1178

1180

1182

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

1158

1160

1162

1164

1166

1168

1170

-0.6

-0.1

0.4

0.9

1.4

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

WATER TABLE ELEVATION, METERS WATER TABLE ELEVATION, METERS WATER TABLE ELEVATION, METERS WATER TABLE ELEVATION, METERS

VERTICAL GRADIENT, + UPWARD VERTICAL GRADIENT, + UPWARD VERTICAL GRADIENT, + UPWARD VERTICAL GRADIENT, + UPWARD

CONSUD/CONSUS

FBK-LO/LI

BOQSUD/BOQSUS

MOSLND/MOSLNS

VERTICAL GRADIENT

SHALLOW: 8.2 M DEEP: 16.2 M

SHALLOW: 4.9 M DEEP: 6.2 M

SHALLOW: 14.0 M DEEP: 51.4 M

SHALLOW: 3.7 M DEEP: 6.12 M

DEEP WELL, WATER LEVEL ELEVATION SHALLOW WELL, WATER LEVEL ELEVATION

Figure 20. Graphs showing vertical gradient and water-level elevation at eight paired wells near the San Pedro River. Wells 

are in order from north at the top to south at the bottom. Locations of wells are shown in figure 1. Solid lines are pressure 

transducer measurements and triangles are tape-down measurements.
32 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

1256

1258

1260

1262

1264

1266

1268

-0.01

-0.03

0.03

0.07

1234

1236

1238

1240

1242

1244

1246

0

0.5

1

1.5

2

1214

1216

1218

1220

1222

1224

1226

0.005

0.007

0.009

0.011

0.013

0.015

0.017

0.019

1225

1227

1229

1231

1233

1235

0

0.02

0.04

0.06

0.08

0.1

WATER TABLE ELEVATION, METERS

VERTICAL GRADIENT, + UPWARD

CONSUD/CLRSUS

VERTICAL GRADIENT, + UPWARD VERTICAL GRADIENT, + UPWARD VERTICAL GRADIENT, + UPWARD

WATER TABLE ELEVATION, METERS WATER TABLE ELEVATION, METERS WATER TABLE ELEVATION, METERS

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

JAN 95 JAN 97 JAN 99 JAN 01 JAN 03 JAN 05 JAN 07 JAN 09

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

JAN 01 JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07 JAN 08 JAN 09 JAN 10

LSP5/LSP1

COTUCD/COTBLM

HERSUD/HERSUS

VERTICAL GRADIENT DEEP WELL, WATER LEVEL ELEVATION SHALLOW WELL, WATER LEVEL ELEVATION

SHALLOW: 19.3 M DEEP: 52.9 M

SHALLOW: 10.5 M DEEP: 54.9 M

SHALLOW: 8.2 M DEEP: 16.2 M

SHALLOW: 25.5 M DEEP: 37.6 M

Figure 20.—Continued.
Base Flow in the San Pedro River near Tombstone 33

at Palominas (station number 09470500, 41.5 km upstream 

of the Tombstone gage), San Pedro River at Charleston (station number 09471000, 14 km upstream of the Tombstone 

gage), and San Pedro River near Tombstone (station number 

09471550). The record at the Palominas gage ends in 1982; 

therefore, the early period common to all three gages is 1968 

to 1981, and the later period is 1997 to 2009. This removes 

a relatively wet period from 1983 to 1986 during which 

streamflow data exist at the Tombstone gage. 

The low-flow data show that the largest decrease in 

streamflow between the early and late periods is at the 

Tombstone gage (fig. 21). A smaller decrease is evident at the 

Charleston gage, and no decrease is evident at the Palominas 

gage. This suggests that changing conditions between the 

Tombstone and Charleston gages and between the Charleston and Palominas gages are more important to the decrease 

in base flow at the Tombstone gage than changing climate, 

as reflected by conditions at the Palominas gage. Changing 

conditions could include a decrease in base flow caused by 

decreased hydraulic gradient near the river or an increase 

in ET withdrawals. Even though ET is small in the winter 

months, its increase in the summer would further deplete 

storage in the near-stream alluvial aquifer and magnify losing 

conditions until that storage is replenished. 

Another feature of interest in the box plots of winter low 

flow (fig. 21) is the change in variability between the gages. 

Winter low flow at the Palominas gage is the most consistent 

(lowest inter-percentile change between the early period and 

late period). Flow at the Tombstone gage, particularly during 

the early period, is more variable, and flow at the Charleston 

gage plots between Palominas and Tombstone flows. This 

increase in variability in downstream distance is caused in part 

by the variation in year-to-year near-stream aquifer storage. 

This is a result of the larger watershed area at downstream 

gages, as the streamflow record integrates the spatial variability of gaining and losing reaches upstream. 

Figure 21. Box plots showing January and February 3-day low flow at San Pedro River at Palominas (station number 09470500), 

San Pedro River at Charleston (station number 09471000), and San Pedro River near Tombstone (station number 09471550). The 

early period of record is 1968 to 1981, and the late period of record is 1997 to 2009.

o

o

o o

o

o

o

o

o

o

o

o

o

o

o

o

o

EXPLANATION 

o

o

o

TOMBSTONE, EARLY

TOMBSTONE, LATE

CHARLESTON, EARLY

CHARLESTON, LATE

PALOMINAS, EARLY

PALOMINAS, LATE

0 20 40 60 80

JANUARY AND FEBRUARY 3-DAY LOW FLOW

CUBIC FEET PER SECOND

OUTLIER DATA

UPPER ADJACENT

75TH PERCENTILE

MEDIAN

25TH PERCENTILE

LOWER ADJACENT
34 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Discussion 

The actual cause of the decline in winter base flow 

between the early and late periods of record at the Tombstone 

gage is most likely a combination of factors. The largest 

decrease in streamflow is in the fall, and the pattern of springtime recession remains largely unchanged. This points to 

higher ET rates due to more vigorous or expansive vegetation 

and (or) a longer growing season due to the later arrival of the 

first frost of the fall. Repeat analysis of aerial imagery shows 

a marked increase in riparian vegetation cover between 1978 

and 2003 (Stromberg and others, 2010). Although this increase 

is minimal immediately upstream of the Tombstone gage, 

every reach above the BOQSUD/BOQSUS wells exhibits an 

increase in Populus-Salix (cottonwood and willow) cover, 

largely at the expense of bare ground rather than a conversion 

of some other vegetation type. In addition, over 40 percent of 

the Populus fremontii population has been established since 

1970. This dramatic increase in vegetation is strong evidence 

that increased ET has had an effect on declining winter base 

flow at the Tombstone gage. 

Although vegetation, and therefore ET, has increased, the 

maximum steady flow rate reached in the winter, when ET is 

minimal, has also declined. While this could be evidence for 

a decline in regional groundwater contribution to streamflow, 

the midwinter steady flow rate is also partially dependent on 

summer runoff. Losing conditions between the Charleston 

gage and the Tombstone gage can explain the decline in the 

midwinter steady flow rate at the Tombstone gage independently of any change in the regional groundwater component 

of winter base flow. This is because the amount of water in 

storage in the near-stream alluvial aquifer depends primarily 

on streamflow from the previous summer and withdrawal by 

ET during the fall and, therefore, varies widely from year to 

year. During the driest years, most of the base flow measured 

at the Charleston gage infiltrates downstream and has little 

influence on the rate of winter base flow at the Tombstone 

gage. The alluvial aquifer never becomes fully saturated, losing conditions do not diminish substantially, and the river does 

not attain a steady flow rate at the Tombstone gage. In this 

way, the maximum flow rate reached in the winter is reflective 

of summer runoff and regional groundwater contributions to 

winter base flow.

The effect of a decline in groundwater contribution to 

winter base flow is more difficult to assess than changes in 

ET or climate. In wet years, this decline would manifest as a 

lower midwinter steady flow rate, which typically exists for a 

period of days to weeks when the alluvial aquifer is saturated 

and when riparian ET and, therefore, seepage loss is minimal. 

In a dry year, however, much of the winter base flow at the 

upstream Charleston gage infiltrates into the evapotranspiration-depleted alluvial aquifer between the gages, and a midwinter steady flow rate is not reached before springtime ET 

begins. Most years during the period 1997 to 2009 were drier 

than average, with several extremely dry years. Therefore, 

the midwinter steady flow rate at the Tombstone gage during 

this period was controlled primarily by the magnitude of the 

alluvial-aquifer storage deficit, caused by ET following the 

previous summer and fall, rather than by the rate of inflow 

from the regional aquifer. 

Because of the difficulty in evaluating the midwinter 

steady flow rate, water levels and hydraulic gradients in the 

alluvial and regional aquifers are used. Data from paired 

piezometers at eight locations upstream of the Tombstone 

gage, in both the alluvial and regional aquifers, indicates 

no trend in water levels or vertical gradient since 2001. The 

percent of regional and alluvial groundwater determined by 

isotopic analysis has also remained relatively constant from 

2000 to 2009. Together, these data show that any decline in 

winter base flow during the past 10 years at the Tombstone 

gage caused by changes in the regional aquifer is minimal.

An important consideration regarding base flow at 

the Tombstone gage is that rainfall varies year-to-year, as 

well as on decadal scales. The later part of the record at the 

Tombstone gaging station, from 1997 to 2009, represents a 

dry period relative to the earlier period, from 1968 to 1986. 

When the long-term precipitation record (1931 to 2009) in the 

Subwatershed is considered, however, the later, drier period of 

record is much closer to the long-term average than the earlier 

period of record (fig. 12). In other words, from 1968 to 1986 

it was unusually wet in the Subwatershed, while from 1997 

to 2009 it has been more typically dry. Nevertheless, when 

climate effects are removed from the base-flow record, there 

remains a significant decrease in winter base-flow discharge in 

the later period.

Changes in near-stream groundwater pumping during 

the study period are not considered in this report. Significant 

amounts of irrigated agricultural land upstream from the 

Charleston gage have been retired since the beginning of the 

streamflow record at the Tombstone gage (Department of 

the Interior, 2005). About 6 km upstream of the Tombstone 

gage, the Boquillas Ranch had irrigated pasture land until it 

was incorporated into the BLM San Pedro Riparian National 

Conservation Area in 1988. An indeterminate amount of 

agricultural pumping occurred on the west side of the river, 

south of Arizona Route 90, between the early 1970s and the 

early 1980s. In 2005, the last significant irrigated acreage in 

the Subwatershed, near Palominas, was retired. Lack of definitive information about the amount and distribution of pumping 

associated with this irrigation precludes detailed analysis. If 

irrigation was responsible for significant withdrawals from 

the alluvial aquifer during the early period of record at the 

Tombstone gage, this would tend to reduce the difference in 

base flow between the early period and late period (that is, the 

early period would have experienced higher base flow without 

the withdrawals for irrigation).

The results of this report have implications for the water 

budget. Base-flow discharge from the Subwatershed at the 

Tombstone gaging station represents surface discharge from 

the Subwatershed of groundwater that has been discharged 

to the stream. As such, an increase in the long-term, mean 
Summary and Conclusion 35

outflow at the Tombstone gaging station would indicate 

an improvement in the regional aquifer condition, and this 

would be reflected in the water budget—more water would 

be available from the regional aquifer to enter the river and 

subsequently exit the Subwatershed as base flow. This condition would imply that other lines in the water budget have also 

changed, such as a reduction in withdrawals (pumping, ET) 

and (or) an increase in recharge (climate change, effluent, secondary water source). Alternatively, if the “Stream base flow” 

line in table 1 is adjusted, because of an improvement in the 

estimation of base flow (as the case in this report), then nothing else in the water budget is affected except for the bottom 

line, which will change by a similar amount; we have simply 

improved the accuracy of the existing water budget. 

As noted in the “Previous Studies” section, above, earlier 

studies that estimated base flow for the San Pedro River at the 

Tombstone gaging station intrinsically included both alluvial 

aquifer discharge and regional aquifer discharge to arrive at 

those estimates. Most estimates of natural recharge in the 

Subwatershed have been back-calculated from estimated base 

flow, because, for a system in equilibrium, the groundwater 

discharging from the system (base flow) must be equal to the 

water entering into the system (recharge). If a water budget 

uses an estimate of natural recharge based on a predevelopment base-flow value that includes all groundwater discharged 

to the stream (both alluvial and regional aquifer discharge), 

then, to be consistent, any refinements to the base-flowdischarge value in the Subwatershed water budget should 

similarly include all groundwater discharged to the stream. 

Alternatively, if the natural recharge value is determined 

directly (and excludes alluvial aquifer recharge) or is based 

solely on an estimate of predevelopment regional groundwater 

discharge, then any refinements to the water-budget base-flow 

discharge value should similarly include only regional groundwater discharge. Complicating this analysis is the possibility 

that the relation between regional and alluvial groundwater 

storage has changed between the predevelopment period and 

the present. If regional groundwater gradients have decreased 

over time, resulting in less regional groundwater discharge to 

the alluvial aquifer and to the stream channel, infiltration of 

streamflow into the alluvial aquifer could increase. In effect, 

this would result in alluvial aquifer storage becoming increasingly derived from streamflow rather than regional groundwater, while total discharge from the alluvial aquifer remains 

relatively constant. In any case, the data needed to evaluate 

this scenario, primarily long-term records of hydraulic gradients within the regional and alluvial aquifer, are not available.

Summary and Conclusion

This report quantifies the amount and sources of winter 

base flow in the San Pedro River near Tombstone. Annual base 

flow is composed entirely of winter base flow, because summer ET rates are higher than summer groundwater discharge, 

resulting in no base-flow contribution to streamflow at the 

Tombstone gage during the summer months. Consequently, 

summer streamflow at the gage is due entirely to intermittent monsoon precipitation, because no flow occurs at the 

gage during much of the summer. Winter streamflow comprises short-duration stormflow owing to direct precipitation, 

previously infiltrated streamflow stored temporarily in the 

near-stream aquifer, and water that is recharged away from the 

river, along the mountain fronts and the ephemeral channels 

of the basin. Analytical methods were used to determine the 

individual amounts of these three components of winter base 

flow. The first was determined by using a base-flow separation technique that was found to perform better than other 

commonly used methods for years when periods of zero flow 

occurred in the fall or spring. After separation of stormflow 

peaks, the remaining winter base-flow record is representative 

of both release from temporary storage in the alluvial aquifer 

and inflow from regional groundwater.

The winter base-flow volume was calculated by summing base flow from the annual hydrograph between a start 

date in the fall and an end date in the spring. The start date 

was determined as either the first day that flow returned to the 

Tombstone gage following its cessation earlier in the fall, the 

first date of continuous increase in streamflow in the fall, or 

more rarely, a day based on the relation found in other years 

between the annual 25th-percentile mean daily flow and the 

winter base-flow volume. Tombstone base flow thus calculated 

varies from a low of 1,220 acre-ft in 1998 to a high of 20,600 

acre-ft in 1985. The period of record at the Tombstone gage 

is from 1967 to 1986 and 1997 to present. Considering every 

year, the median annual base flow is 4,890±1,020 acre-ft. If 

only the early period of record is considered, median base 

flow is 5,830 acre-ft; if only the late period is considered, 

median base flow is 2,880 acre-ft. In dry years, the proportion 

of streamflow that is considered base flow is 100 percent (that 

is, no streamflow was removed in the base-flow separation 

process). In wetter years, 50 percent or less of all streamflow 

is considered base flow.

A locally weighted least squares (LOWESS) model that 

related winter base-flow volume to streamflow during the 

month of October and rainfall during December and January was found to explain 90 percent of the annual variation 

in base-flow volume. After removing the effect of October 

streamflow and December–January rainfall, we determined 

that there is a less than 1 percent chance that there is no difference in base-flow volume between the early period and late 

period (p = 0.003). In other words, there is probably a decrease 

in base flow that is caused by something other than climate. 

Only the two downstream gages, Charleston and Tombstone, 

showed a distinct difference between an early period (1968 

to 1982) and a late period (1997 to 2009), suggesting that the 

decreased flow is caused by conditions below the upstream 

Palominas gage. The decrease in winter base flow at the 

Tombstone gaging station could be due to (1) a decrease in 

inflow from regional groundwater, (2) an increase in ET, either 

because of increased vegetation or a longer growing season 

caused by later freeze dates in the fall, and (or) (3) error in the 

regression model structure or data.
36 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

The relative contribution to base flow of regional 

groundwater and summer monsoon runoff stored as alluvial 

groundwater were determined using environmental isotopes. 

Although the isotopic signature of monsoon water varies 

widely, the 10-yr record of isotope samples along the San 

Pedro River allows for a reasonably accurate assessment. 

Comparing the end-member isotopic compositions to the composition of mixed winter base-flow water at the Tombstone 

gage, 74±10 percent of base flow is derived from regional 

groundwater. Applying this percentage to the median annual 

winter base-flow volume for the later period of record at the 

Tombstone gage gives a value for regional groundwater contribution to winter base flow of 2,130 acre-ft. 

Considering the appropriate amount of base flow to 

include in a water-budget analysis, we realize that base 

flow varies widely from year to year as a function of annual 

rainfall (in particular, late monsoon rain and early winter precipitation). To determine average base flow, we must define 

“average” climate. Similarly, future predictions of base 

flow must make an assumption of future climate. Because 

the early period of record at the Tombstone gage represents 

wetter climate than the long-term average, it alone is not 

representative of base flow. Climate during the late period is 

more representative of the long-term average, but this period 

also exhibits a decline in base flow from the early period 

independent of climate, likely due to an increase in ET. The 

Tombstone gage is more sensitive to changes in ET than the 

upstream Charleston gage, not only because there is simply 

more upstream vegetation, but also because losing conditions 

in the alluvial aquifer between the gages allow base flow to 

be captured if a storage deficit (such as caused by ET) exists. 

Ultimately, the streamflow record at the Charleston gage is 

more representative of common notions of base flow and less 

sensitive to changes in ET. 

Frequently, base flow is considered the minimum amount 

of streamflow that might be expected, in the absence of 

precipitation. At the Tombstone gage, this is not the case—

the variation in annual rainfall has a dominant effect on the 

amount of base flow. Because of losing conditions upstream of 

the Tombstone gage, the amount of base-flow infiltration varies depending on the saturation of the alluvial aquifer after the 

previous monsoon. Following a wet monsoon, little infiltration 

of base flow occurs, and base flow measured at the Tombstone gage is high. In dry years, infiltration is high and a large 

amount of base flow is stored in the alluvial aquifer. The driest 

summer recorded at the Tombstone gage, in 2009, resulted in 

2010 winter base flow that started significantly later (about 1 

month) and at a lower rate than previous years. Without winter 

rain, measured winter flow at the Tombstone gage would have 

been much less than in any previous year. 

Hydraulic gradient and isotope data presented in this 

report provide essential information for understanding base 

flow in the San Pedro River. The extensive monitoring 

network established in the Upper San Pedro Basin is a collaborative effort of the U.S. Geological Survey, the Bureau 

of Land Management, and the Agricultural Research Service 

in cooperation with the organizations and agencies that form 

the Upper San Pedro Patnership. Continued data collection is 

important for future investigations. Further understanding of 

San Pedro base flow would come about through development 

of an integrated surface water/groundwater model, an effort 

for which historic and future data will play an important role.
References Cited 37

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40 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Appendix 1. Annual hydrographs showing measured flow (black) and output 

from base-flow separation (measured flow with storm runoff removed, red). 

Vertical dotted lines are the start date of winter base flow used for base flow 

volume calculation.

1

10

100

1,000

1968

1

10

100

1,000

1969

1

10

100

1,000

1970

1

10

100

1,000

1971

1

10

100

1,000

1972

1

10

100

1,000

1973

1

10

100

1,000

1974

1

10

100

1,000

1975

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL
Appendix 1. 41

1

10

100

1,000

1976

1

10

100

1,000

1977

1

10

100

1,000

1978

1

10

100

1,000

1979

1

10

100

1,000

1980

1

10

100

1,000

1981

1

10

100

1,000

1982

1

10

100

1,000

1983

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

1

10

100

1,000

1984

1

10

100

1,000

1985

10

100

1,000

1986

10

100

1,000

1997

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

UBIC FEET PER SECOND

DISCHARGE, 

UBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL
42 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

1

10

100

1,000

2002

1

10

100

1,000

2003

1

10

100

1,000

2004

1

10

100

1,000

2005

1

10

100

1,000

2006

1

10

100

1,000

2007

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

1

10

1

10

1

10

100

1,000

1986

1

10

100

1,000

1997

1

10

100

1,000

1998

1

10

100

1,000

1999

1

10

100

1,000

2000

1

10

100

1,000

2001

DISCHAR

CUBIC FEET PE

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

DISCHA

CUBIC FEET PE

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL
Appendix 1. 43

1

10

1

10

1

10

100

1,000

2006

1

10

100

1,000

2007

1

10

100

1,000

2008

1

10

100

1,000

2009

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

DISCHAR

CUBIC FEET PE

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHAR

CUBIC FEET PE

DISCHARGE, 

CUBIC FEET PER SECOND

DISCHARGE, 

CUBIC FEET PER SECOND

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL
44 Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona

Produced in the Western Region, Menlo Park, California

Manuscript approved for publication September 19, 2010

Text edited by Jan Zigler

Layout and design by Judy Weathers
Appendix 1. Annual hydrographs showing measured flow (black) and output from base-flow separation (measured flow with storm runoff removed, red). Vertical dotted lines are the start date of winter base flow used for base flow volume calculation. 45

Kennedy and Gungle—Quantity and Sources of Base Flow in the San Pedro River near Tombstone, Arizona—Scientific Investigations Report 2010–5200