Estimating Low-Flow Frequency Statistics and 

Hydrologic Analysis of Selected Streamflow-Gaging Stations, 

Nooksack River Basin, Northwestern Washington and Canada

Scientific Investigations Report 2009–5170

Prepared in cooperation with the Lummi Nation

U.S. Department of the Interior

U.S. Geological Survey
Cover: Photograph of Racehorse Falls near Kendall, Washington. (Photograph taken by 

Christopher A. Curran, 2009.)
Estimating Low-Flow Frequency 

Statistics and Hydrologic Analysis of 

Selected Streamflow-Gaging Stations, 

Nooksack River Basin, Northwestern 

Washington and Canada

By Christopher A. Curran and Theresa D. Olsen

Prepared in cooperation with the Lummi Nation

Scientific Investigations Report 2009–5170

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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Suggested citation:

Curran, C.A., and Olsen, T.D., 2009, Estimating low-flow frequency statistics and hydrologic analysis of selected 

streamflow-gaging stations, Nooksack River basin, northwestern Washington and Canada: U.S. Geological Survey 

Scientific Investigations Report 2009–5170, 44 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................6

Description of Study Area ..................................................................................................................6

Previous Investigations........................................................................................................................7

Low-Flow Frequency Statistics at Continuous-Record Gaging Stations and Miscellaneous 

Measurement Sites .........................................................................................................................7

Estimating Low-Flow Frequency Statistics at Ungaged Sites Using Regional Regression 

Equations ...........................................................................................................................................8

Methods of Regression........................................................................................................................8

Basin Attributes.....................................................................................................................................8

Regression Equations.........................................................................................................................13

Accuracy and Limitations..................................................................................................................14

Hydrologic Analysis of Selected Streamflow-Gaging Stations ...........................................................14

Description of Subbasins ..................................................................................................................14

Racehorse Creek .......................................................................................................................16

Warm Creek ................................................................................................................................18

Clearwater Creek.......................................................................................................................20

Skookum Creek...........................................................................................................................22

Anderson Creek..........................................................................................................................24

Fishtrap Creek.............................................................................................................................26

Evaluation of Redundancy in the Streamflow-Gaging Station Network ...................................28

Hydrograph Comparison Method............................................................................................28

Daily-Value Correlation Method..............................................................................................30

Variable-Space Method............................................................................................................34

Flow-Duration-Ratio Method ...................................................................................................35

Summary of Methods and Prioritization of Streamflow-Gaging Stations ........................37

Summary........................................................................................................................................................39

Acknowledgments.......................................................................................................................................40

References Cited..........................................................................................................................................41

Appendix A. Regression Equations for Estimating Daily Mean Streamflow at Six Gaging 

Stations in the Nooksack River Basin.........................................................................................43
iv

Figures

Figure 1. Map showing location of the Nooksack River basin and major rivers and 

population centers in the basin, Washington and Canada ........................... 2

Figure 2. Map showing locations of streamflow-gaging stations and miscellaneous 

measurement sites in and near the Nooksack River basin, Washington 

and Canada ................................................................................. 3

Figure 3. Map showing location of streamflow-gaging stations in Racehorse, Warm, 

Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins that were 

analyzed for redundancy in the streamflow-gaging station network, 

Nooksack River basin, Washington and Canada ....................................... 15

Figure 4. Satellite image showing oblique view and delineation of the Racehorse 

Creek subbasin with the January 2009 landslide area, Nooksack River basin, 

Washington ................................................................................. 16

Figure 5. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Racehorse Creek 

at North Fork Road, near Kendall, Washington .......................................... 17

Figure 6. Satellite image showing oblique view and delineation of the Warm Creek 

subbasin, Nooksack River basin, Washington .......................................... 18

Figure 7. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Warm Creek near 

Welcome, Washington ..................................................................... 19

Figure 8. Satellite image showing oblique view and delineation of the Clearwater Creek 

subbasin, Nooksack River basin, Washington .......................................... 20

Figure 9. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Clear Water Creek 

near Welcome, Washington ............................................................ 21

Figure 10. Satellite image showing oblique view and delineation of the Skookum Creek 

subbasin, Nooksack River basin, Washington .......................................... 22

Figure 11. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Skookum Creek near 

Wickersham, Washington ............................................................... 23

Figure 12. Satellite image showing oblique view and delineation of the Anderson Creek 

subbasin, Nooksack River basin, Washington .......................................... 24

Figure 13. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Anderson Creek near 

Goshen, Washington ..................................................................... 25

Figure 14. Satellite image showing oblique view and delineation of the Fishtrap Creek 

subbasin, Nooksack River basin, Washington .......................................... 26

Figure 15. Photographs showing view looking upstream (A) and downstream (B) from 

the U.S. Geological Survey streamflow-gaging station on Fishtrap Creek near 

Lynden, Washington ........................................................................ 27

Figure 16. Graph showing daily streamflow runoff at six streamflow-gaging stations in 

the Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek 

subbasins, Nooksack River basin, Washington and Canada, water year 2003 ...... 29
v

Figure 17. Graph showing fifteen-minute streamflow and average tau (τ) values during the 

period of July 11–31 at six gaging stations in the Racehorse, Warm, Clearwater, 

Skookum, Anderson, and Fishtrap Creek subbasins, Nooksack River basin, 

Washington and Canada .................................................................. 30

Figure 18. Scatter plots and correlation coefficients (Pearson’s r) showing relation 

among the natural logs of daily mean streamflows during the summer, winter, 

and spring seasons at each of six gaging stations in the Racehorse, Warm, 

Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins, Nooksack 

River basin, Washington and Canada ................................................... 31

Figure 19. Graph showing drainage area and mean basin elevation for all gaging stations 

used in the regional regression analysis for estimating low-flow frequency 

statistics at ungaged sites, Nooksack River basin, Washington and Canada ...... 35

Figure 20. Graph showing Q90/Q50 ratios for all sites used in the regional regression 

analysis for estimating low-flow frequency statistics at ungaged sites, 

Nooksack River basin, Washington and Canada ....................................... 36

Figure 21. Graph showing Q10/Q50 ratios for all sites used in the regional regression 

analysis for estimating low-flow frequency statistics at ungaged sites, 

Nooksack River basin, Washington and Canada ....................................... 37

Figures—Continued

Tables

Table 1. Streamflow-gaging stations and miscellaneous measurement sites in and 

near the Nooksack River basin, Washington and Canada.............................. 4

Table 2. Low-flow frequency statistics for continuous-record gaging stations and 

miscellaneous measurement sites in and near the Nooksack River basin, 

Washington and Canada .................................................................. 9

Table 3. Basin attributes and their source data considered in the regional regression 

analysis for estimating low-flow frequency statistics at ungaged sites, 

Nooksack River basin, Washington and Canada ....................................... 10

Table 4. Basin attributes for continuous-record gaging stations and miscellaneous 

measurement sites used in the regional regression analysis for estimating 

low-flow frequency statistics at ungaged sites, Nooksack River basin, 

Washington and Canada .................................................................. 11

Table 5. Regression equations for estimating low-flow frequency statistics at 

ungaged sites in the Nooksack River basin, Washington and Canada ............... 13

Table 6. Summary of correlation coefficients (Pearson’s r) showing patterns among 

the natural logs of daily mean streamflows at six gaging stations in the 

Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek 

subbasins during summer, winter, and spring seasons, Nooksack River basin, 

Washington and Canada .................................................................. 34

Table 7. Summary of results by method for determining optimal combinations of 

streamflow-gaging stations to retain in six subbasins, Nooksack River basin, 

Washington and Canada .................................................................. 38

Table 8. Prioritized list of streamflow-gaging stations to retain in six subbasins of the 

Nooksack River basin, Washington and Canada ....................................... 39
vi

Conversion Factors and Datums

Conversion Factors

Inch/Pound to SI

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 0.004047 square kilometer (km2) 

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

cubic foot per second per square 

mile [(ft3/s)/mi2]

 0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

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

°C=(°F-32)/1.8

Datums

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

(NAVD 88).

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

Elevation, as used in this report, refers to distance above the vertical datum.
Estimating Low-Flow Frequency Statistics and 

Hydrologic Analysis of Selected Streamflow-Gaging 

Stations, Nooksack River Basin, Northwestern 

Washington and Canada

By Christopher A. Curran and Theresa D. Olsen

Abstract

Low-flow frequency statistics were computed at 

17 continuous-record streamflow-gaging stations and 8 

miscellaneous measurement sites in and near the Nooksack 

River basin in northwestern Washington and Canada, 

including the 1, 3, 7, 15, 30, and 60 consecutive-day low 

flows with recurrence intervals of 2 and 10 years. Using 

these low-flow statistics, 12 regional regression equations 

were developed for estimating the same low-flow statistics 

at ungaged sites in the Nooksack River basin using a 

weighted-least-squares method. Adjusted R2 (coefficient of 

determination) values for the equations ranged from 0.79 to 

0.93 and the root-mean-squared error (RMSE) expressed as a 

percentage ranged from 77 to 560 percent.

Streamflow records from six gaging stations located 

in mountain-stream or lowland-stream subbasins of the 

Nooksack River basin were analyzed to determine if any of the 

gaging stations could be removed from the network without 

significant loss of information. Using methods of hydrograph 

comparison, daily-value correlation, variable space, and 

flow-duration ratios, and other factors relating to individual 

subbasins, the six gaging stations were prioritized from most 

to least important as follows: Skookum Creek (12209490), 

Anderson Creek (12210900), Warm Creek (12207750), 

Fishtrap Creek (12212050), Racehorse Creek (12206900), 

and Clearwater Creek (12207850). The optimum streamflowgaging station network would contain all gaging stations 

except Clearwater Creek, and the minimum network would 

include Skookum Creek and Anderson Creek.

Introduction 

The Nooksack River and its tributaries (fig. 1) support 

an abundance of wildlife unique to the Northwest region and 

are a major component of Puget Sound fisheries, supporting 

stocks of native salmonid species including Chinook, Chum, 

Coho, Pink, and Steelhead (Washington Department of Fish 

and Wildlife, 2002). The river also supplies some of the water 

needs for residents of Whatcom County, including the City of 

Bellingham with a population of 67,200 (U.S. Census Bureau, 

2000), as well as industrial and agricultural uses in the county. 

Like other large river systems in western Washington, the 

Nooksack River, including its tributaries and ecosystems, 

faces increasing pressures from society for water demand, 

flood protection, and riparian land use. The health and natural 

functioning of the river system is of concern to all residents 

of the Nooksack River basin, and also is vital for maintaining 

the intimate connection between the river and the indigenous 

people of the Northwest. 

The streamflow-gaging station network in the Nooksack 

River basin is an important asset in managing the basin’s water 

resources as it provides the necessary data for quantifying 

water availability, establishing decisions on water use, and 

determining instream-flow requirements (Washington State 

Department of Ecology, 1985). At present (2009), the network 

in the Nooksack River basin consists of 17 streamflow-gaging 

stations and 8 miscellaneous measurement sites operated 

by the U.S. Geological Survey (USGS), Washington State 

Department of Ecology (Ecology), and Environment Canada 

(EC) (fig. 2). An additional 2 streamflow-gaging stations 

and 5 miscellaneous measurement sites maintained by the 

USGS and Ecology are located within 5 mi of the basin 

boundary (fig. 2). Streamflow-gaging stations are automated 

to monitor streamflow, usually at 15-minute intervals, whereas 

miscellaneous measurement sites are locations where discrete 

measurements of streamflow have been made periodically 

over time. Streamflow-gaging stations and miscellaneous 

measurement sites in and near the basin, as well as the years of 

record and operating agencies, are shown in table 1. 

In 1998, under an agreement with the U.S. Bureau of 

Indian Affairs, the USGS installed six streamflow-gaging 

stations for the purpose of monitoring the streamflow of 

tributaries in the Nooksack River basin. This agreement with 

the USGS was later transferred to the Lummi Nation, an 

indigenous tribe of Native Americans in western Washington. 
2 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

tac09-0390 NookLocation_Fig 01

I

5

I

5

SR

542

SR

542

SR

20

SR

542

SR

542

SR

9

SR

9

SR

9

SR

547

SR

547

SR

539

SR

539

Bellingham

Bellingham

Bay

Lummi

Bay

Blaine

Ferndale

Lynden

Sumas

Abbotsford

Everson

Deming

Nooksack

Nooksack

Indian

Reservation

Mount Baker

summit

PugetSound

oF htro N

rk

Nooksack

River

Middle

Fork

Nooksack

Rive r

South

Fork

Nooksack

River

o N ko

as ck

River

WASHINGTON

FigureLocation

EXPLANATION

Population centerLummi Indian ReservationNorth Cascades National Park

Mount Baker Wilderness 0 10 5 20 MILES 15

0 105 20 KILOMETERS 15 Boundary of Nooksack River basin

Base from U.S. Geological Survey digital data, 1996, 1:100,000 UTM zone 10, NAD83.Hillshade from USGS National Elevation Data (NED) 2000, and Shuttle Radar TopoMission (SRTM) 2000 for Canada UTM projection zone 10, NAD83

122°30'

49°48°

30'

122°

British Columbia

Washington

Whatcom County

Skagit County

CANADA

UNITED STATES

Figure 1. Location of the Nooksack River basin and major rivers and population centers in the basin, Washington and Canada.
Introduction 3

tac09-0390 NookLocation_Fig 02

Bellingham

Bay

Lummi

Bay

PugetSound

oF htro N

rk

Nooksack

River

Middle

Fork

Nooksack

Rive r

South

Fork

Nooksack

River

o N ko

as ck

River

0 10 5 20 MILES 150 105 20 KILOMETERS 15

122°30'

49°48°

30'

122°

British Columbia

Washington

CANADA

UNITED STATES

Whatcom County

Skagit County

EXPLANATION

U.S. Geological SurveyWashington State Dept. of EcologyEnvironment CanadaU.S. Geological SurveyWashington State Dept. of Ecology

Boundary of Nooksack River basinBoundary of subbasin

12209490

08MH153

01C070

12210800

01L050

Streamflow-gaging stationMiscellaneous measurement site

01Q070 12213980

01R090

12202450

12202300

12214900

01D100

12212400

12212040

12212050 01M090

12211490 12211480

01P080

12213100 12213030 12210900

12210500

12210800

12210700

12206900

01K050

12208000

01C070

12209490

12209000

12207850

12207750

12205000

12212390

12212430

01L050

01N060

08MH153

Base from U.S. Geological Survey digital data, 1996, 1:100,000 UTM zone 10, NAD83.Hillshade from USGS National Elevation Data (NED) 2000, and Shuttle Radar TopoMission (SRTM) 2000 for Canada UTM projection zone 10, NAD83

Figure 2. Locations of streamflow-gaging stations and miscellaneous measurement sites in and near the Nooksack River basin, Washington and 

Canada.
4 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada Table 1. Streamflow-gaging stations and miscellaneous measurement sites in and near the Nooksack River basin, Washington and Canada. [Low-flow frequency statistics are based on the climatic year, which begins on April 1 and ends on March 31 of the following year. Location of gaging stations and miscellaneous sites are shown in figure 2. Stations highlighted in gray were not used to estimate low-flow frequency statistics. CG, continuous-record gaging station; MS, miscellaneous measurement site; STCG, short-term (less than 7 years of record) continuous-record gaging station; WA, Washington; USGS, U.S. Geological Survey; Ecology, Washington State Department of Ecology; EC, Environment Canada] Station No. Station name Latitude (decimal degrees) Longitude (decimal degrees) Drainage area (mi2

)

Type 

of site

Years of record

(CG sites only)

Number of 

measurements 

(sites only)

Agency 

operating gage

122023001 Olsen Creek near Bellingham, WA 48.75122213 -122.35349758 3.9 CG 7 USGS

122024501 Silver Beach Creek at Maynard Place, at 

Bellingham, WA

48.76927721 -122.40655473 1.1 STCG 6 USGS

12205000 North Fork Nooksack River below Cascade 

Creek, near Glacier, WA

48.90595739 -121.84431036 105 CG 70 USGS

12206900 Racehorse Creek at North Fork Road, near 

Kendall, WA

48.88484196 -122.13320746 10.5 CG 9 USGS

12207750 Warm Creek near Welcome, WA 48.76733993 -121.96459472 4.3 CG 9 USGS

12207850 Clearwater Creek near Welcome, WA 48.78845101 -122.02292921 18.9 CG 7 USGS

12208000 Middle Fork Nooksack River near Deming, WA 48.77928282 -122.10654341 73.3 CG 15 USGS

12209000 South Fork Nooksack River near Wickersham,WA 48.66427931 -122.13348856 103 CG 55 USGS

12209490 Skookum Creek above diversion, near 

Wickersham, WA

48.67150163 -122.13959998 22.4 CG 9 USGS

122105002 Nooksack River at Deming, WA 48.81039369 -122.20487901 584 CG 61 USGS

12210700 Nooksack River at North Cedarville, WA 48.84194444 -122.29305555 589 STCG 2 USGS

12210800 Smith Creek near Goshen, WA 48.85570000 -122.29410000 11..5 MS 13 USGS

12210900 Anderson Creek at Smith Road, near Goshen, WA 48.83261414 -122.33905016 9.0 CG 9 USGS

12211480 Scott Creek at Theil Road, near Lynden, WA 48.91810000 -122.41980000 3.4 MS 12 USGS

12211490 Scott Creek at Blysma Road, near Lynden, WA 48.91900000 -122.46370000 10.4 MS 8 USGS

12212040 Pepin Creek at Lynden, WA 48.94670000 -122.46860000 6.1 MS 11 USGS

12212050 Fishtrap Creek at Front Street, at Lynden, WA 48.93872574 -122.47905316 36.9 CG 9 USGS

12212390 Bertrand Creek at International Boundary 49.00250000 -122.52194440 17.4 STCG 1 USGS

12212400 Bertrand Creek at Bertrand H Street Bridge, near 

Lynden, WA

48.99330000 -122.50940000 18.0 MS 13 USGS

12212430 Unnamed Tributary to Bertrand Creek, near H 

Street, near Lynden, WA

48.98333333 -122.50000000 0.9 STCG 1 USGS

12213030 Deer Creek near Ferndale, WA 48.84510000 -122.54510000 6.4 MS 12 USGS

12213100 Nooksack River at Ferndale, WA 48.84483249 -122.58933890 786 CG 41 USGS
Introduction 5

Table 1. Streamflow-gaging stations and miscellaneous measurement sites in and near the Nooksack River basin, Washington and Canada—Continued[Low-flow frequency statistics are based on the climatic year, which begins on April 1 and ends on March 31 of the following year. Location of gaging stations and miscellaneous sites are shown in figure 2. Stations highlighted in gray were not used to estimate low-flow frequency statistics. CG, continuous-record gaging station; MS, miscellaneous measurement site; STCG, short-term (less than 7 years of record) continuous-record gaging station; WA, Washington; USGS, U.S. Geological Survey; Ecology, Washington State Department of Ecology; EC, Environment Canada]

Station No. Station name Latitude (decimal degrees) Longitude (decimal degrees) Drainage area (mi2) Type of site Years of record (CG sites only) Number of measurements (sites only) Agency operating gage

122139801 North Fork Dakota Creek near Custer, WA 48.95100000 -122.63630000 7.1 MS 13 USGS

122149001 Johnson Creek at Highway 9, at Sumas, WA 48.99290000 -122.26690000 19.8 MS 12 USGS01C070 Hutchison Creek near Acme, WA 48.72444444 -122.15222222 13.2 STCG 4 Ecology

01D1001 Sumas River at Telegraph Road 48.97750000 -122.25250000 30.7 MS 194 Ecology

01K0502 Maple Creek at mouth 48.91416667 -122.07972222 12.0 STCG 3 Ecology

01L050 Anderson Creek at mouth 48.85750000 -122.33583333 13.2 MS 204 Ecology

01M090 Kamm Slough at Northwood Road 48.94972000 -122.40638888 2.9 MS 150 Ecology

01N060 Bertrand Creek at mouth 48.92416667 -122.52861111 12.0 STCG 4 Ecology

01P080 Tenmile Creek above Barrett Lake, WA 48.85722222 -122.52833333 25.6 STCG 4 Ecology

01Q0701 Dakota Creek at Giles Road 48.96277778 -122.68055556 21.4 MS 379 Ecology

01R0901 California Creek at Valley View 48.92138889 -122.65888889 11.4 MS 358 Ecology

08MH153 Fishtrap Creek at International Boundary, Canada 48.00277778 -122.40611111 13.8 CG 19 EC

1Site is located outside of the Nooksack River basin.2Site is discontinued.
6 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

The Lummi Nation has funded the operation of the six 

streamflow-gaging stations from 2000 to the present (2009) 

and has requested that the USGS provide an analysis of 

the accumulated data with a focus on low flows, as well as 

determine whether some of the six stations could be removed 

from the network without significant loss of information.

Purpose and Scope

This report summarizes streamflow data collected in the 

Nooksack River basin, including data from six gaging stations 

funded by the Lummi Nation for the purpose of developing 

regional regression equations to estimate low-flow frequency 

statistics at ungaged sites. The report also evaluates the 

redundancy in streamflow data between the six gaging stations 

and their importance for developing future regional regression 

equations. 

Low-flow frequency statistics, such as the 7Q10 (defined 

as the mean low streamflow that occurs over 7 consecutive 

days with a 10-year recurrence interval) were calculated for 

17 of the streamflow-gaging stations in and near the basin. 

These statistics also were estimated for 8 miscellaneous 

measurement sites based on concurrent streamflow at index 

sites (gaging stations that are nearby or hydrologically 

similar) using established methods. Subbasin drainage areas 

were then delineated upstream of all streamflow sites in the 

study and basin attributes such as mean annual precipitation, 

percent forest cover, and percent surficial geology classified 

as bedrock, were determined using Geographic Information 

System (GIS) methods. 

Using the statistics and basin attributes determined for all 

streamflow sites in the network, regional regression equations 

were developed for estimating low-flow frequency statistics 

at ungaged streams in the Nooksack River basin. Performance 

metrics such as the root-mean-squared error (RMSE) and 

the adjusted coefficient of determination (R2 adjusted) were 

calculated for each of the regression equations developed.

In evaluating the six streamflow-gaging stations 

funded by the Lummi Nation, the subbasins for each of 

the gaging stations were characterized based on land use, 

channel processes, and the stream hydrograph. The Pearson’s 

correlation coefficient, r, was examined between the seasonal 

daily mean streamflow records for each of the gaging stations 

to show where redundancy in daily streamflow information 

exists. The basin attributes for each gaging station as well 

as flow-duration ratios and variable space methods were 

examined to qualitatively assess the priority of each of the six 

gaging stations for remaining in the overall streamflow-gaging 

station network for the basin. 

Description of Study Area 

Located primarily in northwestern Washington, the 

Nooksack River basin (fig. 1) encompasses 822 mi2 of mostly 

forested land, and ranges in elevation from 10,800 ft, the 

summit of Mount Baker in the Cascade Range, to sea level at 

the shores of Puget Sound. The Nooksack River is the product 

of three major tributaries: the North Fork, Middle Fork, and 

South Fork Nooksack Rivers (fig. 1). The largest of these is 

the North Fork, and when added to the length of the mainstem, 

the entire river runs westward about 75 river miles from its 

headwaters in the mountains to Puget Sound. The basin is 

bounded to the north by mountains forming the Fraser River 

valley in Canada and to the south by mountains forming the 

Skagit River valley. Of all Washington State rivers flowing 

into Puget Sound, the Nooksack River is the third largest, with 

an average streamflow of 3,840 ft3/s (U.S. Geological Survey, 

2008).

The Nooksack River basin connects the contrasting 

landscapes of a tectonically and volcanically active mountain 

range and glaciated lowland. The Cascade Range is a 

magmatic arc formed by the subduction of an oceanic plate 

beneath the continental crust and its western edge is an 

assemblage of sedimentary and volcanic rocks of Eocene 

through early Miocene age (Jones, 1999). The comparatively 

flat Puget Lowland lies within the forearc basin formed 

between the colliding plates and has been largely sculpted 

by numerous Pleistocene glaciations which deposited thick 

sedimentary layers of glacial outwash, interspersed with 

finer layers of till (Dragovich and others, 1997b). Presentday surficial geology in the basin reflects the history of 

mountain-building, erosional processes such as landslides and 

lahars, and fluvial processes that erode, transport and deposit 

sediment in post-glacial terrain (Linneman and others, 2007).

Climate in the region is maritime and heavily influenced 

by moist, offshore weather patterns originating in the 

Pacific Ocean and moving inland. The region receives about 

67 percent of annual precipitation from October to March 

(National Oceanic and Atmospheric Administration, 2007), 

with orographic uplift causing more precipitation at high 

elevations, often as snow in the mountains. Winters in the 

region typically are wet and mild in the lowland, while 

summers are warmer and relatively dry. During the most 

recent climate-normal period (1971–2000), mean annual 

precipitation in the Nooksack River basin was about 90 in. and 

ranged from about 32 in. near the mouth of the river to about 

220 in. near the crest of Mount Baker (PRISM Climate Group, 

1998). 

About 70 percent of the Nooksack River basin is forested 

(primarily by coniferous trees in the mountains) while in the 

lowland, agriculture (crops and dairy) is the dominant land use 

accounting for 16 percent of total land cover (Multi-Resolution 

Land Characteristics Consortium, 2001). Urbanized areas in 

the basin are largely concentrated in or around the population 

centers of Ferndale, Lynden, Bellingham (which is largely 

outside of the basin), and Abbotsford, British Columbia. The 

population in the Nooksack River basin was about 55,000 in 

2000 and increased about 25 percent from 1990 to 2000 (U.S. 

Census Bureau, 2000).
Low-Flow Frequency Statistics at Continuous-Record Gaging Stations and Miscellaneous Measurement Sites 7

Previous Investigations

The earliest investigation of low-flow characteristics 

for streams in the Puget Sound region was conducted by 

Hidaka (1973). In that study, streamflow records from 150 

gaging stations throughout the Puget Sound region were 

used to determine low-flow frequency statistics. Indexes 

such as the low-flow yield index (ratio of 7Q2 to drainage 

area, where the 7Q2 is defined as the mean low streamflow 

that occurs over 7 consecutive days with a 2-year recurrence 

interval) and the base-flow index (ratio of 7Q2 to mean annual 

streamflow) also were calculated and related qualitatively to 

basin characteristics such as climate, topography, and geology. 

Subsequent researchers determined low-flow frequency 

curves for streams in selected areas of western Washington 

such as the Olympic and Kitsap Peninsulas, and used simple 

regression methods to estimate low-flow frequency statistics at 

miscellaneous measurement sites (Cummans, 1976; Haushild 

and LaFrance, 1977).

Although no previous studies have documented the 

development of regional regression equations for estimating 

low-flow frequency statistics at ungaged sites in western 

Washington, numerous such studies have recently been 

conducted throughout the country at the State-wide scale (Ries 

and Friesz, 2000; Hortness, 2006; Funkhouser and others, 

2008; and Risley and others, 2008). 

Low-Flow Frequency Statistics at 

Continuous-Record Gaging Stations 

and Miscellaneous Measurement Sites 

Low-flow frequency statistics are useful for estimating 

the probability of water availability in streams during critical 

low-flow periods when conflicting demands for water, for 

example the demands of water supply versus ecosystem 

needs, are likely to exist. These statistics commonly are used 

by Federal, State and local agencies in water-use planning 

and management, as well as in establishing regulatory 

policies relating to instream flows and water quality. Lowflow frequency statistics such as the 7Q10 (defined as the 

mean low streamflow that occurs over 7 consecutive days 

with a 10-year recurrence interval) are determined from the 

mean of consecutive-day low flows of a particular stream, 

usually during a climatic year (April 1 through March 31 of 

the following year) to avoid artificially separating low-flow 

periods by water year. The recurrence interval of a particular 

consecutive-day low-flow event is calculated by fitting the 

annual low-flow series to a log-Pearson Type III distribution 

(Riggs, 1972). In general, it is desirable to compute lowflow frequency statistics such as the 7Q10 at streamflowgaging stations with 10 or more years of streamflow record, 

although previous studies have made exceptions based on the 

range of streamflow conditions during the period of record 

(Hortness, 2006). When the streamflow record for a gaging 

station satisfies a length-of-record criterion, it is considered 

a continuous-record gaging station (CG), and a streamflow 

record that falls short of the criterion is referred to as a 

‘short-term’ continuous-record gaging station (STCG) (Ries 

and Friesz, 2000). Low-flow frequency statistics also can be 

estimated at miscellaneous measurement sites provided that 

a sufficient number of measurements have been made during 

baseflow periods (Funkhouser and others, 2008; Risley and 

others, 2008). Whereas low-flow frequency statistics can be 

computed directly from the record of daily streamflow at a CG 

station, additional methods must be used to estimate similar 

statistics at miscellaneous measurement sites. 

In western Washington, most annual consecutive-day 

low flows occur during the late summer or early autumn, 

and in small or intermittent streams, low-flow frequency 

statistics can have values of zero. In this study, low-flow 

frequency statistics were determined at 15 streamflow-gaging 

stations in the Nooksack River basin, 2 gaging stations just 

outside of the basin, and 8 miscellaneous measurement sites. 

Because of the limited number of gaging stations in the 

Nooksack River basin, CG stations in this study were defined 

as gaging stations with 7 or more years of record covering 

a broad range of streamflow conditions, and stations with 

less than 7 years of record were defined as STCG stations. 

All miscellaneous measurement sites with 10 or more 

measurements made during baseflow periods were initially 

considered in the analysis. Stations with known upstream 

diversions or significant regulation were not included in the 

analysis. For example, USGS gaging station 12208000 on the 

Middle Fork of the Nooksack River was not included because 

significant withdrawals for water supply are made upstream 

of the gaging station. At stations where small upstream 

diversions or regulation may exist but are undocumented (for 

example, stations in the lowland areas where irrigation uses 

may occur), low-flow frequency statistics were determined 

and used in the analysis based on the assumption that effects 

of the upstream modifications were minor. The presence of 

trends in streamflow data in the Nooksack River basin was 

not tested in this analysis and it was assumed that the annual 

low flows recorded at individual stations are independent and 

representative of long-term streamflow conditions. 

At STCG stations, the streamflow record was extended 

to 7 years using the Maintenance of Variance Extension 

version 1.0 (MOVE.1) statistical method (Hirsch, 1982). In 

this method, a log-linear relation of daily streamflow was 

developed based on the overlapping streamflow records of 

the STCG station and a nearby or hydrologically similar 

CG station with a longer record (also referred to as an index 

station). The relation between daily streamflow at both stations 

was used to extend the record at the STCG station. Unlike a 

simple linear regression, which results in streamflow estimates 

that are biased low in their variance, MOVE.1 preserves 

the probability distribution of the estimates (Hirsch, 1982). 
8 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

At miscellaneous measurement sites, the MOVE.1 method 

also was used to estimate streamflow statistics (such as the 

7Q10) based on the log-linear relation between 10 or more 

streamflow measurements at the miscellaneous measurement 

site and concurrent flows at an index station. The calculated 

low-flow frequency statistics for 12 CG stations, 5 STCG 

stations, and 8 miscellaneous measurement sites are shown in 

table 2.

Estimating Low-Flow Frequency 

Statistics at Ungaged Sites Using 

Regional Regression Equations

Water managers, regulators, and scientists are often 

interested in streamflow information at locations in a 

stream network for which measurements do not exist. The 

development of regional regression equations for the purpose 

of estimating streamflow statistics at ungaged sites is a 

common practice and has been well documented in previous 

studies in the Pacific Northwest (Hortness, 2006; Risley 

and others, 2008) and throughout the United States (Ries 

and Friesz, 2000; Funkhouser and others, 2008). Ideally, the 

development of regional regression equations involves an 

existing network of many streamflow-gaging stations with 

long periods of record for which accurate streamflow statistics 

of natural flow conditions can be determined. In practice, the 

number of gaging stations representing natural flow conditions 

is limited, the gaging-station network is often biased toward 

representing larger streams or rivers and the geographic 

placement of the network is unevenly distributed. 

For the Nooksack River basin, regional regression 

equations were developed for estimating the low-flow 

frequency statistics for the 1, 3, 7, 15, 30, and 60 consecutiveday low flows with recurrence intervals of 2 and 10 years 

at ungaged sites in the basin. All equations were developed 

from the streamflow statistics previously determined at 12 CG 

stations, 5 STCG stations, and 8 miscellaneous measurement 

sites, and the basin characteristics at each site.

Methods of Regression

Multiple linear regression methods were used to develop 

relations between streamflow statistics such as the 7Q10 (the 

7-day low-flow with a 10-year recurrence interval), and the 

30Q2 (the 30-day low flow with a 2-year recurrence interval) 

and basin characteristics such as drainage area and mean 

basin elevation. The weighted-multiple-linear-regression 

model (WREG) software (Ken Eng, U.S. Geological Survey, 

written comm., 2009) was used to develop the regression 

equations and three types of multiple linear regression 

methods were considered—ordinary least squares (OLS), 

weighted-least squares (WLS), and generalized-least squares 

(GLS). The most common regression method, OLS, assumes 

that streamflow statistics from all sites are equivalent in 

accuracy. However, low-flow frequency statistics computed 

from continuous-record gaging stations with longer periods 

of record are likely to be more accurate than statistics from 

stations with shorter periods of record, and continuousrecord stations of any length are likely to be more accurate 

than statistics estimated at miscellaneous measurement sites. 

Because the streamflow sites on which the regression models 

are based are not equivalent in their periods of record, the 

OLS method was not used. The WLS and GLS methods are 

preferred for hydrologic regression equations because these 

methods allow for giving more weight (influence in shaping 

the regression model) to streamflow sites with more reliable 

statistics (longer record, smaller variance). In the GLS method, 

weight also is assigned based on the correlation (similarity) 

of streamflow records among sites. For example, sites in 

close proximity may respond similarly to hydrologic events 

compared to sites that are farther apart. In GLS, less weight is 

assigned to sites that are highly correlated, and more weight 

is given to sites that represent different hydrologic responses. 

When all sites are located in the same basin, substantial 

inherent correlation among sites reduces the power of the GLS 

method. This was observed among sites in the Nooksack River 

basin (particularly during the summer season) and for this 

reason, the WLS method was selected over the GLS method. 

Basin Attributes

Basin attributes were derived from a combination of GISbased sources and previous studies in the Puget Sound region. 

The data source for each basin attribute and the 26 attributes 

considered for use in the regression equations are shown in 

table 3. The basin attributes for all continuous-record gaging 

stations and miscellaneous measurement sites considered in 

this study are shown in table 4. Only a limited number of basin 

attributes were selected as explanatory variables in the final 

regression equations to avoid ‘over-fitting’ the model (that is, 

adding complexity without improving model performance). 

Some researchers have suggested limiting the number of 

explanatory variables in a regression equation to one variable 

for every 10–15 observations (Ken Eng, U.S. Geological 

Survey, oral commun., 2009), and this approach was used in 

the present study. 

Basin attributes were first screened for multicollinearity, 

or the degree of correlation between explanatory variables, 

to determine which basin attributes should be incorporated 

into the regression equations. For example, a high correlation 

was found between the basin attributes of mean elevation and 

mean annual precipitation, likely due to orographic uplift that 

causes greater precipitation at high elevations. In this case, 

multicollinearity precludes both of these attributes from being 

used as variables in the same regression equation. Bivariate 

plots were then generated between streamflow statistics and 

basin attributes to determine if variable transformations, 

such as logarithms, would improve the linearity of relations. 
Estimating Low-Flow Frequency Statistics at Ungaged Sites Using Regional Regression Equations 9 Table 2. Low-flow frequency statistics for continuous-record gaging stations and miscellaneous measurement sites in and near the Nooksack River basin, Washington and Canada. [Location of gaging stations and miscellaneous measurement sites are shown in figure 2. Low-flow frequency statistics: xQy, the mean low streamflow that occurs over x consecutive days and has a recurrence interval of y years. CG, continuous-record gaging station; MS, miscellaneous measurement site; STCG, short-term (less than 7 years of record) continuous-record gaging station] Station No. Type of site for low-flow statistics Index site for correlation (STCG or MS sites only) Number of baseflow measurements used for correlation (MS sites only) Correlation coefficient (STCG or MS sites only) Low-flow frequency statistics, in cubic feet per second 1Q10 1Q2 3Q10 3Q2 7Q10 7Q2 15Q10 15Q2 30Q10 30Q2 60Q10 60Q2 12202300 CG 0.16 0.24 0.17 0.24 0.18 0.25 0.2 0.29 0.22 0.34 0.27 0.41 12202450 STCG 12210900 0.880 0 0.01 0 0.02 0 0.02 0 0.03 0 0.03 0.02 0.05 12205000 CG 138 185 141 189 147 198 156 217 176 255 221 337 12206900 CG 1.37 2.6 1.42 2.66 1.49 2.82 1.66 3.29 1.85 4.22 2.49 6.09 12207750 CG 2.43 4.11 2.47 4.2 2.58 4.38 2.79 4.77 3.19 5.32 3.77 6.57 12207850 CG 7.88 11.96 8 12.2 8.21 12.6 8.93 14.4 10.1 17 13.4 25.3 12209000 CG 72.6 95.3 73.3 97.2 75.8 102 80.2 112 88.1 130 103 171 12209490 CG 13.9 18.9 14.6 19.4 15.3 20.6 16.6 22.3 19.3 26.4 21.8 34.7 12210500 CG 606 836 623 866 655 928 742 1,060 849 1,200 1,050 1,460 12210900 CG 0 0.06 0 0.07 0 0.07 0 0.13 0.03 0.17 0.12 0.36 12212040 MS 12212050 11 0.975 0.43 1.05 0.45 1.08 0.48 1.11 0.57 1.21 0.72 1.34 0.87 1.59 12212050 CG 2.05 5.21 2.14 5.37 2.28 5.54 2.74 6.07 3.48 6.75 4.26 8.06 12212400 MS 12212050 13 0.969 0.21 0.80 0.23 0.83 0.25 0.87 0.32 0.99 0.45 1.15 0.60 1.48 12213030 MS 12212050 12 0.962 0.47 0.95 0.48 0.97 0.51 0.99 0.58 1.06 0.70 1.15 0.81 1.32 12213100 CG 622 882 635 904 664 961 729 1,070 826 1,210 1,050 1,480 12213980 MS 12212050 13 0.902 0.19 0.55 0.20 0.57 0.21 0.59 0.26 0.66 0.35 0.75 0.44 0.91 12214900 MS 12212050 12 0.946 4.48 7.73 4.60 7.86 4.77 8.01 5.31 8.45 6.10 8.99 6.87 9.97 01C070 STCG 12206900 0.853 4.17 4.56 4.28 4.78 4.37 4.92 4.57 5.12 4.71 5.68 4.75 6.77 01D100 MS 12212050 46 0.704 6.19 9.59 6.31 9.73 6.50 9.87 7.09 10.30 7.93 10.83 8.72 11.77 01K050 STCG 12212050 0.832 0.52 0.99 0.53 1.02 0.57 1.04 0.61 1.12 0.69 1.3 0.91 1.7 01N060 STCG 12212050 0.938 0.57 1.83 0.7 2.09 0.83 2.27 1.31 2.77 1.48 3.16 2.16 4.22 01P080 STCG 12212050 0.913 1.47 2.56 1.5 2.61 1.61 2.73 1.72 3.11 1.97 3.67 2.4 4.39 01Q070 MS 12212050 32 0.680 0.91 3.02 0.96 3.14 1.04 3.27 1.32 3.68 1.80 4.22 2.33 5.30 01R090 MS 12212050 46 0.914 0.75 1.31 0.77 1.33 0.80 1.35 0.89 1.43 1.03 1.52 1.16 1.69 08MH153 CG 0 1.62 0.22 1.72 0.26 1.89 0.4 2.28 0.59 2.81 1.41 3.67
10 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Table 3. Basin attributes and their source data considered in the regional regression analysis for estimating low-flow frequency 

statistics at ungaged sites, Nooksack River basin, Washington and Canada.

[Data source: 1, U.S. Geological Survey, Streamstats for Washington at http://water.usgs.gov/osw/streamstats/Washington.html; 2, PRISM Climate Group, 

Oregon State University, http://www.prismclimate.org, accessed April 22, 2009; 3, Vaccaro and others, 1998, http://pubs.er.usgs.gov/usgspubs/pp/pp1424D; 

4, Multi-Resolution Land Characteristics Consortium (MRLC), National Land Cover Database (NLCD) 2001 at http://www.mrlc.gov/index.php; 5, Mission 

topographic map (2000), scale 1:50,000, Centre for Topographic Information, Natural Resources Canada; 6, New Westminster topographic map (1989), scale 

1:50,0000, Canada Centre for Mapping, Department of Energy, Mines, and Resources; and 7, Shuttle Radar Topography Mission (SRTM) Elevation Data Set, 

2002, http://seamless.usgs.gov]

Basin attribute Description Data source

Latitude Latitude, NAD83 1

Longitude Longitude, NAD83 1

Drainage area Drainage area, in square miles 1

Precipitation Mean annual precip (1971–2000), in inches 2

Precipitation, minimum Minimum annual precipitation (1971–2000), in inches 2

Precipitation, maximum Maximum annual precipitation (1971–2000), in inches 2

Precipitation, September Mean September precipitation (1971–2000), in inches 2

Relief Relief (maximum minus minimum basin elevation), in feet 1 and 7

Elevation Mean basin elevation, in feet 1 and 7

Elevation, maximum Maximum basin elevation, in feet 1 and 7

Elevation, minimum Minimum basin elevation, in feet 1 and 7

Slope Mean basin slope, in percent 1 and 7

Slope, greater than 30 percent Percentage of area with slope greater than 30 percent 1 and 7

Slope, greater than 30 percent 

facing north

Percentage of area with slope greater than 30 percent and facing north 1 and 7

Bedrock Percentage of area with surficial geology classified as bedrock 3

Fine-grained Percentage of area with surficial geology classified as fine-grained unconsolidated 

sediments

3

Coarse-grained Percentage of area with surficial geology classified as coarse-grained unconsolidated 

sediments

3

Alluvial Percentage of area with surficial geology classified as alluvial sediments 3

Open water Percentage of area with land cover classified as open water 4, 5, 6

Ice/snow Percentage of area with land cover classified as ice/snow 4, 5, 6

Urban Percentage of area with land cover classified as developed land 4, 5, 6

Barren Percentage of area with land cover classified as barren land 4, 5, 6

Forest Percentage of area with land cover classified as forest 4, 5, 6

Shrub/scrub Percentage of area with land cover classified as shrub/scrub 4, 5, 6

Agriculture/grassland/pasture Percentage of area with land cover classified as agriculture/grassland/pasture 4, 5, 6

Wetlands Percentage of area with land cover classified as wetlands 4, 5, 6
Estimating Low-Flow Frequency Statistics at Ungaged Sites Using Regional Regression Equations 11 Table 4. Basin attributes for continuous-record gaging stations and miscellaneous measurement sites used in the regional regression analysis for estimating low-flow frequency statistics at ungaged sites, Nooksack River basin, Washington and Canada.

[Relief: Defined as maximum minus minimum basin elevation]

Station 

No.

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Drainage 

area 

(mi2

)

Precipitation, 1971–2000, in inches

Relief

(feet)

Basin elevation, in feet Mean 

basin slope 

(percent)

Mean 

annual

Minimum 

annual

Maximum 

annual

Mean 

September Mean Minimum Maximum

12202300 48.75122213 -122.35349758 3.9 93 56 117 4.9 2,740 1,750 315 3,060 29.7

12202450 48.76927721 -122.40655473 1.1 55 49 58 2.7 1,200 830 322 1,520 12.5

12205000 48.90595739 -121.84431036 105 101 74 169 4.5 8,390 4,250 1,290 9,680 53.6

12206900 48.88484196 -122.13320746 10.5 103 62 120 4.6 4,560 3,060 420 4,970 49.3

12207750 48.76733993 -121.96459472 4.3 155 140 178 7.0 4,040 4,270 2,720 6,760 51.5

12207850 48.78845101 -122.02292921 18.9 120 105 155 5.3 4,240 3,640 1,660 5,900 47.0

12209000 48.66427931 -122.13348856 103 129 74 190 5.7 6,080 2,720 382 6,460 39.8

12209490 48.67150163 -122.13959998 22.4 138 73 207 6.1 6,570 3,040 421 6,990 42.912210500 48.81039369 -122.20487901 584 103 53 224 4.7 10,600 2,900 219 10,800 41.212210900 48.83261414 -122.33905016 9.0 73 47 116 3.8 2,860 1,130 203 3,070 18.9

12212040 48.94670000 -122.46860000 6.1 61 53 67 3.2 400 221 95 495 6.012212050 48.93872574 -122.47905316 36.9 59 51 68 3.2 443 194 52 495 4.012212400 48.99330000 -122.50940000 18.0 64 58 68 3.4 356 325 122 478 6.012213030 48.84510000 -122.54510000 6.4 40 37 43 2.0 308 180 58 367 2.912213100 48.84483249 -122.58933890 786 90 35 224 4.3 10,800 2,350 12 10,800 33.612213980 48.95100000 -122.63630000 7.1 55 48 58 3.0 362 184 45 408 2.912214900 48.99290000 -122.26690000 19.8 48 56 45 2.7 186 91 35 221 1.301C070 48.72444444 -122.15222222 13.2 90 67 142 4.1 3,680 1,760 538 4,220 30.1

01D100 48.97750000 -122.25250000 30.7 63 46 117 3.5 3,370 682 42 3,410 17.7

01K050 48.91416667 -122.07972222 12.0 68 62 78 3.5 4,200 1,560 508 4,710 32.4

01N060 48.92416667 -122.52861111 34.4 60 48 67 3.2 449 241 33 482 4.0

01P080 48.85722222 -122.52833333 25.6 43 39 46 2.3 292 142 43 335 2.7

01Q070 48.96277778 -122.68055556 21.4 53 46 60 2.8 513 144 14 527 2.3

01R090 48.92138889 -122.65888889 11.4 42 39 47 2.2 347 111 24 371 2.2

08MH153 48.00277778 -122.40611111 13.8 62 59 68 3.4 339 236 141 480 6.0
12 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada Table 4. Basin attributes for continuous-record gaging stations and miscellaneous measurement sites used in the regional regression analysis for estimating low-flow frequency statistics at ungaged sites, Nooksack River basin, Washington and Canada.—Continued

[Relief: Defined as maximum minus minimum basin elevation]

Station 

No.

Percentage of area with Percentage of area with surficial geology classified as Percentage of area with land cover classified as 

Slope 

greater 

than 30 

percent

Slope greater 

than 30 

percent and 

facing north

Bedrock

Finegrained 

unconsolidated 

sediments

Coarsegrained 

unconsolidated 

sediments

Alluvial 

sediments

Open 

water

Ice/ 

snow

Developed 

land

Barren 

land Forest Shrub/ scrub Agriculture/ grassland/ pasture Wetlands

12202300 48.3 10.9 95 0 5 0 0 0 2 0 96 1 0.5 0.5

12202450 0.0 0.0 91 9 0 0 0 0 31 0 60 6 3 0

12205000 84.2 24.4 91 0 6 3 0 6 1 9 64 17 2 1

12206900 89.5 34.5 99 0 1 0 0 0 3 0 85 12 0 0

12207750 85.5 22.0 100 0 0 0 0 1 0 3 80 16 0 0

12207850 83.5 20.6 99 0 1 0 0 0 1 0 83 15 1 0

12209000 69.8 18.5 88 0 11 1 0 0 2 3 76 14 4 1

12209490 75.0 16.6 100 0 0 0 0 0 4 6 70 15 5 0

12210500 68.1 18.3 84 1 9 6 0 2 3 4 72 13 4 2

12210900 21.0 7.5 64 34 2 0 0 0 6 1 67 8 15 3

12212040 1.5 0.3 0 34 52 14 0 0 13 5 27 0 55 0

12212050 0.5 0.1 0 25 59 16 0 0 28 1 10 0 60 1

12212400 0.0 0.0 0 81 13 6 0 0 19 2 22 0 53 4

12213030 0.0 0.0 0 73 24 3 0 0 19 0 22 4 41 14

12213100 54.8 14.8 65 8 17 10 1 2 6 3 59 10 16 3

12213980 0.0 0.0 0 80 20 0 0 0 5 0 41 3 28 23

12214900 0.0 0.0 0 55 23 22 0 0 9 0 4 0 79 8

01C070 53.5 12.9 90 0 0 10 0 0 4 0 76 15 2 301D100 25.8 8.3 41 22 19 18 0 0 6 0 54 3 33 4

01K050 48.5 3.6 70 6 20 4 2 0 5 0 76 9 5 3

01N060 0.0 0.0 0 60 33 7 0 0 13 1 18 0 62 6

01P080 0.0 0.0 1 47 41 11 0 0 14 0 20 3 51 12

01Q070 0.1 0.0 0 37 63 0 0 0 6 0 27 3 49 15

01R090 0.0 0.0 0 34 52 14 0 0 21 0 16 3 43 17

08MH153 0.5 0.1 0 44 47 9 0 0 43 0 12 0 45 0
Estimating Low-Flow Frequency Statistics at Ungaged Sites Using Regional Regression Equations 13

Base 10 logarithmic (referred to as log) transformations of 

streamflow (Q) and drainage area (DA) were justified, and for 

convenience in the final equations, all basin elevations were 

expressed in units of thousands of feet. Finally, a stepwiseregression procedure was performed using S-Plus® statistical 

software (TIBCO Software Inc., 2008) wherein preliminary 

equations were generated for calculating streamflow statistics 

from all combinations of basin attributes. Through iteration 

and screening of Mallow’s Cp statistic (a metric that rewards 

accuracy in the model, while penalizing complexity), the 

stepwise procedure removed those basin attributes that 

contributed least to the explanatory power of the regression 

equation. By repeating the stepwise procedure many times and 

for different combinations of basin attributes, certain attributes 

outperformed others and were retained as variables in the final 

regression equations. For example, although mean annual 

precipitation (P) commonly is found in regression equations 

for estimating high flows, it was outperformed by mean basin 

elevation (E). The basin attributes used in the final regression 

equations were DA and E and these were determined on the 

basis of performance metrics (RMSE, R2, and Cp) computed 

in the stepwise procedure.

Regression Equations

Regression equations were developed for 12 low-flow 

frequency statistics, such as the 7Q10 and the 30Q2. The 

regression equations for estimating flow statistics at ungaged 

sites in the Nooksack River basin and their performance 

metrics are shown in table 5. Because the regressions 

involved log transformations of flow statistics, zero values 

(for example, a 7Q10 equal to 0) cannot be used in the 

regression. Ideally, estimating statistics for these sites would 

be done through the use of logistic regression (Hortness, 2006; 

Funkhouser and others, 2008) and with the availability of a 

large number of similar zero-flow sites. Only a few sites in the 

network had zero flows for some statistics. For these statistics, 

a value of 0.01 ft3/s was added to the value of the statistic at 

all sites for the purpose of performing the regression. Although 

this approach may result in some bias, it was considered 

acceptable for the purposes of the study.

Table 5. Regression equations for estimating low-flow frequency statistics at ungaged sites in 

the Nooksack River basin, Washington and Canada.

[Low-flow statistic: xQy, the mean low streamflow that occurs over x consecutive days and has a recurrence 

interval of y years, in cubic feet per second; R2 adjusted, coefficient of determination adjusted for the number of 

explanatory variables in the regression equation; RMSE, root-mean-squared error; DA, drainage area, in square 

miles; E, mean basin elevation, in thousands of feet; ft3/s, cubic feet per second]

Low-flow 

statistic Regression equation R 2

 adjusted

RMSE

log10 (ft3

/s) percent

1Q10 1Q10 = 0.0170 (DA)1.40 × 100.216(E) 0.79 0.810 560

1Q2 1Q2 = 0.0371 (DA)1.44 × 100.146(E) 0.88 0.544 194

3Q10 3Q10 = 0.0176 (DA)1.42 × 100.210(E) 0.83 0.549 198

3Q2 3Q2 = 0.0436 (DA)1.40 × 100.149(E) 0.88 0.417 123

7Q10 7Q10 = 0.0183 (DA)1.43 × 100.206(E) 0.83 0.527 183

7Q2 7Q2 = 0.0441 (DA)1.40 × 100.150(E) 0.88 0.402 116

15Q10 15Q10 = 0.0205 (DA)1.45 × 100.190(E) 0.83 0.524 181

15Q2 15Q2 = 0.0519 (DA)1.38 × 100.154(E) 0.91 0.356 97.9

30Q10 30Q10 = 0.0262 (DA)1.44 × 100.178(E) 0.88 0.442 134

30Q2 30Q2 = 0.564 (DA)1.38 × 100.162(E) 0.91 0.343 92.9

60Q10 60Q10 = 0.0348 (DA)1.40 × 100.185(E) 0.91 0.354 97.1

60Q2 60Q2 = 0.0716 (DA)1.35 × 100.182(E) 0.93 0.296 76.9
14 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Accuracy and Limitations

In developing regression equations, the number of 

STCG stations (5) and miscellaneous measurement sites (8) 

were relatively large compared to the total number of sites 

used in this analysis (25). Determining estimates of lowflow frequency statistics at STCG stations and miscellaneous 

measurement sites required the selection of a nearby or 

hydrologically similar CG station to serve as an index 

station. Because most STCG stations and miscellaneous 

measurement sites were located in the lowland portion of 

the basin and the number of CG stations in the lowland 

was small (3 stations), the same index station was used in 

estimating low-flow frequency statistics at multiple STCG 

stations and miscellaneous measurement sites. Although this 

fact created undesirable correlation in the data, the benefits of 

retaining STCG stations and miscellaneous measurement sites 

(representing lowland hydrology) in the analysis outweighed 

the disadvantages of their removal. 

The error for each regression equation was quantified by 

the RMSE, which is based on the difference between the value 

of the observed low-flow frequency statistic at each site and 

the value estimated by the regression equation. (The observed 

low-flow frequency statistic is defined as the low-flow 

frequency statistic computed from measured streamflows.) 

Because the regression equations were developed in log 

units, the RMSE was calculated in log units [log (ft3/s)], 

and also expressed as a percentage of the observed low-flow 

frequency statistic. The RMSE expressed as a percentage 

ranged from 77 to 560 percent (table 5). The smallest RMSE 

expressed as a percentage was for the 60Q2 statistic (the 

mean low streamflow for 60 consecutive days with a 2-year 

recurrence interval) and the largest was for the 1Q10 (the 

mean low streamflow for 1 day with a 10-year recurrence 

interval). For a given recurrence interval, the relative errors 

decreased for low-flow frequency statistics of longer duration. 

The largest source of error generally came from sites with 

low-flow frequency statistics of zero, such as Anderson 

Creek (12210900). This finding suggests that when using the 

regression equations at stream sites with a potential for zero or 

small (less than 0.1 ft3/s) low-flow frequency statistics, large 

relative errors may exist in the estimated low-flow frequency 

statistics. Although removing Anderson Creek from the 

regression models reduced the relative RMSE, the influence of 

this site on the regression equation coefficients as determined 

by WREG was small relative to other sites. 

The regression equations developed in this report were 

based on streamflow data recorded at sites in or just outside of 

the Nooksack River basin and should not be used to estimate 

low-flow frequency statistics at sites outside of the basin. 

Furthermore, although the stream sites considered in this study 

contained a large range of values for basin attributes (drainage 

area and mean basin elevation) used in the regression, 

the equations may not be appropriate for sites with basin 

attributes outside of the range of values used in developing the 

equations. 

Hydrologic Analysis of Selected 

Streamflow-Gaging Stations

Streamflow-gaging stations in six subbasins of the 

Nooksack River basin (fig. 3) are operated by the USGS 

in cooperation with the Lummi Nation, and are part of 

the larger streamflow-gaging station network in the basin. 

The gaging stations were individually examined in terms 

of their hydrologic and subbasin characteristics, and their 

streamflow records were analyzed collectively for patterns and 

redundancy in the streamflow-gaging station network. 

Description of Subbasins

Subbasins in the Nooksack River basin (fig. 3) vary in 

size, as well as characteristics such as geology, land cover, 

and precipitation accumulation, but are defined herein as those 

basins containing first- or second-order perennial streams. On 

this basis, subbasins in the Nooksack River basin generally 

fall into one of two types—mountain-stream or lowlandstream subbasins. Racehorse Creek subbasin is an example of 

a mountain-stream subbasin, whereas Fishtrap Creek subbasin 

is an example of a lowland-stream subbasin. Mountainstream subbasins typically are at high elevations, receive 

large amounts of precipitation, have surficial geology that is 

dominated by bedrock, and have a high percentage of land 

cover that is forested. Lowland-stream subbasins are closer 

to sea level, receive moderate precipitation, have surficial 

geology dominated by glacial and river sediments, and have a 

high percentage of land cover that is agricultural or urbanized. 

Mountain-stream subbasins are more likely to have snowmelt 

as a seasonal component of streamflow, and lowland-stream 

subbasins are more likely to have streamflow diverted for 

irrigation use or regulated for flood control.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 15

tac09-0390 LummiBasinsLocation_Fig 03

oF htro N

rk

Nooksack

River

Middle

Fork

Nooksack

River

South

Fork

Nooksack

River

o N ko

as ck

River

Lowland-stream subbasin

Mountain-stream subbasin

0 10 5 20 MILES 150 105 20 KILOMETERS 15

12212050

12210900

12206900

12209490

12207850

12207750

122°30'

49°48°

30'

122°

British Columbia

Washington

CANADA

UNITED STATES

Whatcom County

Skagit County

ClearwaterCreeksubbasin

WarmCreeksubbasin

SkookumCreeksubbasin

AndersonCreeksubbasin

FishtrapCreeksubbasin

RacehorseCreeksubbasin

EXPLANATION

Boundary of s

USGS streamflow-gaging station

elected subbasin

12209490

Boundary of Nooksack River basin

Base from U.S. Geological Survey digital data, 1996, 1:100,000 UTM zone 10, NAD83.Canada UTM projection zone 10, NAD83

Figure 3. Location of streamflow-gaging stations in Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins that were 

analyzed for redundancy in the streamflow-gaging station network, Nooksack River basin, Washington and Canada.
16 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Racehorse Creek

The Racehorse Creek subbasin is 

about 11 mi2 in size, and is located in 

the northeastern part of the Nooksack 

River basin on the northern slope of 

Slide Mountain in the North Fork 

Nooksack River basin. This mountainstream subbasin is carved through a 

mantle of glacial sediments and into 

bedrock composed of massive sandstone, 

conglomerate, and shale (Easterbrook 

and others, 2007). The subbasin has a 

history of landslide occurrence and is in 

a part of the Nooksack River basin that 

remains seismically active (Linneman 

and others, 2007). The subbasin is 

predominantly forested, and interspersed 

with areas of clear-cutting and logging 

roads. Most recently, the subbasin was 

affected by a landslide that occurred 

on January 7, 2009, during a period of 

intense rainfall. The material from this 

failure temporarily dammed the flow 

on Racehorse Creek (which already had 

large flows due to heavy rains) about 1 

mi upstream of the gaging station, and 

after giving way caused an outburst flood 

downstream that significantly modified 

the stream channel in the lower part of 

the subbasin (fig. 4).

Racehorse Creek is a low-order 

stream that drains into the North Fork 

of the Nooksack River about 4 mi 

upstream of the confluence of the Middle 

and North Fork Nooksack Rivers. The 

main channel is about 7 mi long and 

runs westward from Slide Mountain 

at an elevation of about 4,000 ft to 

its confluence with the North Fork 

Nooksack River at an elevation of about 

400 ft. The USGS streamflow-gaging 

station (12206900) is 0.7 mi upstream 

of the mouth of the creek and just 

downstream of a single-span bridge used for logging traffic. 

At flows less than about 20 ft3/s, the stage of the stream is 

controlled by a series of gravel/cobble bars, and at higher 

flows (greater than about 200 ft3/s), the stage is controlled 

by channel geometry and slope. The bankfull width of the 

channel (post-January 2009 flood) is about 75 ft in the reach 

watac09-0390_fig 04-Racehorse

Racehorse Creek Subbasin Racehorse Creek subbasin

USGS gaging station 12206900

North Fork Nooksack River Landslide of January 2009

Slide Mountain

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

Figure 4. Oblique view and delineation of the Racehorse Creek subbasin with the 

January 2009 landslide area, Nooksack River basin, Washington.

just downstream of the gaging station and the top of bank 

elevations are about 6.0 ft above the gage datum (a reference 

datum for measuring river stage only). The reach is fairly 

uniform in channel shape but has been significantly altered by 

the January 2009 flood event, which both widened the channel 

and armored its banks with large woody debris (fig. 5).
Hydrologic Analysis of Selected Streamflow-Gaging Stations 17

watac09-0390_fig 05a,b

A.

B.

Figure 5. View looking upstream (A) and downstream (B) from the U.S. Geological Survey streamflow-gaging 

station on Racehorse Creek at North Fork Road, near Kendall, Washington (12206900). Photographs taken by 

Christopher Curran, U.S. Geological Survey, May 2009.
18 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Warm Creek

The Warm Creek subbasin is about 4 mi2 in size, and 

located in the eastern part of the Nooksack River basin on the 

western edge of Mount Baker in the Middle Fork Nooksack 

River basin. The surficial geology in the lower subbasin is 

predominantly thin layers of colluvial and alpine glacial 

deposits overlying bedrock of sedimentary and igneous origin, 

the latter of which is exposed in the uppermost parts of the 

subbasin. This mountain-stream subbasin is predominantly 

forested with no known logging activity, and in the uppermost 

areas (above 6,000 ft elevation) contains some amount of 

snow throughout most of the year (fig. 6).

Warm Creek is a small low-order stream that drains into 

the Middle Fork of the Nooksack River about 13 mi upstream 

of the confluence of the Middle and North Fork Nooksack 

Rivers. The main channel is about 3 mi long and runs 

Warm Creek subbasin

USGS gaging station 12207750

Mount Baker

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

Figure 6. Oblique 

view and delineation 

of the Warm Creek 

subbasin, Nooksack 

River basin, 

Washington.

westward from an elevation of about 5,000 ft to its confluence 

with the Middle Fork Nooksack River at an elevation of about 

1,500 ft. The USGS streamflow gaging station (12207750) 

is 1 mi upstream of the mouth of the creek. At flows less 

than about 50 ft3/s, the stage of the stream is controlled by a 

series of small boulders that span the channel, and at flows 

greater than about 70 ft3/s, the stage is controlled by channel 

geometry and slope (fig. 7). The bankfull width of the channel 

is estimated to be 40 ft in the reach just upstream of the gaging 

station and the top of bank elevations are estimated at about 

4.0 ft above the gage datum. Access to the gaging station has 

been difficult due to snow accumulation in the winter, and 

most recently the only access road to the gaging station was 

washed out about 6 mi from the gaging station. It is likely that 

the latter took place as a result of heavy rains that occurred in 

the region in January 2009.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 19

watac09-0390_fig 07a,b

A.

B.

Figure 7. View looking upstream (A) and downstream (B) from the U.S. Geological Survey streamflowgaging station on Warm Creek near Welcome, Washington (12207750). Photographs taken by Jeffrey 

Paulat, U.S. Geological Survey, (A) November 2008; (B) January 2009.
20 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Clearwater Creek

The Clearwater Creek subbasin is about 19 mi2 in size, 

and located in the eastern part of the Nooksack River basin, 

adjacent to the Warm Creek subbasin, and also in the Middle 

Fork Nooksack River basin. The surficial geology in the 

subbasin is predominantly thin layers of colluvial and glacial 

deposits overlying bedrock of sedimentary and igneous origin. 

This is a mountain-stream subbasin that is predominantly 

forested and interspersed with large clear-cut areas from 

commercial logging (fig. 8).

Clearwater Creek is a second-order stream that drains 

into the Middle Fork of the Nooksack River about 9 mi 

upstream of the confluence of the Middle and North Fork 

Nooksack Rivers. The main channel is about 6 mi long and 

runs generally west and southwest from an elevation of about 

4,000 ft to its confluence with the Middle Fork Nooksack 

River at an elevation of about 1,100 ft. The USGS streamflowgaging station (12207850) is about 1.8 mi upstream of the 

Clearwater subbasin

USGS gaging station 12207850

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

Figure 8. Oblique view and delineation of the Clearwater Creek subbasin, Nooksack River basin, Washington.

mouth of the creek. At flows less than about 30 ft3/s, the stage 

of the stream is controlled by an irregular but smooth bedrock 

surface that spans the channel (fig. 9A). At medium flows 

(30–100 ft3/s), the stage is controlled by an irregular series of 

large boulders downstream of the gaging station, and at flows 

greater than about 200 ft3/s, the stage is controlled largely by 

channel geometry and slope (fig. 9B). The downstream left 

bank of the channel is a fairly steep bedrock face, whereas the 

downstream right bank is terraced over deposits of colluvial 

sand and gravel. The right bank has large cedar trees and 

massive boulders that constrict high flows and accumulate 

large woody debris. The bankfull width of the channel is about 

65 ft near the gaging station and high-water marks on the right 

bank, deposited during the January 2009 peak, were surveyed 

at 8.9 and 9.2 ft above gage datum on May 21, 2009. In 

November 2007, the gaging station was damaged during high 

flows caused by intense precipitation in the region; the gaging 

station was not restored fully until July 2008.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 21

watac09-0390_fig 09a,b

A.

B.

Figure 9. View looking upstream (A) and downstream (B) from the U.S. Geological Survey 

streamflow-gaging station on Clear Water Creek near Welcome, Washington (12207850). Photographs 

taken by Christopher Curran, U.S. Geological Survey, May 2009.
22 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

watac09-0390_fig 10-Skookum Creek

Skookum Creek subbasin

Twin Sisters Mountain

USGS gaging station 12209490

South Fork Nooksack River

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

Figure 10. Oblique view and delineation of the Skookum Creek subbasin, Nooksack 

River basin, Washington.

Skookum Creek

The Skookum Creek subbasin is 

about 23 mi2 in size, and located in the 

southern part of the Nooksack River 

basin. It extends southward from the 

southern flank of Twin Sisters Mountain 

to the South Fork Nooksack River 

basin. The surficial geology in the lower 

subbasin is predominantly thin layers 

of colluvial and alpine glacial deposits 

that overlie bedrock of sedimentary and 

igneous origin. The uppermost part of 

the basin is exposed igneous-intrusive 

rock that forms the jagged peaks of Twin 

Sisters Mountain. This mountain-stream 

subbasin is predominantly forested 

although interspersed with large clearcuts 

and a system of logging roads. The 

uppermost areas of the basin include the 

southern peak of Twin Sisters Mountain 

(about 7,000 ft elevation) and contains 

snow throughout most of the year 

(fig. 10).

Skookum Creek is a large secondorder stream that drains into the South 

Fork of the Nooksack River about 

14 mi upstream of the confluence of the 

Middle and North Fork Nooksack Rivers. 

The main channel is about 9 mi long 

and runs southward from an elevation 

of about 5,000 ft at the flank of Twin 

Sisters Mountain to its confluence with 

the South Fork Nooksack River at an 

elevation of about 400 ft. The USGS 

streamflow-gaging station (12209490) 

is 0.3 mi upstream of the mouth of the 

creek. Near the gaging station, the creek 

is confined by bedrock on both banks 

and runs fairly straight for about 300 ft. 

At medium and low flows (less than 

about 300 ft3/s), the stage of the stream is 

controlled by bedrock and a series of medium boulders, at higher flows (greater than about 400 ft3/s), the stage is controlled by 

channel geometry and slope (fig. 11). The width of the channel is about 55 ft at the gaging station with no clearly defined top of 

bank. Streamflow data from this station is used by the National Weather Service for calibrating a hydrologic model for the South 

Fork Nooksack River (Brent Bower, National Weather Service, written commun., July 7, 2009). 
Hydrologic Analysis of Selected Streamflow-Gaging Stations 23

watac09-0390_fig 11a,b

A.

B.

Figure 11. View looking upstream (A) and downstream (B) from the U.S. Geological Survey 

streamflow-gaging station on Skookum Creek near Wickersham, Washington (12209490). 

Photographs taken by Jeffrey Paulat, U.S. Geological Survey, June 2009.
24 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Anderson Creek

The Anderson Creek subbasin is about 9 mi2 in size, 

and located in the transition between the Puget Lowland and 

the foothills of the Cascade Range in the Nooksack River 

basin. The surficial geology in this lowland-stream subbasin 

is coarse- to fine-grained glacial deposits in the lower half of 

the subbasin, with thin layers of glacial sediments mantling 

sedimentary bedrock at high elevations. The subbasin is a 

mix of forested land, agricultural land, and residential areas 

(fig. 12).

Anderson Creek is a low-order stream that drains into 

the mainstem of the Nooksack River about 8 mi downstream 

of the confluence of the South Fork and mainstem Nooksack 

Rivers. The stream channel is about 3 mi long and runs 

northward from an elevation of about 3,000 ft to its confluence 

with the Nooksack River at an elevation of about 200 ft. 

Anderson Creek subbasin

USGS gaging station 12210900

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

The USGS streamflow-gaging station (12210900) is 3 mi 

upstream of the mouth of the creek. Just upstream of the 

gaging station, the stream channel is confined by rip-rap on 

both banks that support a single-span overpass. A drainage 

ditch about 0.2 mi long runs parallel to the roadway and enters 

the main channel just upstream of the overpass. At flows less 

than about 20 ft3/s, the stage of the stream is controlled by 

gravel bars, at higher flows (greater than 100 ft3/s), the stage 

is controlled by channel geometry and slope (fig. 13). Channel 

banks are heavily vegetated with brush and overhanging trees. 

In late summer, streamflow in the creek has been observed to 

become so low that it cannot be measured, and is recorded as 

effectively zero flow (Jeffrey Paulat, U.S. Geological Survey, 

oral commun., 2009). The bankfull width of the channel is 

about 48 ft near the gaging station and high-water marks on 

both banks, deposited during the January 2009 peak, were 

surveyed at 11.4 and 11.0 ft above gage datum on May 21, 

2009.

Figure 12. Oblique view and delineation of the Anderson Creek subbasin, Nooksack River basin, Washington.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 25

Figure 13. View looking upstream (A) and downstream (B) from the U.S. Geological Survey 

streamflow-gaging station on Anderson Creek near Goshen, Washington (12210900). Photographs 

taken by Christopher Curran, U.S. Geological Survey, May 2009.

watac09-0390_fig 13a,b

A.

B.
26 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Fishtrap Creek

The Fishtrap Creek subbasin is about 37 mi2 in size 

(26 mi2 of which are in Canada) and located in the Puget 

Lowland in the Nooksack River basin. The surficial geology in 

this lowland-stream subbasin is coarse- to fine-grained glacial 

deposits and coarse-grained alluvial deposits. The subbasin is 

primarily agricultural land and residential areas (fig. 14).

Fishtrap Creek is a second-order stream that enters the 

mainstem of the Nooksack River about 13 mi upstream of 

the mouth. The stream channel is about 11 mi long and runs 

southward from an elevation of about 200 ft to its confluence 

with the Nooksack River at an elevation of about 30 ft. 

Previous investigations in the creek have found fecal bacteria 

and elevated nitrogen concentrations, likely from tile drains 

and ditches that drain agricultural fields and enter the creek 

Lynden, Washington

USGS gaging station 12212050

Fishtrap Creek subbasin

Abbotsford, 

British Columbia

USDA National Agricultural Imagery Program (NAIP) 2006, UTM zone 10 NAD83

(Cox and others, 2005). The USGS streamflow-gaging station 

(12212050) is 3 mi upstream of the mouth of the creek, 

and at the downstream end of a three-section box culvert 

(fig. 15A). At flows less than about 100 ft3/s, the stage of the 

stream is controlled by gravel bars, at higher flows (greater 

than 200 ft3/s), the stage is controlled by channel geometry 

and slope (fig. 15B). Channel banks are heavily vegetated 

with brush and overhanging trees, and a slope failure 

recently occurred on the downstream right bank about 80 ft 

downstream of the gaging station, likely during the January 

2009 flooding. The bankfull width of the channel is about 65 ft 

in the cross section 50 ft downstream of the gaging station 

and high-water marks on both banks, deposited during the 

January 2009 peak, were surveyed at 8.0 and 7.9 ft above gage 

datum on May 21, 2009.

Figure 14. Oblique view and delineation of the Fishtrap Creek subbasin, Nooksack River basin, Washington.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 27

Figure 15. View looking upstream (A) and downstream (B) from the U.S. Geological Survey 

streamflow-gaging station on Fishtrap Creek near Lynden, Washington (12212050). Photographs taken 

by Christopher Curran, U.S. Geological Survey, May 2009.

watac09-0390_fig 15a,b

A.

B.
28 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Evaluation of Redundancy in the StreamflowGaging Station Network

In addition to developing regional regression equations 

for low-flow frequency statistics, the Lummi Nation 

requested that the USGS determine whether some of the 

six streamflow-gaging stations were collecting redundant 

streamflow information and whether some of the gaging 

stations could be removed from the network without 

significant loss of information. Redundancy in this study is 

defined as similarity in the timing, magnitude and frequency 

of streamflow. Because identifying and removing redundancy 

in the streamflow-gaging station network is essentially 

optimizing the network, it is helpful to define an optimal 

network. An optimal streamflow-gaging station network is 

one that contains the fewest number of gaging stations and yet 

provides streamflow information that represents the spectrum 

of hydrologic variability in the basin, while satisfying the 

data needs for various present and future water-resource 

studies and management alternatives. Reducing redundancy 

in a network thus involves identifying elements of hydrologic 

variability (for example the magnitude, frequency, and timing 

of streamflow) and determining which gaging stations are 

essential for explaining the observed variability and which are 

not. 

Four methods were used for considering data 

redundancy: hydrograph comparison, daily-value correlation, 

variable space, and flow-duration ratios. Each method involves 

some aspect of hydrologic variability that can be either 

qualitatively or quantitatively evaluated. The results from 

each method should be considered along with the intended 

long-term use of the data-collection network. For example, the 

daily-value-correlation method is useful in determining which 

gaging stations might provide the best estimate of daily mean 

streamflow in the six subbasins and possibly other subbasins 

of the Nooksack River basin. However, the daily-valuecorrelation method does not address whether the network is 

adequate for improving future regional regressions for low- or 

high-flow frequency statistics. Other methods such as variable 

space, hydrograph comparison, and possibly flow-duration 

ratios are better suited to determine redundancy in the network 

for the purpose of improving future regional regression 

equations for low- and high-flow frequency statistics. 

Hydrograph Comparison Method

Hydrograph comparison is a method for examining 

the similarities and differences of streamflow patterns (the 

timing and magnitude of flow) between gaging stations. A 

hydrograph is a plot of streamflow over time at a gaging 

station, and hydrographs that are similar in the timing and 

magnitude of streamflow share a redundancy in streamflow 

information. Because of the difference in scale between large 

and small streams, hydrograph comparison usually is done 

with streamflow plotted on a logarithmic scale to make visual 

comparisons easier. Physical scaling effects between streams 

also can be further reduced and similarities in streamflow 

patterns can be more easily discerned by normalizing 

streamflow, by dividing daily flow at each gaging station by 

its subbasin drainage area (this ratio also is referred to as 

‘streamflow runoff’). A visual inspection of the normalized 

hydrographs for all six gaging stations in water year 2003 (a 

near-average water year) shows many similarities in the timing 

and relative magnitude of streamflow patterns as well as some 

differences (fig. 16). Although most mountain-stream gaging 

stations (Racehorse, Warm, Clearwater, and Skookum Creeks) 

have a similar runoff response to storm events during the 

winter and spring seasons (mid-October to mid-June), runoff 

patterns are different during the summer season (mid-June to 

mid-October) when baseflow conditions exist. For example, 

mountain-stream gaging stations began the 2003 winter season 

with similar streamflow runoff, but as summer progressed, 

Racehorse Creek was less sustained by baseflow and Warm 

Creek had high runoff due to snowmelt contributions. 

Streamflow runoff generally is less in lowland streams 

than in mountain streams, likely due to lower precipitation 

amounts. Of the two lowland streams, Anderson Creek is the 

only stream with periods of zero flow, whereas streamflow in 

Fishtrap Creek appears more sustained from baseflow during 

the summer season.

A closer inspection of streamflow hydrographs at the 

15-minute time interval during the period of July 11–31, 2002 

(during a wetter than average water year) shows similarities 

and differences in baseflow-recession characteristics between 

the six gaging stations (fig. 17). The slope of the baseflowrecession curve can be quantified as the baseflow-recession 

time constant or simply ‘tau’ (Eng and Milly, 2008), and has 

implications for groundwater recharge to streams. During lowflow periods without significant precipitation, streams with 

large tau exhibit a gradual decrease in streamflow indicating 

more contribution from groundwater recharge, whereas 

streams with smaller tau lack this recharge (possibly losing 

water to the groundwater system) and recede more quickly. 

The value of tau can be determined as follows (Eng and Milly, 

2008):

/ ln( / ),

where

is the baseflow-recession constant or , in days;

is the number of days between streamflow

measurements;

is the streamflow after days, and

is the streamflow at the b

t t t

t t

t

t Q Q

tau

t

Q t

Q

+∆

+∆

τ = ∆

τ

∆

∆

eginning of days. ∆t

(1)
Hydrologic Analysis of Selected Streamflow-Gaging Stations 29

Figure 16. Daily streamflow runoff at six streamflow-gaging stations in the Racehorse, Warm, Clearwater, Skookum, 

Anderson, and Fishtrap Creek subbasins, Nooksack River basin, Washington and Canada, water year 2003.

watac09-0390_fig 16

0.001

0.01

0.1

1

10

100

STREAMFLOW RUNOFF, IN CUBIC FEET PER SECOND PER SQUARE MILE

OCT NOV DEC

2002 2003

JAN FEB MAR APRIL MAY JUNE JULY AUG SEPT

Racehorse Creek

Stream

Warm Creek

Clearwater Creek

Skookum Creek

Anderson Creek

Fishtrap Creek

Average tau values computed for all sites for the 

baseflow-recession period July 11–31 (fig. 17) were similar 

for Racehorse, Clearwater, and Anderson Creeks, whereas 

Skookum and Warm Creeks were more similar to each other. 

Fishtrap Creek had a more gradual baseflow recession than 

any of the other sites during this period. The diurnal pulses 

of streamflow at Warm, Clearwater, and Skookum Creeks 

were caused by snowmelt. The hydrograph for Fishtrap Creek 

shows a small decrease in streamflow mid-way through the 

period, possibly associated with water diversion upstream for 

irrigation.

The hydrograph comparison method suggests that a 

streamflow-gaging station network of two or four stations 

would minimize redundancy in streamflow patterns (timing, 

magnitude) in the six subbasins depending on the priority of 

peak-flow or baseflow conditions. A network prioritized for 

peak streamflow runoff would contain at least two stations, 

including a mountain-stream and lowland-stream site. A 

network of two stations would include Anderson Creek 

(12210900) or Fishtrap Creek (12212050) (lowest peak 

runoff), and either Skookum Creek (12209490), Clearwater 

Creek (12207850), Racehorse Creek (12206900), or Warm 

Creek (12207750) (similar peak runoff). A network with a 

priority for baseflows would contain four stations—Anderson 

Creek (12210900) (smallest tau), Fishtrap Creek (12212050) 

(highest tau), and either Skookum Creek (12209490) or Warm 

Creek (12207750) (similar tau and snowmelt processes), 

and either Clearwater Creek (12207850) or Racehorse Creek 

(12206900) (similar tau).
30 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Daily-Value Correlation Method

A more quantitative method for evaluating redundancy 

in the network of six gaging stations is to examine the 

correlation between the daily mean streamflows of all stations. 

A metric for correlation is Pearson’s r, a coefficient which 

is the square root of the coefficient of determination, r2. A 

large r value between two stations indicates that daily mean 

streamflows at one station can be reasonably estimated as a 

function of daily mean streamflows at the other station. When 

two stations are strongly correlated, one of the two stations 

may be removed from the network without significant loss of 

information. The matrixes in figure 18 show the data plots and 

correlation coefficients for Linear Organic Correlation (LOC) 

regressions of the base e logarithms (natural logs) of daily 

mean streamflows for all six stations during summer (June 

16–Oct. 15), winter (Oct. 16–Feb. 14), and spring (Feb. 15–

June 15). Equivalent regression equations that express daily 

mean streamflow at one station as a function of daily mean 

streamflow at a second station are presented in appendix A. 

In this study, r values ≥ 0.84 (r2 ≥ 0.7) are considered well 

correlated. A summary of r values (table 6) shows that good 

correlation among sites is more common during the winter 

(high flow) season (seven r values ≥ 0.84) than the summer 

(low flow) season (five r values ≥ 0.84) and spring (transition 

flows) season (five r values ≥ 0.84). However, the summer 

season has the highest average correlation for flows among the 

six stations (average r = 0.79), compared to winter (0.78) and 

spring (0.40).

STREAMFLOW, IN CUBIC FEET PER SECOND100

1,000

10

1

0.1

11

JULY 2002

17 24 31

Racehorse Creek

Stream

Warm Creek

Clearwater Creek

Skookum Creek

Anderson Creek

Fishtrap Creek

τ = 10

τ = 13

τ = 35

τ = 21

τ = 26

τ = 15

Figure 17. Fifteen-minute streamflow and average tau (τ) values during the period of July 11–31 at six gaging stations in 

the Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins, Nooksack River basin, Washington 

and Canada. Average values for the baseflow recession time constant (τ), in days, for July 11–31, 2002. 
Hydrologic Analysis of Selected Streamflow-Gaging Stations 31

watac09-0390_fig 18A

NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

 NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

A. Summer season (June 16–Oct. 15) 

0

1

2

3

4

5

2

3

4

5

6

7

0

1

2

3

4

5

0 2 4 6

0 1 2 3 4 5

1 2 3 4 5 6 7

2 3 4 5 6 7

-5 -3 -1 1 3

0

2

4

6

0 1 2 3 4 5

1

2

3

4

5

6

7

-5

-3

-1

1

3

Racehorse

Creek

Warm

Creek

Clearwater

Creek

Skookum

Creek

Anderson

Creek

Fishtrap

Creek

r = 0.82

r = 0.94

r = 0.89

r = 0.80

r = 0.83

r = 0.89

r = 0.90

r = 0.54

r = 0.71

r = 0.92

r = 0.69

r = 0.75

r = 0.63

r = 0.73 r = 0.82

Figure 18. Relation among the natural logs of daily mean streamflows during the summer, winter, and spring seasons 

at each of six gaging stations in the Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins, 

Nooksack River basin, Washington and Canada.
32 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

watac09-0390_fig 18B

B. Winter season (Oct. 16–Feb. 14)

1

2

3

4

5

6

2

3

4

5

6

7

8

1

2

3

4

5

6

1 2 3 4 5 6 7

1 2 3 4 5 6

2 3 4 5 6 7

2 3 4 5 6 7 8

-4 -2 0 4 6

1

2

3

4

5

6

7

1 2 3 4 5 6

2

3

4

2

0

4

6

5

6

7

-4

-2

Racehorse

Creek

Warm

Creek

Clearwater

Creek

Skookum

Creek

Anderson

Creek

Fishtrap

Creek

r =0.87

r =0.94

r =0.94

r =0.77

r =0.75

r =0.92

r =0.88

r =0.59

r =0.62

r =0.92

r =0.65

r =0.65

r =0.71

r =0.17 r =0.86

NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

 NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

Figure 18.—Continued
Hydrologic Analysis of Selected Streamflow-Gaging Stations 33

watac09-0390_fig 18C

C. Spring season (Feb. 15–June 15)

1

2

3

4

5

3

4

5

6

7

2

3

4

5

6

2 3 4 5 6 7 3 4 5 6 7

1 2 3 4 5 3 4 5 6 7

-4 -2 0 2 4 6

2

5

4

3

7

6

2 3 4 5 6

3

4

5

6

7

-4

-2

0

2

6

4

Racehorse

Creek

Warm

Creek

Clearwater

Creek

Skookum

Creek

Anderson

Creek

Fishtrap

Creek

r = 0.74

r = 0.89

r = 0.91

r = 0.31

r = 0.19

r = 0.94

r = 0.78

r = -0.25

r = -0.33

r = 0.88

r = -0.05

r = -0.15

r = 0.20

r = 0.13 r = 0.84

 NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

NATURAL LOG OF DAILY MEAN STREAMFLOW, IN NATURAL LOG OF CUBIC FEET PER SECOND

Figure 18.—Continued
34 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Redundancy of streamflow sites in the network generally 

is assumed when sites correlate strongly during summer, 

winter, and spring. As noted previously, the redundancy 

findings of this method are only useful in determining which 

gaging stations may be eliminated from the network if the 

purpose of the network is to estimate daily mean streamflow 

in any of the six subbasins as a function of measured 

daily mean streamflow in at least one of the six subbasins. 

The redundancy findings of this method are not useful in 

determining which gaging stations may be eliminated from the 

network if the purpose of the network is to estimate regional 

regression equations for flow frequency statistics.

With that caveat, the patterns of correlations among the 

six gaging stations (table 6) indicate that the network could 

be reduced to either two or three stations. To avoid significant 

loss of information, one of the stations retained must be 

Fishtrap Creek (12212050) or Anderson Creek (12210900). 

For a reduced network of only two stations, the other station 

would need to be Skookum Creek (12209490) or Clearwater 

Creek (12207850). If either Skookum or Clearwater were not 

included, both Warm Creek (12207750) and Racehorse Creek 

(12206900) would be needed as these stations do not correlate 

well with each other (r = 0.74 and 0.82 for spring and summer 

season flows, respectively), and this would result in a network 

of three gaging stations. 

Variable-Space Method

For the Nooksack River basin, drainage area (DA) and 

mean basin elevation (E) were the two basin attributes that 

explain the greatest amount of variation in regional regression 

equations for estimating low-flow frequency statistics at 

ungaged sites. One way to evaluate the redundancy in the 

gaging station network is to look at the proximity of stations 

in the variable space defined by DA and E. It is desirable to 

have sites span a large range in the variable space because 

this leads to a more robust regression. Conversely, when two 

or more stations are close to each other in the variable space, 

they share redundant information and do not add explanatory 

power to the regression. 

As shown in figure 19, Clearwater Creek (12207850) 

and Skookum Creek (12209490) plot in close proximity in the 

DA-E variable space and, based on the variable-space method, 

one of these stations could be removed from the network with 

minor effects on regional regression equations for estimating 

low-flow frequency statistics. Fishtrap Creek (12212050) is 

in close proximity to a gaging station operated by Ecology 

(Bertrand Creek near mouth, 01N060) and could be removed 

from the network without significant loss of information, if 

gaging station 01N060 continues to operate.

Results from the variable-space method suggest that a 

network of four or five gaging stations would be optimal for 

future regional regression analyses of low-flow frequency 

statistics in the Nooksack River basin that use the basin 

attributes of drainage area and mean basin elevation. Such 

a network would contain the gaging stations—Racehorse 

Creek (12206900), Warm Creek (12207750), Anderson Creek 

(12210900), Fishtrap Creek (12212050), and Clearwater Creek 

(12207850) or Skookum Creek (12209490). Fishtrap Creek 

could be eliminated if Ecology continues the site at Bertrand 

Creek (01N060).

Table 6. Summary of correlation coefficients (Pearson’s r) showing patterns among the natural logs of daily mean streamflows at six 

gaging stations in the Racehorse, Warm, Clearwater, Skookum, Anderson, and Fishtrap Creek subbasins during summer, winter, and 

spring seasons, Nooksack River basin, Washington and Canada.

[Summer, defined as June 16–October 15; Winter, defined as October 16–February 14; Spring, defined as February 15–June 15. Gray shading indicates 

r values ≥ 0.84]

Racehorse Creek

0.82 0.87 0.74 Warm Creek

0.94 0.94 0.89 0.89 0.92 0.94 Clearwater Creek

0.89 0.94 0.91 0.90 0.88 0.78 0.92 0.92 0.88 Skookum Creek

0.80 0.77 0.31 0.54 0.59 -0.25 0.69 0.65 -0.05 0.63 0.71 0.20 Anderson Creek

0.83 0.75 0.19 0.71 0.62 -0.33 0.75 0.65 -0.15 0.73 0.71 0.13 0.82 0.86 0.84 Fishtrap Creek Summer Winter Spring Summer Winter Spring Summer Winter Spring Summer Winter Spring Summer Winter Spring
Hydrologic Analysis of Selected Streamflow-Gaging Stations 35

wataco9-0390_fig 19 MEAN BASIN ELEVATION, IN FEET

100

1,000

10,000

10

1 10 100 1,000

01N060

12207850

12209490

12212050

DRAINAGE AREA, IN SQUARE MILES

Continuous-record gaging station

Miscellaneous measurement site

Racehorse Creek

Warm Creek

Clearwater Creek

Skookum Creek

Anderson Creek

Fishtrap Creek

Figure 19. Drainage area and mean basin elevation for all gaging stations used in the regional 

regression analysis for estimating low-flow frequency statistics at ungaged sites, Nooksack River 

basin, Washington and Canada.

Flow-Duration-Ratio Method

Flow-duration statistics such as the Q90 (low flow) and 

Q50 (median flow) are defined as the streamflows that are 

exceeded 90 and 50 percent of the time, respectively, at a 

particular site. Because the Q90 or Q50 statistics generally 

increase with stream size, it is useful to remove the scale effect 

(normalize) by evaluating the ratio Q90/Q50. This results 

in a low-flow-duration metric that quantifies the baseflow 

dependence of a stream. A stream with a large Q90/Q50 ratio 

likely receives more baseflow from groundwater or snowmelt 

than a stream with a small ratio. A stream with a small Q90/

Q50 ratio may be more likely to go dry in the summer.

For the purpose of computing regional regression 

equations for low-flow frequency statistics, it is desirable to 

include streams with a range of baseflow characteristics in the 

analysis. As shown in figure 20, Anderson Creek (12210900) 

represents a flow regime with a small Q90/Q50 ratio and 

should remain in the network based on the low-flow-duration 

method. However, Fishtrap Creek (12212050) and Racehorse 

Creek (12206900) have similar Q90/Q50 ratios and one of 

these sites could be removed from the network. Similarly, 

Skookum Creek (12209490) and Warm Creek (12207750) 

also have close Q90/Q50 ratios and one of these sites could 

be removed from the network. Clearwater Creek (12207850), 

which has a Q90/Q50 ratio in between ratios of other stations 

used in the regression analysis, also could be removed. 
36 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

Even though no regional regression equations were 

developed in this study for estimating high-flow frequency 

statistics, it is important to consider how removal of gaging 

stations from the network may affect the ability to develop 

such regressions in the future. As a result, the network was 

assessed for variability in high flows by considering the 

flow-duration statistic Q10, which represents the flow that is 

exceeded 10 percent of the time. Because the Q10 statistic 

generally increases with stream size, it is useful to remove 

the scale effect by normalizing and evaluating the ratio Q10/

Q50 instead. This ratio is a high-flow-duration metric that 

quantifies the responsiveness of a stream to precipitation. A 

responsive or ‘flashy’ stream will have a large Q10/Q50 ratio. 

For the purpose of computing regional regression 

equations for high-flow statistics, it is desirable to include 

streams in the analysis representing different flow regimes, 

that is, streams with a large range of responses to precipitation. 

As shown in figure 21, Anderson Creek (12210900) represents 

an end-member, large Q10/Q50 ratio and should remain in the 

network based on the high-flow-duration method. However, 

Clearwater Creek (12207850), Fishtrap Creek (12212050), 

Racehorse Creek (12206900), Warm Creek (12207750), and 

Skookum Creek (12209490) have similar Q10/Q50 ratios 

and four of these stations could be removed from the network 

with likely minor effects on high-flow regional regression 

equations.

wataco9-0390_fig 20 Q90/Q50 RATIO

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

RANKING

Continuous-record gaging station

Racehorse Creek

Warm Creek

Clearwater Creek

Skookum Creek

Anderson Creek

Fishtrap Creek

Figure 20. Q90/Q50 ratios for all sites used in the regional regression analysis for estimating low-flow 

frequency statistics at ungaged sites, Nooksack River basin, Washington and Canada.
Hydrologic Analysis of Selected Streamflow-Gaging Stations 37

wataco9-0390_fig 21 Q10/Q50 RATIO

RANKING

0

5

4

3

2

1

6

7

8

9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Continuous-record gaging station

Racehorse Creek

Warm Creek

Clearwater Creek

Skookum Creek

Anderson Creek

Fishtrap Creek

Figure 21. Q10/Q50 ratios for all sites used in the regional regression analysis for estimating lowflow frequency statistics at ungaged sites, Nooksack River basin, Washington and Canada.

Summary of Methods and Prioritization of 

Streamflow-Gaging Stations

Four different methods were used to prioritize gaging 

stations for the purpose of optimizing the streamflow-gaging 

station network by reducing the redundancy of streamflow 

information (table 7). The first method, hydrograph 

comparison, was used to examine similarities in the 

streamflow time series for each gaging station at a daily time 

step during a water year and at a 15-minute time step during 

a baseflow recession period. The second method, the dailyvalue-correlation method, was used to determine which of the 

gaging stations collect redundant information if the purpose of 

the network is to estimate daily mean streamflows in the six 

subbasins. The variable-space method was used to determine 

which gaging stations are important for developing low-flow 

regional regression equations using basin attributes of drainage 

area and mean basin elevation. The flow-duration-ratio method 

provided metrics for low flows and high flows (Q90/Q50 

and Q10/Q50, respectively), and was used to evaluate the 

variability of hydrologic response in the network as well as 

the importance of sites for developing regression equations 

for estimating low- and high-flow frequency statistics. Each 

of the methods could be used to suggest a different optimal 

network configuration that would benefit future data analyses 

or needs. Thus, it is difficult to develop a quantitative measure 

to combine these results and create one prioritized list of 

gaging stations. This also means that removing any of the 

gaging stations from the network will result in some loss of 

information and, for example, reduce the accuracy of regional 

regression equations or estimates of daily mean flow in the six 

subbasins of the Nooksack River basin. However, it is possible 

to make a qualitative prioritization of the six streamflowgaging stations.
38 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

The six streamflow-gaging stations were ranked in order 

of priority using a qualitative summary of the four methods 

and, when applicable, other factors relating to individual 

subbasins and gaging stations previously described (table 8). 

The rationale for the priority rankings is discussed below for 

each gaging station.

• Skookum Creek shares the highest rank because, as 

demonstrated by the daily-value correlation method, 

streamflow data from this gaging station would 

likely provide a reasonable estimate of streamflow 

at other mountain streams. However, Skookum 

Creek would likely not provide the best estimate 

of streamflow for lowland streams. Skookum 

Creek shares unique variable space (important 

for regional regression analysis) with Clearwater 

Creek, which was ranked sixth. Streamflow data 

from the Skookum Creek gaging station is used 

by the National Weather Service for calibrating a 

hydrologic model for the South Fork Nooksack 

River.

Table 7. Summary of results by method for determining optimal combinations of streamflow-gaging stations to retain in six subbasins, 

Nooksack River basin, Washington and Canada.

Method Purpose Results

Hydrograph comparison Identifying redundancy in 

timing and magnitude of 

peak flows and baseflowrecession characteristics

Network could be reduced to 2 or 4 stations depending on peak flow or 

baseflow priority

2 stations (peak-flow priority): Anderson Creek or Fishtrap Creek, and Skookum 

or Clearwater Creek or Racehorse or Warm Creek

4 stations (baseflow priority): Anderson Creek, Fishtrap Creek, and Skookum or 

Warm Creek, and Clearwater or Racehorse Creek

Daily-value correlation Identifying redundancy 

in concurrent daily 

streamflow

Network could be reduced to 2 or 3 stations 

2 stations: Fishtrap or Anderson Creek, and Skookum or Clearwater Creek

3 stations: Warm Creek, Racehorse Creek, and Fishtrap or Anderson Creek

Variable space Identifying redundancy in 

the variable space defined 

by basin attributes used 

in regional regression 

analysis

Network could be reduced to 5 stations by eliminating Clearwater Creek 

or Skookum Creek. Network could be reduced to 4 stations by also 

eliminating Fishtrap Creek. However, the latter is only justified if the 

Washington State Department of Ecology continues measurement of 

Bertrand Creek (Ecology no. 01N060)

4 stations: Anderson Creek, Warm Creek, Racehorse Creek, and Skookum or 

Clearwater Creek

5 stations: Anderson Creek, Warm Creek, Fishtrap Creek, Racehorse Creek and 

Skookum or Clearwater Creek

Flow-duration ratio Identifying redundancy in 

the relative frequency 

of extreme flows

Network could be reduced to 2 or 3 stations, depending on low-flow or highflow priority

2 stations (high-flow priority): Anderson Creek, and Warm, Skookum, 

Clearwater, Fishtrap, or Racehorse Creek

3 stations (low-flow priority): Anderson Creek, and Warm or Skookum Creek, 

and Racehorse or Fishtrap Creek

• Anderson Creek shares the highest rank because it 

represents a natural lowland stream, occupies unique 

drainage area-mean basin elevation variable space, 

and has flow-duration ratios for high and low flow 

that make it unique in the basin. Anderson Creek 

also has periods of zero flow during the summer, 

making it valuable for future regional logistic 

regression studies.

• Warm Creek is ranked third because it provides 

unique information in the daily-value correlation 

and variable-space methods. Because of its high 

elevation and thus increased snow accumulation, 

streamflow in the Warm Creek subbasin has a larger 

component of snowmelt per unit area than other 

sites and melting starts later in the season. The 

high elevation combined with a small drainage area 

makes this site unique and it fills an important part 

of the variable space for regression equations.
Summary 39

• Fishtrap Creek is ranked fourth because it represents 

a lowland stream that is affected by agricultural 

activities and urbanization (to a greater degree 

than Anderson Creek) and has baseflow recession 

characteristics that are different from the other 

gaging stations. This station represents an important 

index station that was consistently selected to 

estimate streamflow characteristics at most of 

the miscellaneous measurement sites in the basin 

based on geographic proximity and similar variable 

space (drainage area and mean basin elevation). 

The priority ranking of this gaging station could 

be lowered if Ecology continues to operate the 

gaging station on Bertrand Creek (01N060) and EC 

continues to operate the gaging station upstream on 

Fishtrap Creek (0MH153).

• Racehorse Creek is ranked fifth because although it 

occupies unique variable space, it is similar to other 

stations for most of the methods used. The subbasin 

measured by the gaging station recently experienced 

profound channel changes that could make it 

difficult to maintain an accurate stage-discharge 

relation at this station for the foreseeable future.

• Clearwater Creek is ranked sixth because it is similar 

to Skookum Creek in daily-value correlation and 

variable space. The creek is in close proximity 

to Warm Creek and has baseflow recession 

characteristics similar to Racehorse Creek. The 

streamflow record for Clearwater Creek also is 

shorter than for the other stations and is missing data 

from October 2006 to July 2008 (21 months) due to 

a flood that damaged the gaging station.

Overall, it appears that a minimal network should 

contain two gaging stations: Skookum Creek, which is a 

mountain-stream station, and Anderson Creek, which is a 

lowland-stream station. The optimal streamflow-gaging 

station network should contain five stations, representing (1) 

tributaries for each fork of the Nooksack River, (2) mountainstream and lowland-stream subbasins, and (3) different 

baseflow recession characteristics. Clearwater Creek could 

be removed because it consistently appears as a redundant 

site among all methods used. Of all the methods used to 

analyze the network, the daily-value-correlation and variablespace methods are the most important to consider, as these 

relate directly to further quantitative uses of the data, such as 

estimating missing streamflow at gaged sites and developing 

regional regression equations to estimate streamflowfrequency statistics at ungaged sites. The priority of one of 

these methods over the other depends on the purpose of the 

streamflow-gaging station network.

Summary

The Nooksack River, including its tributaries and 

ecosystems, faces increasing pressures for water demand, 

flood protection, and riparian land use. The streamflow-gaging 

station network in the Nooksack River basin is an important 

asset in managing the basin’s water resources as it provides the 

necessary data for water managers, regulators, and scientists 

to monitor water availability. The streamflow-gaging station 

network in the basin consists of 17 streamflow-gaging stations 

and 8 miscellaneous measurement sites operated by Federal, 

State, and Canadian government agencies. The Lummi Nation, 

an indigenous tribe of Native Americans, has funded operation 

of six of the streamflow-gaging stations operated by the USGS 

for the past 10 years, and has requested that the USGS provide 

an analysis of the streamflow data.

The study documented in this report assembled 

streamflow data from 12 continuous-record gaging stations 

(CG), 5 short-term continuous-record gaging stations 

Table 8. Prioritized list of streamflow-gaging stations to retain in six subbasins of the Nooksack River basin, Washington and Canada.

[WA, Washington]

Station No. Station name Latitude 

(decimal degrees)

Longitude 

(decimal degrees)

Priority ranking for 

retaining station in 

streamflow-gaging 

station network

12209490 Skookum Creek above diversion, near Wickersham, WA 48.67150163 -122.13959998 1

12210900 Anderson Creek at Smith Road, near Goshen, WA 48.83261414 -122.33905016 1

12207750 Warm Creek near Welcome, WA 48.76733993 -121.96459472 3

12212050 Fishtrap Creek at Front Street, at Lynden, WA 48.93872574 -122.47905316 4

12206900 Racehorse Creek at North Fork Road, near Kendall, WA 48.88484196 -122.13320746 5

12207850 Clearwater Creek near Welcome, WA 48.78845101 -122.02292921 6
40 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

(STCG), and 8 miscellaneous measurement sites in or near the 

Nooksack River basin, and determined low-flow frequency 

statistics for 1, 3, 7, 15, 30, and 60 consecutive-day low flows 

with recurrence intervals of 2 and 10 years. Streamflow-gaging 

stations with 7 or more years of continuous streamflow record 

were considered CG stations; stations with less than 7 years 

of record were considered STCG stations. Miscellaneous 

measurement sites with 10 or more measurements of 

streamflow during baseflow periods were used in the analysis 

of low-flow frequency statistics. Whereas low-flow frequency 

statistics were computed directly from the streamflow record 

at CG stations, the Maintenance of Variance Extension version 

1 (MOVE.1) statistical method was first used to extend the 

record at STCG stations to 7 years before low-flow frequency 

statistics were computed. At miscellaneous measurement sites, 

MOVE.1 was used to estimate low-flow frequency statistics 

using similar statistics from nearby or hydrologically similar 

CG stations.

Because the Lummi Nation is interested in estimating 

streamflow at locations in the Nooksack River basin where 

streamflow-gaging stations or miscellaneous measurement 

sites do not exist, regional regression equations were 

developed for estimating the low-flow frequency statistics 

at ungaged sites. Equations were developed for estimating 

low-flow frequency statistics for the 1, 3, 7, 15, 30, and 

60 consecutive-day low flows with recurrence intervals of 

2 and 10 years. The equations were developed from the 

streamflow statistics previously determined at 12 CG and 

5 STCG stations, 8 miscellaneous measurement sites, and 

the basin characteristics determined at each site. A total of 

26 basin characteristics, such as drainage area, mean annual 

precipitation, and percentage of area with surficial geology 

classified as bedrock were examined for use as explanatory 

variables in the regression equations. The stepwise regression 

analysis and tests for multicollinearity were used iteratively to 

select the final basin characteristics, drainage area and mean 

basin elevation, as explanatory variables in the regression 

equations. The USGS software program WREG (version 1.0) 

was used to develop weighted-least-squares (WLS) regression 

equations for estimating low-flow frequency statistics at 

ungaged sites in the Nooksack River basin. The WLS method 

used gave more weight in the regression models to sites with 

longer periods of record and thus presumably more accurate 

streamflow statistics. Performance metrics such as the 

coefficient of determination (R2) and root-mean-squared error 

(RMSE) expressed as a percentage were calculated for each of 

the regression equations and ranged from 0.79 to 0.93 and 77 

to 560 percent, respectively.

In addition to developing regional regression equations 

for low-flow frequency statistics, the Lummi Nation 

requested that the USGS determine whether some of the 

six streamflow-gaging stations were collecting redundant 

streamflow information and if some of the gaging stations 

could be removed from the network without significant loss 

of information. Four methods were used for considering data 

redundancy: hydrograph comparison, daily-value correlation, 

variable space, and flow-duration ratios. The hydrographcomparison method found similarities and differences between 

gaging stations in the streamflow record during a water year 

at a daily time step and during the baseflow recession period 

at a 15-minute time step. The daily-value-correlation method 

identified which of the gaging stations collect redundant 

information and is a useful method if the purpose of the 

network is to estimate daily mean streamflows in the six 

subbasins. The variable-space method identified which gaging 

stations occupy unique variable space and is important for 

determining the relative importance of gaging stations for 

developing regional regression equations. The flow-durationratio method provided metrics for low flows and high flows 

(Q90/Q50 and Q10/Q50, respectively), and was used to 

evaluate the variability of hydrologic response in the network. 

The results from each method should be considered along with 

the intended long-term use of the data-collection network. In 

evaluating the six gaging stations, the subbasins for each of 

the gaging stations also were characterized based on land use, 

surficial geology, and streamflow characteristics. Although 

each of the methods could be used to suggest a different 

optimal network configuration, a qualitative prioritization 

of the six gaging stations was made from most to least 

important as follows: Skookum Creek (12209490), Anderson 

Creek (12210900), Warm Creek (12207750), Fishtrap Creek 

(12212050), Racehorse Creek (12206900), and Clearwater 

Creek (12207850). The optimum streamflow-gaging 

station network would contain all gaging stations except 

Clearwater Creek, and the minimum network would include 

Skookum Creek and Anderson Creek. The optimal network 

configuration depends largely on the expected future use of the 

streamflow-gaging station network.

Acknowledgments

The authors gratefully acknowledge the dedication 

of the hydrologic technicians at the USGS Sedro Wooley 

Field Office in collecting high-quality streamflow data and 

maintaining the streamflow-gaging stations in the Nooksack 

River basin, without which this study would not have been 

possible. 
References Cited 41

References Cited

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42 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

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Appendix A 43

Appendix A. Regression Equations for Estimating Daily Mean Streamflow at Six 

Gaging Stations in the Nooksack River Basin

As part of the daily-value correlation method, 

regression analyses were conducted in natural 

log space using Linear Organic Correlation to 

determine redundancy in streamflow information 

among six streamflow-gaging stations in the 

Nooksack River basin. By transforming the 

resulting regression equations from natural log 

space back into standard space, a set of equations 

resulted (table A1) that can be used to estimate 

daily mean streamflow at any one of the six 

stations as a function of daily mean streamflow 

at another of the six stations. The ability to 

estimate daily mean streamflow may be useful 

for filling in periods of missing record at any of 

the six gages, or extending the record at gages 

that may be discontinued. When estimating daily 

mean streamflow using regression equations, the 

equation for the appropriate season and with the 

largest correlation coefficient should be selected 

(table 6).

Table A1. Regression equations for estimating daily mean streamflow at six 

gaging stations, Nooksack River basin, Washington and Canada.

[All units of streamflow are in cubic feet per second. Equations highlighted in gray have 

r values ≥ 0.84; A, is daily mean streamflow for Racehorse Creek at USGS gaging station 

12206900. B, is daily mean streamflow for Warm Creek at USGS gaging station 12207750; 

C, is daily mean streamflow for Clearwater Creek at USGS gaging station 12207850. D, is 

daily mean streamflow for Skookum Creek at USGS gaging station 12209490; E, is daily 

mean streamflow for Anderson Creek at USGS gaging station 12210900; F, is daily mean 

streamflow for Fishtrap Creek at USGS gaging station 12212050]

Summer

(June 16–Oct. 15)

Winter 

(Oct. 16–Feb. 14)

Spring

 (Feb. 15–June 15)

A = 0.468 × B1.2 A = 1.393 × B1.2 A = 3.56× B0.866

A = 0.192 × C1.12 A = 0.397 × C1.09 A = 0.783 × C0.892

A = 0.035 × D1.46 A = 0.256 × D1.11 A = 0.415 × D1.01

A = 17.4 × E0.769 A = 7.78× E0.662 A = 14.7 × E0.544

A = 0.252 × F1.57 A = 0.430 × F1.1 A = 0.446 × F1.16

B = 1.89 × A0.836 B = 0.758 × A0.835 B = 0.231 × A1.15

B = 0.474 × C0.938 B = 0.350 × C0.907 B = 0.174 × C1.03

B = 0.115 × D1.22 B = 0.243 × D0.924 B = 0.084 × D1.16

B = 20.6 × E0.643 B = 4.21 × E0.553 B = 101× E-0.628

B = 0.596 × F1.31 B = 0.375 × F0.916 B = 5,710 × F-1.34

C = 4.36 × A0.892 C = 2.34 × A0.921 C = 1.32 × A1.12

C = 2.22 × B1.07 C = 3.18 × B1.1 C = 5.47 × B0.971

C = 0.220 × D1.3 C = 0.669 × D1.02 C = 0.491 × D1.13

C = 55.7 × E0.686 C = 15.5 × E0.61 C = 486 × E-0.61

C = 1.28 × F1.4 C = 1.08 × F1.01 C = 24,300 × F-1.31

D = 9.89 × A0.684 D = 3.42× A0.904 D = 2.40 × A0.993

D = 5.88 × B0.818 D = 4.61 × B1.08 D = 8.46 × B0.86

D = 3.20 × C0.767 D = 1.48 × C0.981 D = 1.88 × C0.886

D = 69.9 × E0.526 D = 21.9 × E0.598 D = 34.5 × E0.54

D = 3.85 × F1.07 D = 1.60 × F0.991 D = 1.08 × F1.16

E = 0.024 × A1.3 E = 0.045 × A1.51 E = 0.007 × A1.84

E = 0.009 ×B1.55 E = 0.074 ×B1.81 E = 1,570 ×B-1.59

E = 0.003 × C1.46 E = 0.011 × C1.64 E = 25,300 × C-1.64

E = 0.0003 × D1.9 E = 0.006 × D1.67 E = 0.001 × D1.85

E = 0.004 × F2.04 E = 0.013 × F1.66 E = 0.002 × F2.14

F = 2.41 × A0.638 F = 2.16 × A0.912 F = 2.00 × A0.859

F = 1.48 × B0.763 F = 2.92 × B1.09 F = 626 × B-0.744

F = 0.840 × C0.716 F = 0.929 × C0.99 F = 2,300 × C-0.766

F = 0.284 × D0.933 F = 0.624 × D1.01 F = 0.938 × D0.866

F = 14.9 × E0.491 F = 14.0 × E0.604 F = 20.1 × E0.468
44 Estimating Low-Flow Frequency Statistics and Hydrologic Analysis, Nooksack River Basin, Washington and Canada

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Curran and Olsen— Estimating Low-Flow Frequency Statistics, Nooksack River Basin, Northwestern Washington and Canada—Scientific Investigations Report 2009–5170