U.S. Department of the Interior 

U.S. Geological Survey 

Trends in Streamflow of the San Pedro River,

Southeastern Arizona, and Regional Trends

in Precipitation and Streamflow in

Southeastern Arizona and

Southwestern New Mexico

Professional Paper 1712
Inside Front Cover

Blank
Trends in Streamflow of the San Pedro River, 

Southeastern Arizona, and Regional Trends in 

Precipitation and Streamflow in Southeastern 

Arizona and Southwestern New Mexico

By Blakemore E. Thomas and Don R. Pool

Professional Paper 1712

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

P. Lynn Scarlett, Acting Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia: 2006

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Suggested citation:

Thomas, B.E., Pool, D.R., 2006, Trends in Streamflow of the San Pedro River, Southeastern Arizona, and Regional 

Trends in Precipitation and Streamflow in Southeastern Arizona and Southwestern New Mexico: U.S. Geological 

Survey Professional Paper 1712, 79 p.

Library of Congress Cataloging-in-Publication Data

Thomas, Blakemore E.

Trends in streamflow of the San Pedro River, Southeastern Arizona, and regional trends in precipitation and 

streamflow in Southeastern Arizona and Southwestern New Mexico / by Blakemore E. Thomas and Don R. Pool.

 p. cm. –(U.S. Geological Survey professional paper ; 1712)

Includes bibliographic references.

1. Streamflow–Arizona. 2. Streamflow–San Pedro River (New Mexico and Arizona). 3. Rain and rainfall–Arizona. 

4. Rain and rainfall–San Pedro River Watershed (New Mexico and Ariz.) I. Pool, D.R. II. Geological Survey (U.S.) 

III. Trends in streamflow of the San Pedro River, Southeastern Arizona, and regional trends in precipitation and 

streamflow in Southeastern Arizona and Southwestern New Mexico. IV. Series: U.S. Geological Survey 

professional paper; 1712.

GB1225.A6T56 2005

551.48’309791—dc22

2005027019

ISBN 1-411-30668-6
iii

Contents

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................3

Physical Setting.....................................................................................................................................3

Previous Studies ...................................................................................................................................7

Methods...........................................................................................................................................................8

Regional Trends.....................................................................................................................................8

Trends in the San Pedro River Basin...............................................................................................10

Trends in Precipitation and Streamflow.................................................................................10

Trends in Streamflow Caused by Factors Other than Precipitation..................................11

Monotonic Trends.............................................................................................................12

Step Trends ........................................................................................................................12

Regional Trends............................................................................................................................................13

Trends in Precipitation.......................................................................................................................13

Trends in Streamflow .........................................................................................................................15

Temporal Patterns or Cycles in Precipitation and Streamflow...................................................19

Trends in the San Pedro River Basin........................................................................................................22

Hydrologic Water Budgets and Relation to Streamflow Trends.................................................22

Trends in Precipitation and Streamflow..........................................................................................24

Trends in Streamflow Caused by Factors Other than Precipitation...........................................30

Monotonic Trends......................................................................................................................30

Step Trends .................................................................................................................................46

Causes of Trends in Streamflow.......................................................................................................50

Fluctuations in Precipitation ....................................................................................................50

Fluctuations in Air Temperature..............................................................................................52

Changes in Seasonal Distribution of Flow between the San Pedro River 

and Storage in the Stream Bank and Alluvial Aquifer ...........................................52

Changes in Watershed Characteristics .................................................................................56

Human Activities........................................................................................................................57

Summary and Conclusions.........................................................................................................................61

References Cited..........................................................................................................................................63

Appendix 1—Evaluation of Effects of Different Streamflow-Gaging Station 

Locations on Trend Analysis.........................................................................................................66

Appendix 2—Supplemental Data for Analysis of Step Trends in Streamflow...................................77
iv

Figures

1. Graphs showing trends in annual and seasonal streamflow of the San Pedro 

River at Charleston, Arizona .......................................................................................................3

2. Map showing location of regional study area and data-collection sites ...........................4

3. Map showing location of the Upper San Pedro River Basin and Charleston 

watershed, southeastern Arizona and northern Sonora, Mexico........................................5

4. Maps showing ratios of summer to annual value. A, Precipitation; B, Streamflow..........6

5. Graphs showing: A, Average monthly total precipitation at Tombstone, Arizona, 

and B, Historical distribution of daily streamflows for the San PedroRiver at 

Charleston, Arizona ......................................................................................................................7

6. Maps showing regional trends in precipitation, 1950–2002. A, Winter; 

B, Summer; C, Annual ................................................................................................................15

7. Maps showing regional trends in streamflow, 1950–2002. A, Winter; 

B, Summer; C, Annual ................................................................................................................18

8–22. Graphs showing:

8. Trends in regional normalized seasonal precipitation, southeastern Arizona 

and southwestern New Mexico...............................................................................................20

9. Trends in normalized seasonal streamflow for the San Pedro River at Charleston, 

Arizona, and regional normalized streamflow for the northwest and northeast 

parts of the study area, southeastern Arizona and southwestern New Mexico.............21

10. Trends in annual and seasonal precipitation at Tombstone, Arizona................................24

11. Step trends in central tendency and variability of precipitation at Tombstone, 

Arizona, and streamflow of the San Pedro River at Charleston, Arizona..........................29

12. LOWESS fits between precipitation at Tombstone, Arizona, and selected 

monthly total streamflows of the San Pedro River at Charleston, Arizona.......................31

13. Trends in monthly total streamflow and monthly total streamflow adjusted 

for variation in precipitation, January–December, San Pedro River at 

Charleston, Arizona ....................................................................................................................40

14. Trends in monthly low flow and monthly low flow adjusted for variation in 

precipitation, January–December, San Pedro River at Charleston, Arizona ...................42

15. Trends in maximum daily storm runoff and maximum daily storm runoff 

adjusted for variation in precipitation, selected months, San Pedro River 

at Charleston, Arizona................................................................................................................44

16. Regression relations between precipitation at Tombstone, Arizona, and 

monthly total streamflow for February through December for three time 

periods, San Pedro River at Charleston, Arizona..................................................................48

17. Regression relations between precipitation at Tombstone, Arizona, and 

maximum daily storm runoff for July through September for three time 

periods, San Pedro River at Charleston, Arizona..................................................................50

18. Annual average temperature at Tombstone, Arizona, 1913–2002 ......................................52

19. Correlations between monthly total streamflows and total streamflows 

for 24 previous months, San Pedro River at Charleston, Arizona, 1913–2002...................53

20. Correlations between monthly low flows and total streamflows for 

24 previous months, San Pedro River at Charleston, Arizona, 1931–2002.........................54

21. Correlations between monthly precipitation and precipitation for 

24 previous months, Tombstone, Arizona, 1913–2002...........................................................55

22. Ground-water pumpage in the Upper San Pedro River Basin, Sierra Vista 

subwatershed, Arizona and Sonora, Mexico, 1940–2002 ....................................................58
Tables

1. Data-collection sites for analysis of regional trends in precipitation, 

southeastern Arizona and southwestern New Mexico .........................................................9

2. Data-collection sites for analysis of regional trends in streamflow, 

southeastern Arizona and southwestern New Mexico .......................................................10

3. Regional trends in precipitation for 11 time periods, 1930-2002, southeastern 

Arizona and southwestern New Mexico ................................................................................14

4. Trends in seasonal and annual total streamflow at 6 gaging stations for 

11 time periods, 1930–2002, southeastern Arizona and southwestern 

New Mexico ................................................................................................................................16

5. Trends in seasonal and annual total streamflow at 21 gaging stations for 

periods of record, southeastern Arizona and southwestern New Mexico ......................17

6. Predevelopment water budget for the watershed of the San Pedro River 

at Charleston, Arizona................................................................................................................22

7. Predevelopment water budget for ground-water system in the watershed 

of the San Pedro River at Charleston, Arizona ......................................................................23

8. Water budget for seasonal streamflow of the San Pedro River at 

Charleston, Arizona ....................................................................................................................23

9. Trends in monthly, seasonal, and annual precipitation at Tombstone, 

Arizona, 1913–2002 .....................................................................................................................25

10. Trends in monthly, seasonal, and annual total precipitation at Tombstone, 

Arizona, for selected time periods...........................................................................................26

11. Changes in seasonal and annual total streamflow and low flow from 

the predevelopment period to 1991–2002, San Pedro River at 

Charleston, Arizona ....................................................................................................................27

12. Trends in seasonal total streamflow of the San Pedro River at Palominas, 

Charleston, and Redington, Arizona, for selected time periods .........................................28

13. Seasonal relations between low flow, total flow, and maximum daily 

storm runoff, San Pedro River at Charleston, Arizona, 1931–2002 .....................................30

14. Results of LOWESS regression analyses between monthly precipitation 

at Tombstone, Arizona, and monthly total streamflow for the San Pedro 

River at Charleston, Arizona; and between precipitation at Tombstone 

and time, 1913–2002....................................................................................................................32

15. Explanatory variables for LOWESS regression equations between 

monthly precipitation at Tombstone, Arizona, and monthly streamflow 

for the San Pedro River at Charleston, Arizona.....................................................................33

16. Results of LOWESS regression analyses between monthly precipitation 

at Tombstone, Arizona, and monthly low flow for the San Pedro River 

at Charleston, Arizona, and between precipitation at Tombstone and 

time, 1931–2002 ...........................................................................................................................35

17. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and maximum daily storm runoff for the San Pedro 

River at Charleston, Arizona; and between precipitation at Tombstone 

and time, 1913–2002, for selected months..............................................................................36

18. Trends in monthly total streamflow and monthly total streamflow adjusted 

for variation in precipitation, San Pedro River at Charleston, Arizona, 

1913–2002 .....................................................................................................................................37
vi

Tables—Continued

19. Trends in monthly low flow and monthly low flow adjusted for variation 

in precipitation, San Pedro River at Charleston, Arizona, 1931–2002 ................................38

20. Trends in maximum daily storm runoff and maximum daily storm runoff 

adjusted for variation in precipitation, by month, San Pedro River at 

Charleston, Arizona, 1913–2002................................................................................................39

21. Results of significance tests for differences among regression relations 

between precipitation at Tombstone, Arizona, and monthly total 

streamflow for the San Pedro River at Charleston, Arizona, for three 

time periods .................................................................................................................................47

22. Results of significance tests for differences among regression relations 

between precipitation at Tombstone, Arizona, and maximum daily storm 

runoff for the San Pedro River at Charleston, Arizona, for July, August, 

and September, for three time periods ...................................................................................47

24. Changes from 1913 to 2002 in monthly average precipitation at Tombstone, 

Arizona, and monthly average streamflow for San Pedro River at 

Charleston, Arizona ....................................................................................................................51

23. Factors that could cause trends in seasonal streamflow of the San Pedro 

River at Charleston, Arizona .....................................................................................................51

25. Changes in estimated annual base flow for San Pedro River from

predevelopment period to 1977–2002, previous studies, and this study ...........................59

1A. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and monthly total streamflow for the San Pedro 

River at Charleston, Arizona, and between precipitation at Tombstone 

and time, 1943–2002....................................................................................................................67

1B. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and monthly low flow for the San Pedro River 

at Charleston, Arizona, and between precipitation at Tombstone 

and time, 1943–2002....................................................................................................................68

1C. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and maximum daily storm runoff for the San Pedro 

River at Charleston, Arizona, and between precipitation at Tombstone 

and time, 1943–2002, for selected months..............................................................................69

1D. Trends in monthly total streamflow and monthly total streamflow adjusted 

for variation in precipitation, San Pedro River at Charleston, Arizona, 

1943–2002 .....................................................................................................................................70

1E. Trends in monthly low flow and monthly low flow adjusted for variation 

in precipitation, San Pedro River at Charleston, Arizona, 1943–2002 ................................71

1F. Trends in maximum daily storm runoff and maximum daily storm runoff 

adjusted for variation in precipitation, by month, San Pedro River at 

Charleston, Arizona, 1943–2002................................................................................................72

1G. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and station-adjusted monthly total streamflow 

for the San Pedro River at Charleston, Arizona, and between 

precipitation at Tombstone and time, 1913–2002...................................................................73

1H. Results of LOWESS regression analyses between precipitation at 

Tombstone, Arizona, and station-adjusted maximum daily storm 

runoff for the San Pedro River at Charleston, Arizona, and between 

precipitation at Tombstone and time, 1913–2002, for selected months.............................74
vii

Tables—Continued

1I. Trends in station-adjusted monthly total streamflow and station-adjusted 

monthly total streamflow adjusted for variation in precipitation, San Pedro 

River at Charleston, Arizona, 1913–2002 .................................................................................75

1J. Trends in station-adjusted maximum daily storm runoff and station-adjusted 

maximum daily storm runoff adjusted for variation in precipitation, by month, 

San Pedro River at Charleston, Arizona, 1913–2002 .............................................................76

2A. Results of least-squares regression analyses between precipitation at 

Tombstone, Arizona, and monthly total streamflow for the San Pedro River 

at Charleston, Arizona, for selected time periods.................................................................77

2B. Results of least-squares regression analyses between precipitation at 

Tombstone, Arizona, and maximum daily storm runoff for the San Pedro 

River at Charleston, Arizona, for selected time periods.......................................................79

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2) 

acre 0.004047 square kilometer (km2)

square foot (ft2) 929.0 square centimeter (cm2)

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3) 28.32 cubic decimeter (dm3) 

cubic foot (ft3) 0.02832 cubic meter (m3) 

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

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

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

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

°F = 1.8(°C) + 32

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD 27).

Elevation, as used in this report, refers to the distance above or below NGVD 29.
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Trends in Streamflow of the San Pedro River, 

Southeastern Arizona, and Regional Trends in 

Precipitation and Streamflow in Southeastern 

Arizona and Southwestern New Mexico

By Blakemore E. Thomas and Don R. Pool

Abstract

This study was done to improve the understanding of 

trends in streamflow of the San Pedro River in southeastern 

Arizona. Annual streamflow of the river at Charleston, 

Arizona, has decreased by more than 50 percent during the 

20th century. The San Pedro River is one of the few remaining 

free-flowing perennial streams in the arid Southwestern United 

States, and the riparian forest along the river supports several 

endangered species and is an important habitat for migratory 

birds.

Trends in seasonal and annual precipitation and 

streamflow were evaluated for surrounding areas in 

southeastern Arizona and southwestern New Mexico to 

provide a regional perspective for the trends of the San Pedro 

River. Seasonal and annual streamflow trends and the relation 

between precipitation and streamflow in the San Pedro River 

Basin were evaluated to improve the understanding of the 

causes of trends.

There were few significant trends in seasonal and 

annual precipitation or streamflow for the regional study 

area. Precipitation and streamflow records were analyzed for 

11 time periods ranging from 1930 to 2002; no significant 

trends were found in 92 percent of the trend tests for 

precipitation, and no significant trends were found in 

79 percent of the trend tests for streamflow. For the trends in 

precipitation that were significant, 90 percent were positive 

and most of those positive trends were in records of winter, 

spring, or annual precipitation that started during the midcentury drought in 1945–60. For the trends in streamflow 

that were significant, about half were positive and half were 

negative.

Trends in precipitation in the San Pedro River Basin 

were similar to regional precipitation trends for spring and 

fall values and were different for summer and annual values. 

The largest difference was in annual precipitation, for which 

no trend tests were significant in the San Pedro River Basin, 

and 23 percent of the trend tests were significantly positive in 

the rest of the study area. Streamflow trends for the San Pedro 

River were different from regional streamflow trends. All 

seasonal flows for the San Pedro River, except winter flows, 

had significant decreasing trends, and seasonal flows for 

most streams in the rest of the study area had either no trend 

or a significant increasing trend. Two streams adjacent to the 

San Pedro River Basin (Whitewater Draw and Santa Cruz 

River), however, had significant decreasing trends in summer 

streamflow.

Factors that caused the decreasing trends in streamflow 

of the San Pedro River at Charleston were investigated. 

Possible factors were fluctuations in precipitation and air 

temperature, changes in watershed characteristics, human 

activities, or changes in seasonal distribution of bank storage. 

This study statistically removed or accounted for the variation 

in streamflow caused by fluctuations in precipitation. Thus, 

the remaining variation or trend in streamflow was caused by 

factors other than precipitation.

Two methods were used to partition the variation 

in streamflow and to determine trends in the partitioned 

variation: (1) regression analysis between precipitation and 

streamflow using all years in the record and evaluation of 

time trends in regression residuals, and (2) development of 

regression equations between precipitation and streamflow for 

three time periods (early, middle, and late parts of the record) 

and testing to determine if the three regression equations 

were significantly different. The methods were applied to 

monthly values of total flow (average flow) and storm runoff 

(maximum daily mean flow) for 1913–2002, and to monthly 

values of low flow (3-day low flow) for 1931–2002.

Statistical tests provide strong evidence that factors 

other than precipitation caused a decrease in streamflow of 

the San Pedro River. Factors other than precipitation caused 

significant decreasing trends in streamflows for late spring 

through early winter and did not cause significant trends for 

late winter through early spring. Total flows had significant 

decreasing trends in June through December, low flows had 

significant decreasing trends in May through December, and 

 
storm runoff had significant decreasing trends in July through 

September. The effects of factors other than precipitation were 

tested only for July through October for storm runoff.

Besides fluctuations in precipitation, the principal factors 

that could have caused decreasing streamflow trends are 

(1) changes in watershed characteristics such as changes in 

riparian vegetation, changes in upland vegetation, and changes 

in stream-channel morphology, and (2) human activities such 

as ground-water pumping, construction of runoff-detention 

structures, urbanization, and cattle ranching (grazing). 

Changes in upland and riparian vegetation likely were 

major factors in the decreasing trends in total streamflows 

and low flows. Total flows and low flows in summer 

and fall were significantly affected by factors other than 

precipitation, but late winter flows were not significantly 

affected. The significant effects coincide with high rates 

of transpiration from vegetation in the summer and the 

nonsignificant effects coincide with low rates of transpiration 

in the late winter. Another piece of evidence that implicates 

vegetation as a cause is that the upland and riparian vegetation 

of the San Pedro River Basin changed during the 20th century. 

The relative proportions of different species changed in upland 

vegetation (woody plants increased and grasses decreased), 

and the areal extent and density of riparian vegetation 

increased substantially.

Ground-water pumping in the United States and Mexico 

had a mixed influence on streamflow trends at Charleston, 

Arizona; statistical analyses indicate that seasonal pumping 

from wells near the river for irrigation in the spring and 

summer was a major factor in the decrease in low flows and 

that year-round pumping from wells in the regional aquifer 

away from the river was not a major factor in the decrease 

in low flows. If regional pumping had caused a trend, the 

pumping should have affected low flows for all months of 

the year, but factors other than precipitation did not cause 

significant trends in low flows for January, February, March, 

and May. Most of the local pumping near the river was 

during the spring and summer, and this seasonal pumping 

probably caused some decreases in summer low flows. 

These conclusions are for trends from 1913 to 2002, and 

regional pumping in the United States and Mexico could 

affect streamflow at Charleston in the future, because 

regional ground-water pumping often has a delayed effect 

on streamflows.

Introduction

Concerns about trends in precipitation and streamflow 

have increased in the Southwestern United States, where the 

population is increasing at a rapid rate and water supplies 

are limited because of an arid or semiarid climate (Hurd and 

others, 1999; Webb and others, 2004). Resource managers 

need to understand the characteristics and the causes of these 

trends. Precipitation and streamflow can have a monotonic 

increasing or decreasing trend, can shift from high to low 

values for extended periods of time, or can alternate in cycles 

from high to low values. Information about these trend 

characteristics is useful because the same characteristics 

might continue in the future. The cause of a streamflow 

trend is usually difficult to determine and quantify. Trends 

are commonly a result of natural fluctuations in precipitation, 

but trends can also result from other factors, such as human 

activities or changes in watershed characteristics. Resource 

managers need to know if precipitation fluctuations or other 

factors caused the trend. Land- and water-management 

decisions can be more effective when the cause of a trend 

is known.

This report presents results of a study of trends in 

streamflow for a river in the Southwestern United States. 

Total streamflow and low flow in the San Pedro River in 

southeastern Arizona has decreased during the past 90 years 

(Pool and Coes, 1999), and resource managers and the 

public have a great interest in learning more about the trend 

and more about possible causes of the trend. The San Pedro 

River is one of the few remaining free-flowing perennial 

streams in the arid Southwest. The riparian forest along 

the river supports several endangered species and is an 

important habitat for migratory birds. The decreasing trends 

in streamflow of the San Pedro River are causing concerns 

that riparian habitat may be damaged and that overall longterm water supply in the watershed may be threatened. 

In 1988, Congress established the San Pedro Riparian National 

Conservation Area (SPRNCA) to preserve and protect the 

riparian area. From 1994 to 2005, the U.S. Geological Survey, 

in cooperation with the Bureau of Land Management and 

Cochise County, Arizona, has conducted studies to improve 

the understanding of the hydrology of the Upper San Pedro 

River Basin. This study of streamflow trends was done during 

2003–04 and was part of the larger cooperative program.

The decreases in streamflow of the San Pedro River at 

Charleston, Arizona have been substantial: changes in total 

streamflow from the first 20 years of streamflow record 

(1913–36) to the last 20 years of record (1983–2002) were 

-54 percent for annual flows, -70 percent for summer flows, 

and -20 percent for winter flows (fig. 1). These decreasing 

trends are anomalous compared to generally increasing 

streamflow trends during the 20th century in most of the 

United States (Lins and Slack, 1999).

Potential causes of the decreasing streamflow trends 

of the San Pedro River are (1) fluctuations in precipitation, 

(2) fluctuations in temperature, (3) changes in watershed 

characteristics, (4) human activities, and (5) changes in the 

seasonal distribution of bank storage. Possible watershed 

characteristics that may have influenced streamflow trends are 

changes in riparian vegetation, changes in upland vegetation, 

and changes in stream-channel morphology. Possible human 

activities that may have influenced streamflow trends are 

ground-water pumping, construction of runoff-detention 

structures, urbanization (increased impervious areas and 

diversions of runoff), and cattle ranching (grazing).

 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
 Purpose and Scope

This report presents results of a study of trends in 

streamflow of the San Pedro River in southeastern Arizona 

and regional trends in precipitation and streamflow in 

southeastern Arizona and southwestern New Mexico. The 

study objective was to improve the understanding of trends 

and the causes of trends in streamflow of the San Pedro River. 

The decreasing streamflow trends of the San Pedro River 

have been well documented by other studies (Hereford, 1993; 

Sharma and others, 1997; Stromberg, 1998; Pool and Coes, 

1999; and Rojo and others, 1999), but no study has thoroughly 

investigated the nature and causes of the trends. Determining 

the causes of the decrease in streamflow is difficult because 

the many possible factors are interrelated and there are meager 

data on the historical changes in some of the factors. This 

study took several different approaches and used statistical 

analysis as the primary tool. Statistical analysis can sort out 

complex interactions and determine the relative importance 

of each factor affecting streamflow, and it provides objective 

measures of the strength of evidence (probabilities) for 

determining if trends are statistically significant or if trends 

occurred by chance.

The first step in the analysis was to place the trends in 

San Pedro River streamflow in a regional perspective. Trends 

in seasonal precipitation and streamflow for surrounding areas 

were determined and compared to trends in the San Pedro 

River Basin. The second step was a detailed evaluation of 

trends in seasonal precipitation and streamflow in the basin. 

The third step was to evaluate trends in monthly streamflows 

of the San Pedro River and to distinguish between the 

effects of precipitation and the effects of factors other than 

precipitation. The variation in streamflow caused by variation 

in precipitation was removed, and the remaining variation was 

attributed to factors other than precipitation, such as human 

activities or changes in watershed characteristics. The last step 

incorporated results of all the analyses to evaluate the specific 

causes of streamflow trends.

Physical Setting

The regional study area is about 7,000 mi2, and the 

San Pedro River Basin at Charleston, Arizona, is 1,234 mi2

(figs. 2 and 3). About 696 mi2 of the basin is in Mexico. The 

regional boundaries were selected to include an area of similar 

climate and physiography as the San Pedro River Basin. 

The western boundary is near the Santa Cruz River Basin; 

areas to the west of that are much drier than the San Pedro 

River Basin. The northern boundary is near the southern 

part of the Salt River Basin; areas to the north of that are 

at a consistently higher elevation and are much wetter and 

cooler than the San Pedro River Basin. The eastern boundary 

extended much further than the western boundary because 

the climate in much of southwestern New Mexico is similar 

to that of the San Pedro River Basin. The eastern boundary is 

about 50 miles east of the Arizona-New Mexico border. The 

southern boundary is the upper watershed of the San Pedro 

River in Sonora, Mexico, and the international boundary 

between the United States and Mexico to the west and east of 

the watershed.

The regional study area (fig. 2) has a wide range of landsurface elevation, precipitation, and vegetation. Precipitation 

and vegetation generally correlate with elevation; precipitation 

increases with increased elevation, and vegetation changes 

from desert shrubs and cacti in the lowlands to grassland 

and oak woodland in the mid-elevations and conifers in the 

highlands. Land-surface elevations range from about 2,000 to 

11,000 ft, and mean annual precipitation ranges from about 

10 in. in the lowest elevations to about 40 in. in the highest 

elevations. In the Upper San Pedro River Basin, land-surface 

elevations range from about 3,900 to 9,500 ft, and mean 

annual precipitation ranges from about 14 to 30 in. (fig. 3). 

Figure 1. Trends in annual and seasonal streamflow of the 

San Pedro River at Charleston, Arizona. Blue line is LOWESS fit 

to data.

100

10

1,000

1

100

10

1,000

1

100

10

1,000

1

100

10

1,000

1

19101915192019251930193519401945195019551960196519701975198019851990199520002005

FALL AVERAGE STREAMFLOW

SUMMER AVERAGE STREAMFLOW

WINTER AVERAGE STEAMFLOW

ANNUAL AVERAGE STREAMFLOW

STREAMFLO

W, IN CUBIC FEET PER SECOND

Figure 1. Trends in annual and seasonal streamflow of San Pedro

River at Charleston, Arizona. Blue line is LOWESS fit to data.

Introduction 
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16 

11 

30 

29 

26 

36 

1 

1 

0 25 MILES 

0 25 KILOMETERS 

Enlarged 

area 

UPPER SAN PEDRO BASIN 

CHARLESTON 

Base from U.S. Geological Survey WATERSHED 

digital data, 1:100,000, 1982 

Universal Transverse Mercator 

projection, Zone 12 

EXPLANATION 

Northwest Northeast 

Southwest Southeast 

U.S. GEOLOGICAL SURVEY 

 STREAMFLOW-GAGING 

 STATION AND NUMBER 

 (See table 2) 

NATIONAL WEATHER SERVICE 

 PRECIPITATION STATION 

 AND NUMBER (See table 1) 

R 

o g 

C 

o 

r e e k 

l l o n M 

i 

M i m b 

R i v e r 

r e s 

v e r 

T u l a r o s a 

D a r 

A 

h i te wat e r W 

r a v i p a a 

r 

k e e C 

S o o i t a 

C r e e k n 

P a 

a n o 

n 

a s W h 

t 

S a n C a r l o s R i ver 

w 

S 

n a n a r F 

o c s i c i R 

2 

23 

19 

6 

21

Figure 2. Location of regional study area and data-collection sites.

 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
110o45’ 30’ 15’ 110o 109o45’

15’

31o

30’

45’

32o

32o15’

0 5 MILES

0 5 KILOMETERS

Base from U.S. Geological Survey

digital data, 1:100,000, 1982

Universal Transverse Mercator

projection, Zone 12

ARIZONA

SONORA

UNITED STATES

MEXICO

PIMA COUNTY

SANTA CRUZ

COUNTY

Palominas

Benson

Bisbee

St. David

Charleston

P

de ro i

R

B

ari

abocom

iver

COCHISE COUNTY

92

90

90

82

TOMBSTONE

HILLS

WHETSTONE MOUNTAINS

MULE

MOUNTAINS

The Narrows

Fairbank

Cananea

80

10

Tombstone

CHARLESTON WATERSHED

Sierra Vista

SIERRA VISTA

SUBWATERSHED

San Pedro

Riparian

National

Conservation

Area

SUBWATERSHED

BENSON

R ver

EXPLANATION

U.S. GEOLOGICAL SURVEY

 STREAMFLOW-GAGING

 STATION

BOUNDARY OF CHARLESTON

 WATERSHED

Huachuca City

Tucson

A R I Z O N A

Upper San Pedro

Basin and

Charleston watershed

San

UNITED STATES

MEXICO

Fort Huachuca

Figure 3. Location of the Upper San Pedro River Basin and Charleston watershed, southeastern Arizona and 

northern Sonora, Mexico.

Introduction 
The climate of the study area is arid or semiarid with a 

biseasonal distribution of precipitation in summer and winter. 

Seasons have different precipitation characteristics because 

there are several sources of moisture and several types of 

storms that transport the moisture and deliver the precipitation. 

In the winter, mid-latitude frontal systems bring moisture from 

the Pacific Ocean, and the precipitation generally has a long 

duration, low intensity, and widespread extent. Spring is a dry 

transitional period, and frontal systems usually move to the 

north of the study area. In the summer, moisture moves into 

the study area from the Gulf of Mexico, Gulf of California, 

and Pacific Ocean, and convective thunderstorms (monsoons) 

deliver short-duration and high-intensity precipitation. The 

thunderstorms have a small spatial extent and are somewhat 

random in their location. Fall is a transitional period that can 

have precipitation from monsoonal thunderstorms, frontal 

systems, and dissipating tropical cyclones. Residual moisture 

from tropical cyclones can be carried northward with weak 

monsoonal flow or with cutoff low-pressure systems from the 

Pacific Ocean, and storms from this source can result in some 

of the largest and most widespread floods in the study area 

(Webb and others, 2004). 

The southwest part of the study area (fig. 2), which 

includes the Upper San Pedro River Basin (fig. 3), is generally 

similar to the rest of the study area in its physical environment 

with the exception of the seasonal distribution of precipitation 

and streamflow. In the southwest part of the study area, 

percentages of annual precipitation and streamflow that occur 

in the summer are larger than percentages in the rest of the 

study area (fig. 4). In the southwest part, about 48 percent of 

the precipitation and 56 percent of the streamflow occur in the 

summer. In the rest of the study area, about 39 percent of the 

precipitation and 22 percent of the streamflow occur in the 

summer. Thus, changes in summer precipitation have a greater 

effect on overall water supply in the southwest part compared 

to the rest of the study area.

The seasonal characteristics of precipitation at 

Tombstone, Arizona, and streamflow of the San Pedro River 

are similar: most of the annual volume of water is in the 

summer, and the least amount of water is in the spring (fig. 5). 

Summer also has the largest difference between high and 

low streamflows.

Figure 4. Ratios of summer to annual value. A, Precipitation; B, Streamflow.

0 25 MILES 

0 25 KILOMETERS 

EXPLANATION 

RANGE IN RATIO:

0.10 TO 0.39 0.40 TO 0.49 0.50 TO 0.75

111o 110o 109o 108o 

34o 

33o 

32o 

B. Streamflow 

111o 110o 109o 108o 

34o 

33o 

32o 

ARIZONA NEW MEXICO ARIZONA NEW MEXICO 

A. Precipitation 

Northwest Northeast 

Southwest 

Southeast 

Northwest Northeast 

Southwest 

Southeast 

 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Figure 5. A, Average monthly total precipitation at Tombstone, Arizona, and B, Historical distribution of daily streamflows for the 

San Pedro River at Charleston, Arizona.

Previous Studies

In addition to the studies that have noted the large 

decrease in streamflow of the San Pedro River, many other 

studies have investigated changes or trends in precipitation and 

watershed characteristics during the 20th century. There were 

small changes in precipitation patterns and intensity, but no 

large changes in precipitation magnitude (Hereford, 1993; 

Sharma and others, 1997; Pool and Coes, 1999; and Rojo 

and others, 1999). Upland and riparian vegetation changed 

in areal extent, density, and relative proportion of different 

species (Hereford, 1993; Stromberg, 1998; Kepner and 

Edmonds, 2002; and Turner and others, 2003). Stream-channel 

morphology of the San Pedro River changed substantially 

from 1880 to 1955 (Hereford, 1993). From 1880 to 1910, the 

channel incised and deepened, and from 1910 to 1955, the 

channel migrated laterally and widened.

Several ground-water models have been constructed 

of the ground-water system in the Upper San Pedro Basin 

(Freethey, 1982; Vionnett and Maddock, 1992; Corell and 

others, 1996; and Goode and Maddock, 2000). These models 

were constructed to improve the understanding of the groundwater system and its interaction with the San Pedro River, 

and to estimate effects of future ground-water pumping. 

The models simulated changes in the ground-water and 

surface-water systems from a predevelopment period (prior 

to 1940) to the late 1970s or 1990s. Ground-water pumping 

caused simulated decreases in annual base flow that ranged 

from 33 to 65 percent of the predevelopment flow.

4

A. Average monthly precipitation

90th percentile

10th percentile

PRECIPITATION, IN INCHES 

3

2

1

JAN. 

Average monthly precipitation from

1913 to 2002 at Tombstone, Arizona

Historical distribution of daily streamflows from 1913 to 2002

for the San Pedro River at Charleston, Arizona

FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. 

0

B. Daily streamflows

DAILY MEAN DISCHARGE, IN CUBIC FEET PER SECOND

1,000

100

10

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. 

1

1,200

Median

Introduction 
Methods

Regional Trends

Regional trends in precipitation and streamflow were 

determined by evaluating records at 38 National Weather 

Service precipitation sites and 21 U.S. Geological Survey 

(USGS) streamflow-gaging stations (fig. 2, tables 1 and 2). 

Precipitation data are more complete than streamflow data. 

Most precipitation sites have data from 1950 to 2002, and 

some sites have data from 1930 or earlier. Streamflow-gaging 

stations have more missing data than precipitation sites, 

and some streams have two or more gaging stations. Only 

10 gaging stations have mostly complete data from 1950 to 

2002. Most of the missing streamflow data were from gaging 

stations that were discontinued for blocks of time within 

their records.

Annual and seasonal values of precipitation and 

streamflow were analyzed. Seasons were defined on the basis 

of the type of storms that cause precipitation and runoff. 

Winter was defined as November through March, spring was 

April through June, summer was July and August, and fall was 

September and October. In the San Pedro River Basin, about 

27 percent of the annual precipitation falls in winter, 6 percent 

in spring, 49 percent in summer, and 18 percent in fall.

An evaluation of trends is dependent on the period of 

record that is evaluated. During the 20th century, precipitation 

and streamflow in the study area followed decadal-scale 

cycles of high and low values (McCabe and Dettinger, 1999). 

The 1950s had low precipitation and streamflow, and the 

1980s had high precipitation and streamflow. Consequently, 

several time periods were analyzed to obtain results that were 

not biased by a particular position on a cycle. Trends were 

analyzed for 11 time periods starting every 5 years from 

1930 to 1980, and ending in 2002 (for example, 1930–2002, 

1935–2002, and 1940–2002).

A nonparametric Kendall tau test was used to determine 

if there were significant trends in precipitation or streamflow 

(Helsel and Hirsch, 1992, p. 326–328). The Kendall tau 

non-parametric test is considered more appropriate than 

parametric tests (such as linear regression) for precipitation 

and streamflow data because these data usually have many 

outliers that unduly influence parametric tests, and these data 

usually are not normally distributed. The Kendall tau test is for 

monotonic trends. A monotonic trend generally increases or 

decreases in magnitude throughout a time period. There may 

be short reversals of the increasing or decreasing trend, but the 

predominant trend is in one direction. A set of data in which 

the magnitudes of data steadily increase for half the time 

period and steadily decrease for the other half would have no 

monotonic trend.

Several statistical tests were made in this study and all 

used a threshold significance level of a p-value equal to 0.05. 

A p-value less than 0.05 means the test is significant. 

The p-value of 0.05 is a commonly used significance level 

(Sokal and Rohlf, 1995, p. 163–164); however, p-values 

between 0.05 and 0.10 are also important and indicate a strong 

association. Tests with a p-value between 0.05 and 0.10 were 

called “nearly significant” in this report.

Results of the trend tests for the precipitation sites 

and streamflow-gaging stations were plotted on maps of 

the regional study area. The results were also summarized 

for five parts of the study area: the San Pedro River Basin 

and four quadrants—southwest, including the San Pedro 

River Basin; northwest; northeast; and southeast (fig. 2). 

The boundaries of the four quadrants were selected on the 

basis of similar climatic and streamflow characteristics.

Temporal patterns or cycles in seasonal precipitation 

and streamflow were evaluated using typical or average 

values for the study area. Typical values of precipitation and 

streamflow were compared for the southwest part (including 

the San Pedro River Basin) and the rest of the study area. 

These two parts were compared because an objective of the 

study was to determine how trends in the basin compare to 

regional trends. Typical values were represented by computing 

regional normalized values from site values in the two parts. 

A normalized seasonal value was computed at each site by 

dividing each seasonal value of precipitation or streamflow by 

the mean for the entire record, and regional normalized values 

were computed by taking the mean of all the normalized 

seasonal values for each site.

Regional normalized precipitation was computed for 

the southwest part of the study area using four sites and was 

computed for the rest of the study area using 11 sites (table 1 

and fig. 2). No regional normalized streamflow was computed 

for the southwest part of the study area because streamflow 

trends of the San Pedro River were severe and would have 

obscured any temporal patterns or cycles in streamflow of 

other streams in the southwest part. Regional normalized 

streamflow was computed for the rest of the study area using 

three sites (San Carlos River near Peridot, Arizona; Gila 

River near Gila, New Mexico; and San Francisco River near 

Glenwood, New Mexico; table 2). The precipitation and 

streamflow sites used for the regional normalized values were 

selected because they all had mostly complete records for 

1931–2002 and they had similar precipitation or streamflow 

characteristics within their part of the study area.

 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1. Data-collection sites for analysis of regional trends in precipitation, southeastern Arizona and southwestern New Mexico

Map 

number1

National 

Weather Service 

identification number Name2 State

Period of 

record

Years 

of data

Land-surface 

elevation 

(feet)

Mean annual 

precipitation3

(inches)

1 0159 Alpine4 Arizona 1931–2002 72 8,050 20.5

2 0808 Black River Pumphouse Arizona 1947–2002 56 6,040 16.2

3 0958 Bowie4 Arizona 1931–2002 65 3,760 11.5

4 1664 Chiricahua National Monument Arizona 1948–2002 55 5,300 19.5

5 1849 Clifton4 Arizona 1901–2002 100 3,520 13.1

6 2140 Coronado National Monument Arizona 1956–2002 47 5,242 20.9

7 2664 Douglass FAA Airport Arizona 1948–2002 55 4,150 13.0

8 2754 Duncan Arizona 1942–2002 61 3,660 11.2

9 3120 Fort Huachuca Arizona 1955–1997 43 4,670 15.1

10 5418 McNeal5 Arizona 1931–2002 71 4,170 11.6

11 26119 Oracle 2 SE Arizona 1950–2002 53 4,510 23.1

12 6280 Patagonia5 Arizona 61931–2002 55 4,190 17.6

13 6353 Pearce Sunsites Arizona 1953–2002 43 4,350 12.2

14 7036 Redington Arizona 1942–2002 60 2,940 13.8

15 7334 Rucker Canyon5 Arizona 1931–2002 72 5,370 19.0

16 7390 Safford Ag Center Arizona 1949–2002 54 2,954 9.2

17 27480 San Carlos Reservoir Arizona 1931–1997 67 2,530 15.5

18 27593 Santa Rita Experiment Range Arizona 1950–2002 53 4,300 22.3

19 8619 Tombstone5 Arizona 1905–2002 93 4,610 13.6

20 28815 Tucson, University of Arizona4 Arizona 1901–2002 102 2,440 11.6

21 28865 Tumacacori National Monument Arizona 1946–2002 57 3,270 15.8

22 9334 Willcox Arizona 1940–2002 62 4,175 12.5

23 9562 Y Lightning Ranch Arizona 1939–2002 64 4,590 14.1

24 0417 Animas4 New Mexico 1931–2002 72 4,420 11.2

25 0818 Beaverhead Ranger Station New Mexico 1939–2002 62 6,670 14.9

26 1910 Cliff 11 SE New Mexico 1944–2002 59 4,780 14.6

27 2024 Columbus New Mexico 1941–2002 61 4,160 9.6

28 2436 Deming4 New Mexico 61901–2002 93 4,300 9.5

29 3157 Faywood New Mexico 1946–2002 55 5,190 11.6

30 3265 Fort Bayard4 New Mexico 1931–2002 72 6,140 15.2

31 3368 Gage 4 ESE New Mexico 1901–2002 100 4,410 10.2

32 3775 Hachita New Mexico 1931–2002 70 4,510 10.5

33 4009 Hillsboro4 New Mexico 1905–2002 84 5,270 12.7

34 5079 Lordsburg 4 SE4 New Mexico 1931–2001 71 4,250 11.6

35 5273 Luna Ranger Station4 New Mexico 1931–2002 72 7,050 15.9

36 5754 Mimbres Ranger Station New Mexico 1931–1997 67 6,240 17.3

37 7340 Redrock4 New Mexico 1931–2002 68 4,150 12.9

38 9691 White Signal New Mexico 1949–2002 54 6,070 15.2

1

See figure 2.

2

All sites were operated by the National Weather Service.

3

Values are for 1950-2002, or for period of record if the period began after 1950.

4

Site was used in the analysis of regional normalized precipitation in northwest, northeast, and southeast part of study area (fig. 8).

5

Site was used in the analysis of regional normalized precipitation in southwest part of study area (fig. 8).

6

Site has more than 10 years of missing data in a continuous block of time within period of record.

Methods 
Trends in the San Pedro River Basin

Trends in the San Pedro River Basin were analyzed 

in more detail than the trends in the regional study area. 

Trends in seasonal precipitation and streamflow were 

evaluated, trends in monthly streamflow caused by factors 

other than precipitation were evaluated, and causes of trends 

were evaluated. Trends from 1913 to 2002 were evaluated 

using precipitation data from the National Weather Service 

site at Tombstone, Arizona, and streamflow data from the 

USGS gaging station San Pedro River at Charleston, Arizona 

(station 09471000). These sites were used because they have 

the longest and most complete data records in the San Pedro 

River Basin.

The gaging station for San Pedro River at Charleston was 

moved three times during 1913 to 2002, but it has been at the 

same location since 1943. The analyses presented in this report 

were done on the complete record from 1913 to 2002. There is 

some uncertainty, however, about the possible effects of the 

Table 2. Data-collection sites for analysis of regional trends in streamflow, southeastern Arizona and southwestern New Mexico

[nr, near; NA, data not available]

Map 

number1

Gagingstation 

number Name2 State

Period of 

record

Years 

of data

Drainage area 

(square miles)

Mean 

basin 

elevation 

(feet)

Mean annual 

precipitation3

(inches)

1 09468500 San Carlos River nr Peridot Arizona 1930-2002 73 1,026 4,480 17.2

2 09470500 San Pedro River at Palominas Arizona 41931-2002 46 737 4,950 17.9

3 09471000 San Pedro River at Charleston Arizona 1913-2002 86 1,234 4,840 16.5

4 09472000 San Pedro River nr Redington Arizona 1944-1997 50 2,927 4,660 15.5

5 09473000 Aravaipa Creek nr Mammoth Arizona 41932-2002 46 537 4,530 16.2

6 09480000 Santa Cruz River nr Lochiel Arizona 1950-2002 53 82.2 5,150 18.2

7 09480500 Santa Cruz River nr Nogales Arizona 1931-2002 70 533 4,850 18.7

8 09481500 Sonoita Creek nr Patagonia Arizona 1931-1972 40 209 4,800 19.3

9 09482500 Santa Cruz River at Tucson Arizona 41913-2002 75 2,222 4,050 16.9

10 09484000 Sabino Creek nr Tucson Arizona 41933-2002 55 35.5 6,300 22.6

11 09484600 Pantano Wash nr Vail Arizona 41960-2002 28 457 4,500 15.4

12 09485000 Rincon Creek nr Tucson Arizona 41953-2002 36 44.8 4,850 19.2

13 09485850 Rillito Creek nr Tucson Arizona 1914-1975 61 892 4,400 15.5

14 09537500 Whitewater Draw nr Douglas Arizona 1931-1982 48 1,023 4,740 14.8

15 08477000 Mimbres River nr Mimbres New Mexico 1931-1976 46 152 5,972 NA

16 09430500 Gila River nr Gila New Mexico 1929-2002 74 1,864 8,100 18.0

17 09430600 Mogollon Creek nr Cliff New Mexico 1968-2002 35 69.0 NA NA

18 09431500 Gila River nr Redrock New Mexico 1931-2002 65 2,829 6,280 17.0

19 09442680 San Francisco River nr Reserve New Mexico 1960-2002 43 350 5,820 17.0

20 09442692 Tularosa River abv Aragon New Mexico 1967-1996 30 94.0 7,720 13.0

21 09444000 San Francisco River nr Reserve New Mexico 1928-2002 75 1,653 4,560 17.6

1

See figure 2.

2

All gaging stations were operated by the U.S. Geological Survey.

3

Precipitation is the mean for the entire drainage basin and is based mostly on 1931–1960 data.

4

Gaging station has more than 10 years of missing data in a continuous block of time within period of record.

different station locations on the trend analyses. These effects 

were primarily evaluated by performing the same analyses on 

the data since 1943 and comparing those results to the results 

from the analyses on the complete data set. The evaluation 

found minor changes in trends and effects of factors other 

than precipitation, but the overall conclusions were the same. 

The evaluation of the effects of station location on the trend 

analyses is shown in appendix 1.

Trends in Precipitation and Streamflow

Monotonic trends in monthly and seasonal precipitation 

from 1913 to 2002 were evaluated to determine possible 

seasonal differences, and monotonic trends for shorter time 

periods during 1913 to 2002 were evaluated to determine 

possible changes in trends over time. Changes in streamflow 

from the predevelopment period to 2002 were evaluated to 

determine the overall decrease in flow during the time of 

human influences on the streamflow record. The period prior 

10 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
to 1940 is generally considered the predevelopment period 

(Corell and others, 1996; Rojo and others, 1999). Streamflow 

records at Palominas (09470500), Charleston (09471000), 

and Redington (09472000; fig. 2 and table 2) were analyzed 

for different time periods to provide insight into the causes 

of trends. Finally, step trends or shifts in precipitation and 

streamflow were evaluated to gain a better understanding of 

the characteristics of the trends.

Monotonic trends in precipitation were determined using 

the Kendall tau test. For trends in seasonal precipitation, 

measures of the total volume, maximum value, frequency, 

and volume per storm were evaluated. Total volume was total 

inches, maximum value was maximum daily precipitation, 

frequency was number of days with precipitation, and volume 

per storm was total volume divided by number of days with 

precipitation.

Step trends in seasonal precipitation and streamflow 

were evaluated to provide additional information on the 

changes over time. Monotonic trend tests incorporate all the 

increasing, level, or decreasing trends or cycles in a record and 

provide a summary statistic of the overall trend for the entire 

period of record. Possible cycles or step trends within the 

record are lost or obscured in this type of analysis. To evaluate 

step trends or cycles in seasonal precipitation and streamflow, 

the years of data were grouped into six successive time 

periods and measures of the central tendency and variability 

were computed for each time period. The six time periods 

were selected so each period has about an equal number of 

years (about 14). The central tendency was represented by 

the median value, and the variability was represented by the 

interquartile range (IQR). The IQR is the difference between 

the 75th percentile and 25th percentile of the data. Two types 

of seasonal data were used in the step-trend analysis: (1) total 

precipitation or streamflow for each year in the time period 

and (2) maximum daily precipitation or streamflow for each 

year in the time period. The median and IQR for each season 

were computed using the 14 values in each time period. 

Thus, these medians and IQRs measure the interannual 

central tendency and variability.

To normalize the results for comparison between 

precipitation and streamflow, the medians and IQRs for 

each time period were divided by the median or IQR for 

the entire record. All four seasons were analyzed, but only 

winter, summer, and fall values are discussed because spring 

precipitation and streamflow are a small percentage of the 

volume or maximum values for the year.

Trends in Streamflow Caused by Factors Other 

than Precipitation

The last and most detailed analysis of streamflow of 

the San Pedro River was of trends in monthly values of 

total flow, low flow, and storm runoff, and of trends in these 

streamflow components that were caused by factors other 

than precipitation. Analysis of trends in monthly values 

and different streamflow components provides information 

about the cause of trends, because the influence of each 

human activity and each watershed characteristic is different 

depending on the month of the year and the streamflow 

component. Pumping from the regional ground-water system 

should have a constant effect on low flows and total flows 

throughout all months of the year, and have little effect on 

storm runoff. Vegetation and associated transpiration have a 

much larger effect on streamflow during the warm summer 

months than during the cool winter months.

The three components of streamflow analyzed in this 

study (total flow, low flow, and storm runoff) were represented 

as follows: (1) total flow was the average flow for each month, 

(2) low flow was the 3-day low flow for each month, and 

(3) storm runoff was the maximum daily mean flow for each 

month with direct runoff from precipitation. The 3-day low 

flow can be considered an index of regional ground-water 

discharge, but it can also include flow from local bank storage 

and discharge from the local alluvial ground-water system. 

Several methods are available to estimate base flow or groundwater discharge, but all have some limitations, and the 3-day 

low flow was used because it is unbiased, repeatable, and not 

dependent on assumptions. Average flows and storm runoff 

were analyzed for the entire record (1913–2002). Low flows 

were analyzed for 1931–2002, because data for daily low 

flows during 1913–30 were not considered sufficiently 

accurate. Low flows for several consecutive days were often 

averaged into a single value in the streamflow record. 

The monthly 3-day low flow is used as an approximation 

of monthly base flow of the San Pedro River. Base flow 

has sometimes been confused with an estimate of all the 

ground water that moves to a stream and discharges to a 

stream. Base flow, as used in this study and in the groundwater models of the Upper San Pedro Basin (Freethey, 1982; 

Vionnett and Maddock, 1992; Corell and others, 1996; 

Goode and Maddock, 2000), is the actual flow in the river 

that is sustained by ground-water discharge. The total quantity 

of ground water that moves to the San Pedro River equals 

base flow plus water that is removed by evapotranspiration 

from shallow ground water in the flood plain and near the 

stream channel. 

The record of storm-runoff peaks was not complete for 

most months during 1913 to 2002. The analysis was intended 

for actual storm runoff—mostly overland flow of water from 

an intense storm that causes a steep rise in the hydrograph of 

daily flows. Almost every year had at least one storm-runoff 

peak during the summer months, but many years could go by 

where precipitation was not sufficient to generate storm runoff 

during the other months. To construct a record of storm-runoff 

peaks for each month, the annual hydrographs of daily mean 

flows for all years in the record were evaluated, and stormrunoff peaks were selected from the appearance of sharp 

peaks of runoff. This procedure resulted in a complete record 

for August (84 peaks), one missing peak for July (83 peaks), 

71 peaks for September, about 35 peaks for June and October, 

about 20 peaks for November to March, and fewer than 

10 peaks for April and May.

Possible trends in San Pedro River streamflow caused 

by factors other than precipitation were determined by 

partitioning the temporal variation in streamflow into two 

parts: (1) the variation caused by variation in precipitation 

and (2) the variation caused by other factors, such as 

human activities and changes in watershed characteristics. 

The variation in streamflow caused by factors other than 

precipitation was then tested for trends.

Methods 11
The partitioning of the variation in streamflow and testing 

to determine trends in the streamflow variation caused by 

factors other than precipitation was done using two methods: 

(1) regression analysis between precipitation and streamflow 

for all years in the record and evaluation of time trends in 

regression residuals, and (2) development of regression 

equations between precipitation and streamflow for three time 

periods (early, middle, and late parts of the record) and testing 

to determine if the three regression equations are significantly 

different. Method 1 is an evaluation of monotonic change 

for the entire record, and method 2 is an evaluation of step 

changes during three time periods in the record.

Monotonic Trends

The first method was a four-step method of regression 

modeling and monotonic trend testing (Helsel and Hirsch, 

1992, p. 323–337). The first step was to develop regression 

relations between precipitation and streamflow for the 

monthly streamflow components using all years in the record 

(about 80 data pairs for each month). The residuals from the 

regression analysis represent streamflow values that have had 

the variation caused by variation in precipitation removed. 

The second step was to test for monotonic trends in the 

residuals over time using a Kendall tau test; trends in these 

residuals can be attributed to factors other than precipitation.

A potential limitation or shortcoming of this method is 

that a drift or trend in precipitation over time could cause a 

bias in the relation between the regression residuals and time, 

and the test of the relation between regression residuals and 

time could lose some statistical power. Careful attention to the 

results of the regression analysis and the third and fourth steps 

in the method were used in this study to mitigate this possible 

shortcoming. All the regression equations were thoroughly 

evaluated to ensure the residuals had no bias or trend 

compared to the predicted streamflow values. The third step 

in the method, developed by Alley (1988), was to remove the 

effect of precipitation on time. The variation in time caused 

by trends in precipitation was removed using regression 

analysis between precipitation and time. The fourth step was 

to perform a Kendall tau test of monotonic trend using the 

precipitation-streamflow residual as the Y variable and the 

precipitation-time residual as the X variable. This fourth step 

has more statistical power than step two, and the relation 

between precipitation-streamflow residuals and precipitationtime residuals is free of the influence of precipitation (the 

degree of the removal of influence is related to the accuracy of 

the regression analyses in the first and third steps).

The relation between precipitation at Tombstone and 

streamflow of the San Pedro River is not linear for most 

monthly flows, so a locally weighted regression-smoothing 

technique was used to determine the fitted values and residuals 

for trend analysis. The technique called locally weighted 

scatterplot smoothing (LOWESS) was used (Cleveland, 

1979; Helsel and Hirsch, 1992). A multiple-variable form 

of LOWESS was used (Insightful, 2001) to provide enough 

flexibility to explain variation in streamflow. In LOWESS, a 

different weighted least-squares regression is used to compute 

each fitted value. The weights for each equation are a function 

of a user specified window width and the magnitude of the 

residual from the previous regression. The window width 

(called a span in the software used in this study; Insightful, 

2001) specifies the number of data points that are used to fit 

the equation. A larger span will, therefore, have a smoother 

fitted model than a smaller span. A span of 0.60 indicates that 

60 percent of the data are used to fit each equation.

For monthly total flow and low flow, the explanatory 

variables investigated in the LOWESS analyses were months 

of precipitation for the same month as streamflow and for 

different combinations of 9 previous months of precipitation. 

For storm runoff (a daily flow), the explanatory variables 

investigated were precipitation for the day of runoff and 

several combinations of precipitation for up to 60 days 

previous to the day of runoff (for example days 1–5, 

days 1–10, days 11–30, and days 31–60). LOWESS analysis 

and the same explanatory variables for precipitation also were 

used for the regression of precipitation versus time.

Step Trends

The second method used to determine trends in 

streamflow caused by factors other than precipitation was 

to split the streamflow record into three time periods (early, 

middle, and late), develop monthly regression relations 

between precipitation and streamflow for each time period, 

and determine if the regression relations for the three time 

periods were significantly different. A change in the regression 

equations (precipitation-streamflow relations) between the 

time periods indicates a step change in streamflow caused by 

factors other than precipitation.

This test of step trends in the precipitation-streamflow 

relation over time was done on monthly total streamflow 

(average flow) and on storm runoff (maximum daily mean 

flow for each month). Low flows were not tested because this 

method uses a single explanatory variable of precipitation to 

explain streamflow, and single-variable equations could not be 

developed to sufficiently explain low flows.

A simple test is available to determine if regression 

relations are significantly different. This test must be 

performed on linear regression relations developed by the 

least-squares technique. The relation between precipitation 

and streamflow is not linear for most monthly flows; 

however, the relation is only nonlinear on the margins of the 

data, and the relation can be made linear by removing some 

precipitation-streamflow data pairs at low and high values of 

precipitation. These outliers were removed for the analysis; 

the removal is justified because most of the data remain in the 

analysis, and most of the data that were removed were for low 

values of precipitation where there was no runoff or response 

of streamflow. Thus, it is a test of the precipitation-runoff 

relation for values of precipitation that have runoff, but it is not 

a test of the complete precipitation-streamflow relation. More 

information about the data that were removed is presented in 

the “Step Trends” section on pages 46–47 and in “Appendix 

2” of this report.

12  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
The statistical test used for determining differences in 

regression relations over time was a nested F test (Helsel and 

Hirsch, 1992, p. 315–319; Ott, 1993, p. 716–721). This is 

similar to an analysis of covariance in which regression and 

analysis of variance are combined into one test. A simple 

model (1) is developed between precipitation and streamflow, 

then a more complex model (2) is developed by adding 

in variables for time, and the most complex model (3) is 

developed by adding interaction terms between precipitation 

and time. Streamflow and precipitation are continuous 

variables and time is a discrete variable used to represent the 

three time periods.

The streamflow record was divided into three time 

periods so that about an equal number of years were in each 

time period. The optimum time periods were 1913–42, 

1943–76, and 1977–2002. Because of missing data (mostly 

missing precipitation values), the three time periods for 

a given month typically had an unequal number of years. 

A random procedure was used to remove data so that an equal 

number of data pairs were in each time period. This was done 

to eliminate any potential unequal weighting and unequal 

variance for time periods or bias in the results (Tabachnick and 

Fidell, 2001, p. 46–47).

The following equations were used to determine if 

there were significant differences in the regression equations 

developed for three time periods. The three regression 

equations can be combined into the following equations using 

two dummy or binary variables (T1 and T2):

Q = B0 + B1P + E, (1)

Q = B0 + B1P + B2T1 + B3T2 + E, (2)

Q = B0 + B1P + B2T1 + B3T2 + B4PT1 + B5PT2 + E, (3)

where

Q = streamflow,

P = precipitation,

T1 and T2 = dummy variables representing three time 

periods,

PT1 and PT2 = interaction terms between precipitation 

and time,

B0 = regression intercept,

B1-5 = regression coefficients, and

E = error term.

The first step is to determine if there is a significant 

difference in slopes of the regression equations for the three 

time periods. This is done by comparing models 2 and 3. The 

interaction terms in model 3 represent the regression slopes. 

The models are statistically compared using a nested 

F statistic:

F = (SSEs – SSEc)/(dfs – dfc), (4)

(SSEc/dfc)

The s subscript refers to the simpler model (fewer explanatory 

variables) and the c subscript refers to the more complex 

model (more explanatory variables). The SSE is the error sums 

of squares and df is the degrees of freedom.

If the F statistic is significant (p-value < 0.05) in 

comparing models 2 and 3, then model 3 is a significant 

improvement on model 2 and the regression slopes are 

significantly different. A second step is to determine if the 

regression intercepts are significantly different. A test of 

differences in regression intercepts is similar to an analysis of 

covariance. If the regression slopes are significantly different, 

then the test of intercepts cannot be performed because an 

assumption of the intercepts test is that the slopes are equal for 

all time periods. The test of regression intercepts is to compare 

models 1 and 2. This is the same nested F test as the test for 

slopes; the complex model is model 2 and the simple model is 

model 1.

Regional Trends

Regional trends in precipitation and streamflow were 

evaluated for about a 7,000-mi2 study area in southeastern 

Arizona and southwestern New Mexico (fig. 2). By most 

measures of precipitation and streamflow in the regional 

analysis, the San Pedro River Basin is similar to other basins 

in the southwest part of the study area and is generally not 

similar to basins in the rest of the study area. The southwest 

part of the study area includes the San Pedro River Basin, the 

Whitewater Draw Basin to the east, and the Santa Cruz River 

Basin to the west.

Trends in Precipitation

Seasonal and annual precipitation had no trends for most 

of the 11 analyzed time periods; 92 percent of the 1,760 trend 

tests performed on individual sites were not significant 

(table 3). The trends that were detected were related to time 

periods and seasons. Most significant trends in winter and 

spring precipitation were for time periods that started during 

the mid-century drought in 1945–60. Most significant trends 

in summer precipitation were for time periods that started 

during 1930–50. Significant trends in annual precipitation 

were more widespread across time periods and were found in 

time periods starting during 1930–65. Ninety percent of the 

147 significant trends in precipitation were positive. Summer 

precipitation had most of the significant negative trends; a few 

other negative trends were scattered in other seasons.

Precipitation trends in the southwest part of the study area 

were generally different from trends in the rest of the study 

area, and trends in the San Pedro River Basin were similar 

to trends at other sites in the southwest part of the study area 

(fig. 6 and table 3). The difference between the southwest part 

and the rest of the study area is most pronounced in annual 

precipitation. Ninety-five percent of the 97 trend tests on 

annual precipitation were not significant in the southwest part 

of the study area, and 28 percent of the 255 trend tests were 

significantly positive in the rest of the study area.

Regional Trends 13
Table 3. Regional trends in precipitation for 11 time periods, 1930-2002, southeastern Arizona and southwestern New Mexico

Season1

Part of 

study area2

Percentage of sites with significant trend (p-value < 0.05)

3

(p is positive trend and n is negative trend)

Starting year for trend test (data for tests end in 2002)

4

1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

Winter San Pedro River Basin5 0 0 0 0 0 0 0 0 0 0 0

southwest 0 0 0 0 11 p 8 p 0 0 0 0 0

northwest 0 0 0 11 p 0 0 0 0 0 0 9 n

northeast 0 0 0 13 p 22 p 11 p 0 0 0 0 0

southeast 0 0 0 17 p 33 p 17 p 0 0 0 0 0

Spring San Pedro River Basin5 0 0 0 50 p 0 0 75 p 0 0 0 0

southwest 0 0 0 33 p 0 8 p 50 p 0 0 0 0

northwest 0 0 0 0 0 9 p 18 p 0 0 0 0

northeast 0 0 0 0 0 11 p 0 0 0 0 0

southeast 0 0 0 0 17 p 17 p 33 p 0 0 0 0

Summer San Pedro River Basin5 100 n 100 n 50 n 50 n 50 n 25 n 0 0 0 25 p 0

southwest 25 n 25 n 20 n 17 n 22 n 8 n 0 0 0 9 p 0

northwest 0 40 p 25 p 11 p 0 0 9 p 0 0 0 0

northeast 80 p 80 p 50 p 50 p 22 p 11 p 22 p 0 0 0 0

southeast 20 p 40 p 0 0 0 0 0 0 0 0 0

Fall San Pedro River Basin5 0 0 0 0 0 0 0 0 0 0 0

southwest 0 0 0 0 11 p 0 8 p 0 0 0 0

northwest 0 0 0 0 0 0 9 n 0 0 0 0

northeast 0 0 0 0 0 0 0 0 0 11 n 0

southeast 0 0 0 0 0 0 0 0 0 0 0

Annual San Pedro River Basin5 0 0 0 0 0 0 0 0 0 0 0

southwest 0 0 0 33 p 0 0 0 0 0 0 27 n

northwest 40 p 40 p 50 p 78 p 55 p 27 p 18 p 9 p 0 0 9 n

northeast 60 p 60 p 67 p 100 p 78 p 33 p 11 p 22 p 0 0 0

southeast 0 20 p 17 p 67 p 50 p 33 p 17 p 17 p 0 0 0

Part of study area2

Number of sites with data for significance testing

Starting year for trend test (data for all tests end in 2002)

4

1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

San Pedro River Basin5 1 1 2 2 2 4 4 4 4 4 4

southwest 4 4 5 6 9 12 12 12 11 11 11

northwest 5 5 8 9 11 11 11 11 11 11 11

northeast 5 5 6 8 9 9 9 9 9 9 9

southeast 5 5 6 6 6 6 6 6 6 6 6

1

Winter is November-March, spring is April-June, summer is July-August, and fall is September-October.

2

See figure 2.

3

A Kendall tau trend test was made on seasonal and annual total precipitation.

4

Most sites have data through 2002. Three sites have data ending in 1997, and one site has data ending in 2001.

5

San Pedro River Basin is in the southwest part of the study area, and it includes precipitation sites 6, 9, 19, and 23 (table 1).

14  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Trends in Streamflow

The analysis of regional trends in streamflow was 

limited by the incomplete records and spatial distribution 

of streamflow data in the study area. Whereas 21 gaging 

stations had at least 25 years of data, only 6 stations 

had complete records that could be used for a rigorous 

analysis of regional trends during 1930–2002 (table 4). 

There were 10 gaging stations on 4 rivers (table 2), so 

6 of those stations could not be used because of spatial 

correlation. Another 9 stations were not used because the 

records had large blocks of time when the stations were 

discontinued. The streamflow data from the 15 gaging 

stations not used for the rigorous regional comparison 

were still evaluated, but with attention to their limitations 

(table 5).

Seasonal and annual streamflow had no trends for 

most of the 11 analyzed time periods; 79 percent of 

the 330 trend tests performed on individual sites were 

not significant (table 4). The time periods that did have 

significant streamflow trends were not as clustered about 

the mid-century drought as were the significant trends for 

precipitation. Sixty-six percent of the significant trends 

were for time periods that started before 1955. Most 

significant trends in winter, spring, fall, and annual flows 

were positive, and 95 percent of the significant trends in 

summer flows were negative.

Figure 6. Regional trends in precipitation, 1950–2002. A, Winter; B, Summer; C, Annual.

Northwest Northeast 

Southwest 

Southeast 

111o 110o 109o 108o 

34o 

33o 

32o 

111o 110o 109o 108o 

34o 

33o 

32o 

ARIZONA NEW MEXICO ARIZONA NEW MEXICO 

A. Winter B. Summer 

111o 110o 109o 108o 

34o 

33o 

32o 

C. Annual 

0 25 MILES 

0 25 KILOMETERS 

EXPLANATION 

SIGNIFICANT TREND—p–value 

less than 0.05:

NONE

POSITIVE

NEGATIVE

Figure 6. Regional trends in precipitation, 1950–2002. A, Winter; B, Summer; C, Annual. 

ARIZONA NEW MEXICO 

Northwest Northeast 

Southwest 

Southeast 

Northwest Northeast 

Southwest 

Southeast 

Regional Trends 15
Table 4. Trends in seasonal and annual total streamflow at 6 gaging stations for 11 time periods, 1930–2002, southeastern Arizona and 

southwestern New Mexico

[<, less than; nr, near; AZ, Arizona; NM, New Mexico; NA, data are not sufficient for significance testing (< 20 years)]

Season1 Gaging station name

Part of 

study area2

Significant trend in flow (p-value < 0.05)

3

(p is positive trend and n is negative trend)

Starting year for trend test (data for all tests end in 2002)

1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

Winter San Pedro River at Charleston, AZ southwest

Santa Cruz River nr Nogales, AZ

San Carlos River nr Peridot, AZ northwest n

Sabino Creek nr Tucson, AZ NA NA

Gila River nr Gila, NM northeast

San Francisco River nr Glenwood, NM p p p p

Spring San Pedro River at Charleston, AZ southwest n n n n n

Santa Cruz River nr Nogales, AZ

San Carlos River nr Peridot, AZ northwest p p p p p p p

Sabino Creek nr Tucson, AZ NA NA

Gila River nr Gila, NM northeast

San Francisco River nr Glenwood, NM p

Summer San Pedro River at Charleston, AZ southwest n n n n n n n n n

Santa Cruz River nr Nogales, AZ n n n n n n n n n

San Carlos River nr Peridot, AZ northwest

Sabino Creek nr Tucson, AZ NA NA

Gila River nr Gila, NM northeast p

San Francisco River nr Glenwood, NM

Fall San Pedro River at Charleston, AZ southwest n

Santa Cruz River nr Nogales, AZ

San Carlos River nr Peridot, AZ northwest p p n

Sabino Creek nr Tucson, AZ NA NA

Gila River nr Gila, NM northeast p p p

San Francisco River nr Glenwood, NM p p

Annual San Pedro River at Charleston, AZ southwest n n n n n n

Santa Cruz River nr Nogales, AZ

San Carlos River nr Peridot, AZ northwest p n

Sabino Creek nr Tucson, AZ p p p p NA NA

Gila River nr Gila, NM northeast p p p p p

San Francisco River nr Glenwood, NM p p p p p

1

Winter is November-March, spring is April-June, summer is July-August, and fall is September-October.

2

See figure 2.

3

A Kendall tau trend test was made on seasonal and annual average streamflow.

16  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 5. Trends in seasonal and annual total streamflow at 21 gaging stations for periods of record, southeastern Arizona and 

southwestern New Mexico

[<, less than; Slp, slope; nr, near; Riv, river; Cr, creek; >, greater than]

Part of 

study area1

Map 

no.1 Gaging-station name

Period of 

record

Kendall tau trend test2

Winter3 Spring3 Summer3 Fall3 Annual

Slp4 p-value Slp4 p-value Slp4 p-value Slp4 p-value Slp4 p-value

southwest 2 San Pedro Riv at Palominas 51931–2002 n 0.032 n 0.041 n 0.024 n 0.295 n 0.049

3 San Pedro Riv at Charleston 1913–2002 n .132 n .042 n <.001 n .011 n <.001

4 San Pedro Riv nr Redington 1944–1997 p .927 n .539 n <.001 n .870 n .018

6 Santa Cruz Riv nr Lochiel 1950–2002 p .004 p <.001 n .175 p .575 p .581

7 Santa Cruz Riv nr Nogales 1931–2002 n .792 n .601 n .005 p .959 p .980

8 Sonoita Cr nr Patagonia 1931–1972 p .322 p .152 n .470 n .699 p 1.000

9 Santa Cruz Riv at Tucson 51913–2002 p .742 p .014 n .035 p .538 n .202

14 Whitewater Draw nr Douglas 1931–1982 n <.001 n <.001 n .081 n .036 n .010

northwest 1 San Carlos Riv nr Peridot 1930–2002 p .571 p .012 n .070 p .112 p .571

5 Aravaipa Cr nr Mammoth 51932–2002 p .405 p .029 n .222 n .883 p .501

10 Sabino Cr nr Tucson 51933–2002 p .695 p .240 p .220 p .194 p .046

11 Pantano Wash nr Vail 51960–2002 n .314 p .953 n .228 n .073 n .260

12 Rincon Cr nr Tucson 51953–2002 p .662 p .361 n .307 p .354 p .892

13 Rillito Cr nr Tucson 1914–1975 n .501 n .107 n .013 n .544 n .058

northeast 15 Mimbres Riv nr Mimbres 1931–1976 n .373 n .272 n .872 p .883 n .857

16 Gila Riv nr Gila 1929–2002 p .236 n .889 p .487 p .197 p .152

17 Mogollon Cr nr Cliff 1968–2002 n .842 n .349 p .132 p .573 n 1.000

18 Gila Riv nr Redrock 1931–2002 p .479 p .879 p .479 p .520 p .308

19 San Francisco Riv nr Reserve 1960–2002 n .900 p .675 n .630 n .713 n .786

20 Tularosa Riv abv Aragon 1967–1996 p .205 p .284 p .112 p .034 p .090

21 San Francisco Riv nr Glenwood 1928–2002 p .127 p .437 n .044 p .705 p .179

1

See figure 2.

2

Trend test was made on seasonal and annual average streamflow.

3

Winter is November-March, spring is April-June, summer is July-August, and fall is September-October.

4

Slope of trend: n is negative and p is positive.

5

Gaging station has more than 10 years of missing data in a continuous block of time within period of record.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

p nearly significant positive trend 0.05–0.10

p significant positive trend < 0.05

Regional Trends 17
Geographic patterns in streamflow trends were similar to 

the geographic patterns in precipitation trends—streamflow 

trends of the San Pedro River Basin were generally similar to 

streamflow trends of other streams in the southwest part of 

the study area, and trends in the southwest part were different 

from trends in the rest of the study area (fig. 7 and tables 4 

and 5). The two rivers in the southwest part that had complete 

records—San Pedro River and Santa Cruz River—had 

consistently different trends from rivers in the rest of the study 

area. The San Pedro and Santa Cruz Rivers had consistent 

negative summer trends, and other streams had no summer 

trends. For annual flows, the San Pedro River had a negative 

trend, the Santa Cruz River had no trend, and the rest of the 

study area had no trends or positive trends. 

The patterns of the trends in streamflow at the six 

gaging stations with complete records were also found in 

the trends for the gaging stations that did not have complete 

and consistent records (table 5). Whitewater Draw is the next 

major watershed to the east of the San Pedro Basin. It had 

data only from 1931 to 1982, but it had similar streamflow 

trends as the San Pedro River. All seasons except summer 

had significant negative trends, and the p-value for summer 

trends was nearly significant at 0.081. Streamflow at other 

stations with incomplete records in the northwest and 

northeast parts of the study area had few significant trends, 

but most significant trends at the six stations with complete 

records were for time periods starting in 1930–50 and ending 

in 2002, and the records at these other stations did not cover 

that time period.

Northwest Northeast 

Southwest 

Southeast 

Northwest Northeast 

Southwest 

Southeast 

Northwest Northeast 

Southwest 

Southeast 

111o 110o 109o 108o 

34o 

33o 

32o 

111o 110o 109o 108o 

34o 

33o 

32o 

ARIZONA NEW MEXICO ARIZONA NEW MEXICO 

A. Winter B. Summer 

111o 110o 109o 108o 

34o 

33o 

32o 

C. Annual 

0 25 MILES 

0 25 KILOMETERS 

EXPLANATION 

SIGNIFICANT TREND—p–value 

less than 0.05:

NONE

POSITIVE

NEGATIVE

Figure 7. Regional trends in streamflow, 1950–2002. A, Winter; B, Summer; C, Annual. 

ARIZONA NEW MEXICO 

Figure 7. Regional trends in streamflow, 1950–2002. A, Winter; B, Summer; C, Annual.

18  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
The decreasing trends in summer flows for Whitewater 

Draw, the San Pedro River, and the Santa Cruz River could 

have similar causes. The three watersheds had similar 

historical changes: upland vegetation changed from primarily 

grasslands to mostly mesquite woodlands, riparian vegetation 

increased substantially, and ground-water pumping increased 

substantially (Turner and others, 2003; Robert H. Webb, 

U.S. Geological Survey, oral commun., 2004).

Temporal Patterns or Cycles in Precipitation 

and Streamflow

There are long-term temporal patterns or cycles in 

precipitation and streamflow in the study area. Understanding 

these cycles is important because (1) the cycles influence 

long-term changes in water supply, vegetation, and other 

watershed characteristics, (2) the cycles tend to repeat and 

their magnitude and duration can be used for land- and watermanagement decisions, and (3) trend analyses are strongly 

affected by the cycles.

Long-term patterns or cycles in precipitation from 

1930 to 2002 are shown in graphs of regional normalized 

precipitation for the study area (fig. 8). Regional normalized 

values are an average of the long-term data in the region. 

Winter and spring precipitation had much more pronounced 

cycles than did summer or fall precipitation. Winter and 

spring precipitation were generally high in the 1930s, low in 

the 1950s and 1960s, high in the 1980s, and low in the late 

1990s and early 2000s. The seasons had different interannual 

variability; spring and fall precipitation had the most 

variability, winter had moderate variability, and summer had 

small variability.

The normalized precipitation trends for the southwest 

part of the study area generally followed the same patterns as 

the normalized trends for the rest of the study area. The only 

notable difference was in summer precipitation from 1930 

to 2002; summer precipitation appeared to decrease slightly 

in the southwest part and increase slightly in the rest of the 

study area.

Long-term cycles in streamflow from 1930 to 2002 

are shown using normalized values for the San Pedro 

River at Charleston and regional normalized values for the 

northwest and northeast parts of the study area (fig. 9). 

Regional normalized streamflow for winter, spring, and fall 

in the northwest and northeast parts of the study area had 

long-term patterns similar to those in the precipitation data. 

A big difference between precipitation and streamflow in 

those areas was in the summer: summer precipitation had no 

apparent cycles and small interannual variability, and summer 

streamflow had large cycles and large interannual variability.

In contrast to the pronounced streamflow cycles in the 

northwest and northeast parts of the study area, streamflow 

in the San Pedro River mostly just decreased steadily. 

Precipitation in all parts of the study area had long-term 

cycles, and the influence of those precipitation cycles appears 

in streamflow in the northeast and northwest parts of the study 

area but not in streamflow of the San Pedro River. This lack 

of response to precipitation cycles is one indication that other 

factors besides precipitation could be affecting streamflow of 

the San Pedro River.

Effects of the recent drought (about the past 5 years) 

appear as decreasing trends in many of the plots of normalized 

precipitation and streamflow for all parts of the study area 

(figs. 8 and 9). There are downturns from 1990 to 2002 in 

precipitation and streamflow for both winter and spring. 

Effects of the drought do not appear in summer precipitation 

in any part of the study area, and other seasonal precipitation 

and streamflow show mixed effects.

Regional Trends 19
Figure 8. Trends in regional normalized seasonal precipitation, southeastern Arizona and southwestern New Mexico. Blue line is 

LOWESS fit to data. 1930 1935 1940 1945

195019551960196519701975198019851990199520002005

Figure 8. Trends in regional nomalized seasonal precipitation, southeastern Arizona and southwestern New Mexico. Blue line is LOWESS

fit to data.

NORMALIZED PRECIPITATION FOR SOUTHWEST

PART OF STUDY AREA (4 SITES)

1

0

2

3

4

WINTER

1

0

2

3

4

SUMMER

1

0

2

3

4

FALL

1

0

2

3

4

SPRING

REGIONAL NORMALIZED PRECIPITATION

1930193519401945195019551960196519701975198019851990199520002005

NORMALIZED PRECIPITATION FOR NORTHWEST, NORTHEAST,

AND SOUTHEAST PARTS OF STUDY AREA (11 SITES)

1

0

2

3

4

WINTER

1

0

2

3

4

SUMMER

1

0

2

3

4

FALL

1

0

2

3

4

SPRING

REGIONAL NORMALIZED PRECIPITATION

20 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
1930

193519401945195019551960196519701975198019851990199520002005

NORMALIZED STREAMFLOW FOR

SAN PEDRO RIVER AT CHARLESTON

1

0

2

3

4

WINTER

1

0

2

3

4

SUMMER

1

0

2

3

4

FALL

1

0

2

3

4

SPRING

NORMALIZED STREAMFLOW

1930193519401945195019551960196519701975198019851990199520002005

REGIONAL NORMALIZED STREAMFLOW FOR NORTHWEST

AND NORTHEAST PARTS OF STUDY AREA (3 SITES)

1

0

2

3

4

WINTER

1

0

2

3

4

SUMMER

1

0

2

3

4

FALL

1

0

2

3

4

SPRING

REGIONAL NORMALIZED STREAMFLOW

Figure 9. Trends in nomalized seasonal streamflow for San Pedro River at Charleston, Arizona and regional normalized seasonal streamflow

for the northwest and northeast parts of study area, southeastern Arizona and southwestern New Mexico. Blue line is LOWESS fit to data.

Figure 9. Trends in normalized seasonal streamflow for the San Pedro River at Charleston, Arizona, and regional normalized 

streamflow for the northwest and northeast parts of the study area, southeastern Arizona and southwestern New Mexico. Blue line is 

LOWESS fit to data.

Regional Trends  21
Trends in the San Pedro River Basin

Trends in the San Pedro River Basin were analyzed in 

three steps. First, the general significance and characteristics 

of trends in precipitation and streamflow were analyzed. 

Second, trends in streamflow caused by factors other than 

precipitation were analyzed. Finally, all the results were used 

for an evaluation of the causes of trends in streamflow.

Hydrologic Water Budgets and Relation to 

Streamflow Trends

Before results of the study of the San Pedro River 

Basin are presented, it is useful to describe hydrologic water 

budgets for the entire watershed, the ground-water system, 

and the streamflow of the San Pedro River. These budgets 

describe the relation between the sources of water (inflow) and 

the components of outflow. They can be used to evaluate how 

changes in one component can affect other components of a 

budget, or how a change in a component can affect streamflow 

trends.

The source of all water in the watershed is precipitation 

(table 6). Water moves through the watershed as runoff, 

ground-water flow and discharge, and evapotranspiration. 

The water can also go into storage or be removed from 

storage. Water can be stored for short periods of time (1) as 

interception by vegetation where it rapidly evaporates, or 

(2) on land surface where it either evaporates or infiltrates the 

soil. Water can also be stored for longer periods in soils or 

as ground water. In most watersheds, change in storage over 

long periods is minimal and only the three major processes 

are active—runoff, ground-water flow and discharge, and 

evapotranspiration.

Components of the predevelopment watershed budget 

(table 6) were estimated using information from previous 

studies and data from this study. The predevelopment period is 

prior to 1940; it is assumed that before 1940, human activities 

had a minimal effect on the watershed budget and long-term 

inflow equaled long-term outflow. Precipitation was estimated 

using an average value of 16.5 in. for the entire watershed 

(table 2), runoff was estimated using measured flow data 

from 1913 to 1940 for the San Pedro River at Charleston, 

ground-water recharge and discharge were estimated 

using estimates of base flow from this study and estimates 

of other components from Corell and others (1996), and 

evapotranspiration for the watershed was the residual. Notable 

items of the budget are that watershed evapotranspiration 

is more than 90 percent of precipitation and ground-water 

discharge is less than 2 percent of precipitation.

The effects of human activities or changes in watershed 

characteristics can be evaluated using the watershed budget 

(table 6). If precipitation stays constant over time and there 

is no change in storage in the watershed, any increase in 

an outflow component must be balanced by a decrease in 

another outflow component. For example, an increase in 

evapotranspiration must be balanced by a decrease in runoff or 

ground-water discharge.

Table 6. Predevelopment water budget for the watershed of 

the San Pedro River at Charleston, Arizona

Components of 

watershed budget

Pre-development 

water budget 

(acre-feet per year)

Percent 

of water 

budget

Inflow

Precipitation 1,100,000 100

Outflow

1) Runoff 49,800 4.5

2) Ground-water flow and 

discharge

14,000 1.5

3) Evapotranspiration 

from all sources except 

directly from ground 

water1

1,036,000 94.0

Change in storage

4) Interception and surface 

storage

0 0

5) Soil moisture 0 0

6) Ground water 0 0

1

Evapotranspiration can come from (1) intercepted precipitation, 

(2) surface water, (3) soil moisture, (4) upland vegetation, and (5) flood 

plain and riparian vegetation.

The ground-water budget for the San Pedro River 

watershed describes the recharge (inflow) and discharge 

(outflow) for the ground-water system (table 7). Most recharge 

occurs near the mountain fronts by infiltration in mountains 

and subsurface inflow and percolation of runoff in stream 

channels that originate in the mountains. Runoff amounts from 

mountainous areas typically are large because of the large 

amount of precipitation (more than 25 in./yr), the steep terrain, 

and the low infiltration rates. About 10–20 percent of the total 

recharge probably is from infiltration of runoff in ephemeralstream channels throughout the watershed. Another small 

percentage of the recharge, probably less than a few percent, 

is from direct infiltration of precipitation on upland areas 

and the valley floor of the watershed (Coes and Pool, 2005). 

Ground water discharges (1) to the San Pedro River as base 

flow, (2) as evapotranspiration from the shallow water table in 

the San Pedro River flood plain, (3) as underflow north of the 

watershed, or (4) by pumping from wells.

Predevelopment ground-water discharge was estimated 

using streamflow data from this study and information 

from previous studies (table 7). Base flow was estimated 

using monthly 3-day low flows for 1931–45. The median 

3-day low flow was computed for each month (in acre-ft) 

and the monthly values were summed for the annual total. 

22  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 7. Predevelopment water budget for groundwater system in the watershed of the San Pedro River at 

Charleston, Arizona

Components of 

ground-water budget

Pre-development 

water budget 

(acre-feet per year)

Percent 

of water 

budget

Recharge (inflow)1 14,000 100

1) Mountain-front inflow (

2

) (2)

2) Seepage of runoff in 

ephemeral stream channels

(

2

) (

2

)

3) Infiltration and percolation 

of precipitation directly into 

ground-water system

(

2

) (2)

Discharge (outflow)

1) Base flow of San Pedro 

River3

7,900 56

2) Evapotranspiration4 5,700 41

3) Underflow north of 

watershed5

400 3

4) Pumping from wells 

(withdrawals)

0 0

Change in storage 0 0

1

Recharge is sum of discharge components 1–3.

2

Proportion of recharge from three sources is unknown.

3

Estimated using monthly low-flow data from this study.

4

From shallow water table in flood plain of San Pedro River. Estimated 

by Corell and others (1996; fig. 7 and table 4).

5

Estimated by Freethey (1982) and Corell and others (1996).

If recharge is assumed to be constant, any increase 

in an outflow component must be balanced by a decrease 

in storage or another outflow component (table 7). For 

example, an increase in ground-water pumping must be 

balanced by a decrease in ground-water storage, base flow, 

or evapotranspiration. Underflow north of the watershed also 

could decrease but its relative magnitude is small (3 percent of 

the budget) and it could not balance any appreciable pumping.

The budget for seasonal streamflow of the San Pedro 

River shows the components of inflow (gains) and components 

of outflow (losses) at a given point along the river (Charleston; 

table 8). Inflow is from runoff of precipitation, ground-water 

discharge, and flow from bank storage or short-term storage in 

the alluvial aquifer. Outflow from the stream is by flow to the 

alluvial aquifer (long-term), flow to bank storage or short-term 

storage in the alluvial aquifer, direct evapotranspiration from 

the water surface, or transpiration from riparian vegetation 

adjacent to the stream channel. The streamflow at Charleston 

is the net addition and subtraction of all these components 

acting on streamflow upstream from Charleston.

It is clear that a decrease in a source of inflow to the 

river, such as runoff or ground-water discharge, would cause 

a decrease in streamflow. An increase in a component of 

outflow, however, could also cause a decrease in streamflow.

Several of the years of August 3-day low flow contained 

runoff or flow from bank storage, so the median August 

3-day low flow was not representative of base flow. The 

median August low flow was, therefore, estimated as the 

average of the July and September median low-flow values. 

Evapotranspiration was estimated by Corell and others 

(1996), and underflow north of the watershed was estimated 

by Freethey (1982) and Corell and others (1996). Recharge 

was estimated as the sum of the three discharge components, 

under the assumption that the system was in equilibrium. 

This estimated ground-water budget (14,000 acre-ft/yr) is 

smaller than previous estimates that ranged from 16,000 to 

19,000 acre-ft/yr (Freethey, 1982; Vionnett and Maddock, 

1992; and Corell and others, 1996). One reason why this 

budget is smaller is that the previous studies were for the 

Sierra Vista subwatershed and the San Pedro Basin in Mexico 

(fig. 3), which is larger than the Charleston watershed. 

Table 8. Water budget for seasonal streamflow of the 

San Pedro River at Charleston, Arizona

Components of inflow and outflow

Inflow to stream (gains)

1) Runoff of precipitation

A) Overland flow and tributary streamflow from 

upland areas

B) Shallow subsurface stormflow from upland areas

C) Overland flow from saturated soils in San Pedro River 

flood plain

2) Ground-water discharge

A) Regional aquifer

B) Local alluvial aquifer (long-term sustained discharge)

3) Flow from bank storage or short-term storage in alluvial

 aquifer

Outflow from stream (losses)

1) Flow to alluvial aquifer (long-term sustained flow)

2) Direct evaporation from water surface

3) Transpiration from riparian vegetation adjacent to the 

stream channel

4) Flow to bank storage or short-term storage in alluvial aquifer

Trends in the San Pedro River Basin  23
Trends in Precipitation and Streamflow

Monotonic trends for the following characteristics 

of monthly and seasonal precipitation at Tombstone were 

evaluated: total volume, intensity, frequency, and volume per 

storm. Most characteristics of precipitation and most months 

and seasons had no significant trends for 1913-2002 (fig. 10 

and table 9). Precipitation in July and summer were the only 

month and (or) season with a significant decreasing trend. 

The monotonic trends shown in table 9 are for the entire 

record of precipitation at Tombstone. To determine if some 

shorter periods of time within 1913–2002 had significant 

trends in total precipitation, trend tests were made on early and 

late subsets of that record with breakpoints at 1950, 1960, and 

1970 (table 10). Only a few of the monthly or seasonal values 

of precipitation had significant trends. November precipitation 

had significant decreasing trends for 1913–50 and 1913–60, 

summer precipitation had a significant decreasing trend for 

1951–2002, and annual precipitation had a nearly significant 

(p-value = 0.061) decreasing trend for 1913–70. The time 

periods of no trends and decreasing trends for summer and 

annual precipitation can be seen in figure 10. 

Changes in seasonal total streamflow and low flow for 

the San Pedro River at Charleston were calculated from the 

predevelopment period (prior to 1940) to 1991–2002. Annual 

total flow decreased by 62 percent from 57,700 acre-ft/yr in 

the predevelopment period to 22,000 acre-ft/yr in 1991–2002 

(table 11). Changes in summer flows dominated the changes 

in annual flows; 70 percent of the decrease in annual flow was 

from the decrease in summer flow. Annual low flow decreased 

by 46 percent from 7,900 acre-ft/yr to 4,300 acre-ft/yr 

(table 11). This low flow is roughly analogous to base flow, 

which has been evaluated and discussed in many previous 

studies (Corell and others, 1996; Pool and Coes, 1999; and 

Rojo and others, 1999). About 60 percent of the decrease 

in annual low flow was during the fall and early winter 

(September–January).

Trends in seasonal total streamflow for several time 

periods were determined for the San Pedro River at Palominas, 

Charleston, and Redington (fig. 2 and table 12). Differences 

or similarities in trends at the three different sites on the 

river can potentially provide some insight on the causes of 

streamflow trends. The drainage areas for the three sites 

are 737 mi2 at Palominas, 1,234 mi2 at Charleston, and 

2,927 mi2 at Redington. The vegetation, land-surface relief, 

and elevations of the three watersheds are similar; however, 

human activities are different. Ground-water pumping in 

the Palominas watershed has been primarily for a mine in 

Mexico, and a small amount has been for agriculture and 

domestic uses. In the watershed between Palominas and 

Charleston, water is pumped for public supply, domestic 

use, and agriculture. In the watershed between Charleston 

and Redington, water is pumped for a military base 

(Fort Huachuca) and for agriculture.

Figure 10. Trends in annual and seasonal precipitation at 

Tombstone, Arizona. Blue line is LOWESS fit to data. 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985

1990199520002005

Figure 10. Trends in annual and seasonal precipitation at Tombstone,

Arizona. Blue line is LOWESS fit to data.

FALL PRECIPITATION–Trend test p-value=0.838

0

SUMMER PRECIPITATION–Trend test p-value=0.011

WINTER PRECIPITATION–Trend test p-value=0.781

5

30

0

10

15

20

25

5

30

0

10

15

20

25

5

30

10

15

20

25

0

5

30

10

15

20

25

ANNUAL PRECIPITATION–Trend test p-value=0.133

PRECIPITATION, IN INCHES

24  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 9. Trends in monthly, seasonal, and annual precipitation at Tombstone, Arizona, 1913–2002

[>, greater than; <, less than]

Month or 

season1

Kendall tau trend test for 1913–2002

Total precipitation

Maximum daily 

precipitation

Number of days 

with precipitation

Total precipitation 

divided by number of days 

with precipitation

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

January 81 n 0.915 81 n 0.530 81 p 0.902 81 n 0.565

February 81 n .886 81 p .803 81 n .130 81 p .508

March 85 p .240 85 p .316 85 p .455 85 p .131

April 84 n .476 84 n .595 84 n .528 84 n .743

May 85 p .541 85 p .592 85 p .414 85 p .459

June 85 p .845 85 p .414 85 n .459 85 p .380

July 84 n .036 84 n .002 84 n .262 84 n .027

August 83 n .509 83 n .312 83 n .984 83 n .140

September 85 n .936 85 n .949 85 n .825 85 p .823

October 85 p .533 85 p .894 85 p .067 85 n .988

November 82 p .965 82 p .665 82 n .954 82 p .432

December 81 n .997 81 n .710 81 p .802 81 n .756

Winter 76 n .781 76 n .339 75 n .687 75 p .725

Spring 84 p .611 84 p .309 84 n .499 81 p .184

Summer 82 n .011 82 n .105 82 n .465 82 n .016

Fall 85 p .838 85 p .921 85 p .276 85 n .841

Annual 72 n .133 72 n .149 72 n .661 68 n .560

1

Winter is November–March, spring is April–June, summer is July–August, and fall is September–October.

2

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n significant negative trend < 0.05

p nearly significant positive trend 0.05–0.10

Trends in the San Pedro River Basin  25
Table 10. Trends in monthly, seasonal, and annual total precipitation at Tombstone, Arizona, for selected time periods

[Slp, slope; >, greater than; <, less than]

Month or 

season1

Kendall tau trend test on monthly and seasonal total precipitation

Breakpoint at 1950 Breakpoint at 1960 Breakpoint at 1970

1913–1950 1951–2002 1913–1960 1961–2002 1913–1970 1971–2002

n2 Slp3 p-value n2 Slp3 p-value n2 Slp3 p-value n2 Slp3 p-value n2 Slp3 p-value n2 Slp3 p-value

January 31 n 0.919 40 n 0.428 37 p 0.360 34 0.0 1.000 44 n 0.678 27 n 0.428

February 31 n .696 40 p .186 37 n .619 34 p .131 44 n .199 27 p .388

March 31 n .221 40 p .629 37 n .783 34 p .583 44 n .855 27 0.0 1.000

April 31 n .140 40 p .076 37 n .060 34 p .145 44 n .074 27 p .154

May 31 n .033 40 p .749 37 n .301 34 p .432 44 n .229 27 n .448

June 31 n .754 40 n .691 37 p .801 34 p .464 44 n .775 27 n .966

July 31 n .696 40 n .217 37 n .556 34 n .134 44 n .413 27 n .150

August 31 p .696 40 n .477 37 p .513 34 p .906 44 p .401 27 p .478

September 31 p .786 40 p .537 37 n .374 34 n .533 44 p .879 27 p .632

October 31 n .276 40 n .834 37 n .675 34 n .789 44 n .331 27 n .133

November 31 n .037 40 p .408 37 n .027 34 n .678 44 n .103 27 n .532

December 31 n .959 40 p .118 37 n .186 34 p .414 44 n .321 27 p .370

Winter 29 n .119 38 p .359 35 n .334 32 p .417 42 n .278 25 p .640

Spring 30 n .532 40 p .454 36 n .902 34 p .106 43 n .229 27 p .602

Summer 30 p .775 40 n .017 36 p .595 34 n .146 43 n .683 27 n .381

Fall 30 n .402 40 n .825 36 n .231 34 n .131 43 n .464 27 n .156

Annual 30 n .101 40 n .718 36 n .282 34 0.0 1.000 43 n .061 27 n .478

1

Winter is November–March, spring is April–June, summer is July–August, and fall is September–October.

2

Number of years analyzed.

3

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

p nearly significant positive trend 0.05–0.10

26  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 11. Changes in seasonal and annual total streamflow and low flow from the predevelopment period to 1991–2002, 

San Pedro River at Charleston, Arizona

Flow1 Season2

Streamflow for time period3

(acre-feet per year) Change in streamflow Percent 

of annual 

Predevelopment change 4 1991–2002

Total 

(acre-feet per year) Percent

Total flow Late winter 3,100 3,100 0 0 0

Spring 2,500 1,300 -1,200 -48 3

Summer 31,400 6,300 -25,100 -80 70

Fall 11,800 4,800 -7,000 -59 20

Early winter 8,900 6,500 -2,400 -27 7

Annual 57,700 22,000 -35,700 -62 100

(cubic-feet per second) (79.7) (30.4) (-49.3)

Low flow Late winter 1,600 1,400 -200 -13 5

Spring 1,200 700 -500 -42 14

Summer 900 300 -600 -67 17

Fall 1,500 400 -1,100 -73 31

Early winter 2,700 1,500 -1,200 -44 33

Annual 7,900 4,300 -3,600 -46 100

(cubic-feet per second) (10.9) (5.9) (-5.0)

1

Total flow is calculated from monthly average flows and low flow is calculated from monthly 3-day low flows.

2

Late winter is February-March, spring is April-June, summer is July-August, fall is September-October, and early winter is November-January.

3

Seasonal total streamflow is the seasonal average streamflow for the time period. Seasonal low flow was calculated differently so it can be a surrogate 

for base flow of the stream. First the median low flow was computed for each month for the time period. Then the seasonal low flow was computed as the 

average of the median monthly low flows in each season.

4

Predevelopment period; total flow was 1913-40 and low flow was 1931-45.

Trends in the San Pedro River Basin  27
Seasonal trends in total streamflow at the three sites 

were similar (table 12). Summer flows at Charleston and 

Redington significantly or nearly significantly decreased for 

all time periods, and summer flows at Palominas significantly 

or nearly significantly decreased from 1931 and 1951 to 2002. 

The nonsignificant trends in summer flows at Palominas from 

1961 and 1971 to 2002 may be related to the large gap in the 

flow record from 1982 to 1995. Trends in winter flows at the 

three sites were similar in that there were no significant trends 

at all three sites from 1951, 1961, and 1971 to 2002. Spring 

and fall flows had mixed trends, but generally were similar at 

the three sites. These results indicate that the same factor or 

factors likely were influential in the streamflow trends at all 

three sites. 

Step trends or shifts in seasonal values of total and 

maximum precipitation and streamflow were evaluated for 

six time periods during 1913–2002. The advantage of this 

approach was that trends in both the central tendency and the 

variability could be evaluated and short-term trends within 

1913-2002 could be evaluated. The central tendency was 

represented by the median, and the variability was represented 

by the IQR.

Median values of precipitation had no large step trends 

(fig. 11). The variability of precipitation had some larger 

step changes over time. The interannual variability of winter 

total precipitation appears to have increased after about 1976. 

The interannual variability of maximum daily precipitation 

changed appreciably over time for all three seasons; winter 

variability had a step change to higher values after 1976, 

summer variability changed frequently with the highest value 

in 1943–60, and fall variability had a general decreasing trend 

over time. 

Table 12. Trends in seasonal total streamflow of the San Pedro River at Palominas, Charleston, and Redington, Arizona, for selected 

time periods

[<, less than; ---, no data]

Site

Time period 

tested

Kendall tau trend test on seasonal total streamflow

Winter1 Spring1 Summer1 Fall1

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

No. of 

years Slope2 p-value

Palominas 1931–02 46 n 0.032 46 n 0.041 46 n .024 45 n 0.295

1951–02 38 n .801 38 p .841 38 n .056 37 p 0.353

1961–02 28 n .859 28 p .030 28 n .374 27 0.0 1.000

1971–02 18 0.0 1.000 18 n .940 18 n .880 17 n .592

Charleston 1931–02 70 n .087 70 n .001 70 n <.001 70 n .019

1951–02 52 p .642 52 n .172 52 n <.001 52 n .856

1961–02 42 n .812 42 n .854 42 n .013 42 n .233

1971–02 32 n .323 32 n .016 32 n .089 32 n .158

Redington 1931–97 --- --- --- --- --- --- --- --- --- --- --- ---

1951–97 47 n .963 47 n .523 47 n <.001 46 n .977

1961–97 37 n .513 37 n .207 37 n <.001 36 n .072

1971–97 27 n .983 27 n .270 27 n <.001 26 n .061

1

Winter is November-March, spring is April-June, summer is July-August, and fall is September-October.

2

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

p significant positive trend < 0.05

28  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Interannual IQR of total streamflow

350

300

250

200

150

100

0

1913–27 1928–42 1943–60 1961–76 1977–89 1990–2002

50

Interannual IQR of total precipitation

350

300

250

200

150

100

0

50

PERCENTAGE OF INTERQUARTILE RANGE (IQR) FOR ENTIRE RECORD

Median of total streamflow for years in time period

350

300

250

200

150

100

0

1913–27 1928–42 1943–60 1961–76 1977–89 1990–2002

50

Median of total precipitation for years in time period

350

300

250

200

150

100

0

50

PERCENTAGE OF MEDIAN FOR ENTIRE RECORD

Interannual IQR of maximum daily mean streamflow

350

300

250

200

150

100

0

1913–27 1928–42 1943–60 1961–76 1977–89 1990–2002

50

Interannual IQR of maximum daily precipitation

350

300

250

200

150

100

0

50

PERCENTAGE OF INTERQUARTILE RANGE (IQR) FOR ENTIRE RECORD

Median of maximum daily mean

streamflow for years in time period

350

300

250

200

150

100

0

1913–27 1928–42 1943–60 1961–76 1977–89 1990–2002

50

Median of maximum daily precipitation

for years in time period

350

300

250

200

150

100

0

50

PERCENTAGE OF MEDIAN FOR ENTIRE RECORD

EXPLANATION

Winter Summer Fall

Figure 11. Step trends in central tendency and variability of precipitation at Tombstone, Arizona, and streamflow of the San Pedro 

River at Charleston, Arizona. IQR is the interquartile range; 75th percentile minus the 25th percentile,

Trends in the San Pedro River Basin  29
Streamflow had larger changes over time in median 

values and variability than did precipitation (fig. 11). For 

median total and maximum streamflows, there is a step change 

at about 1943; before 1943 all seasonal flows were high, and 

after 1942 all seasonal flows were generally low. The behavior 

of the median seasonal flows after 1942 is different; summer 

median flows decreased continuously, and fall and winter 

median flows were mostly steady except for higher values 

during 1977–89. 

The interannual variability of seasonal streamflows 

also had patterns. The variability of winter maximum flow 

had two distinct step changes; the variability was high 

during 1913–42, low during 1943–76, and high again during 

1977–2002. Variability of summer total flow decreased 

monotonically during the entire record, and variability of 

summer maximum flow had a step change from high to low 

values at 1960. Variability of fall total and maximum flow was 

generally similar for the entire record except for a high period 

during 1977–89.

Trends in Streamflow Caused by Factors Other 

than Precipitation

Two methods were used to evaluate trends in streamflow 

caused by factors other than precipitation. Both methods used 

regression analysis to remove or account for the variation 

in streamflow caused by variation in precipitation. Once 

the variation was removed or accounted for, the remaining 

variation in streamflow was tested for trends over time. One 

method tested for monotonic trends and the other method 

tested for step trends.

The two methods were applied to monthly values of 

total flow, low flow, and storm runoff. Total flow (average 

flow) provides information about the total quantity of flow in 

the river each month. Low flow (3-day low flow) is a rough 

approximation of base flow—the flow sustained by groundwater discharge. Storm runoff (maximum daily mean flow) is 

the quick response of the watershed to rainfall. Preliminary 

analyses of the monthly flow data showed that low flow 

is about 80 percent of total flow in the winter and about 

10 percent of total flow in the summer (table 13). Summer 

total flow is, therefore, mostly runoff of precipitation. The 

storm runoff analyzed in this study was the maximum daily 

mean flow for the month; this flow component represents a 

1-day response to rainfall. Storm runoff (in ft3/s) was about 

five times greater than monthly total flow (in ft3/s) in the 

winter and eight times greater than monthly total flow in the 

other seasons (table 13).

Monotonic Trends

LOWESS multiple-variable regression analyses 

and Kendall tau statistical tests were used to determine 

monotonic trends in monthly streamflow caused by factors 

other than precipitation. Before the LOWESS analyses were 

performed, all variables (precipitation and streamflow) were 

log transformed to improve the accuracy of the LOWESS 

equations and to decrease the heteroscedasticity of the data 

(variance of streamflow increases as values of precipitation 

increase). The analyses were performed on total flow (average 

flow), low flow (3-day low flow), and storm runoff (maximum 

daily mean flow).

Table 13. Seasonal relations between low flow, total flow, and maximum daily storm runoff, San Pedro River at Charleston, Arizona, 

1931–2002

[---, no data]

Season1

Percentage of total streamflow2

Ratio of maximum daily storm 

runoff to total monthly flow5 Low flow3 Runoff + flow from bank storage4

Winter 82 18 4.8

Early spring 72 28 ---

Late spring 55 45 9.7

Summer 8 92 7.7

Early fall 22 78 7.0

Late fall 67 33 6.7

1

Season: winter is November-March, early spring is April-May, late spring is June, summer is July-August, early fall is September, and late fall is October.

2

The ratio of monthly low flow, in cubic feet per second, to total flow, in cubic feet per second, was computed for each month during 1931-2002. The 

median value of the ratios was then computed for each month. The seasonal percentage is the average of the median ratios for each month in the season.

3

Low flow is the 3-day low flow.

4

Runoff + flow from bank storage is the difference between total flow and low flow.

5

The ratio of maximum daily mean flow, in cubic feet per second, to average flow, in cubic feet per second, was computed for each month during 1931-

2002. The median value of the ratios was then computed for each month. The seasonal ratio is the average of the median ratios for each month in the season.

30 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
The final LOWESS equations had several combinations 

of monthly precipitation for the explanatory variables. The 

final equations were selected on the basis of whether they were 

physically reasonable and various measures of statistical fit 

including highest R 2 value; lowest standard error of estimate; 

lack of any extreme outliers; and best overall distribution of 

residuals compared to a normal distribution, fitted values, and 

explanatory variables.

A simple illustration of a multiple-variable LOWESS 

fit to a streamflow-precipitation relation is not possible, 

therefore, some examples are shown to illustrate how singlevariable LOWESS equations fit the nonlinear relation between 

monthly precipitation and total streamflow (fig. 12). LOWESS 

analysis is especially needed for the February, September, and 

November flows, and it also is a better fit than a least-squares 

linear fit to the July flows.

The R 2 values for the multiple-variable LOWESS 

regression equations for monthly total streamflow ranged from 

0.50 to 0.81 (table 14). Thus, precipitation explained between 

50 and 81 percent of the variation in monthly streamflows. 

The number of months of precipitation in the equations 

ranged from three to four, and the equations generally 

used precipitation for the same month as streamflow and 

precipitation for months immediately prior to the streamflow 

(table 15). During June–January, precipitation for the same 

month as streamflow was the best single month for explaining 

total streamflow. During February–May, the best single month 

of precipitation varied from 1 to 4 months prior to streamflow.

Precipitation for the same month as streamflow is a 

measure of the amount of direct runoff that contributes to 

streamflow. Precipitation during months prior to a monthly 

streamflow affects the streamflow in two ways: (1) it builds up 

storage in watershed soils that results in decreased infiltration 

of precipitation and increased runoff, and (2) it increases 

runoff and streamflow in preceding months that results in 

increased bank storage and storage in the alluvial aquifer. This 

increased storage increases flow by decreasing the loss of the 

current flow into storage or by releasing water from storage 

and contributing to the current flow.

FEBRUARY

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

PRECIPITATION FOR MONTH, IN INCHES

1.0 10.0 20.0

1,000

1

0 0.1

JULY

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

PRECIPITATION FOR MONTH, IN INCHES

1.0 10.0 20.0

1,000

1

0 0.1

SEPTEMBER

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

PRECIPITATION FOR MONTH, IN INCHES

1.0 10.0 20.0

1,000

1

0 0.1

NOVEMBER

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

PRECIPITATION FOR MONTH, IN INCHES

1.0 10.0 20.0

1,000

1

0 0.1

Figure 12. LOWESS fits between precipitation at Tombstone, Arizona, and selected monthly total streamflows of the San Pedro River 

at Charleston, Arizona. Blue line is LOWESS fit to data.

Trends in the San Pedro River Basin  31
Table 14. Results of LOWESS regression analyses between monthly precipitation at Tombstone, Arizona, and monthly total 

streamflow for the San Pedro River at Charleston, Arizona; and between precipitation at Tombstone and time, 1913–2002

[R 2, coefficient of multiple determination]

Month

Number 

of years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Total streamflow

(cubic feet per second)

Time

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span3 R2

Standard error 

(years) Span3

January 72 Oct., Nov., Dec., and Jan. 0.81 0.260 0.75 0.51 28.14 0.75

February 72 Dec., Jan., and Feb. .80 .182 .60 .29 28.70 .75

March 76 Jan., Feb., and Mar. .66 .187 .75 .51 26.69 .50

April 76 Jan., Feb., and Mar. .50 .178 .75 .51 26.69 .50

May 76 Jan., Feb., and Mar. .52 .182 .75 .51 26.69 .50

June 73 Dec., Jan., Mar., and June .73 .346 .75 .69 30.01 .50

July 76 Jan., May, June, and July .70 .433 .75 .64 27.00 .60

August 74 Feb., July, and Aug. .64 .349 .75 .39 27.35 .60

September 79 May, Aug., and Sept. .62 .404 .75 .23 28.64 .75

October 79 May, Sept., and Oct. .77 .340 .60 .27 30.60 .60

November 77 June., Oct., and Nov. .74 .196 .60 .26 27.30 .75

December 76 Oct., Nov., and Dec. .78 .267 .50 .38 26.76 .60

1

Time period for analyses was 1913–2002.

2

LOWESS regression models:

Response variable, total streamflow: log Qn = log P1 + log P2 + log Pn where Qn is average streamflow for month n, in cubic feet per second, and Pn is 

precipitation for month n, in inches.

Response variable, time: Tn = log P1 + log P2 + log Pn where Tn is time for month n, in years, and Pn is precipitation for month n, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

32  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 15. Explanatory variables for LOWESS regression equations between monthly precipitation at Tombstone, Arizona, and monthly 

streamflow for the San Pedro River at Charleston, Arizona

[R 2, coefficient of multiple determination]

A. Total flow (monthly average flow)

Explanatory variables Response variable LOWESS R2 value

Precipitation

Average flow in 

indicated month

Month with best 

R2 value1 All months

Previous months Current 

8 7 6 5 4 3 2 1 month

Oct Nov Dec Jan January 0.42 0.81

Dec Jan Feb February .41 .80

Jan Feb Mar March .29 .66

Jan Feb Mar April .28 .50

Jan Feb Mar May .21 .52

Dec Jan Mar June June .28 .73

Jan May June July July .33 .70

Feb July Aug August .39 .64

May Aug Sept September .41 .62

May Sept Oct October .49 .77

June Oct Nov November .47 .74

Oct Nov Dec December .53 .78

B. Low flow (monthly 3-day low flow)

Explanatory variables Response variable LOWESS R2 value

Precipitation

Low flow in 

indIcated month

Month with best 

R2 value1 All months

Previous months Current 

8 7 6 5 4 3 2 1 month

Oct Nov Dec Jan January 0.28 0.80

Nov Dec Jan February .46 .82

Jan Feb Mar March .33 .58

Jan Feb Mar April .25 .60

Nov Dec Jan Mar May .14 .75

Dec Jan June June .21 .57

April May June July July .14 .81

Dec July Aug August .18 .67

Jan Aug Sept September .38 .60

May Aug Sept October .32 .66

Aug Oct November .50 .65

Aug Oct Nov December .37 .59

1 

 

Month of precipitation with the best R 2 value for a single-variable LOWESS equation.

Trends in the San Pedro River Basin  33
The R 2 values for the multiple-variable LOWESS 

regression equations for monthly low flow ranged from 

0.57 to 0.82 (table 16). The number of months of precipitation 

in the equations ranged from two to four. The combination of 

months in the low-flow equations was generally different from 

the combination of months used in the total-flow equations 

(table 15). Precipitation for the same month as low flow 

was used less often, and months of precipitation prior to the 

flow were much more important. This makes physical sense 

because low flows should be less influenced by precipitation 

and direct runoff for the same month and more influenced 

by the amount of storage in the stream bank and alluvial 

aquifer. Precipitation and associated total flows can build 

up bank storage over many months, and the storage can be 

released to low flows several months after the precipitation. 

Low flows during February–June were mostly influenced 

by precipitation in the previous winter. Low flows during 

September–December were mostly influenced by precipitation 

in the previous summer or fall. 

The multiple-variable LOWESS regression equations 

for storm runoff were successful for some months and not 

successful for other months (table 17). Most months of the 

year could not be analyzed because of insufficient data; only 

June, July, August, September, and October had enough 

data for analysis. The equations were successful for July, 

September, and October; R 2 values ranged from 0.57 to 0.84. 

The equation for June had an R 2 of 0.32, and the equation for 

August had an R 2 of 0.35; these equations are considered to 

be too inaccurate for use in the next step of trend analysis. 

The periods of precipitation that were most successful in 

explaining maximum daily runoff were precipitation for the 

same day as runoff and precipitation for combinations of days 

1 to 60 prior to the day of runoff.

The next step of this monotonic trend analysis was to 

use LOWESS analysis to remove the variation in time caused 

by variation in precipitation. The LOWESS equations for 

precipitation and time used the same explanatory variables 

that were used in the LOWESS equations for precipitation and 

streamflow. These precipitation-time equations had R 2 values 

ranging from 0.23 to 0.69 for total flows (table 14), 0.26 to 

0.73 for low flows (table 16), and 0.46 to 0.62 for storm runoff 

(table 17).

The next step of the trend analysis was to use the 

Kendall tau test to determine significant trends. Three sets 

of data were tested for comparison: (1) streamflow values 

and time (years); (2) the LOWESS precipitation-streamflow 

residuals and time; and (3) the LOWESS precipitationstreamflow residuals and the LOWESS precipitation-time 

residuals. The LOWESS residuals can be called “precipitationadjusted” or “adjusted” values. Trend tests on the second and 

third sets of data (adjusted values) can be used to determine if 

there were significant trends in streamflow caused by factors 

other than precipitation.

Factors other than precipitation caused significant 

decreasing trends in streamflow (adjusted flow is significantly 

related to adjusted time; tables 18–20). Adjusted total flows 

and low flows had similar seasonal trends; summer, fall, and 

early winter flows (June–December) significantly decreased, 

and late winter and early spring flows (January–March) had 

no significant trends. Only 3 months of storm runoff could 

be tested for trends in adjusted values. Adjusted storm runoff 

for July and September had significant decreasing trends, and 

adjusted storm runoff for October had a nearly significant 

decreasing trend (p = 0.079). Unadjusted storm runoff for the 

winter and early spring had no significant decreasing trends, 

but it is not known if there were effects of factors other than 

precipitation.

Trends in unadjusted and adjusted total flows for all 

months are shown in figure 13. The adjusted total flows in 

the figure are LOWESS residuals plus the mean of the log 

monthly flows for the entire record. The adjusted streamflows 

generally had lower slopes and much less interannual 

variability than the unadjusted streamflows. Unadjusted flows 

for July, August, September, and October appeared to have a 

break in the time trend between 1950 and 1970; the later flows 

have a steeper decrease over time than the earlier flows. The 

adjusted streamflows also had similar breaks in slope, but the 

difference in slopes between early and later flows is much 

less than that for the unadjusted flows. The steeper slopes of 

adjusted flows after 1950–70 indicate that factors other than 

precipitation had a stronger effect on the decreasing flows in 

the later time periods rather than in the earlier time periods. 

Trends in unadjusted and adjusted monthly low flows had 

similar patterns as those for monthly total flows (fig. 14). The 

adjusted low flows had less interannual variability and lower 

slopes than the unadjusted low flows. Also, some breaks or 

shifts in the trends or slopes in the adjusted low flows are less 

pronounced than those in the unadjusted low flows.

Trends in unadjusted storm runoff are shown in figure 15 

for all months except April and May, which had too few runoff 

events (fewer than 10). Trends in adjusted storm runoff are 

also shown for July, September, and October. The difference 

in trends of unadjusted flows compared to adjusted flows is 

clearly shown in the trends for October storm runoff. The 

trend in unadjusted flows had a sharp rise from 1970 to 2002, 

an overall positive slope for the record, and a trend-test pvalue of 0.333 (table 20). This rise was caused by larger than 

average October precipitation. Total precipitation from 1970 

to 2002 was 35 percent larger than the long-term average 

(1913–2002), and maximum daily precipitation was 16 percent 

larger than the long-term average (1913–2002). When this 

effect of precipitation is removed from the storm runoff, the 

trend in adjusted storm runoff had an overall negative slope 

and a trend test p-value of 0.347.

34  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 16. Results of LOWESS regression analyses between monthly precipitation at Tombstone, Arizona, and monthly low flow for 

the San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1931–2002

[R 2, coefficient of multiple determination]

Month

Number of 

years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Low flow 

(cubic feet per second)

Time

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span3 R2

Standard error 

(years) Span3

January 55 Oct., Nov., Dec., and Jan. 0.80 0.163 0.75 0.54 23.43 0.75

February 55 Nov., Dec., and Jan. .82 .141 .50 .61 19.38 .50

March 60 Jan., Feb., and Mar. .58 .138 .75 .61 20.55 .50

April 60 Jan., Feb., and Mar. .60 .139 .50 .61 20.55 .50

May 55 Nov., Dec., Jan., and Mar. .75 .178 .75 .73 23.41 .60

June 56 Dec., Jan., and June .57 .246 .75 .67 18.63 .50

July 63 Apr., May, June, and July .81 .368 .60 .72 20.41 .60

August 54 Dec., July, and Aug. .67 .377 .75 .27 23.08 .75

September 59 Jan., Aug., and Sept. .60 .270 .60 .32 22.51 .60

October 62 May, Aug., and Sept. .66 .249 .75 .44 19.86 .75

November 62 Aug. and Oct. .65 .154 .60 .26 20.43 .60

December 61 Aug., Oct., and Nov. .59 .124 .75 .47 21.84 .50

1

Time period for analyses was 1931–2002.

2

LOWESS regression models:

Response variable, low flow: log Qn = log P1 + log P2 + log Pn

where Qn is 3-day low flow for month n, in cubic feet per second, and Pn is precipitation for month n, in inches.

Response variable, time: Tn = log P1 + log P2 + log Pn

where Tn is time for month n, in years, and Pn is precipitation for month n, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

Trends in the San Pedro River Basin  35
Table 17. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and maximum daily storm runoff for 

the San Pedro River at Charleston, Arizona; and between precipitation at Tombstone and time, 1913–2002, for selected months

[R 2, coefficient of multiple determination]

Month

Number of 

years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Maximum daily storm runoff 

(cubic feet per second)

Time 

(years)

Monthly precipitation 

(inches) R2

Standard 

error 

(log units) Span3 R2

Standard 

error 

(years) Span3

June 34 p0 and p1–10 0.32 0.613 0.75 ( 4 ) ( 4 ) ( 4 )

July 78 p0, p1–10, p11–30, and p31–60 .64 .462 .75 .62 26.77 .60

August 78 p0 and p1–30 .35 .440 .75 ( 4 ) ( 4 ) ( 4 )

September 71 p0, p1–10, and p11–30 .57 .550 .60 .46 29.24 .50

October 36 p0 and p1–30 .84 .427 .50 .50 26.33 .60

1

Time period for analyses was 1913–2002.

2

LOWESS regression models:

Response variable, maximum daily storm runoff: log Qn = log P1 + log P2 + log Pm, where Q is maximum daily mean flow for month n, in cubic feet per 

second, and Pm is precipitation for indicated days previous to day of runoff, in inches (p0 is precipitation for day of runoff, p1–10 is cumulative precipitation for 

days 1 through 10 prior to runoff).

Response variable, time: Tn = log P1 + log P2 + log Pm, where T is time for month n, in years, and Pm is precipitation for indicated days previous to day of 

runoff, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

4

LOWESS regression analysis between precipitation and time was not done because the LOWESS equation between precipitation and maximum runoff was 

not sufficiently accurate (R 2 < 0.50).

36  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 18. Trends in monthly total streamflow and monthly total streamflow adjusted for variation in precipitation, San Pedro River at 

Charleston, Arizona, 1913–2002

[<, less than; >, greater than]

Month

Total streamflow (1913–2002)

1

Number of 

years analyzed

Kendall tau trend test

Streamflow and time Adjusted streamflow and time2

Adjusted streamflow 

and adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 72 n 0.017 n 0.208 n 0.061

February 72 n .930 p .428 p .198

March 76 n .996 p .487 p .300

April 76 p .542 p .638 p .854

May 76 n .081 n .449 n .135

June 73 n .001 n <.001 n .018

July 76 n <.001 n .007 n <.001

August 74 n <.001 n .001 n <.001

September 79 n <.001 n <.001 n <.001

October 79 n .029 n <.001 n <.001

November 77 n <.001 n <.001 n <.001

December 76 n .018 n <.001 n <.001

1

Average streamflow.

2

Variation in streamflow that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in streamflow and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

Trends in the San Pedro River Basin  37
Table 19. Trends in monthly low flow and monthly low flow adjusted for variation in precipitation, San Pedro River at Charleston, 

Arizona, 1931–2002

[<, less than; >, greater than]

Month

Low flow (1931–2002)

1

Number of 

years analyzed

Kendall tau trend test

Flow and time Adjusted flow and time2

Adjusted flow and 

adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 55 n 0.014 n 0.089 n 0.245

February 55 n .292 n .965 n .532

March 60 p .527 p .342 p .178

April 60 n .139 n .293 n .030

May 55 n <.001 n .007 n .163

June 56 n <.001 n .002 n .001

July 63 n <.001 n .073 n <.001

August 54 n <.001 n .002 n <.001

September 59 n <.001 n <.001 n <.001

October 62 n <.001 n .003 n <.001

November 62 n .007 n <.001 n <.001

December 61 n .003 n <.001 n <.001

1

Three-day low flow.

2

Variation in low flow that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in low flow and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

38  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 20. Trends in maximum daily storm runoff and maximum daily storm runoff adjusted for variation in precipitation, by month, 

San Pedro River at Charleston, Arizona, 1913–2002

[<, less than; >, greater than]

Month

Maximum daily storm runoff (1913–2002)

1

Number of 

years analyzed

Kendall tau trend test

Runoff and time Adjusted runoff 

and time2

Adjusted runoff and 

adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 18 n 0.820 (

6

) (

6

) (

6

) (

6

)

February 17 n .902 (

6

) (

6

) (

6

) (

6

)

March 15 p .020 (

6

) (

6

) (

6

) (

6

)

April 7 (

5

) (

5

) (

5

) (

5

) (

5

) (

5

)

May 3 (

5

) (

5

) (

5

) (

5

) (

5

) (

5

)

June 34 n .382 (

7

) (

7

) (

7

) (

7

)

July 78 n <.001 n .005 n .010

August 78 n <.001 (

7

) (

7

) (

7

) (

7

)

September 71 n .002 n .013 n .007

October 36 p .333 n .347 n .079

November 17 n .265 (

6

) (

6

) (

6

) (

6

)

December 19 p .624 (

6

) (

6

) (

6

) (

6

)

1

Maximum daily mean streamflow for month.

2

Variation in runoff that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in runoff and time that were caused by variation in precipitation were yremoved by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

5

Sufficient data were not available to perform trend analysis.

6

Sufficient data were not available to perform LOWESS regression analysis and to create adjusted values of runoff and time.

7

LOWESS regression equations for June and August runoff were not accurate enough to use for adjusted values of runoff and time.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

p significant positive trend < 0.05

Trends in the San Pedro River Basin  39
Figure 13. Trends in monthly total streamflow and monthly total streamflow adjusted for variation in precipitation, January–December, 

San Pedro River at Charleston, Arizona. Blue line is LOWESS fit to data.

100 

10 

1,000 

1910191519201925193019351940194519501955196019651970197519801985199019952000200519101915192019251930193519401945195019551960196519701975198019851990199520002005

1

AVERAGE FLOW

JANUARY–Trend test

p-value=0.017

100 

10 

1,000 

1

100 

10 

1,000 

1

FEBUARY–Trend test p-value=0.930

100 

10 

1,000 

100 

10 

1,000 

1

MARCH–Trend test p-value=0.996

JANUARY–Trend test p-value= 0.208

FEBUARY–Trend test p-value= 0.428

MARCH–Trend test p-value=0.487

100 

10 

1,000 

100 

10 

1,000 

1

APRIL–Trend test p-value=0.542

100 

10 

1,000 

1

100 

10 

1,000 

1

1

1

1

1

MAY–Trend test p-value=0.081

100 

10 

1,000 

100 

10 

1,000 

1

JUNE–Trend test p-value=0.001

APRIL–Trend test p-value=0.638

MAY–Trend test p-value = 0.449

JUNE–Trend test p-value is less than 0.001

100 

10 

1,000 

AVERAGE FLOW ADJUSTED FOR VARIATION IN PRECIPITATION

STREAMFLO

W, IN CUBIC FEET PER SECOND 

STREAMFLO

W, IN CUBIC FEET PER SECOND 

40 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Figure 13. Continued.

100 

10 

1,000 

1910191519201925193019351940194519501955196019651970197519801985199019952000200519101915192019251930193519401945195019551960196519701975198019851990199520002005

1

AVERAGE FLOW

JULY–Trend test p-value is less than 0.001

100 

10 

1,000 

1

100 

10 

1,000 

1

AUGUST–Trend test p-value is less than 0.001

100 

10 

1,000 

100 

10 

1,000 

1

SEPTEMBER–Trend test p-valueis less than 0.001

JULY–Trend test p-value=0.007

AUGUST–Trend test p-value=0.001

SEPTEMBER–Trend test p-valueis less than 0.001

100 

10 

1,000 

100 

10 

1,000 

1

OCTOBER–Trend test p-value=0.029

100 

10 

1,000 

1

100 

10 

1,000 

1

1

1

1

1

NOVEMBER–Trend test p-value is less than 0.001

100 

10 

1,000 

100 

10 

1,000 

1

DECEMBER–Trend test p-value=0.018

OCTOBER–Trend test p-value is less than 0.001

NOVEMBER–Trend test p-valueis less than 0.001

DECEMBER–Trend test p-valueis less than 0.001

100 

10 

1,000 

AVERAGE FLOW ADJUSTED FOR VARIATION IN PRECIPITATION

STREAMFLO

W, IN CUBIC FEET PER SECOND 

STREAMFLO

W, IN CUBIC FEET PER SECOND 

Trends in the San Pedro River Basin  41
Figure 14. Trends in monthly low flow and monthly low flow adjusted for variation in precipitation, January–December, San Pedro 

River at Charleston, Arizona. Blue line is LOWESS fit to data.

LOW FLOW

JUNE–Trend test p-value is less than 0.001

1

100 

10

0.1

LOW FLOW ADJUSTED FOR VARIATION IN PRECIPITATION

STREAMFLO

W, IN CUBIC FEET PER SECOND 

1930193519401945195019551960196519701975198019851990199520002005

MAY–Trend test p-valueis less than 0.001

1

100

10

0.1

APRIL–Trend test p-value=0.139

1

100

10

0.1

MARCH–Trend test p-value=0.527

1

100

10

0.1

FEBRUARY–Trend test p-value=0.292

1

100

10

0.1

JANUARY–Trend test p-value=0.014

1

100

10

0.1

JUNE–Trend test p-value=0.002

1

100

10

0.1

STREAMFLO

W, IN CUBIC FEET PER SECOND

1930193519401945195019551960196519701975198019851990199520002005

MAY–Trend test p-value=0.007

1

100

10

0.1

APRIL–Trend test p-value=0.293

1

100

10

0.1

MARCH–Trend test p-value=0.342

1

100

10

0.1

FEBRUARY–Trend test p-value=0.965

1

100

10

0.1

JANUARY–Trend test p-value=0.089

1

100

10

0.1

42  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Figure 14. Continued.

LOW FLOW

DECEMBER–Trend test p-value=0.003

1

100 

10

0.1

LOW FLOW ADJUSTED FOR VARIATION IN PRECIPITATION

STREAMFLO

W, IN CUBIC FEET PER SECOND 

1930193519401945195019551960196519701975198019851990199520002005

NOVEMBER–Trend test p-value=0.007

1

100

10

0.1

OCTOBER–Trend test p-value is less than 0.001

1

100

10

0.1

SEPTEMBER–Trend test p-value is less than 0.001

1

100

10

0.1

AUGUST–Trend test p-value is less than 0.001

1

100

10

0.1

JULY–Trend test p-value

is less than 0.001

1

100

10

0.1

DECEMBER–Trend test p-value is less than 0.001

1

100

10

0.1

STREAMFLO

W, IN CUBIC FEET PER SECOND

1930193519401945195019551960196519701975198019851990199520002005

NOVEMBER–Trend test p-value is less than 0.001

1

100

10

0.1

OCTOBER–Trend test p-value=0.003

1

100

10

0.1

SEPTEMBER–Trend test p-value is less than 0.001

1

100

10

0.1

AUGUST–Trend test p-value=0.002

1

100

10

0.1

JULY–Trend test p-value=0.073

1

100

10

0.1

Trends in the San Pedro River Basin  43
Figure 15. Trends in maximum daily storm runoff and maximum daily storm runoff adjusted for variation in precipitation, selected 

months, San Pedro River at Charleston, Arizona. Blue line is LOWESS fit to data. 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Figure 15. Trends in maximum daily storm runoff and maximum daily storm runoff adjusted for variation in precipitation, selected 

months, San Pedro River at Charleston, Arizona. Blue line is LOWESS fit to data. 

MAXIMUM DAILY MEAN FLOW

100 

10 

1,000 

10,000 

1

JUNE–Trend test p-value=0.382

100 

10 

1,000 

10,000 

1

MARCH–Trend test p-value=0.020

100 

10 

1,000 

10,000 

1

FEBRUARY–Trend test p-value=0.902

100 

10 

1,000 

10,000 

1

JANUARY–Trend test p-value=0.820

STREAMFLO

W, IN CUBIC FEET PER SECOND 

19101915192019251930193519401945195019551960196519701975198019851990199520002005

MAXIMUM DAILY MEAN FLOW

100 

10 

1,000 

10,000 

1

OCTOBER–Trend test p-value=0.333, positive slope

100 

10 

1,000 

10,000 

1

SEPTEMBER–Trend test p-value=0.002

100 

10 

1,000 

10,000 

1

AUGUST–Trend test p-value is less than 0.001

100 

10 

1,000 

10,000 

1

JULY–Trend test p-value is less than 0.001

STREAMFLO

W, IN CUBIC FEET PER SECOND 

44  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Figure 15. Continued. 1910 1915 1920 1925 1930

193519401945195019551960196519701975198019851990199520002005

Figure 15. Continued. 

MAXIMUM DAILY MEAN FLOW ADJUSTED FOR VARIATION IN PRECIPITATION

100 

10 

1,000 

10,000 

1

OCTOBER–Trend test p-value=0.347, negative slope

100 

10 

1,000 

10,000 

NOTE: August flows were not adjusted

 for variation in precipitation

1

SEPTEMBER–Trend test p-value=0.013

100 

10 

1,000 

10,000 

1

JULY–Trend test p-value=0.005

STREAMFLO

W, IN CUBIC FEET PER SECOND 

19101915192019251930193519401945195019551960196519701975198019851990199520002005

MAXIMUM DAILY MEAN FLOW

100 

10 

1,000 

10,000 

1

DECEMBER–Trend test p-value=0.624

100 

10 

1,000 

10,000 

1

NOVEMBER–Trend test p-value=0.265

STREAMFLO

W, IN CUBIC FEET PER SECOND 

Trends in the San Pedro River Basin  45
relation was much different from that for the majority of the 

data. These high outliers had to be deleted to have a linear 

relation between precipitation and streamflow. Results of the 

final linear regression analyses for all time periods are shown 

in appendix 2.

Storm runoff (maximum daily mean flow) was analyzed 

for July, August, and September. Other months did not have 

enough data for the analysis. Three explanatory variables 

were tested for the single-variable regression equations: 

precipitation for (1) the day of runoff, (2) the day of runoff 

plus one previous day, and (3) the day of runoff plus 

10 previous days. Other possible combinations of days of 

precipitation were not tested because results of the previous 

LOWESS analysis of the relation between storm runoff and 

precipitation showed the other combinations of days were not 

significant as single-variable predictors of runoff. The linear 

regression analysis found that precipitation for the day of 

runoff was not a good explanatory variable for these single 

variable equations. Many days of runoff had zero precipitation 

for the same day, which resulted in low R2 values and high 

standard errors of regression. The other two explanatory 

variables were better, although they were not strongly related 

to storm runoff. Results of the final linear regression analyses 

for all time periods are shown in appendix 2.

Factors other than precipitation caused significant 

step trends in total monthly streamflow from 1913 to 2002 

(table 21). The step-trend results were similar to results 

of the previous monotonic trend analysis. The regression 

relations between precipitation and monthly total flows were 

significantly different for summer, fall, and early winter (June 

through December) and not significantly different for late 

winter and spring (February through May). The regression 

relations between precipitation and maximum daily storm 

runoff were significantly different for all the months tested: 

July, August, and September (table 22). Regressions for storm 

runoff are shown for two explanatory variables: 2 days of 

precipitation and 11 days of precipitation. There were slightly 

different results, but the overall conclusion is the same. 

Linear regression relations between precipitation 

and monthly total flows for 3 time periods are shown 

for 11 months in figure 16. The regression relations for 

February–May are clearly similar, and the regression relations 

are not significantly different. The regression relations 

for June–December have significantly different slopes or 

intercepts indicating that the precipitation-streamflow relation 

changed over time for those months. In June–September, 

the precipitation-streamflow relation for the late time period 

(1977–2002) is significantly lower than the relations for the 

two earlier time periods (1913–76). Thus, for a given amount 

of precipitation, there was less streamflow (runoff) during 

1977–2002 than during 1913–76. 

Linear regression relations for three time periods for 

storm runoff in July, August, and September are shown in 

figure 17. These relations are similar to those for monthly total 

flow in which the regression relation (precipitation-streamflow 

relation) for the late time period is at a consistently lower level 

than the other two regression relations. 

Step Trends

Step trends in streamflow caused by factors other than 

precipitation were determined by developing linear regression 

relations between precipitation and streamflow for three time 

periods (1913–42, 1943–76, and 1977–2002), and testing to 

determine if the three regression relations are significantly 

different. Linear least-squares regression relations were 

developed for monthly total streamflow (average flow) and 

storm runoff (maximum daily mean flow for each month). 

The explanatory variables (precipitation) and response 

variables (streamflow) were log transformed before the 

regression analysis.

The step-trend analysis was done using single-variable 

linear regression equations (one explanatory variable for 

precipitation). Multivariable linear equations similar to those 

used in the LOWESS equations (tables 14–17) were not 

used because (1) they did not improve the accuracy and fit 

and (2) the nested F-tests used for determining step trends 

(equation 4) would lose statistical power. Single-variable 

linear equations had similar R 2 values as multivariable 

linear equations using the same explanatory variables as the 

LOWESS equations. In LOWESS, multivariable equations 

significantly improved the fit compared to single-variable 

equations, but in linear least squares, single-variable equations 

were as good as multivariable equations. Statistical power 

is lost in the nested F-tests with multivariable equations by 

losing degrees of freedom. For example, a single variable 

for precipitation results in n-6 degrees of freedom for the 

complex model (equation 3), and n-6 degrees of freedom 

in the denominator of the F-test (equation 4); four variables 

for precipitation results in n-15 degrees of freedom in the 

denominator of the F-test.

Three explanatory variables were tested for the singlevariable equations for monthly total flow: precipitation for 

(1) the same month as flow, (2) the same month and previous 

month, and (3) the same month and two previous months. 

The best equation was selected using the R 2 value, standard 

error, and distribution of residuals. This best equation 

was then used for the test of effects of factors other than 

precipitation. The linear regression is a parametric analysis, 

so several assumptions had to be met for the analysis to be 

valid. Among the more important assumptions are that (1) the 

relation between precipitation and streamflow must be linear, 

(2) outliers must not unduly influence the regression, and 

(3) residuals must be independent, have zero mean, have a 

constant variance, and follow a normal distribution (Draper 

and Smith, 1981, p. 141–192). 

To meet the necessary assumptions, several low and 

high outliers had to be deleted from the analysis of monthly 

total flows. There were no outliers in the analysis of storm 

runoff. The regression relations between monthly total flows 

and precipitation were not linear for values of precipitation 

less than about 0.3 in (fig. 12). This threshold existed for 

all monthly flows; generally, there is minimal or no runoff 

(response of streamflow) when precipitation is less than 0.3 in. 

So, all streamflow-precipitation data pairs were deleted if 

the precipitation was less than 0.3 in. The resulting monthly 

total flows, therefore, are flows that have at least some runoff 

from precipitation. Some of the months also had data pairs 

that were high outliers where the precipitation-streamflow 

46  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 21. Results of significance tests for differences among regression relations between precipitation at Tombstone, Arizona, and 

monthly total streamflow for the San Pedro River at Charleston, Arizona, for three time periods

[---, no data; <, less than; >, greater than]

Month

Months of cumulative 

precipitation used for 

explanatory variable1

Number 

of years 

analyzed

p-values for significance 

tests of differences 

among regression relations 

for three time periods2

p-values for significance tests of difference between 

regression relations for two time periods2

1913–42 versus

1943–76

1943–76 versus

1977–2002

1913–42 versus

1977–2002

Slope3 Intercept4 Slope3 Intercept4 Slope3 Intercept4 Slope3 Intercept4

January5 --- --- --- --- --- --- --- --- --- ---

February 3 60 .213 .814 .111 .419 .635 .769 .131 .736

March 3 66 .663 .961 .705 .892 .337 .820 .745 .951

April 63 72 .302 .810 .308 .908 .026 (

7

) .957 .570

May 63 72 .188 .198 .100 .883 .097 .051 .533 .228

June 1 36 .451 .008 .560 .138 .537 .072 .212 .004

July 2 75 .002 (

7

) .561 .249 .003 (

7

) .005 (

7

)

August 1 75 .239 <.001 .946 .568 .113 .001 .249 <.001

September 2 72 .889 <.001 .654 .024 .967 .010 .687 <.001

October 2 66 .014 (

7

) .065 .135 .004 (

7

) .496 .035

November 3 54 .731 .002 .465 .558 .533 .004 .836 .004

December 3 63 <.001 (

7

) .002 (7) .018 (

7

) .180 .002

1

Precipitation for same month as streamflow and indicated number of previous months (1 is precipitation for same month, and 2 is precipitation for same month and one 

previous month).

2

Data were grouped into three time periods, early is 1913–42, middle is 1943–76, and late is 1977–2002. For each time period, a linear regression analysis was made between 

precipitation and monthly average streamflow. A nested F test of simpler versus complex models was used to determine the significance of the difference among regression relations.

3

Slope of regression relations.

4

Intercept of regression relations.

5

Linear regression relations could not be adequately fit to data.

6

Months of cumulative precipitation are January, February, and March.

7

Significance test for difference among regression intercepts is not valid when the 

slopes are significantly different.

Table 22. Results of significance tests for differences among regression relations between precipitation at Tombstone, Arizona, and 

maximum daily storm runoff for the San Pedro River at Charleston, Arizona, for July, August, and September, for three time periods

[<, less than; >, greater than]

Month

Days of cumulative 

precipitation used for 

explanatory variable1

Number 

of years 

analyzed

p-values for significance 

tests of differences among 

regression relations for three 

time periods2

p-values for significance tests of difference between 

regression relations for two time periods2

1913–42 versus

1943–76

1943–76 versus

1977–2002

1913–42 versus

1977–2002

Slope3 Intercept4 Slope3 Intercept4 Slope3 Intercept4 Slope3 Intercept4

July 2 72 0.845 <.001 0.501 0.469 0.724 <.001 0.820 .001

11 72 .504 <.001 .701 .393 .498 <.001 .292 <.001

August 2 69 .028 ( 5 ) .034 ( 5 ) .015 ( 5 ) .734 <.001

11 69 .195 <.001 .081 .065 .989 .050 .104 <.001

September 2 69 .676 .015 .619 .043 .421 .316 .687 .005

11 69 .480 .024 .374 .066 .268 .330 .885 .008

1

Precipitation for same day as runoff and indicated number of previous days, in inches (2 is same day and 1 previous day, 11 is same day and 10 previous days).

2

Data were grouped into three time periods, early is 1913–42, middle is 1943–76, and late is 1977–2002. For each time period, a linear regression analysis was made between 

precipitation and monthly maximum daily mean streamflow. A nested F test of simpler versus complex models was used to determine the significance of the difference among 

regression relations.

3

Slope of regression relations.

4

Intercept of regression relations.

5

Significance tests for difference among regression intercepts is not valid when the 

slopes are significantly different.

Trends in the San Pedro River Basin  47

p-value 

no significant difference > 0.10

nearly significant difference 0.05–0.10

significant difference < 0.05

p-value 

no significant difference > 0.10

nearly significant difference 0.05–0.10

significant difference < 0.05
STREAMFLO

W FOR JUNE,

IN CUBIC FEET PER SECOND

Figure 16. Regression relations between precipitation at Tombstone, Arizona and monthly total streamflow for February through December

for three time periods, San Pedro River at Charleston, Arizona.

0.2 20

1

1 10

1,000

100

10

STREAMFLO

W FOR APRIL,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR JANUARY,

FEBRUARY, AND MARCH, IN INCHES

0.2 20

1

1 10

1,000

100

10

STREAMFLO

W FOR FEBRUARY,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR DECEMBER,

JANUARY, AND FEBRUARY, IN INCHES

0.2 20

1

1 10

p-value (slope)=0.213

p-value (intercept)=0.814

1,000

100

10

STREAMFLO

W FOR JULY,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR JUNE

AND JULY, IN INCHES

0.2 20

1

1 10

p-value (slope)=0.002

1,000

100

10

STREAMFLO

W FOR MAY,

IN CUBIC FEET PER SECOND

PRECIPITATION FOR JANUARY,

FEBRUARY, AND MARCH, IN INCHES

0.2 20

1

1 10

1,000

100

10

p-value (slope)=0.188

p-value (intercept)=0.198

STREAMFLO

W FOR MARCH,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR JANUARY,

FEBRUARY, AND MARCH, IN INCHES

0.2 20

1

1 10

p-value (slope)=0.663

p-value (intercept)=0.961

1,000

100

10

PRECIPITATION FOR JUNE, IN INCHES

p-value (slope)=0.451

p-value (intercept)=0.008

p-value (slope)=0.302

p-value (intercept)=0.810

FEBRUARY MARCH

APRIL MAY

JUNE JULY

Figure 16. Regression relations between precipitation at Tombstone, Arizona, and monthly total streamflow for February through 

December for three time periods, San Pedro River at Charleston, Arizona.

48  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Figure 16. Continued.

Trends in the San Pedro River Basin  49

STREAMFLO

W FOR DECEMBER,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR OCTOBER,

NOVEMBER, AND DECEMBER, IN INCHES

0.2 20

1

1 10

1,000

100

10

STREAMFLO

W FOR OCTOBER,

IN CUBIC FEET PER SECOND

CUMULATIVE PRECIPITATION FOR SEPTEMBER,

AND OCTOBER, IN INCHES

0.2 20

1

1 10

1,000

100

10

STREAMFLO

W FOR AUGUST,

IN CUBIC FEET PER SECOND

PRECIPITATION FOR AUGUST, IN INCHES

0.2 20

1

1 10

p-value (slope)=0.239

p-value (intercept) is

 less than 0.001

1,000

100

10

0.2 20

1

1 10

1,000

100

10

0.2 20

1

1 10

1,000

100

10

NOTE: p-values are for difference

 in regression relations

EXPLANATION

1913–42

1943–76

1977–2002

CUMULATIVE PRECIPITATION FOR SEPTEMBER,

OCTOBER, AND NOVEMBER, IN INCHES

p-value (slope)=0.731

p-value (intercept)=0.002

p-value (slope)=0.014

p-value (slope) is less than 0.001

CUMULATIVE PRECIPITATION FOR AUGUST,

AND SEPTEMBER, IN INCHES

p-value (slope)=0.889

p-value (intercept) is

 less than 0.001

NOTE: One data point not shown in figure;

 precipitation= 7.53 and streamflow=1,890 

STREAMFLO

W FOR SEPTEMBER,

IN CUBIC FEET PER SECOND

STREAMFLO

W FOR NOVEMBER,

IN CUBIC FEET PER SECOND

AUGUST SEPTEMBER

OCTOBER NOVEMBER

DECEMBER
Causes of Trends in Streamflow

This study found that factors other than precipitation 

caused a significant decrease in streamflow of the San Pedro 

River (tables 18–22). The factors that caused the decrease 

in flows are more difficult to extract because of interaction 

among the different factors and because historical data on 

the possible factors is more qualitative than quantitative. 

In addition, there was a cumulative effect from the individual 

effects of several factors. Evaluation of the relations among 

components of streamflow, seasonal trends, and historical 

information helped to sort out the most influential factors 

from the least influential.

Five general factors could have caused the decreasing 

trends in seasonal streamflow of the San Pedro River: 

(1) fluctuations in precipitation; (2) fluctuations in air 

temperature; (3) changes in watershed characteristics, such as 

changes in riparian vegetation, upland vegetation, and streamchannel morphology; (4) human activities such as groundwater pumping, urbanization, construction of runoff-detention 

structures, and cattle ranching (grazing); and (5) changes in 

seasonal distribution of flow between the San Pedro River and 

storage in the stream bank and alluvial aquifer (table 23).

The factors causing trends were evaluated by comparing 

how the factors affect the stream budget (sources of inflow 

and components of outflow; table 8) and how the factors 

relate to the results of this study. Examples of factors and 

their relation to the stream budget include: (1) fluctuations 

in precipitation that have a strong effect on the two principal 

inflow components of streamflow (runoff and ground-water 

discharge) and a weak and indirect effect on the outflow 

components, (2) ground-water pumping that can decrease 

inflow from ground-water discharge and increase outflow by 

flow to the alluvial aquifer, and (3) changes in vegetation and 

associated evapotranspiration that can directly or indirectly 

affect almost all components. These vegetation changes can 

affect inflow from runoff and ground-water discharge and 

outflow by flow to the alluvial aquifer and transpiration.

Fluctuations in Precipitation

Fluctuations in precipitation were a major factor in the 

total variation in streamflow, and a decrease in precipitation 

likely had some influence on streamflow trends. The 

LOWESS regression equations showed that precipitation was 

significantly related to streamflow (tables 14, 16, and 17). 

In those equations, precipitation explained an average of 

69 percent of the variation in monthly total flows, 68 percent 

of the variation in monthly low flows, and 68 percent of the 

variation in storm runoff for July, September, and October.

The portion of the decrease in streamflow caused by 

fluctuations or a decrease in precipitation could not be 

estimated with available data. Quantitative data on changes 

over time and on physical processes are needed for all the 

major factors that influenced streamflow trends (table 23), 

and such data were available only for precipitation and 

ground-water pumping. A simple comparison between 

the changes in monthly precipitation and streamflow, 

Figure 17. Regression relations between precipitation at 

Tombstone, Arizona, and maximum daily storm runoff for July 

through September for three time periods, San Pedro River at 

Charleston, Arizona.

CUMULATIVE PRECIPITATION FOR DAY OF

RUNOFF AND 10 PREVIOUS DAYS, IN INCHES

0.02 10.0

10

0.1 1.0

SEPTEMBER

p-value (slope)=0.480

p-value (intercept)=0.024

10,000

1,000

100

MAXIMUM DAILY MEAN STREAMFLO

W, IN CUBIC FEET PER SECOND

10

AUGUST

p-value (slope)=0.195

p-value (intercept) is

 less than 0.001

10,000

1,000

100

10

JULY

p-value (slope)=0.504

p-value (intercept) is

 less than 0.001

10,000

1,000

100

NOTE: p-values are for difference

 in regression relations

EXPLANATION

1913–42

1943–76

1977–2002

50 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
however, can show some useful relations. Changes in 

monthly average precipitation and streamflow from 1913 to 

2002 were estimated by fitting a linear regression relation 

between precipitation and years and between log streamflow 

and years, and then using the change in fitted values from 

1913 and 2002 as the change in average values. Streamflow 

was log transformed because high outliers in untransformed 

data result in fitted regression relations that are not 

representative of average values in 1913 and 2002.

From 1913 to 2002, most months had little or no 

changes in precipitation and large decreases in streamflow 

(table 24). Precipitation decreased moderately by 0.46 in. 

(13 percent) in August and 0.34 in. (44 percent) in November, 

and it decreased substantially by 1.53 in. (36 percent) in July. 

Streamflow decreased in 9 months, with substantial decreases 

of more than 70 percent in June–September and moderate 

decreases of between 35 and 55 percent in November–January. 

The decrease in precipitation in July, August, and November 

likely caused some of the decrease in streamflow, especially 

in the summer; but streamflow had much larger changes than 

precipitation, which indicates that other factors must have 

been involved. 

Table 24. Changes from 1913 to 2002 in monthly average precipitation at Tombstone, Arizona, and monthly average streamflow for 

San Pedro River at Charleston, Arizona

Month

Average precipitation1

(inches)

Change in average 

precipitation

Average streamflow2

(acre-feet)

Change in average 

streamflow

1913 2002

Total 

(inches) Percent 1913 2002

Total 

(acre-feet) Percent

January 0.78 0.98 0.20 26 1,780 1,160 -620 -35

February .76 .64 -.12 -16 1,240 1,310 70 6

March .49 .66 .17 35 1,060 1,170 110 10

April .26 .24 -.02 -8 640 760 120 19

May .16 .24 .08 50 500 380 -120 -24

June .44 .60 .16 36 650 190 -460 -71

July 4.25 2.72 -1.53 -36 14,800 1,600 -13,200 -89

August 3.55 3.09 -.46 -13 18,100 3,450 -14,650 -81

September 1.53 1.44 -.09 -6 5,420 1,020 -4,400 -81

October .60 1.17 .57 95 950 680 -270 -28

November .78 .44 -.34 -44 1,270 570 -700 -55

December .94 1.04 .10 13 1,620 1,010 -610 -38

1

Linear least squares regression was performed between year and monthly precipitation using data from 1913 to 2002. Precipitation values 

for 1913 and 2002 were determined from the fitted regression equations. These fitted values are estimates of the average precipitation at 

the beginning and end of the record. 2

The same linear-regression procedure as used for precipitation was used for streamflow, except the regression equations were fit to year and 

the log of streamflow.

Table 23. Factors that could cause trends in seasonal 

streamflow of the San Pedro River at Charleston, Arizona

Factors

1) Fluctuations in precipitation

2) Fluctuations in air temperature 

3) Changes in watershed characteristics

A) Upland vegetation

B) Riparian vegetation

C) Stream-channel morphology

4) Human activities

A) Ground-water pumping

B) Urbanization

C) Construction of runoff-detention structures

D) Cattle ranching (grazing)

5) Changes in seasonal distribution of flow between the San Pedro 

River and storage in the stream bank and alluvial aquifer

Trends in the San Pedro River Basin  51
Fluctuations in Air Temperature

Average air temperature increased by about 2 degrees 

Fahrenheit during the past century (fig. 18). This temperature 

increase could have caused changes in vegetation in 

the watershed and increased the length of the growing 

season, which in turn could have changed the amount of 

evapotranspiration. There are no detailed studies of the 

effects of temperature change on vegetation in the San Pedro 

watershed. Temperature changes, if they had any effect on 

streamflow, would appear indirectly in the effects of changes 

in vegetation on streamflow. These effects of vegetation are 

discussed later in this section.

61

66

65

64

63

62

67

19101915192019251930193519401945195019551960196519701975198019851990199520002005

ANNUAL AVERAGE TEMPERATURE–Trend test p-value=0.001

Figure 18. Annual average temperature at Tombstone, Arizona,

1913–2002. Blue line is LOWESS fit to data. TEMPERATURE, IN DEGREES FAHRENHEIT

Figure 18. Annual average temperature at Tombstone, Arizona, 

1913–2002. Blue line is LOWESS fit to data.

a monthly total flow is the correlation coefficient between 

that month’s flow and each of the 24 monthly total flows 

prior to that month. The correlation plots for low flows were 

computed between monthly low flows and the 24 prior months 

of total flows. A significant positive correlation between a 

current monthly flow and a previous month’s flow is a good 

indication that the previous month’s flow contributed some 

bank storage which is then released during the current month. 

Larger positive coefficients for a previous month indicate 

more influence of bank storage on the monthly flow, and a 

series of significant positive correlations with previous months 

indicates a longer and more persistent influence of bank 

storage. 

There is a strong seasonal pattern in the correlation plots 

for monthly total flows (fig. 19). Winter and spring total flows 

are significantly correlated with about five previous months of 

flows. Summer total flows have little correlation with previous 

months because of the low spring flows where bank storage 

is drained each year. Fall total flows are correlated with the 

previous summer flows.

Monthly low flows have similar seasonal relations as 

those for the monthly total flows (fig. 20). Winter and spring 

low flows are correlated with many months of previous total 

flow, and summer and fall flows are correlated with only a few 

months of previous total flow. Monthly low flows generally 

are correlated with previous total flows for a longer time 

period than monthly total flows. 

A third correlation plot was made for monthly 

precipitation to show that the streamflow persistence is 

primarily related to bank storage and is not related to 

persistence of monthly precipitation (fig. 21). None of the 

months of precipitation have a pattern of persistent significant 

correlations with precipitation in previous months. 

It was impossible to quantitatively determine the degree 

of influence on streamflow trends of changes over time in 

the flow between the San Pedro River and bank storage. 

The correlation data indicated there were some seasonal 

differences. Bank storage has the most influence on spring 

and winter flows, a moderate influence on fall flows, and 

the least influence on summer flows (figs. 19 and 20). The 

number of previous months with significant correlations was 

about five for spring and winter flows, 2–3 for fall flows, and 

1–2 for summer flows. The average correlation coefficient for 

total flows and low flows for 3 previous months was 0.60 for 

spring and winter flows, 0.44 for fall flows, and 0.24 for 

summer flows.

Bank storage has a stronger influence on monthly 

low flows than on monthly total flows. This influence is 

indicated by the total number of previous months of flow with 

significant correlations; low flows had 70 significant months 

and total flows had 53 significant months (figs. 19 and 20). 

Bank storage also appeared to have a different duration and 

strength of influence on fall low flows compared to fall total 

flows. Fall low flows had about 4 significant previous months 

and fall total flows had about 2 significant previous months. 

The average correlation coefficient for 3 previous months was 

0.53 for fall low flows and 0.36 for fall total flows.

Changes in Seasonal Distribution of Flow 

between the San Pedro River and Storage in the 

Stream Bank and Alluvial Aquifer

Changes in the seasonal distribution of flow between the 

San Pedro River and storage in the stream bank and alluvial 

aquifer likely had some influence on trends in fall and winter 

streamflows and had little or no influence on the trend in 

summer streamflows. The relation between streamflow and 

nearby storage is complex and is strongly related to seasons 

and streamflow components.

Bank storage of the San Pedro River is water that is 

stored in alluvial material near the stream channel. During 

high streamflows, some of the water will flow from the river 

into bank storage, and when flow subsides after high flows, 

water will typically drain from bank storage and flow back 

into the river. The time period of the storage and release 

of storage can be as short as daily and as long as several 

months (seasonal). Short-term storage in the alluvial aquifer 

is included in this factor because the boundary between bank 

storage and alluvial-aquifer storage is not clearly defined. For 

convenience, the two types of storage are called bank storage 

in this discussion.

Bank storage and its effect on streamflows can be 

illustrated by plots of correlation coefficients between 

monthly total flows and total flows for 24 previous months 

and between monthly low flows and monthly total flows for 

24 previous months (figs. 19 and 20). The correlation plot for 

52  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

SUMMER TOTAL FLOWS

1.0

0.5

0

–0.5

–1.0

SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

FALL TOTAL FLOWS

1.0

0.5

0

–0.5

–1.0

WINTER TOTAL FLOWS

DECEMBER JANUARY

MARCH

SEPTEMBER

OCTOBER

NOVEMBER

FEBRUARY

1.0

0.5

0

–0.5

–1.0

SPRING TOTAL FLOWS

1.0

0.5

0

–0.5

–1.0

MONTH PRIOR TO MONTHLY STREAMFLOW MONTH PRIOR TO MONTHLY STREAMFLOW

EXPLANATION

Correlations not significant at 5 percent level

APRIL

MAY

JUNE

JULY

AUGUST

Figure 19. Correlations between monthly total streamflows and total streamflows for 24 previous months, San Pedro River at 

Charleston, Arizona, 1913–2002.

Trends in the San Pedro River Basin  53
SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

SUMMER LOW FLOWS

1.0

0.5

0

–0.5

–1.0

SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

FALL LOW FLOWS

1.0

0.5

0

–0.5

–1.0

WINTER LOW FLOWS

JANUARY

DECEMBER

MARCH

APRIL

MAY

JULY

AUGUST SEPTEMBER

OCTOBER

JUNE

FEBRUARY NOVEMBER

1.0

0.5

0

–0.5

–1.0

SPRING LOW FLOWS

1.0

0.5

0

–0.5

–1.0

MONTH PRIOR TO MONTHLY STREAMFLOW MONTH PRIOR TO MONTHLY STREAMFLOW

EXPLANATION

Correlations not significant at 5 percent level

Figure 20. Correlations between monthly low flows and total streamflows for 24 previous months, San Pedro River at Charleston, 

Arizona, 1931–2002.

54  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

SUMMER PRECIPITATION

1.0

0.5

0

–0.5

–1.0

SPEARMAN CORRELATION COEFFICIENT

0 2 4 6 8 10 12 14 16 18 20 22 24

FALL PRECIPITATION

1.0

0.5

0

–0.5

–1.0

WINTER PRECIPITATION

JANUARY

DECEMBER

MARCH

OCTOBER SEPTEMBER

NOVEMBER

FEBRUARY

1.0

0.5

0

–0.5

–1.0

SPRING PRECIPITATION

1.0

0.5

0

–0.5

–1.0

MONTH PRIOR TO MONTHLY PRECIPITATION MONTH PRIOR TO MONTHLY PRECIPITATION

EXPLANATION

Correlations not significant at 5 percent level

APRIL MAY JUNE

AUGUST JULY

Figure 21. Correlations between monthly precipitation and precipitation for 24 previous months, Tombstone, Arizona, 1913–2002.

Trends in the San Pedro River Basin  55
The correlations among bank storage, seasons, low 

flows, and total flows (figs. 19 and 20) provide information 

that needs to be considered in analyzing trends of monthly 

and seasonal flows. The long duration and strong influence of 

bank storage on winter and spring flows indicate that trends 

in previous months (up to about 5) could have affected trends 

in winter and spring flows. The short duration and generally 

weak influence of bank storage on summer flows indicate that 

summer flows likely were not affected by trends in any other 

seasonal flow. The short but strong influence of bank storage 

on fall flows, especially low flows, indicates that trends in 

summer flows could have affected trends in fall flows.

The seasonal difference in flow volumes is another 

streamflow characteristic that needs to be considered in 

analyzing the influence of bank storage on streamflow 

trends. Summer and early fall flows provide most of the 

annual volume of streamflow (fig. 5); flows during July 

through September were 70 percent of the annual flow in the 

predevelopment period. A large decrease in this summer total 

flow over time would affect trends in fall and early winter 

flows. As summer flows decrease, fall and early winter flows 

would also decrease because there would be less summer 

bank storage and less release of that bank storage in the fall 

and early winter. In the fall and winter, flows generally are 

low to moderate in magnitude (fig. 5) and large runoff events 

occur infrequently. Thus, only trends in the large runoff events 

would likely have any influence on subsequent seasonal 

flows. In the spring, flows are low in magnitude and runoff 

occurs infrequently. Thus, trends in spring flows would have 

no influence on subsequent summer flows. Bank storage also 

drains during the spring, so summer flows start out each year 

with little or no influence from bank storage.

The trends determined for adjusted streamflows 

(streamflow with effects of precipitation removed) account 

for some of the effects of changes in bank storage. All the 

LOWESS equations used to remove effects of precipitation 

from streamflow had precipitation in previous months as 

explanatory variables (table 15). Changes in previous month’s 

precipitation over time would likely be correlated with 

changes in bank storage over time. Thus, some of the effects 

of changes in bank storage have been removed from the 

adjusted streamflows.

In summary, changes in bank storage over time had 

a minimal effect on trends in summer flows, so the causes 

of decreasing trends in summer flows could have been 

fluctuations in precipitation and temperature, changes in 

watershed characteristics, or human activities. Parts of the 

decreasing trend in fall and early winter flows, however, 

were likely caused by the decreasing bank storage from 

the decreasing trend in summer total flows. Understanding 

the causes of decreasing summer total flows is, therefore, 

important to understanding the causes of the overall decrease 

in annual flows and the causes of the decrease in fall and early 

winter flows. 

Changes in Watershed Characteristics

Riparian and upland vegetation.—Changes in upland and 

riparian vegetation were likely major factors in the decreasing 

trends in total streamflow and low flow of the San Pedro 

River. Change in vegetation was identified as important, but 

this study could not distinguish if change in upland vegetation 

or riparian vegetation was more important. The evidence that 

vegetation was a major factor is: (1) that summer streamflow 

trends were different from winter streamflow trends, (2) that 

riparian and upland vegetation changed substantially during 

the 20th century, and (3) that evapotranspiration dominates 

the watershed budget, and small changes in evapotranspiration 

could cause large changes in streamflow.

A seasonal difference in significant trends in adjusted 

streamflow supports vegetation as a major cause of decreasing 

streamflow, because significant trends were found during the 

months of highest transpiration and significant trends were not 

found during months of low transpiration. Factors other than 

precipitation caused significant decreasing trends in total flows 

and low flows during summer and early fall (June–September) 

and did not cause significant trends in most late winter flows 

(January–March; tables 18–20). Significant decreasing 

trends were also determined for months of moderate to low 

transpiration (October–December), but part of those trends 

can be explained by the decreasing water available from bank 

storage as summer total flows decreased over time. 

Data on vegetation changes in the watershed during the 

20th century also support vegetation as a major cause of the 

decrease in streamflow. Two studies found large changes 

in upland vegetation during the 20th century (Kepner and 

Edmonds, 2002; Turner and others, 2003). Kepner and 

Edmonds (2002) used satellite data to determine changes 

in vegetation from 1973 to 1997 for the San Pedro River 

watershed above Redington. These changes should be similar 

to the changes in the watershed above Charleston. From 1973 

to 1997, the area of grasslands decreased by 16 percent, the 

area of desert scrub decreased by 22 percent, and the area of 

mesquite woodland increased by 400 percent. Quantitative 

data are not available for changes before 1970, but repeat 

photographs in the late 1800s, early 1960s, and 1994 (Turner 

and others, 2003) show large changes from grasslands to 

woody plants, primarily mesquite.

The changes in upland vegetation from grasslands 

to woody plants can affect high flows (runoff) and low 

flows (ground-water discharge). The changes can decrease 

runoff by (1) increasing interception of precipitation, which 

would increase evaporation from intercepted precipitation, 

56  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
and by (2) increasing transpiration, which would decrease 

soil-moisture storage and increase the amount of storage 

space available for infiltration of precipitation. Increased 

transpiration from the upland vegetation would also ultimately 

decrease low flows because ground-water recharge and 

discharge would be decreased. Measurements of water use 

by vegetation in the San Pedro River flood plain just east of 

Sierra Vista showed larger water-use rates for mesquite than 

for grasslands (Scott and others, 2000). Water use (evaporation 

and transpiration) from grasslands was about equal to 

precipitation, and water use from mesquite woodland was 

about 1.5 times the precipitation. Almost all the water use at 

those study sites in a flood plain was from soils and not from 

ground water, so the results can apply to the upland vegetation 

of the watershed where ground water is not accessible by 

plants.

Riparian vegetation near the San Pedro River generally 

increased during the 20th century in a pattern of about three 

shifts or step changes. The primary types of trees were 

Fremont cottonwood, mesquite, Goodding willow, and 

saltcedar. Before about 1900, the stream valley was mostly 

marshland and there was only a small riparian forest; from 

1900 to the 1930s, riparian vegetation increased slowly but 

was still limited in areal extent and density; from the 1930s to 

1960, vegetation increased at a rapid rate and approximately 

doubled in area; and after 1960, the areal extent and density 

increased at a slow rate or stabilized, but there were many 

changes in the relative abundance of different species (Lacey 

and others, 1975; Hereford, 1993; Stromberg, 1998; Rojo and 

others, 1999).

Changes in riparian vegetation on the stream bank or 

nearby flood plain can affect low flows and high flows. 

Increased riparian vegetation or change to a species that uses 

more water can decrease low flows by (1) intercepting and 

removing ground water that would have discharged to the 

river, (2) increasing the amount of water that is transpired from 

the river (the water moves from the river through soils and 

into plant roots), and (3) lowering the ground-water level near 

the river during the growing season, which creates a larger 

storage volume for downward seepage and loss of streamflow. 

Increased riparian vegetation can decrease high flows by 

lowering the ground-water level and increasing seepage losses.

Another reason that vegetation change is likely an 

important factor in the decrease in streamflow is that small 

changes in watershed vegetation could result in large 

changes in streamflow; evapotranspiration accounts for about 

90 percent of the precipitation that falls on the watershed 

(table 6).

Stream-channel morphology.—Changes in streamchannel morphology likely had some influence on streamflow 

trends. The channel migrated laterally and increased its 

sinuosity and flood plain area during the 20th century 

(Hereford, 1993). There were two distinct periods of 

geomorphic activity. Before 1955, the stream channel was 

active and it widened substantially by lateral migration and 

expansion of meanders. After 1955, the stream channel was 

fairly stable; lateral and vertical changes were small. 

The increased sinuosity and flood plain area could cause 

high flows to decrease by increased attenuation, infiltration, 

and storage of water. Those changes could cause low flows 

to decrease by increased flow to more available bank storage 

and indirectly by increased riparian vegetation in a larger 

floodplain. The changes could also cause low flows to 

increase: high flows in a more sinuous channel and a larger 

floodplain would lose more water to bank storage, which 

would then drain back to the river in subsequent months and 

increase low flows. 

Changes in channel morphology probably had some 

influence on trends in high flows because there is a physical 

explanation for how the changes could have caused decreases 

in flows. The influence probably was not major, however, 

because the changes in morphology should have had the 

same effect on all seasonal total flows, and trends in seasonal 

total flows were different (tables 18, 20, and 21). Changes 

in morphology were likely a minor factor in low-flow trends 

because the changes could have increased and decreased low 

flows and thus balanced out any potential effect on trends.

Human Activities

Ground-water pumping.—Results of this study indicate 

that ground-water pumping had a mixed influence on 

streamflow trends at Charleston; the degree of influence 

depends on the location of pumping wells and the amount of 

pumping. Statistical analyses indicate that seasonal pumping 

from wells near the river for irrigation in the spring and 

summer was a major factor in the decreasing trends in low 

flows and that year-round pumping from the regional aquifer 

in wells away from the river was not a major factor.

Ground-water pumping from the regional basinfill aquifer and floodplain alluvial aquifer is considered 

a possible cause of the decreasing streamflows because 

pumping increased substantially during the second half of 

the 20th century (fig. 22). Total pumping in the Sierra Vista 

subwatershed in Arizona and the San Pedro Basin in Mexico 

(fig. 3) was generally less than 2,000 acre-ft/yr prior to 1940. 

There was pumping for mining activities near Tombstone 

during the first decade of the 20th century, but Tombstone is 

downstream of Charleston, and the pumping should have had 

a minimal effect on streamflow at Charleston from 1913 to 

2002. Total pumping increased steadily from 3,600 acre-ft/yr 

in 1940 to about 28,000 acre-ft/yr in the 1970s and increased 

at a more rapid rate to about 53,000 acre-ft/yr in 2002 (Corell 

and others, 1996; Consultores en Agua Subterranea S.A., 

2000; De Aguinaga, 2002; Arizona Department of Water 

Resources, 2005).

Trends in the San Pedro River Basin  57
Figure 22. Ground-water pumpage in the Upper San Pedro River Basin, Sierra Vista subwatershed, Arizona and Sonora, Mexico, 

1940–2002.

In the United States, pumping was for agriculture, public 

supply, domestic supply, and a military base (Fort Huachuca). 

After 1950, most of the pumping in the United States was 

(1) for nonagricultural uses, (2) from the regional aquifer away 

from the San Pedro River near Sierra Vista and Fort Huachuca, 

and (3) distributed year round. The agricultural pumping in 

the United States was near the river and most was in the spring 

and summer. There were three distinct periods of agricultural 

pumping; average rates were about 3,200 acre-ft/yr during 

1940–63, 8,100 acre-ft/yr during 1964–85, and 4,600 acre-ft/yr 

during 1986–2002 (fig. 22).

In Mexico, pumping was for mining activities, 

agriculture, public supply, and domestic supply. Pumping for 

mining activities mostly was year round and steady at about 

5,100 acre-ft/yr from 1945 to 1980, and then it fluctuated 

and increased to about 16,000 acre-ft/yr in 2002. Agricultural 

pumping, mostly near the river and during spring and summer, 

accounted for about 90 percent of the other pumping (nonmine) in Mexico (De Aguinaga, 2002). The agricultural 

pumping was less than about 1,000 acre-ft/yr before the late 

1970s and increased steadily from about 3,700 acre-ft/yr in 

1980 to 10,700 acre-ft/yr in 2002 (fig. 22). 

From 1906 to 1986, ground water was pumped to 

dewater the Copper Queen mine near Bisbee, Ariz. (fig. 22). 

This pumping was assumed to have a minimal effect on 

discharge to the San Pedro River from the regional basinfill aquifer because (1) the pumping was from ground water 

in bedrock, (2) the pumping was near a surface-water and 

ground-water divide with the adjacent basin to the east, and 

(3) most of the pumped water was transported to evaporation 

ponds and for irrigation south of Bisbee. Seepage from the 

evaporation ponds and return flow from irrigation added some 

artificial recharge to the basin-fill aquifer (Southwest GroundWater Consultants, 2004). The pumping from the Copper 

Queen mine was, therefore, not considered as a possible factor 

in the decreasing streamflow trends and was not added to 

the total pumping discussed for the study area and shown in 

figure 22.

Ground-water pumping can decrease low flows or total 

flows in streams by three principal mechanisms that are 

related to a decrease in ground-water levels: (1) in stream 

reaches that receive ground-water discharge (gaining stream), 

the hydraulic gradient from the aquifer to the stream is 

decreased, and the decreased gradient results in a decrease in 

ground-water discharge to the stream; (2) in stream reaches 

where water flows from the stream to the aquifer and there is 

no unsaturated material between the streambed and the water 

table (losing stream), the hydraulic gradient from the stream 

to the aquifer is increased, and the increased gradient results 

in increased flow of water from the stream to the aquifer; 

and (3) a combination of mechanisms 1 and 2 in which the 

hydraulic gradient and flow direction between the aquifer and 

stream is reversed—initially water moves from the aquifer to 

the stream, then it changes so water moves from the stream to 

the aquifer (Alley and others, 1999). In addition to the above 

three mechanisms that act mostly on low flows, ground-water 

pumping can also decrease total flows during moderate and 

high flows. When ground-water levels are lowered near a 

stream, the storage space in unsaturated material is increased, 

which allows more water to infiltrate the ground and be lost 

from the stream.

58  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM GROUND-WATER PUMPAGE, IN ACRE-FEET PER YEAR

50,000

40,000

30,000

20,000

10,000

0

60,000

19401945195019551960196519701975198019851990199520002005

U.S. AGRICULTURE

COPPER QUEEN MINE

TOTAL PUMPAGE—Excluding

Copper Queen mine

MEXICAN MINING

MEXICAN OTHER

U.S. OTHER
Many previous studies have analyzed the groundwater system and its interaction with the upper San Pedro 

River during the past 40–60 years, and all concluded that 

ground-water pumping caused a decrease in annual base 

flow of the San Pedro River (table 25). Two ground-water 

models estimated an average decrease in base flow of 

49 percent at Charleston (Vionnett and Maddock, 1992; 

Goode and Maddock, 2000), and two models estimated an 

average decrease in base flow of 40 percent at Fairbank, 

Ariz. (Freethey, 1982; Correll and others, 1996). Separate 

analyses of streamflow data estimated a decrease in base flow 

of 49 percent at Charleston (Corell and others, 1996) and 

22 percent at Fairbank (Rojo and others, 1999).

The results of this statistical study appear to be different 

from results of the previous ground-water model simulations. 

This study indicates that seasonal pumping from wells near 

the river was a major factor in the decrease in low flows 

(base flows) at Charleston, but year-round regional pumping 

was not a major factor. If regional pumping had caused a 

trend, the pumping should have affected low flows for all 

months of the year, but factors other than precipitation did not 

cause significant trends in low flows for January, February, 

March, and May (table 19). The influence of seasonal 

pumping near the river fits into this study’s results because 

Table 25. Changes in estimated annual base flow for San Pedro River from predevelopment period to 1977–2002, previous studies, 

and this study

Source

Method of 

estimating base flow

Location 

of estimated 

base flow

Last time period 

for estimated 

base flow

Base flow in acre-feet per year 

and cubic feet per second1 Change in flow

Predevelopment2

Last 

time period

(acre-feet and 

cubic feet per second) (percent)

Vionnett and Maddock 

(1992)

Ground-water model Charleston 1988 8,300

(11.5)

2,900

(4.0)

-5,400

(-7.5)

-65

Corell and others 

(1996)

Base-flow analysis of 

streamflow data

Charleston 1985–1991 9,500

(13.1)

4,800

(6.6)

-4,700

(-6.5)

-49

Goode and Maddock 

(2000)

Ground-water model Charleston 1997 9,600

(13.2)

6,400

(8.9)

-3,200

(-4.3)

-33

This study Measured 3-day 

monthly low flows

Charleston 1991–2002 7,900

(10.9)

4,300

(5.9)

-3,600

(-5.0)

-46

Freethey (1982) Ground-water model Fairbank 1977 7,500

(10.4)

4,500

(6.2)

-3,000

(-4.2)

-40

Corell and others 

(1996)

Ground-water model Fairbank 1990 9,500

(13.1)

5,700

(7.9)

-3,800

(-5.2)

-40

Rojo and others 

(1999)

Previous models and 

statistical analysis

Fairbank 1990 9,500

(13.1)

7,400

(10.2)

-2,100

(-2.9)

-22

1

Base flow is discharge of the San Pedro River during times of no runoff. It is ground-water discharge minus evapotranspiration from nearby riparian 

vegetation.

2

Predevelopment period is prior to 1940.

most of that pumping is in the summer, and pumping during 

the summer could cause a decrease in ground-water discharge 

in the summer and no decrease in the winter. Previous 

ground-water models simulated all pumping (near-stream 

and regional) in annual time periods; thus, the simulations 

could not distinguish between effects of seasonal nearstream pumping and effects of year-round regional pumping. 

A decrease in annual base flow could result from a large 

decrease in base flow during the spring, summer, and fall, 

and no decrease in base flow during the winter. It is possible, 

therefore, that much of the simulated decreases in annual base 

flow at Charleston were from seasonal pumping of nearstream wells and that results of this study are similar to results 

of previous models.

Seasonal near-stream ground-water pumping has a 

similar effect on base flow as transpiration from riparian 

vegetation. Both factors can decrease base flow by removing 

ground water and causing a decrease in the hydraulic gradient 

between ground water and the stream, and both factors can 

cause a base-flow decrease in the summer and no decrease in 

the winter. Thus, it was not possible to distinguish between 

the effects of these two factors using a statistical analysis of 

the available data on precipitation, streamflow, near-stream 

pumping, and riparian vegetation.

Trends in the San Pedro River Basin  59
If the conclusion about year-round regional pumping 

is incorrect (not a major factor), the most likely reason is 

that there was some factor that caused an increase in winter 

low flows that balanced out a decrease caused by regional 

pumping. For example, an increase in winter flows of 3.0 ft3/s 

from 1931 to 2002 could have balanced out a decrease in 

winter flows of 3.0 ft3/s caused by regional pumping. 

Urbanization and runoff-detention basins in Sierra Vista 

are potential factors that could have caused this balancing 

effect by increasing ground-water recharge and resulting 

discharge to the San Pedro River (see next section), but this 

seems unlikely because most of the increased discharge 

to the river would have been in the 1980s, 1990s, or later. 

Urbanization would not have caused an appreciable increase 

in recharge until the size of Sierra Vista increased beyond a 

small town; the population increased from 6,700 in 1970 to 

25,000 in 1980 (City of Sierra Vista, 2005). Runoff-detention 

basins substantial enough to create appreciable recharge 

were not constructed until the late 1980s (Upper San Pedro 

Partnership, 2002).

To evaluate this study’s conclusion about regional 

pumping, trends in precipitation-adjusted low flows were 

evaluated for 1931 to 1980, which is before any potential 

balancing effect from urbanization or runoff-detention 

structures in Sierra Vista. The study conclusion was supported, 

because there were no significant trends in adjusted low flows 

for January, February, March, and May during 1931–80. 

The conclusion from this study that year-round regional 

ground-water pumping was not a major influence on baseflow trends is only for trends in low flows from 1931 to 

2002 at Charleston. Regional U.S. and Mexico pumping 

could affect streamflow at Charleston in the future because 

regional ground-water pumping often has a delayed effect 

on streamflows. Ground-water pumping from wells far from 

a stream may not affect streamflows for years, decades, or 

longer (Alley and others, 1999). 

Urbanization, cattle ranching (grazing), and runoffdetention structures.—Urbanization, cattle grazing, and 

runoff-detention structures probably had some influence on 

streamflow trends. These three factors typically have opposite 

effects on low flows compared to high flows. Urbanization 

and cattle grazing usually cause an increase in high flow and 

a decrease in low flow, and runoff-detention structures usually 

cause a decrease in high flow and an increase in low flow.

Urbanization typically increases high flows by causing 

more runoff from increased impervious areas, and it typically 

decreases low flows by decreasing infiltration of precipitation, 

ground-water recharge, and eventually ground-water 

discharge. Urbanization in Sierra Vista probably caused a 

small increase in high flows of the San Pedro River after the 

1970s when the population and corresponding impervious area 

increased appreciably (City of Sierra Vista, 2005). The effect 

of urbanization in Sierra Vista on low flows appears to be 

different from the typical effect of urbanization in more humid 

areas. Some preliminary studies indicate that urbanization 

may increase ground-water recharge, which would eventually 

result in an increase in low flow (GeoSystems Analysis, 

2004; David C. Goodrich, U.S. Department of AgricultureAgricultural Research Service, written commun., 2002). 

The increased runoff from urban impervious areas is 

concentrated and diverted to ephemeral stream channels where 

much of the runoff infiltrates and becomes recharge. Without 

the concentrated runoff in the urban area, rainfall would be 

diffuse and would not be sufficient to percolate to the water 

table. As in high flows, the increase in low flows would have 

occurred after the 1970s.

Cattle grazing, and specifically overgrazing, in a 

watershed can increase high flows by decreasing landcover vegetation and compacting soils, which decreases the 

infiltration capacity of a soil and increases runoff. Overgrazing 

can decrease low flows in areas where there is naturally 

occurring recharge, because more water runs off and less 

water is available to percolate to the ground-water system and 

become recharge and eventually discharge. Cattle grazing can 

also result in a change in the types of vegetation, which may 

have different effects on runoff.

From 1880 to 1930, there was likely some overgrazing 

and damage to vegetation and soils in the Upper San Pedro 

River Basin, and after 1930 there was no widespread damage 

because the cattle population slowly decreased to relatively 

low levels (Rodgers, 1965). During 1880 to 1900, there were 

about 15,000 to 35,000 cattle in the Upper San Pedro Basin—

many more than the estimated carrying capacity of about 

10,000 (the number of cattle that the land can sustain with no 

damage). During 1900 to 1930, there were about 10,000 to 

20,000 cattle—still more than the estimated carrying capacity. 

After 1930, the cattle population was at or below the carrying 

capacity, and it has decreased slowly as land use has changed 

from mostly ranching and agriculture to more urban and 

residential. In 1988, cattle were excluded from the SPRNCA.

The influence of cattle grazing on streamflow trends of 

the San Pedro River is difficult to determine because grazing 

may be one cause of the changes in vegetation that occurred 

during the 20th century. Results of this study indicate that 

changes in upland and riparian vegetation were a major factor 

in the decreasing trends in high flows and low flows. If cattle 

grazing was a major factor in the vegetation changes, then it 

was also a major indirect factor in the decreasing streamflow 

trends. This study did not evaluate the potential influence of 

cattle grazing on changes in vegetation; previous studies have 

suggested that there were three principal causes of vegetation 

changes—changes in climate, cattle grazing, and fire 

suppression (Hereford, 1993; Turner and others, 2003).

The overgrazing in the late 1800s and early 1900s could 

have caused an increase in high flows during that time by 

compacting soils, causing soil erosion, and damaging or 

removing vegetation. After the 1930s, when damage from 

grazing likely was minimal, soils and vegetation could have 

recovered slowly, which would have decreased high flows. 

The combination of the effects of overgrazing/recovery would 

result in a decreasing high-flow trend from before 1930 to 

after 1930. The same overgrazing/recovery could result in 

60 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
an increasing trend in low flows. It is impossible to separate 

the recovery process from overgrazing from the concurrent 

changes in vegetation, which could have been caused by 

changes in climate. This study can, therefore, only conclude 

that cattle grazing might have been a major indirect factor in 

the decreasing trends of high flows and low flows.

Numerous small runoff-detention structures were built 

on small tributaries throughout the watershed of the upper 

San Pedro River during the last 100 years (Hereford, 1993). 

These structures typically decrease high flows by capturing 

or slowing down runoff, and they increase low flows by 

increasing ground-water recharge and discharge. High-flow 

runoff (total flows and storm runoff) would be decreased 

immediately after construction and low flows would be 

increased months or years later.

Runoff-detention structures in the watershed probably 

were a factor in the decreasing trends in high flows; the 

degree of influence, however, is difficult to determine because 

accurate quantitative data on the number, size, location, and 

dates of construction are not available. The structures likely 

were not a major factor in the streamflow trends for two 

reasons. First, most of the structures likely were built in the 

first half of the 20th century and have been operating during 

most of the 20th century. This would result in a fairly constant 

effect of decreased high flows from the early 20th century 

until 2002 and no decreasing trend over time. The relative 

dates of construction are supported by some topographic 

maps and an assumed correlation between runoff-detention 

structures and cattle population. An evaluation of five 

7.5-minute topographic maps published in the 1950s and 

revised in the 1980s showed that more than 90 percent of the 

runoff-detention structures shown on the maps were built 

before the 1950s. The number and dates of construction of 

runoff-detention structures likely have a moderate correlation 

with the cattle population in the watershed because many 

of the structures were built to create stock ponds for cattle 

(Hereford, 1993). Second, the structures should have had the 

same effect on all seasonal total flows, and trends in seasonal 

total flows were different (tables 18, 20, and 21).

Runoff-detention structures likely caused no trend or a 

minor increase in low flows. Increased recharge and eventually 

discharge is possible because water that originally flowed 

freely down a channel is impounded behind a structure where 

it could infiltrate and become recharge. An appreciable 

increasing trend in recharge and low flows is unlikely because 

(1) an evaluation of ten 7.5-minute topographic maps showed 

that many of the structures are on upland areas where there is 

minimal or no recharge potential, (2) Coes and Pool (2005) 

measured rapid infiltration rates of runoff in ephemeralstream channels of about 1 to 9 ft/hr, so much of the runoff 

could infiltrate before being impounded by a runoff-detention 

structure, and (3) runoff-detention structures may have had a 

constant effect on streamflows for the entire 20th century, with 

no resulting trend in low flows.

Summary and Conclusions

This study was done to improve the understanding of 

trends in streamflow of the San Pedro River in southeastern 

Arizona. Annual streamflow of the river at Charleston, 

Arizona, has decreased by more than 50 percent during the 

20th century. The San Pedro River is one of the few remaining 

free-flowing perennial streams in the arid Southwestern United 

States, and the riparian forest along the river supports several 

endangered species and is an important habitat for migratory 

birds. To make effective and informed decisions, resource 

managers and the public need to have a better understanding 

of the characteristics of the streamflow trends and the causes 

of the trends.

The first step in this study was to place the trends in 

streamflow of the San Pedro River in a regional perspective. 

Relations and trends in seasonal and annual precipitation 

and streamflow for surrounding areas (7,000 mi2) were 

determined and compared to trends in the San Pedro River 

Basin (1,230 mi2). The second step was a detailed evaluation 

of trends in seasonal and annual precipitation and streamflow 

in the San Pedro River Basin. The third step evaluated 

trends in monthly streamflows of the San Pedro River and 

statistically distinguished between the effects of precipitation 

and the effects of factors other than precipitation. The last step 

incorporated results of all the analyses to evaluate the specific 

causes of streamflow trends.

Regional trends in seasonal and annual precipitation and 

streamflow were determined by analyzing precipitation data 

from 38 sites and streamflow data from 21 sites. The data were 

analyzed for 11 time periods starting every 5 years from 

1930 to 1980, and ending in 2002 (for example, 1930–2002, 

1935–2002, and 1940–2002). No significant trends were 

found in 92 percent of the trend tests for precipitation, and no 

significant trends were found in 79 percent of the trend tests 

for streamflow. Most significant trends in spring, fall, and 

winter precipitation were for time periods that started during 

the mid-century drought in 1945–60. The time periods with 

significant trends in streamflow were not as clustered about 

the mid-century drought as were the precipitation trends. 

Significant streamflow trends generally started before 1955.

For the trends in precipitation that were significant, 

90 percent were positive and most of the significant negative 

trends were for summer precipitation. For the significant 

trends in streamflow, about half were positive and half 

were negative.

There are long-term temporal patterns or cycles in 

precipitation and streamflow in the study area. Winter and 

spring precipitation had much more pronounced cycles than 

summer or fall precipitation. Winter and spring precipitation 

was generally high in the 1930s, low in the 1950s and 1960s, 

high in the 1980s, and low in the late 1990s and early 2000s. 

Winter, spring, and fall streamflow in the northwest and 

northeast parts of the study area had similar long-term patterns 

as those seen in the precipitation data. In contrast to the 

obvious streamflow cycles in the northwest and northeast parts 

of the study area, streamflow in the San Pedro River mostly 

just decreased steadily.

Summary and Conclusions  61
By most measures of precipitation and streamflow in 

the regional analysis, trends in the San Pedro River Basin are 

similar to trends in other basins in the southwest part of the 

study area and are generally not similar to trends in basins in 

the rest of the study area. The southwest part of the study area 

includes the San Pedro River Basin, the Whitewater Draw 

Basin to the east, and the Santa Cruz River Basin to the west. 

The only appreciable difference between the San Pedro Basin 

and other basins in the southwest part was in the degree of 

streamflow trends; trends in streamflow of the San Pedro River 

were more severe than trends in streamflow of Whitewater 

Draw and the Santa Cruz River, but all three streams still had 

similar seasonal patterns in trends.

There are several implications of the regional analysis: 

• The southwest part of the study area is more vulnerable 

to changes in summer monsoon storms than the rest 

of study area, because more than half the annual 

precipitation and streamflow in the southwest part 

occurs in the summer. 

• The southwest part of the study area appears to have 

more long-term problems with a decreasing surfacewater supply than the rest of the study area. Most 

significant trends in precipitation and streamflow in 

the southwest part were negative, and most significant 

trends in the rest of the study area were positive. The 

decreasing flow in the San Pedro River is well known, 

but the Santa Cruz River and Whitewater Draw also 

had significant decreasing trends in summer flows.

• There were more significant decreasing trends in 

streamflow than significant decreasing trends in 

precipitation in the southwest part of the study area. 

This indicates that some other factors besides 

precipitation may have influenced the streamflow 

trends.

To improve the understanding of trends in streamflow of 

the San Pedro River, a detailed evaluation was made of trends 

in precipitation, trends in streamflow, and trends in streamflow 

caused by factors other than precipitation. Trends from 1913 to 

2002 were evaluated using precipitation data from Tombstone, 

Arizona, and streamflow data at Charleston, Arizona.

From 1913 to 2002, annual, winter, spring, and fall 

precipitation at Tombstone had no significant trends and 

summer precipitation had a significant decreasing trend. 

Changes in seasonal total flow and low flow for the San Pedro 

River were calculated from the predevelopment period (prior 

of 1940) to the 1990s. Annual total flow decreased from 

57,700 to 22,000 acre-ft/yr, and summer total flow decreased 

from 31,400 to 6,300 acre-ft/yr. Annual low flow decreased 

from 7,900 to 4,300 acre-ft/yr, and summer low flow 

decreased from 900 to 300 acre-ft/yr.

The characteristics of trends in precipitation and 

streamflow during 1913 to 2002 were investigated by 

evaluating step trends over six time periods in the central 

tendency and variability of winter, summer, and fall values. 

Precipitation had mostly no trends in central tendency or 

variability. Streamflow, however, had both monotonic and 

step trends, and several notable differences in trends for the 

different seasons.

There was a step change in the central tendency of 

streamflows at about 1943; before 1943 all seasonal flows 

were high, and after 1943 all seasonal flows were generally 

low. The behavior of the seasonal flows after 1943 was 

different; summer flows decreased continuously, and fall 

and winter flows were mostly steady except for high values 

during 1977–89.

 The interannual variability of seasonal streamflows also 

had patterns. The variability of winter streamflow had two 

distinct step changes; the variability was high during 1913–42, 

low during 1943–76, and high again during 1977–2002. 

Summer interannual variability decreased monotonically 

during the entire record. Fall interannual variability was 

generally similar for the entire record except for a high period 

during 1977–89.

Factors that caused the decreasing trends in streamflow 

of the San Pedro River at Charleston were investigated. 

Possible factors were fluctuations in precipitation and air 

temperature, changes in watershed characteristics, human 

activities, or changes in seasonal distribution of bank 

storage. This study statistically removed or accounted 

for the variation in streamflow caused by fluctuations in 

precipitation. Thus, the remaining variation or trend in 

streamflow was caused by factors other than precipitation.

Partitioning of the variation in streamflow and testing to 

determine trends in the partitioned variation was done using 

two methods: (1) regression analysis between precipitation 

and streamflow using all years in the record and evaluation 

of time trends in regression residuals, and (2) development of 

regression equations between precipitation and streamflow for 

three time periods (early, middle, and late parts of the record) 

and testing to determine if the three regression equations are 

significantly different. Method 1 is an evaluation of monotonic 

changes for the entire record, and method 2 is an evaluation 

of step changes over three time periods in the record. 

The methods were applied to monthly values of total flow 

(average flow) and storm runoff (maximum daily mean flow) 

for 1913–2002, and to monthly values of low flow (3-day low 

flow) for 1931–2002.

Statistical tests provide strong evidence that factors 

other than precipitation caused a decrease in streamflow of 

the San Pedro River. Factors other than precipitation caused 

significant decreasing trends in streamflows for late spring 

through early winter, and did not cause significant trends for 

late winter through early spring. Total flows had significant 

trends in June through December, low flows had significant 

trends in May through December, and storm runoff had 

significant trends in July through September. The effects 

of factors other than precipitation were only tested for July 

through October for storm runoff.

The specific factor or factors (besides precipitation) that 

caused the decreasing streamflow of the San Pedro River 

is difficult to determine because of interaction among the 

different factors and because historical data on the possible 

factors is more qualitative than quantitative. Possible changes 

in watershed characteristics that may have influenced 

streamflow trends are changes in riparian vegetation, 

changes in upland vegetation, and changes in stream-channel 

morphology. Possible human activities that may have 

62  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
influenced streamflow trends are ground-water pumping, 

construction of runoff-detention structures, urbanization, and 

cattle ranching (grazing). 

Changes in upland and riparian vegetation likely were 

major factors in the decreasing trends in total streamflows 

and low flows. Total flows and low flows in summer 

and fall were significantly affected by factors other than 

precipitation, but late winter flows were not significantly 

affected. The significant effects coincide with high rates 

of transpiration from vegetation in the summer, and the 

nonsignificant effects coincide with low rates of transpiration 

in the late winter. Another piece of evidence that implicates 

vegetation as a cause is that the upland and riparian vegetation 

of the San Pedro River Basin changed during the 20th century. 

The relative proportions of different species changed in upland 

vegetation (woody plants increased and grasses decreased), 

and the areal extent and density of riparian vegetation 

increased substantially. 

Ground-water pumping in the United States and Mexico 

had a mixed influence on streamflow trends at Charleston; 

the degree of influence depends on the location of pumping 

wells and the amount of pumping. Statistical analyses indicate 

that seasonal pumping from wells near the river for irrigation 

in the spring and summer was a major factor in the decrease 

in low flows and that year-round pumping from wells in the 

regional aquifer away from the river was not a major factor 

in the decrease in low flows. If regional pumping had caused 

a trend, the pumping should have affected low flows for all 

months of the year, but factors other than precipitation did not 

cause significant trends in low flows for January, February, 

March, and May. Most of the local pumping near the river 

was during the spring and summer, and this seasonal pumping 

probably caused some decreases in summer low flows. 

These conclusions are for trends from 1913 to 2002, and 

regional U.S. and Mexico pumping could affect streamflow 

at Charleston in the future, because regional ground-water 

pumping often has a delayed effect on streamflows.

Other factors (besides precipitation, vegetation, and 

seasonal ground-water pumping near the river) had varying 

degrees of influence on the streamflow trends of the San Pedro 

River. Changes in stream-channel morphology, runoffdetention structures, and cattle grazing likely were factors in 

the decreasing trends in total flows. Some physical processes 

and historical data support the factors as a cause of decreasing 

total flows, but statistical tests in this study indicated each 

factor was not a major influence. Although not major factors 

in themselves, their cumulative effect could have been major. 

Change in bank storage over time likely was another factor in 

some of the decreasing tends in seasonal low flows. The large 

decreasing trends in total flows during the summer would 

have decreased bank storage over time and decreased the 

subsequent release of bank storage during the fall and early 

winter. This decreased bank storage likely had an effect on the 

decreasing trends in fall and early winter low flows.

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64  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Appendices 1–2

 
Appendix 1

Evaluation of Effects of Different StreamflowGaging Station Locations on Trend Analysis

The gaging station San Pedro River at Charleston, 

Arizona (09471000), was moved several times during 

the record from 1913 to 2002. There were three general 

locations that were appreciably different. The first location 

was near Fairbank, Arizona, from September 12, 1912, to 

September 30, 1926. During that time the station was moved 

once about 1,000 ft, but there were no tributaries between the 

two locations, so the streamflow record can be considered 

equivalent from 1912 to 1926. The Fairbank site was about 

7 mi. downstream from the current site, and the drainage area 

of the Fairbank site was about 1,300 mi2. The station was at 

its second location from May 1928 to November 30, 1942. 

That station was about 1.7 mi. downstream from the current 

site and the drainage area was about 1,250 mi2. The station 

has been at its current location since December 1, 1942, and 

its drainage area is 1,234 mi2.

The effects of the different station locations on the trend 

analyses of streamflow performed in this study could not be 

directly determined. Three analyses were made, however, 

to indirectly evaluate the effects of the different locations. 

First, the graphs of precipitation-adjusted streamflow versus 

time were visually inspected to determine if there were any 

obvious breaks or jumps in the data after a station move. 

Such a break or jump might indicate an important difference 

in the effects of factors other than precipitation that was 

caused by the move. The second more rigorous analysis 

was to perform the same trend analysis of streamflow and 

adjusted streamflow for only the period of record where the 

station was at one location—from 1943 to 2002. Values of 

monthly total flow (average flow), monthly low flow (3-day 

low flow), and storm runoff (maximum daily mean flow for 

each month) were analyzed. The third analysis was to adjust 

the flows from the earlier records according to the drainagearea ratio of the station sites, and then perform the same trend 

analysis of streamflow and adjusted streamflow. From 1913 

to 1926, the drainage-area ratio was 0.947, and from 1928 

to 1942, the ratio was 0.987. Thus, flows in the early record 

are adjusted downward to make them more equivalent to the 

flows from the current station location. Monthly total flow 

and maximum daily storm runoff were analyzed. Low flows 

were not analyzed using station-adjusted flows; low flows 

should have little correlation to size of drainage area because 

most low flow is ground-water discharge.

Visual inspection of the plots of adjusted streamflow 

versus time show no apparent breaks or jumps in the plots 

at the time of station moves—1926 and 1943 (figs. 13–15). 

Results of the trend analysis of streamflow data using the 

record from the current station location from 1943 to 2002 

(tables 1A-1F) are similar to the results of the analysis of 

data for the entire record from 1913 to 2002 (tables 14–20). 

There were differences in the magnitude of trends (p-values) 

and a couple monthly-flow trends changed from significant 

to nonsignificant, but the overall conclusions about seasonal 

trends did not change. Results of the analysis of streamflows 

adjusted for station location (tables 1G–1J) were very similar 

to results of the analysis of the flows not adjusted for location 

(tables 14–20). Trends in monthly total flows for February–

December were the same, and January total flow changed 

from nearly significant to not significant. Trends in storm 

runoff were the same.

66  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1A. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and monthly total streamflow for the 

San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1943–2002

[R 2, coefficient of multiple determination]

Month

Number of 

years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Total streamflow 

(cubic feet per second)

Time 

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span3 R2

Standard error 

(years) Span3

January 48 Nov., Dec., and Jan. 0.82 0.283 0.50 0.47 15.49 0.90

February 48 Dec, Jan., and Feb. .74 .209 .75 .66 17.88 .50

March 51 Jan., Feb., and Mar. .87 .174 .50 .60 16.76 .60

April 51 Jan., Feb., and Mar. .67 .136 .60 .60 16.76 .60

May 51 Jan., Feb., and Mar. .63 .191 .50 .60 16.76 .60

June 50 Dec., Mar., and June .78 .303 .50 .42 19.58 .60

July 54 May, June, and July .74 .440 .60 .42 18.45 .60

August 53 June, July, and Aug. .68 .370 .75 .56 16.38 .60

September 54 May, Aug., and Sept. .70 .372 .75 .49 18.16 .60

October 55 May, Sept., and Oct. .89 .290 .60 .61 18.44 .50

November 54 June, Oct., and Nov. .84 .162 .50 .58 17.48 .50

December 53 Oct., Nov., and Dec. .80 .296 .50 .53 19.72 .50

1

Time period for analysis was 1943–2002.

2

LOWESS regression models:

Response variable, total streamflow: log Qn = log P1 + log P2 + log Pn where Qn is average streamflow for month n, in cubic feet per second, 

and Pn is precipitation for month n, in inches.

Response variable, time: Tn = log P1 + log P2 + log Pn where Tn is time for month n, in years, and Pn is precipitation for month n, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

Appendix 1  67
Table 1B. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and monthly low flow for the 

San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1943–2002

[R 2, coefficient of multiple determination]

Month

Number 

of years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Low flow 

(cubic feet per second)

Time 

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span3 R2

Standard error 

(years) Span3

January 49 Oct., Dec., and Jan. 0.78 0.163 0.60 0.66 17.73 0.50

February 48 Nov., Dec., and Jan. .82 .145 .60 .47 15.49 .90

March 51 Jan., Feb., and Mar. .73 .139 .60 .60 16.76 .60

April 51 Jan., Feb., and Mar. .58 .134 .60 .60 16.76 .60

May 48 Nov., Dec., Jan., and Mar. .76 .150 .90 .74 15.94 .80

June 49 Dec., Jan., and June .64 .247 .60 .41 16.62 .90

July 54 Apr., May, June, and July .79 .389 .75 .80 18.62 .60

August 53 July and Aug. .51 .420 .50 .44 16.13 .50

September 54 Aug. and Sept. .52 .239 .80 .38 17.77 .50

October 54 May, Aug., and Sept. .71 .224 .90 .49 18.16 .60

November 54 Aug. and Oct. .74 .147 .50 .25 17.03 .75

December 53 Aug., Oct., and Nov. .73 .134 .50 .53 16.99 .60

1

Time period for analysis was 1943–2002.

2

LOWESS regression models:

Response variable, low flow: log Qn = log P1 + log P2 + log Pn where Qn is 3-day low flow for month n, in cubic feet per second, and Pn is precipitation for 

month n, in inches

Response variable, time: Tn = log P1 + log P2 + log Pn where Tn is time for month n, in years, and Pn is precipitation for month n, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

68  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1C. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and maximum daily storm runoff for 

the San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1943–2002, for selected months

[R 2, coefficient of multiple determination]

Month

Number of 

years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Maximum daily storm runoff 

(cubic feet per second)

Time

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span3 R2

Standard error 

(years) Span3

June 20 p0 and p1 –10 0.54 0.689 0.60 0.51 15.98 0.90

July 54 p0, p1 –10, and p11 –30 .67 .471 .60 .45 16.26 .80

August 55 p0 and p1 –30 .32 .470 .75 ( 4 ) ( 4 ) ( 4 )

September 49 p0, p1 –10, and p11 –30 .63 .621 .60 .49 16.16 .80

October 23 p0 and p1 –30 .85 .442 .80 .47 16.26 .90

1

Time period for analysis was 1943–2002.

2

LOWESS regression models:

Response variable, maximum daily storm runoff: log Qn = log P1 + log P2 + log Pm, where Q is maximum daily mean flow for month n, in cubic feet per 

second, and Pm is precipitation for indicated days previous to day of runoff (p0 is precipitation for day of runoff, p1-10 is cumulative precipitation for days 1 

through 10 prior to runoff), in inches

Response variable, time: Tn = log P1 + log P2 + log Pm, where T is time for month n, in years, and Pm is precipitation for indicated days previous to day of 

runoff, in inches.

3

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

4

LOWESS regression analysis between precipitation and time was not done because the LOWESS equation between precipitation and maximum runoff was 

not sufficiently accurate (R 2 < 0.50).

Appendix 1  69
Table 1D. Trends in monthly total streamflow and monthly total streamflow adjusted for variation in precipitation, San Pedro River at 

Charleston, Arizona, 1943–2002

[<, less than; >, greater than]

Month

Total streamflow (1943–2002)

1

Number of 

years analyzed

Kendall tau trend test

Streamflow and time

Adjusted streamflow 

and time2

Adjusted streamflow 

and adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 48 n 0.145 n 0.180 n 0.077

February 48 p .729 n .351 n .259

March 51 p .852 p .987 p .909

April 51 p .673 n .455 n .626

May 51 n .014 n .229 n .015

June 50 n .004 n .015 n .001

July 54 n <.001 n .005 n <.001

August 53 n .003 n .031 n .005

September 54 n .202 n .011 n <.001

October 55 n .147 n .117 n .212

November 54 n .031 n .066 n .017

December 53 n .145 n .003 n <.001

1

Average streamflow.

2

Variation in streamflow that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in streamflow and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

70 Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1E. Trends in monthly low flow and monthly low flow adjusted for variation in precipitation, San Pedro River at Charleston, 

Arizona, 1943–2002

[<, less than; >, greater than]

Month

Low flow (1943–2002)

1

Number of 

years analyzed

Kendall tau trend test

Flow and time Adjusted flow and time2 Adjusted flow and adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 49 n .208 n 0.211 0.0 1.000

February 48 n .709 p .810 n 0.576

March 51 p .757 p .721 p 0.330

April 51 n .354 n .047 n 0.015

May 48 n .002 n .282 n 0.143

June 49 n <.001 n .017 n 0.010

July 54 n .001 n .026 n 0.016

August 53 n <.001 n .014 n < 0.001

September 54 n .042 n <.001 n 0.001

October 54 n .055 n .006 n 0.001

November 54 n .063 n .002 n 0.001

December 53 n .036 n .041 n < 0.001

1

Three-day low flow.

2

Variation in flow that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in flow and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

Appendix 1  71
Table 1F. Trends in maximum daily storm runoff and maximum daily storm runoff adjusted for variation in precipitation, by month, 

San Pedro River at Charleston, Arizona, 1943–2002

[<, less than; >, greater than]

Month

Storm runoff (1943–2002)

1

Number of 

years analyzed

Kendall tau trend test

Runoff and time Adjusted runoff and time2

Adjusted runoff and 

adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 11 p 0.640 ( 6 ) ( 6 ) ( 6 ) ( 6 )

February 9 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

March 9 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

April 6 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

May 3 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

June 20 n .256 n .770 n .183

July 54 n <.001 n .001 n <.001

August 55 n .008 ( 7 ) ( 7 ) ( 7 ) ( 7 )

September 49 n .305 n .103 n .013

October 23 p .161 p .833 p .751

November 10 n .858 ( 6 ) ( 6 ) ( 6 ) ( 6 )

December 12 p .193 ( 6 ) ( 6 ) ( 6 ) ( 6 )

1

Maximum daily mean streamflow for month.

2

Variation in runoff that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in runoff and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

5

Sufficient data were not available to perform trend analysis.

6

Sufficient data were not available to perform LOWESS regression analysis and to create adjusted values of runoff and time.

7

LOWESS regression equations for June and August runoff were not accurate enough to use for adjusted values of runoff and time.

p-value 

n or p no significant trend > 0.10

n significant negative trend < 0.05

72  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1G. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and station-adjusted monthly total 

streamflow for the San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1913–2002

[R 2, coefficient of multiple determination]

Month

Number of 

years 

analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Station-adjusted total streamflow3

(cubic feet per second)

Time 

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span4 R2

Standard error 

(years) Span4

January 72 Oct., Nov., Dec., and Jan. 0.81 0.259 0.75 0.51 28.14 0.75

February 72 Dec., Jan., and Feb. .80 .184 .60 .29 28.70 .75

March 76 Jan., Feb., and Mar. .66 .188 .75 .51 26.69 .50

April 76 Jan., Feb., and Mar. .50 .180 .75 .51 26.69 .50

May 76 Jan., Feb, and Mar. .51 .184 .75 .51 26.69 .50

June 73 Dec., Jan., Mar., and June .73 .344 .75 .69 30.01 .50

July 76 Jan., May, June, and July .70 .430 .75 .64 27.00 .60

August 74 Feb., July, and Aug. .64 .346 .75 .39 27.35 .60

September 79 May, Aug., and Sept. .62 .400 .75 .23 28.64 .75

October 79 May, Sept., and Oct. .77 .339 .60 .27 30.60 .60

November 77 June, Oct., and Nov. .74 .195 .60 .26 27.30 .75

December 76 Oct., Nov., and Dec. .78 .266 .50 .38 26.76 .60

1

Time period for analysis was 1913–2002.

2

LOWESS regression models:

Response variable, station-adjusted total streamflow: log Qn = log P1 + log P2 + log Pn where Qn is average streamflow for month n (adjusted for station 

location), in cubic feet per second, and Pn is precipitation for month n, in inches

Response variable, time: Tn = log P1 + log P2 + log Pn where Tn is time for month n, in years, and Pn is precipitation for month n, in inches.

3

Station adjusted total streamflow is the flow adjusted for different station locations. From 1913 to 1926, the flow was multiplied times 0.947; from 1928 to 

1942, the flow was multiplied times 0.987; and from 1943 to 2002, the flow was not changed. 

4

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

Appendix 1  73
Table 1H. Results of LOWESS regression analyses between precipitation at Tombstone, Arizona, and station-adjusted maximum 

daily storm runoff for the San Pedro River at Charleston, Arizona, and between precipitation at Tombstone and time, 1913–2002, for 

selected months

[R 2, coefficient of multiple determination]

Month

Number of 

years analyzed1

LOWESS regression models2

Explanatory variables

Response variable

Station-adjusted maximum 

daily storm runoff 3

(cubic feet per second)

Time

(years)

Monthly precipitation 

(inches) R2

Standard error 

(log units) Span4 R2

Standard error 

(years) Span4

June 34 p0 and p1-10 0.32 0.613 0.75 ( 5 ) ( 5 ) ( 5 )

July 78 p0, p1-10, p11-30, and p31-60 .64 .460 .75 .62 26.77 .60

August 78 p0 and p1-30 .35 .438 .75 ( 5 ) ( 5 ) ( 5 )

September 71 p0, p1-10, and p11-30 .57 .548 .60 .46 29.24 .50

October 36 p0 and p1-30 .84 .424 .50 .50 26.33 .60

1

Time period for analysis was 1913–2002.

2

LOWESS regression models:

Response variable, station-adjusted maximum daily storm runoff: log Qn = log P1 + log P2 + log Pm, where Q is maximum daily mean streamflow for 

month n (adjusted for station location), in cubic feet per second, and Pm is precipitation for indicated days previous to day of runoff (p0 is precipitation 

for day of runoff, p1–10 is cumulative precipitation for days 1 through 10 prior to runoff), in inches.

Response variable, time: Tn = log P1 + log P2 + log Pm, where T is time for month n, in years, and Pm is precipitation for indicated days previous to day of 

runoff, in inches.

3

Station-adjusted monthly runoff is the runoff adjusted for different station locations. From 1913 to 1926, the runoff was multiplied times 0.947; from 1928 

to 1942, the runoff was multipled times 0.987; and from 1943 to 2002, the runoff was not changed.

4

Span is a parameter that controls the window width and smoothness of the fitted LOWESS model. As the span is increased, the window width is increased 

and more points influence the magnitude of the fitted values. Thus, a larger span will have a smoother fitted model than a smaller span.

5

LOWESS regression analysis between time and precipitation was not done because the LOWESS equation between maximum streamflow and precipitation 

was not sufficiently accurate (R 2 < 0.50).

74  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 1I. Trends in station-adjusted monthly total streamflow and station-adjusted monthly total streamflow adjusted for variation in 

precipitation, San Pedro River at Charleston, Arizona, 1913–2002

[<, less than; >, greater than]

Month

Station-adjusted total streamflow (1913–2002)

1

Number of 

years analyzed

Kendall tau trend test

Streamflow and time

Adjusted streamflow 

and time2

Adjusted streamflow and 

adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 72 n 0.031 n 0.296 n 0.119

February 72 p .892 p .379 p .131

March 76 p .872 p .317 p .174

April 76 p .432 p .459 p .587

May 76 n .116 n .569 n .224

June 73 n .001 n <.001 n .034

July 76 n <.001 n .008 n .001

August 74 n <.001 n <.001 n <.001

September 79 n <.001 n <.001 n <.001

October 79 n .037 n <.001 n .001

November 77 n .001 n .001 n <.001

December 76 n .031 n .001 n <.001

1

Monthly average streamflow adjusted for different station locations. From 1913 to 1926, the flow was multiplied times 0.947; from 1928 to 1942, the flow ws 

multiplied times 0.987; and from 1943 to 2002, the flow was not changed. 

2

Variation in streamflow that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in streamflow and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

p-value 

n or p no significant trend > 0.10

n significant negative trend < 0.05

Appendix 1  75
Table 1J. Trends in station-adjusted maximum daily storm runoff and station-adjusted maximum daily storm runoff adjusted for 

variation in precipitation, by month, San Pedro River at Charleston, Arizona, 1913–2002

[<, less than; >, greater than]

Month

Station-adjusted storm runoff (1913–2002)

1

Number of 

years analyzed

Kendall tau trend test

Runoff and time Adjusted runoff and time2

Adjusted runoff and 

adjusted time3

Slope4 p-value Slope4 p-value Slope4 p-value

January 18 n 0.820 ( 6 ) ( 6 ) ( 6 ) ( 6 )

February 17 n .967 ( 6 ) ( 6 ) ( 6 ) ( 6 )

March 15 p .018 ( 6 ) ( 6 ) ( 6 ) ( 6 )

April 7 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

May 3 ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 ) ( 5 )

June 34 n .406 ( 7 ) ( 7 ) ( 7 ) ( 7 )

July 78 n <.001 n .007 n .013

August 78 n <.001 ( 7 ) ( 7 ) ( 7 ) ( 7 )

September 71 n .002 n .015 n .010

October 36 p .313 n .361 n .084

November 17 n .303 ( 6 ) ( 6 ) ( 6 ) ( 6 )

December 19 p .624 ( 6 ) ( 6 ) ( 6 ) ( 6 )

1

Maximum daily mean streamflow for month adjusted for different station locations. From 1913 to 1926, the flow was multiplied times 0.947; from 1928 to 

1942, the flow was multiplied times 0.987; and from 1943 to 2002, the flow was not changed.

2

Variation in runoff that was caused by variation in precipitation was removed by LOWESS regression analysis.

3

Variations in runoff and time that were caused by variation in precipitation were removed by LOWESS regression analysis.

4

Slope of trend: n is negative and p is positive.

5

Sufficient data were not available to perform trend analysis.

6

Sufficient data were not available to perform LOWESS regression analysis and to create adjusted values of runoff and time.

7

LOWESS regression equations for June and August runoff were not accurate enough to use for adjusted values of runoff and time.

p-value 

n or p no significant trend > 0.10

n nearly significant negative trend 0.05–0.10

n significant negative trend < 0.05

p significant positive trend < 0.05

76  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Appendix 2

Supplemental Data for Analysis of Step Trends in Streamflow

Table 2A. Results of least-squares regression analyses between precipitation at Tombstone, Arizona, and monthly total streamflow 

for the San Pedro River at Charleston, Arizona, for selected time periods

[R 2, coefficient of determination; ---, no data; <, less than; >, greater than]

Month

Months of 

cumulative 

precipitation 

used for 

explanatory 

variable1

Number 

of low 

outliers 

removed2

Number 

of high 

outliers 

removed2

Number 

of years 

analyzed

Time 

period 

analyzed

Least squares linear regression equation3

Coefficients Statistics

Intercept Slope R2

Standard 

error 

(log units)

F-test 

p-value

January4 --- --- --- --- --- --- --- --- ---

February 3 0 6 60 1913–02 1.11 0.47 0.42 0.161 <.001

0 2 20 1913–42 1.00 .74 .51 .163 <.001

0 0 20 1943–76 1.16 .35 .19 .162 .058

0 4 20 1977–02 1.12 .44 .54 .160 <.001

March 3 2 4 66 1913–02 1.12 .41 .33 .155 <.001

1 1 22 1913–42 1.12 .41 .18 .176 .049

1 0 22 1943–76 1.15 .33 .40 .121 .002

0 3 22 1977–02 1.10 .48 .42 .175 .001

April 53 2 0 72 1913–03 .98 .27 .15 .186 .001

1 0 24 1913–42 .93 .36 .08 .278 .195

1 0 24 1943–76 1.01 .11 .14 .078 .075

0 0 24 1977–02 .96 .38 .40 .150 .001

May 53 2 0 72 1913–02 .78 .25 .10 .209 .007

1 0 24 1913–42 .72 .51 .14 .278 .074

1 0 24 1943–76 .85 .07 .02 .120 .482

0 0 24 1977–02 .69 .33 .24 .183 .014

June 1 43 0 36 1913–02 1.01 .80 .21 .450 .005

12 0 12 1913–42 1.35 1.33 .51 .400 .009

18 0 12 1943–76 1.05 .96 .31 .408 .059

13 0 12 1977–02 .73 .58 .18 .396 .174

July 2 0 0 75 1913–02 .94 1.61 .36 .470 <.001

0 0 25 1913–42 1.57 .97 .40 .309 .001

0 0 25 1943–76 1.61 .74 .20 .284 .023

0 0 25 1977–02 .13 2.51 .53 .438 <.001

  77
Table 2A. Results of least-squares regression analyses between precipitation at Tombstone, Arizona, and monthly total streamflow 

for the San Pedro River at Charleston, Arizona, for selected time periods—Continued

Month

Months of 

cumulative 

precipitation 

used for 

explanatory 

variable1

Number 

of low 

outliers 

removed2

Number 

of high 

outliers 

removed2

Number 

of years 

analyzed

Time period 

analyzed

Least squares linear regression equation3

Coefficients Statistics

Intercept Slope R2

Standard 

error 

(log units)

F-test 

p-value

August 1 0 0 75 1913–02 1.51 1.26 0.41 0.373 < 0.001

0 0 25 1913–42 1.61 1.39 .38 .307 .001

0 0 25 1943–76 1.55 1.42 .67 .325 <.001

0 0 25 1977–02 1.46 .81 .22 .346 .018

September 2 0 0 72 1913–02 .62 1.52 .39 .426 <.001

0 0 24 1913–42 .82 1.61 .38 .399 .001

0 0 24 1943–76 .71 1.39 .58 .325 <.001

0 0 24 1977–02 .44 1.37 .35 .394 .002

October 2 5 3 66 1913–02 .84 .82 .29 .359 <.001

2 0 22 1913–42 .90 1.01 .30 .360 .008

3 2 22 1943–76 .96 .29 .11 .280 .139

0 1 22 1977–02 .57 1.32 .52 .345 <.001

November 3 4 5 54 1913–02 .89 .46 .28 .185 <.001

2 3 18 1913–42 .94 .51 .25 .182 .035

2 0 18 1943–76 .99 .32 .26 .144 .029

0 2 18 1977–02 .78 .45 .35 .177 .010

December 3 3 5 63 1913–02 1.11 .45 .29 .209 <.001

0 1 21 1913–42 1.05 .94 .48 .207 .001

2 1 21 1943–76 1.18 .19 .18 .153 .058

1 3 21 1977–02 .97 .59 .52 .175 <.001

1

Precipitation for same month as streamflow and indicated number of previous months (1 is precipitation for same month, and 2 is precipitation for same 

month and one previous month).

2

See page 31 for explanation of outliers

3

Regression equation is log Q = B1 + B2 log P,

 where

Q = monthly average streamflow, in cubic feet per second;

P = cumulative precipitation for indicated months, in inches;

B1 = regression intercept; and

B2 = regression slope.

4

Linear regression equations could not be adequately fit to data.

5

Months of cumulative precipitation are January, February, and March.

p-value 

no significant regression equation > 0.10

nearly significant regression equation 0.05–0.10

significant regression equation < 0.05

78  Trends in Streamflow of the San Pedro River and Regional Trends in Precipitation and Streamflow, AZ and NM
Table 2B. Results of least-squares regression analyses between precipitation at Tombstone, Arizona, and maximum daily storm runoff 

for the San Pedro River at Charleston, Arizona, for selected time periods

[R 2, coefficient of determination;<, less than]

Month

Days of 

cumulative 

precipitation 

used for 

explanatory 

variable1

Number 

of years 

analyzed

Time period 

analyzed

Least squares linear regression equation2

Coefficients Statistics

Intercept Slope R2

Standard 

error F-test p-value

July 2 72 1913–02 2.88 0.15 0.03 0.548 0.154

24 1913–42 3.13 .07 .02 .382 .493

24 1943–76 3.11 .21 .06 .307 .232

24 1977–02 2.35 .11 .02 .524 .538

11 72 1913–02 2.73 .60 .16 .509 <.001

24 1913–42 3.06 .28 .11 .365 .118

24 1943–76 2.95 .39 .14 .294 .070

24 1977–02 2.28 .65 .16 .484 .053

August 2 69 1913–02 3.08 .21 .10 .478 .008

23 1913–42 3.27 .10 .03 .376 .400

23 1943–76 3.29 .46 .39 .425 .001

23 1977–02 2.69 .04 .01 .444 .701

11 69 1913–02 2.89 .42 .10 .478 .007

23 1913–42 3.08 .83 .51 .269 <.001

23 1943–76 2.92 .24 .05 .530 .297

23 1977–02 2.64 .23 .02 .440 .474

September 2 69 1913–02 2.62 .22 .09 .582 .015

23 1913–42 2.87 .21 .12 .440 .102

23 1943–76 2.64 .31 .17 .540 .053

23 1977–02 2.32 .12 .03 .672 .452

11 69 1913–02 2.51 .57 .16 .557 .001

23 1913–42 2.74 .46 .10 .446 .150

23 1943–76 2.50 .84 .29 .499 .008

23 1977–02 2.28 .39 .11 .642 .120

1

Precipitation for same day as daily runoff and indicated number of previous days (2 is same day and 1 previous day, and 11 is same day and 10 previous days).

2

Regression equation is log Q = B1 + B2 log P,

 where

Q = monthly maximum daily mean streamflow, in cubic feet per second;

P = cumulative precipitation for indicated days, in inches;

 B1 = regression intercept; and

 B2 = regression slope.

Appendix 2  79

p-value 

no significant regression equation > 0.10

nearly significant regression equation 0.05–0.10

significant regression equation < 0.05
Manuscript approved for publication, May 09, 2005.

Prepared by the Reports Section, U.S. Geological Survey, 

Tucson, Arizona.

USGS Publishing staff

Steve A. Longsworth, Supervisory Hydrologist

Tracey L. Suzuki, Technical Editor

John Callahan, Illustrator

For more information concerning the research in this report, contact 

the Arizona Water Science Center Director,

U.S. Geological Survey, 520 N. Park Ave., Suite 221

Tucson, AZ 85719

http://az.water.usgs.gov
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Thomas and Pool—TRENDS IN STREAMFLOW OF THE SAN PEDRO RIVER, SOUTHEASTERN ARIZONA, AND 

REGIONAL TRENDS OF PRECIPITATION AND STREANFLOW IN SOUTHEASTERN ARIZONA AND 

SOUTHWESTERN NEW MEXICO—U.S. Geological Survey Professional Paper 1712