U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2006–3004

May 2006 Printed on recycled paper

Introduction

Total annual streamflow of the 

San Pedro River at Charleston 

in southeastern Arizona (fig. 1) 

decreased by about 66 percent from 

1913 to 2002 (fig. 2). 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. The decreasing trend 

in streamflow has led to concerns that 

riparian habitat may be damaged and 

that overall long-term water supply 

for a growing population may be 

threatened. Resource managers and 

the public have an interest in learning 

more about the trend and the possible 

causes of the trend.

Thomas and Pool (2006) 

investigated the decreasing trends in 

Figure 2. Trends in annual and seasonal 

streamflow of San Pedro River at Charleston, 

Arizona. Lines are LOWESS fit to data.

Prepared in cooperation with the

BUREAU OF LAND MANAGEMENT

Trends in Streamflow of the San Pedro River, 

Southeastern Arizona

Tucson r r d Pe o San evi R

Charleston

Watershed of the

San Pedro River at Charleston

UNITED S

MEXICO

TATES

A R I Z O N A

Phoenix

streamflow of the San Pedro River. Their study evaluated trends 

in seasonal streamflows and trends in the relation between 

precipitation and streamflow. The purpose of this fact sheet is 

to summarize results of the detailed study by Thomas and Pool 

(2006).

Changes in total annual streamflow of the San Pedro River 

at Charleston, Arizona, were greater than changes in annual 

precipitation at Tombstone, Arizona, for the same period 

(1913–2002; figs. 2 and 3). Annual precipitation decreased by 

13 percent, and annual streamflow decreased by 66 percent. 

Winter precipitation and streamflow changed by a small 

amount, but summer precipitation decreased by 26 percent, and 

summer streamflow decreased by 85 percent. 

Possible factors that could have caused the decreasing 

trends in streamflow were trends in precipitation, changes 

in watershed characteristics, and human activities. The 

variation in streamflow caused by variation in precipitation 

was statistically removed. Thus, 

the remaining variation or trend in 

streamflow can be attributed to factors 

other than precipitation.

Summer flow (–85%),

trend test p-value less than 0.001

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

1,000

11910

1920193019401950196019701980199020002005

Winter flow (–13%),

trend test p-value= 0.115

100

10

1,000

1

Annual flow (–66%),

trend test p-value less than 0.001

100

10

1,000

1

19101920193019401950196019701980199020002005

20

15

10

25

5

0

20

15

10

25

5

0

20

15

10

25

5

0

PRECIPITAION, IN INCHES

Annual (–13%),

trend test p-value= 0.133

Summer (–26%),

trend test p-value= 0.011

Winter (+6%),

trend test p-value= 0.781

Figure 3. Trends in annual and seasonal precipitation at Tombstone, Arizona. Lines are 

LOWESS fit to data.

Figure 1. Location of study area.
Methods

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 

and statistical tests 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 (rainfall-runoff relations) are significantly 

different. Method 1 was applied to monthly values of total flow 

(average flow) and low flow (3-day low flow), and method 2 

was applied to total flows. The low flows are roughly analogous 

to base flow, which is ground-water discharge to the river.

An important feature of the statistical analysis in the study 

is that it provides objective criteria for making decisions and 

interpretations about the data The statistical tests for trends 

result in a p-value. The p-value is a measure of the strength of 

evidence (data) for determining if the change in flow over time 

is a random occurrence or if it is a significant trend that did 

not occur by chance. As the p-value decreases, the evidence to 

support a conclusion for a trend becomes stronger. A threshold 

significance level of 0.05 was used in the study; a p-value of 

less than 0.05 means that the trend is considered significant. A 

p-value of 0.05 means that there is a 5-percent probability that 

the conclusion for a trend is incorrect.

The regression analysis between precipitation and 

streamflow (method 1) was done by using a regressionsmoothing technique called locally weighted scatterplot 

smoothing (LOWESS) (Cleveland, 1979; Insightful, 2001). 

This nonlinear technique was used because the relation between 

precipitation and streamflow is not linear. Examples of the 

nonlinear relations are shown for February and July in figure 4.

Figure 4. Examples of LOWESS fits to precipitation at Tombstone 

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

February and July.

Results of Regressions and Trend Tests

The LOWESS analyses were successful in explaining 

much of the variation in streamflow (tables 1 and 2). 

Generally, precipitation for the same month as streamflow 

and precipitation for several preceding months were used 

in the LOWESS equations. The R2 values shown in tables 1 

and 2 represent the amount of variation in streamflow that is 

explained by precipitation. Thus, precipitation in December, 

January, and February explained 80 percent of the variation 

in total streamflow for February. The advantage of using 

several months of precipitation instead of just one month of 

precipitation is evident in the comparison of the R2 values 

of single-variable LOWESS equations to the R2 values of 

multivariable equations. For February, the R2 value was 0.36 for 

a single-variable equation and 0.80 for a multivariable equation; 

for July, the R2 value was 0.33 for one variable and 0.70 for 

multiple variables (table 1 and fig. 4).

To determine if factors other than precipitation caused trends 

in total flows and low flows, the residuals from the LOWESS 

multivariable analyses were tested for trends using a Kendall 

tau statistical test (Helsel and Hirsch, 1992). The LOWESS 

residual (measured minus predicted value) represents streamflow 

with the variability caused by precipitation removed. Trends in 

the residuals are trends caused by factors other than variation 

in precipitation. Residual trends are also trends in the relation 

between precipitation and streamflow.

Factors other than precipitation caused significant trends in 

total flows for June-December and did not cause significant 

trends for January-May (table 3). For low flows, factors other 

than precipitation caused significant trends for May, June, 

Table 1. Results of LOWESS regression analyses between monthly 

precipitation at Tombstone, Arizona, and monthly total streamflow for 

the San Pedro River at Charleston, Arizona

[R2, coefficient of multiple determination]

Month of

total 

streamflow1

Months of precipitation used in 

LOWESS regression equation2

R2 for regression 

equation

Jan. Oct., Nov., Dec., Jan. 0.81

Feb. Dec., Jan., Feb. .80

Mar. Jan., Feb., Mar. .66

Apr. Jan., Feb., Mar. .50

May Jan., Feb., Mar. .52

June Dec., Jan., Mar., June .73

July Jan., May., June, July .70

Aug. Feb., July, Aug. .64

Sept. May, Aug., Sept. .62

Oct. May, Sept., Oct. .77

Nov. June, Oct., Nov. .74

Dec. Oct., Nov., Dec. .78

1Time period for analysis was 1913–2002.

2LOWESS regression model: 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.

Table 2. Results of LOWESS regression analyses between monthly 

precipitation at Tombstone, Arizona, and monthly low flow for the San 

Pedro River at Charleston, Arizona

[R2, coefficient of multiple determination]

Month of 

low flow1

Months of precipitation used in 

LOWESS regression equation2

R2 for regression

equation

Jan. Oct., Nov., Dec., Jan. 0.80

Feb. Nov., Dec., Jan. .82

Mar. Jan., Feb., Mar. .58

April Jan., Feb., Mar. .60

May Nov., Dec., Jan., Mar. .75

June Dec., Jan., June .57

July Apr., May, June, July .81

Aug. Dec., July, Aug. .67

Sept. Jan., Aug., Sept. .60

Oct. May, Aug., Sept. .66

Nov. Aug. and Oct. .65

Dec. Aug., Oct., Nov. .59

1Time period for analysis was 1931–2002.

2LOWESS regression model: 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.

February

R2= 0.36

STREAMFLOW, IN CUBIC

FEET PER SECOND

PRECIPITATION FOR MONTH, IN INCHES

100

10

20.0

1,000

1

July

R2= 0.33

000.110.020.01.00.110.01.0
Table 3. Trends in monthly total streamflow and monthly total 

streamflow adjusted for variation in precipitation, San Pedro River at 

Charleston, Arizona, 1913–2002

[<, less than]

Month

Total streamflow, 1913–2002

Kendall tau trend test

Streamflow and time Adjusted streamflow

and time1

Slope2 p-value Slope2 p-value

Jan. n 0.017 n 0.208

Feb. n .930 p .428

Mar. n .996 p .487

Apr. p .542 p .638

May n .081 n .449

June n .001 n <.001

July n <.001 n .007

Aug. n <.001 n .001

Sept. n <.001 n <.001

Oct. n .029 n <.001

Nov. n <.001 n <.001

Dec. n .018 n <.001

1

Variation in streamflow that was caused by variation in precipitation was 

removed by LOWESS regression analysis.

2

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

p-value

n or p not significant 0.05 to 1.00

n significant <0.05

Streamflow adjusted for

precipitation, p-value= 0.428

STREAMFLOW, IN CUBIC FEET PER SECOND

100

10

1,000

11910

192019301940195019601970198019902000

100

FEBRUARY JULY

10

1,000

1

Streamflow adjusted for

precipitation, p-value= 0.007

Streamflow, p-value= 0.930

Streamflow,

p-value less than 0.001

200519101920193019401950196019701980199020002005

Figure 5. Trends in streamflow and adjusted streamflow for February 

and July, San Pedro River at Charleston, Arizona. Lines are LOWESS 

fit to data.

February,

p-value (slope)= 0.213

p-value (intercept)= 0.814

STREAMFLOW, IN CUBIC

FEET PER SECOND

PRECIPITATION FOR DECEMBER,

JANUARY, AND FEBRUARY, IN INCHES

1913–42

1913–42

1943–76

1943–76

1977–2002

1977–2002

PRECIPITATION FOR JUNE,

AND JULY, IN INCHES

100

10

0.210.020.0

1,000

1

July,

p-value

(slope)= 0.002

1.00.210.01.020.0

and August-December and did not cause significant trends 

for January-April and July (table 4). Thus, a seasonal pattern 

was determined with significant trends in summer, fall, and 

early winter flows, and no significant trends in late winter and 

spring flows. Examples of trends in streamflow and trends in 

streamflow adjusted for variation in precipitation (LOWESS 

residuals) are shown for February and July in figure 5.

Trends in rainfall-runoff relations for three time periods 

were evaluated by comparing regression relations between 

precipitation and streamflow for 1913–42, 1943–76, and 1977–

02. The difference among regression relations was determined 

with a nested F-test (Helsel and Hirsch, 1992). The results 

of the nested F-tests were similar to results of the LOWESS 

residual tests—trends in summer, fall, and late winter flows 

were significant, and trends in other parts of the year were 

not significant (table 5). Examples of trends in rainfall-runoff 

relations for February and July are shown in figure 6.

Factors Affecting Trends

The primary factors that could have caused decreasing 

streamflow trends and changes in rainfall-runoff relations are 

decreases in precipitation, natural or human-induced changes 

in watershed characteristics, and increases in ground-water 

pumping. Examples of watershed characteristics that can 

change over time are riparian vegetation, upland vegetation, 

and stream-channel morphology. Annual precipitation 

decreased by 13 percent from 1913 to 2002, and the decrease 

likely resulted in some of the decrease in streamflow; however, 

statistical analyses provide strong evidence that other factors 

also contributed to the decrease in streamflow. 

Figure 6. Trends in rainfall-runoff relations for February and July, 

San Pedro River at Charleston, Arizona, 1913 to 2002.

Table 4. Trends in monthly low flow and monthly low flow adjusted 

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

1931–2002

[<, less than]

Month

Low flow, 1931–2002

Kendall tau trend test

Streamflow and time Adjusted streamflow

and time1

Slope2 p-value Slope2 p-value

Jan. n 0.014 n 0.089

Feb. n .292 n .965

Mar. p .527 p .342

Apr. n .139 n .293

May n <.001 n .007

June n <.001 n .002

July n <.001 n .073

Aug. n <.001 n .002

Sept. n <.001 n <.001

Oct. n <.001 n .003

Nov. n .007 n <.001

Dec. n .003 n <.001

1Variation in low flow that was caused by variation in precipitation was 

removed by LOWESS regression analysis.

2Slope of trend: n is negative and p is positive

p-value

n or p not significant 0.05 to 1.00

n significant <0.05
Changes in upland and riparian vegetation were likely major 

factors in the decreasing trends in total streamflows and low 

flows. Factors other than precipitation caused significant trends 

in total flows and low flows in the summer and fall, but those 

factors did not cause significant trends in late winter flows. The 

significant trends coincide with high rates of transpiration from 

vegetation in the summer, and the nonsignificant trends coincide 

with low rates of transpiration in the late winter. Another piece 

of evidence that implicates vegetation as a cause of decreased 

flows 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 

(Rojo and others, 1999; Kepner and Edmonds, 2002; as 

referenced in Thomas and Pool, 2006).

Ground-water pumping in the upper San Pedro watershed 

in Mexico and the United States had a mixed influence on 

streamflow trends at Charleston. Pumping increased from less 

than 2,500 acre-ft/yr before 1940 to about 53,000 acre-ft/yr in 

2002 (Thomas and Pool, 2006). 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. The analyses also indicate 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 April (table 4). These conclusions are for 

trends from 1913–2002, and regional pumping in the United 

States and Mexico could affect streamflow at Charleston in 

the future, because regional ground-water pumping can have a 

delayed effect on streamflows (Alley and others, 1999).

—Blakemore E. Thomas

References

Alley, W.M., Reilly, T.E., and Franke, O.L., 1999, Sustainability 

of ground-water resources: U.S. Geological Survey Circular 

1186, 79 p.

Cleveland, W.S., 1979, Robust locally weighted regression and 

smoothing scatterplots: Journal of the American Statistical 

Association, v. 74, p. 829– 836.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elesevier Science Publishing 

Company, Inc., 522 p.

Insightful, 2001, S-Plus 6 for windows guide to statistics, V. 1, 

Seattle, Washington, Insightful Corporation, 730 p.

Thomas, B.E., and Pool, D.R., 2006, Trends in streamflow 

of the San Pedro River, southeastern Arizona, and trends 

in precipitation and streamflow in northwestern New 

Mexico and southeastern Arizona: U.S. Geological Survey 

Professional Paper 1712, 79 p.

For further information, contact:

Blakemore E. Thomas 

U.S. Geological Survey

Arizona Water Science Center

520 North Park Avenue, Suite 221

Tucson, Arizona, 85719-5035

Email: bthomas@usgs.gov or visit home page 

http://az.water.usgs.gov

Table 5. 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]

Month

Months of 

cumulative 

precipitation used for 

explantory 

variable1

p-values for significance tests of difference among regression relations for 

three time periods2

Slope3 Intercept4

Jan.5 --- --- ---

Feb. 3 0.213 0.814

Mar. 3 0.663 0.961

Apr. 63 0.302 0.810

May 63 0.188 0.198

June 1 0.451 0.008

July 2 0.002 ( 7 )

Aug. 1 0.239 <0.001

Sept. 2 0.889 <0.001

Oct. 2 0.014 ( 7 )

Nov. 3 0.731 0.002

Dec. 3 <0.001 ( 7 )

1Precipitation for same month as streamflow and indicated number of 

previous months (2 months is the same month and the previous month)

2Data were grouped into three time periods (1913–42, 1943–76, and

1977–2002). For each time period, a linear regression analysis was made 

between precipitation and monthly average streamflow. The difference among 

regression relations was tested with a nested F-test.

3Slope of regression relations.

4Intercept of regression relations.

5Linear regression relations could not be fit.

6Months of cumulative precipitation are January, February, and March.

7Significance test for difference among regression intercepts is not valid 

when the slopes are significantly different.

p-value

not significant 0.05 to 1.00

significant <0.05