Prepared in cooperation with the U.S. Fish and Wildlife Service

A National Streamflow Network Gap Analysis

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5013
Cover (clockwise from top left). Top left: U.S. Geological Survey (USGS) streamgage 01634000, 

North Fork Shenandoah River near Strasburg, Virginia; photograph by Julie Kiang. USGS streamgage 

13039500, Henrys Fork near Lake, Idaho; photograph by Nathan Jacobson, USGS. USGS streamgage 

10336660, Blackwood Creek near Tahoe City, California; photograph by Jesse Juchtzer, USGS. USGS 

streamgage 15960000, Tamayariak River near Kaktovik, Alaska; photograph by Ryan Hollins, USGS. 

USGS streamgage 12056500, North Fork Skokomish River below Staircase Rapids near Hoodsport, 

Washington; photograph by Julie Kiang.
A National Streamflow Network Gap Analysis

By Julie E. Kiang, David W. Stewart, Stacey A. Archfield, Emily B. Osborne, and Ken Eng

Prepared in cooperation with the U.S. Fish and Wildlife Service

Scientific Investigations Report 2013–5013

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Kiang, J.E., Stewart, D.W., Archfield, S.A., Osborne, E.B., and Eng, Ken, 2013, A national streamflow network gap 

analysis: U.S. Geological Survey Scientific Investigations Report 2013–5013, 79 p. plus one appendix as a separate 

file, http://pubs.usgs.gov/sir/2013/5013/.
iii

Acknowledgements

The U.S. Fish and Wildlife Service provided funding for this project and their support is gratefully 

acknowledged. Todd Koenig and Kernell Ries of the U.S. Geological Survey (USGS) queried the 

National Streamflow Statistics (NSS) database and provided the resulting data. James Falcone 

of the USGS provided a draft of Geospatial Attributes of Gages for Evaluating Streamflow 

(GAGES) version II for use in this study, with significantly more streamgages than were available 

in the original GAGES dataset.

v

Contents

Acknowledgements......................................................................................................................................iii

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

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

Objectives of the Streamgage Gap Analysis.............................................................................................1

Study Area and Data .....................................................................................................................................2

Streamgage Gap Analysis for Gaged Locations.......................................................................................3

Spatial Gap Analysis.............................................................................................................................7

Temporal Gap Analysis ......................................................................................................................11

Calculation of Flow Statistics ...........................................................................................................11

Uncertainty of Estimated Statistics .................................................................................................12

Mean Annual Flow.....................................................................................................................13

Monthly Flow Statistics ............................................................................................................18

Peak Flow Statistics ..................................................................................................................26

Low-Flow Statistics ...................................................................................................................29

Streamgage Gap Analysis for Ungaged Locations ................................................................................29

Previous Regional Analyses .............................................................................................................29

Availability of Index Streamgages ...................................................................................................31

Correlation Analysis ..................................................................................................................31

Estimation of Correlation ..........................................................................................................31

Estimation of Correlation Using Observed Streamflow..............................................31

Mapping of Correlation for Ungaged Locations ..........................................................36

Distribution of Correlations Across the United States ........................................................36

Relation Between Distance and Correlation.........................................................................37

Map Correlation Across the United States ...........................................................................37

Basin Attribute Coverage ..................................................................................................................54

Summary and Conclusions.........................................................................................................................55

Spatial Gap Analysis...........................................................................................................................55

Temporal Gap Analysis ......................................................................................................................55

Uncertainty Analysis ..........................................................................................................................55

Previous Regression Studies............................................................................................................55

Correlation............................................................................................................................................56

Basin Attribute Similarity...................................................................................................................56

Further Work.................................................................................................................................................56

References Cited..........................................................................................................................................58

Appendix 1. Gages Used in the Reference-Quality Streamgage Dataset ......................................61

Appendix 2. Basin Attributes at Gageable Watersheds and Gaged Basins 

for Each Hydrologic Unit Code Region....................................................................................63
vi

Figures

1. Maps showing streamgages used in this analysis for the datasets that 

contain A, all (complete) and B, reference-quality streamgages ........................................4

2. Map showing hydrologic unit code regions for the United States ......................................5

3. Maps showing level II ecoregions of North America present in the 

United States .................................................................................................................................6

4. Maps showing the spatial coverage of streamgages in the complete 

dataset that have upstream watersheds with drainage area A, less 

than 20,000 square miles (mi2); B, less than 2,000 mi2; C, less than 1,000 mi2; 

and D, less than 500 mi2 ...............................................................................................................8

5. Map showing spatial coverage of reference-quality streamgage drainages .................10

6. Graphs showing percentage of hydrologic unit code regions gaged ...............................11

7. Graphs showing the percentages of ecoregions gaged .....................................................12

8. A, Map showing streamgage drainage basins less than or equal to 2,000 

square miles (mi2) with at least 50 years of record collected between 

1900 and 2009 and B, graph showing percentages of conterminous 

United States with at least 50 years of record, by size of gaged drainage area .............14

9. Map showing the median years of record for the reference-quality 

streamgages found in each hydrologic unit code region....................................................15

10. Map showing the coefficient of variation of the mean annual flow ..................................16

11. Maps showing A, standard error of mean annual flow for 10 years for 

each streamgage in the reference-quality streamgage dataset and 

B, median standard error of the mean annual flow for stations in each 

hydrologic unit code region ......................................................................................................19

12. Maps showing standard error of mean annual flow for A, 50 and B, 100 years..............20

13. Map showing the number of years of record needed in each hydrologic 

unit code region to estimate mean annual flow with a (fractional) standard 

error of 0.1....................................................................................................................................21

14. Graph showing the number of years of streamflow record needed in 

hydrologic unit code region 9 (Souris-Red-Rainy) to estimate mean 

annual flow with a specified standard error..........................................................................26

15. Maps showing standard error of 10 percent annual exceedance probability 

flood (10-year flood) for A, a record length of 10 years and B, for a record 

length of 100 years......................................................................................................................27

16. Maps showing standard error of selected peak flow quantiles by hydrologic 

unit code region ..........................................................................................................................28

17. Maps showing the standard error of A, prediction and B, the estimate 

for regression equations used to predict mean annual flow ..............................................32

18. Maps showing the standard error of A, prediction and B, the estimate for 

regression equations used to predict the 1 percent annual exceedance 

probability flood ..........................................................................................................................33

19. Maps showing the standard error of A, prediction and B, the estimate for 

regression equations used to predict the 10 percent annual exceedance 

probability flood ..........................................................................................................................34

20. Graphs showing the standard error of A, prediction and B, the estimate 

for regression equations used to predict the 7-day average, 10-year 

minimum flow ..............................................................................................................................35
vii

 21. Graphs showing the distribution of Pearson’s correlation coefficient 
viii

Tables

1. Cumulative percentage of hydrologic unit code regions that are gaged ...........................7

2. Cumulative percentage of level II ecoregions in the United States that 

are gaged .......................................................................................................................................9

3. Percentage of hydrologic unit code regions with at least 10 years of 

gaged record collected at streamgages draining less than or equal to 

2,000 square miles ......................................................................................................................13

4. Percentage of level II ecoregions with at least 10 years of gaged record 

collected at streamgages draining less than or equal to 2,000 square miles ..................17

5. Median coefficient of variation of annual mean flow of streamgages .............................18

6. Median coefficient of variation for hydrologic unit code regions......................................22

7. Median coefficient of variation for level II ecoregions in the United States ...................24

8. Basin attributes commonly used in regression studies......................................................30

9. Basin attributes appearing in regression equations developed by the USGS 

and included in the National Streamflow Statistics (NSS) database................................30

10. Summary of key findings by hydrologic unit code (HUC) region ........................................57

Conversion Factors and Datum

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)

mile, nautical (nmi) 1.852 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

square mile (mi2) 2.590 square kilometer (km2

)

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

°F=(1.8×°C)+32

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

°C=(°F-32)/1.8

Vertical coordinate information is referenced to 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.
ix

Abbreviations

HUC hydrologic unit code

LPIII log Pearson type III statistical distribution

NSS National Streamflow Statistics software

NWIS National Water Information System

RMSE root mean square error

SE standard error

USGS U.S. Geological Survey

WIE Weighted Independent Estimates software

A National Streamflow Network Gap Analysis

By Julie E. Kiang, David W. Stewart, Stacey A. Archfield, Emily B. Osborne, and Ken Eng

Abstract

The U.S. Geological Survey (USGS) conducted a gap analysis to evaluate how well the USGS streamgage network meets 

a variety of needs, focusing on the ability to calculate various 

statistics at locations that have streamgages (gaged) and that do 

not have streamgages (ungaged). This report presents the results 

of analysis to determine where there are gaps in the network of 

gaged locations, how accurately desired statistics can be calculated with a given length of record, and whether the current network allows for estimation of these statistics at ungaged locations.

The analysis indicated that there is variability across the 

Nation’s streamflow data-collection network in terms of the 

spatial and temporal coverage of streamgages. In general, the 

Eastern United States has better coverage than the Western 

United States. The arid Southwestern United States, Alaska, 

and Hawaii were observed to have the poorest spatial coverage, 

using the dataset assembled for this study. Except in Hawaii, 

these areas also tended to have short streamflow records. Differences in hydrology lead to differences in the uncertainty of 

statistics calculated in different regions of the country. Arid and 

semiarid areas of the Central and Southwestern United States 

generally exhibited the highest levels of interannual variability 

in flow, leading to larger uncertainty in flow statistics.

At ungaged locations, information can be transferred from 

nearby streamgages if there is sufficient similarity between the 

gaged watersheds and the ungaged watersheds of interest. Areas 

where streamgages exhibit high correlation are most likely to be 

suitable for this type of information transfer. The areas with the 

most highly correlated streamgages appear to coincide with mountainous areas of the United States. Lower correlations are found 

in the Central United States and coastal areas of the Southeastern 

United States. Information transfer from gaged basins to ungaged 

basins is also most likely to be successful when basin attributes 

show high similarity. At the scale of the analysis completed in 

this study, the attributes of basins upstream of USGS streamgages 

cover the full range of basin attributes observed at potential locations of interest fairly well. Some exceptions included very high or 

very low elevation areas and very arid areas.

Introduction

To understand streamflow in the context of ecological services, water availability, or interactions with water 

quality, streamflow information is needed for a wide variety 

of hydrologic conditions. Statistics providing information on 

the magnitude, timing, and frequency of streamflow events are 

needed at the location of interest.

Ideally, a gaged streamflow record is available at the location of interest, and statistics can be calculated directly from 

the streamflow time series. To estimate reliable statistics and 

identify trends in streamflow, long-term streamflow records are 

essential. The extent of the U.S. Geological Survey (USGS) 

streamflow network and the accuracy of statistics calculated 

from records of limited length are assessed in this report. 

Whereas other government agencies and private organizations 

may also collect streamflow information in some areas of the 

United States, this report focuses exclusively on the USGS 

streamgage network because USGS streamflow data are readily 

accessible from a single database and consistent quality control 

procedures have been applied to the entire dataset.

Because it is impossible to maintain a streamgage at 

every location of interest, methods have been developed to 

transfer streamflow information at gaged locations to estimate 

information at ungaged locations. These methods generally 

require that flow records at the gaged locations be relatively 

unaltered by upstream land-use change, flow regulation, 

discharges, or withdrawals. This report assesses the suitability 

of the USGS streamflow network for transferring information 

from gaged locations to ungaged locations.

For the purpose of estimating statistics, areas of the 

country that are not covered by the streamgage network and 

where there is low suitability for applying statistical methods 

for estimating statistics are priority areas for the addition of 

streamgages. Additional streamgages can be located strategically, if information about gaps is available. The goal of this 

report is to help identify where there are gaps in the streamflow network. Filling in these gaps with new streamgages will 

not only allow estimation of statistics directly from a new 

gaged record, but will also allow better estimation of streamflow statistics at ungaged locations.

Objectives of the Streamgage Gap 

Analysis

Streamgage gap analysis for gaged locations.—The 

objective of the streamgage gap analysis for gaged locations is 

to assess the spatial and temporal extent of the existing USGS 
2 A National Streamflow Network Gap Analysis

streamgage network. There are three main components to this 

part of the analysis:

• spatial gap analysis to characterize the spatial extent 

and coverage of the current streamgage network

• temporal gap analysis to characterize the change in 

the network over time and the coverage of long-term 

streamgages (50 years of record or more)

• uncertainty analysis to evaluate the accuracy of statistics calculated at gaged locations in different parts of 

the country

Streamgage gap analysis for ungaged locations.—The 

streamgage gap analysis for ungaged locations provides an 

assessment of the suitability of the USGS streamgage network 

for estimating statistics at ungaged locations. Two approaches 

are commonly taken for transferring information from the 

streamgage network to an ungaged location. The first involves 

the selection of one or more index streamgages whose 

upstream watershed is thought to be similar to the ungaged 

location. Streamflow characteristics calculated for the index 

streamgages are then adjusted and applied to the ungaged 

location. The second approach to information transfer utilizes 

regional relationships among streamflow characteristics and 

upstream basin characteristics. This part of the streamgage 

gap analysis considers the following approaches to assess the 

suitability of the USGS streamgage network for estimating 

statistics at ungaged locations:

• identify where an existing long-term continuous record 

index station is likely to be suitable or unsuitable for 

transfer of information using correlation analysis and 

basin attribute analysis

• evaluate the accuracy of regional regression analyses for estimation of streamflow statistics across the 

country

Study Area and Data

The network analysis examined the USGS streamgage 

network for the entire United States, including Alaska, Hawaii, 

and Caribbean (for purposes of this report, Puerto Rico), 

although some elements of the analysis were possible only 

for the conterminous United States. Only USGS streamgages 

included in the National Water Information System (NWIS) 

database were considered.

A total of 9,929 USGS streamgages were used in this 

study (highlight 1). The bulk of the dataset consisted of the 

9,323 streamgages included in the Geospatial Attributes of 

Gages for Evaluating Streamflow (GAGES) dataset, developed by Falcone and others (2010), as updated in March 2011. 

This 2011 update, referred to as GAGES–II-prelim, includes 

all streamgages active in water year1 2010 and all current and 

1

A water year is a 12-month period starting October 1 and continuing to the 

following September 30. The water year is designated by the calendar year in 

which it ends.

Highlight 1. Datasets Used 

in the National Streamflow 

Network Gap Analysis

Complete dataset.—Consists of a total of 9,929 

streamgages (fig. 1A), including reference- and nonreference-quality streamgages. Consists of GAGES–

II-prelim streamgages and additional streamgages 

from Wieczorek (2011).

Reference-quality streamgages dataset.—A total 

of 1,630 streamgages are identified in GAGES–IIprelim as having reference-quality data and at least 

20 years of record (fig. 1B). The reference-quality 

streamgages are judged to be largely free of human 

alterations to flow, whereas nonreference-quality 

streamgages may have substantial human alterations to flow (Falcone and others, 2010). Reference 

streamgages were used for statistical analyses (uncertainty of statistics and analysis of flow correlation) 

that require long-term records. In the basin similarity 

analysis, streamgages were included as long as they 

are identified to be of reference quality, regardless of 

the record length.

There are small differences between the 

streamgages identified as being reference quality 

in the final GAGES–II dataset (Falcone, 2011) and 

those identified as reference quality in the preliminary version used in this study. The GAGES–II 

dataset was not finalized until October 2011, after 

the completion of the analysis for this study. As a 

result of review of the final Falcone (2011) dataset by 

the U.S. Geological Survey, 19 streamgages classified as reference quality in the preliminary dataset 

were removed from that designation. In addition, 15 

streamgages were reclassified as being of reference 

quality. The 19 reclassified streamgages that were 

included as reference-quality streamgages in the 

preliminary dataset and used in this analysis met all 

other criteria for assignment into the reference-quality classification. Because of this, and because of the 

small number of streamgages that were reclassified, 

use of the preliminary dataset is not believed to have 

a substantive effect on the results of this analysis. 

Appendix 1 lists the reference-quality streamgages 

with 20 or more years of record that were used in this 

study and notes the streamgages whose classification 

changed in the final GAGES–II dataset.
Streamgage Gap Analysis for Gaged Locations 3

discontinued USGS streamgages with at least 20 years of 

record beginning after 1950. Similar to the original GAGES 

dataset, GAGES–II-prelim includes delineated drainage 

basins for the streamgages as well as values of a variety of 

basin characteristics calculated for the upstream watershed, 

such as mean annual precipitation, mean basin elevation, and 

land use descriptors. For this study, the GAGES–II-prelim 

dataset was supplemented by an additional 606 streamgages 

with 20 or more years of record (where record started before 

1950) for which automated geographic information system 

(GIS) delineations (Wieczorek, 2011) match NWIS-reported 

drainage areas within 20 percent. This complete dataset was 

used for most of the GIS-based analysis to identify temporal 

and geographical gaps in the streamgage network. For most 

of this work, the complete dataset was further restricted to 

streamgages measuring flow for drainage areas less than 

or equal to 20,000 square miles (mi2). The locations of the 

streamgages used in this study are shown in figure 1A.

Each of the streamgages included in the GAGES–II-prelim 

dataset are classified as being of either reference or nonreference 

quality. Reference-quality streamgages are those judged to be 

largely free of human alterations to flow, whereas nonreference 

quality streamgages may have substantial human alterations to 

flow (Falcone and others, 2010). All streamgages were screened 

and categorized as either reference quality or nonreference 

quality by calculating a hydrologic disturbance index (presence 

of dams, change in reservoir storage, number of canals, road 

density, proximity to major pollutant discharge site, estimates 

of water withdrawals, and fragmentation of undeveloped land), 

reviewing historical digital maps and imagery for evidence of 

hydrologic alteration and human activity, and reviewing comments in USGS annual water data reports for information on 

regulation or diversions. The streamgages that were identified in 

the GAGES–II-prelim dataset as of reference quality were the 

focus of many parts of the network analysis because these are the 

streamgages that facilitate estimation of natural flow statistics at 

gaged and ungaged locations. Daily streamflow data for 1,630 

reference-quality streamgages with 20 or more years of record 

were downloaded from NWIS. These 1,630 streamgages are 

shown in figure 1B and listed in appendix 1.

The statistics that were considered in this analysis are 

listed in highlight 2. The flow statistics are divided into four 

categories: statistics describing long-term mean conditions, 

peak flows, low flows, and variability in flow. All the statistics 

chosen are commonly used by ecologists, flood plain managers, and water resource planners.

Many components of this study are conducted by or summarized by hydrologic unit code (HUC) 2-digit water resource 

regions (HUC regions; fig. 2). The Missouri River Basin 

(HUC region 10) is very large and has been separated into 

Upper Missouri (HUC region 10A) and Lower Missouri (HUC 

region 10B). Some parts of the analysis are also summarized 

by level II ecoregions of North America (ecoregions; fig. 3), 

as defined by the Commission for Environmental Cooperation (1997). Hawaii and Puerto Rico are not included in the 

ecoregions classification.

Highlight 2. Statistics Used in

Streamgage Gap Analysis

• Long-term mean.—

• Mean annual flow

• Mean monthly flows (mean daily flow 

throughout the month)

• Maximum monthly flows (maximum daily 

flow during the month)

• Minimum monthly flows (minimum daily 

flow during the month)

• Peak flows.—

• 1 percent chance annual exceedance flood 

(100-year flood)

• 2 percent chance annual exceedance flood 

(50-year flood)

• 4 percent chance annual exceedance flood 

(25-year flood)

• 10 percent chance annual exceedance flood 

(10-year flood)

• Low flows.—

• 7Q2 (7-day average minimum flow experienced on average once in 2 years)

• 7Q10 (7-day average minimum flow experienced on average once in 10 years)

• Variability in flow.—Coefficient of variation of 

flow (interannual variability)

Streamgage Gap Analysis for Gaged 

Locations

A streamgage network should have a wide spatial extent, 

with streamgages covering the variety of watershed conditions experienced in the network area. To accurately estimate 

flow statistics at gaged locations, long periods of record are 

generally preferable. This part of the analysis focuses on the 

following questions:

• Where are large geographical gaps located in the 

streamgage network (Spatial Gap Analysis section)?

• Where are large temporal gaps located in the 

streamgage network (Temporal Gap Analysis section)?

• How accurately can commonly used statistics be estimated at streamgage locations (Accuracy of Estimated 

Statistics section)?
4 A National Streamflow Network Gap Analysis

A

Alaska Hawaii Puerto Rico

GAGES II-prelim gages

Supplemental gages

EXPLANATION

Reference streamgage

Alaska Hawaii Puerto Rico

B

EXPLANATION

Figure 1. Maps showing 

streamgages used in this 

analysis for the datasets 

that contain A, all (complete) 

and B, reference-quality 

streamgages.
Streamgage Gap Analysis for Gaged Locations 

5

Puerto Rico Hawaii Alaska

01

02

03

04

06

05

08

09

07

10A10B

11

12

12

13

14

15

16

17

18

19

20

21

HUC boundary, and number

EXPLANATION

Figure 2. Map showing hydrologic unit code (HUC) regions for the United States. HUC regions shown in this map are indicated by two-digit codes.
6 A National Streamflow Network Gap Analysis Level II Ecoregions 2.2 Alaska Tundra 2.3 Brooks Range Tundra 3.1 Alaska Boreal Interior 3.2 Taiga Cordillera 5.2 Mixed Wood Shield 5.3 Atlantic Highlands 6.1 Boreal Cordillera 6.2 Western Cordillera 7.1 Marine West Coast Forest 8.1 Mixed Wood Plains

8.2 Central USA Plains8.3 Southeastern USA Plains8.4 Ozark and Ouachita Appalachian Forest8.5 Mississippi Alluvial and SE USA Coastal Plains9.2 Temperate Prairies9.3 West Central Seimarid Prairies9.4 South Central Semiarid Prairies9.5 Texas-Louisiana Coastal Plain9.6 Tamaulipas-Texas Semiarid Plain10.1 Cold Deserts10.2 Warm Deserts11.1 Mediterranean California12.1 Western Sierra Madre Piedmont13.1 Upper Gila Mountains15.4 Everglades

2.2

2.3

3.1

3.2

5.2

5.3

6.1

6.2

7.1

8.1

8.2

8.3

8.4

8.5

8.1

6.2

9.2

9.3

9.4

9.5

9.6

10.1

10.2

11.1

13.1

12.1

15.4

8.4

8.3

7.1

10.2

EXPLANATION

Figure 3. Maps showing level II ecoregions of North America present in the United States; from Commission for Environmental Cooperation (1997).
Streamgage Gap Analysis for Gaged Locations 7

Spatial Gap Analysis

The extent of the existing streamgage network was 

assessed using GIS analysis. The drainage area covered by 

streamgages was mapped to highlight locations where there is 

sparse coverage by existing USGS streamgages. Differences 

in the geographical distribution of streamgages by region also 

were explored using GIS.

The size of a drainage basin affects scaling properties of 

hydrologic processes. For example, if upstream basin characteristics are similar, streamflow in a very small basin will tend to 

increase and decrease in response to precipitation events faster 

than in a large basin. Further, a large basin generally averages 

a hydrologic response over a large heterogeneous area; subbasins within the larger area may experience different amounts of 

precipitation, and different responses may occur. Consequently, 

a very large basin may not provide a great deal of information about local watershed response—even for a small basin 

contained within the large basin. Similarly sized watersheds are 

generally preferred when transferring information from a gaged 

location to an ungaged location. The reference-quality gages 

used in this analysis have upstream drainage areas ranging from 

less than 1 mi2

 to nearly 20,000 mi2. To stay roughly within 

this range of drainage area, the spatial analysis of the USGS 

streamgage network focused on streamgages that measure 

drainage areas of less than 20,000 mi2

.

Figure 4 shows the spatial coverage of USGS streamgages 

in the complete dataset. When basins of drainage areas less than 

20,000 mi2 are considered, approximately 72 percent of the 

conterminous United States is gaged. The percentage of the land 

area that is gaged decreases to 45 percent for basins less than 

or equal to 2,000 mi2, 33 percent for basins less than or equal 

to 1,000 mi2, and 20 percent for basins less than or equal to 500 

mi2 in size. No attempt was made to assess the contribution of 

streamgages maintained by other agencies or organizations.

For the small basin sizes (fig. 4A, B), the streamgages in 

the complete dataset cover a larger percentage of the total area 

in the Eastern United States than in the Central and Western 

United States. In part, this is because the stream density is 

higher in the more humid Eastern United States than in many 

parts of the Western and Central United States, which are 

arid or semiarid. Areas with greater streamgage density also 

generally correspond to areas with high population. For large 

basin sizes (fig. 4C, D), the differences in spatial coverage of 

streamgages across the country are somewhat less apparent. 

The information on spatial coverage is summarized in table 1, 

which lists the percentage of each HUC region that is gaged 

by streamgages in the complete dataset by basin size. Some 

Table 1. Cumulative percentage of hydrologic unit code regions that are gaged.

[HUC, hydrologic unit code; DA, drainage area; ≤ , less than or equal to; mi2, square mile]

HUC region

Cumulative percentage gaged by all streamgages Cumulative percentage gaged by reference gages

DA

≤500 mi2

DA

≤1,000 mi2

DA

≤1,500 mi2

DA

≤2,000 mi2

DA

≤20,000 mi2

DA

≤500 mi2

DA

≤1,000 mi2

DA

≤1,500 mi2

DA

≤2,000 mi2

DA

≤20,000 mi2

1 New England 36 44 56 60 74 6 9 13 13 13

2 Mid-Atlantic 45 55 59 61 78 10 12 12 12 12

3 South Atlantic-Gulf 26 39 47 50 79 7 9 10 11 11

4 Great Lakes 33 50 57 60 73 8 11 13 13 13

5 Ohio 38 52 58 63 86 9 10 11 11 11

6 Tennessee 34 46 51 56 69 10 13 13 13 13

7 Upper Mississippi 22 41 53 59 88 6 8 10 10 11

8 Lower Mississippi 15 30 38 43 63 3 6 6 6 6

9 Souris-Red-Rainy 14 32 42 55 65 5 11 15 23 25

10A Upper Missouri 11 22 30 37 70 4 6 8 9 11

10B Lower Missouri 17 31 43 49 84 3 5 7 9 16

11 Arkansas-White-Red 14 28 37 43 79 3 6 7 8 10

12 Texas-Gulf 18 29 35 40 79 5 8 9 9 10

13 Rio Grande 7 12 16 17 40 1 1 3 3 3

14 Upper Colorado 20 28 35 39 77 4 4 4 4 4

15 Lower Colorado 9 17 23 32 66 3 3 3 5 5

16 Great Basin 8 13 16 17 31 1 1 1 1 1

17 Pacific Northwest 23 37 44 48 76 8 10 11 11 13

18 California 24 35 40 41 62 5 8 8 8 8

19 Alaska 1 2 2 4 10 0 1 1 2 9

20 Hawaii 10 10 10 10 10 1 1 1 1 1

21 Caribbean 51 51 51 51 51 4 4 4 4 4
8 A National Streamflow Network Gap Analysis

Alaska Hawaii Puerto Rico

Alaska

AlaskaAlaska

Hawaii Puerto Rico

Hawaii Puerto Rico Hawaii Puerto Rico

B A

C D

EXPLANATION

Gaged drainage area

HUC region boundary

Figure 4. Maps showing the spatial coverage of streamgages in the complete dataset (GAGES–II-prelim streamgages plus 606 streamgages with at least 20 years of record) that have upstream watersheds with drainage area A, less than 20,000 square miles (mi2); B, less than 2,000 mi2; C, less than 1,000 mi2; and D, less than 500 mi2.
Streamgage Gap Analysis for Gaged Locations 9

HUC regions have low streamgage coverage across all basin 

sizes. In particular, the arid Rio Grande (HUC region 13) and 

Great Basin (HUC region 16) have only 30 to 40 percent areal 

coverage. Alaska (HUC region 19) and Hawaii (HUC region 

20) have even poorer areal coverage, about 10 percent.

Figure 5 shows the spatial coverage of the gaged drainages 

in the reference-quality streamgage dataset. In the conterminous 

United States, 8.6 percent of the total land area is gaged by a 

streamgage in the reference-quality streamgage dataset. Figure 6 

compares the spatial coverages of the complete dataset and the 

reference-quality streamgage dataset by HUC region. The bars 

in the figure are labeled with the number of streamgages in the 

HUC region. The regions with the greatest coverage in the complete dataset are not necessarily the same as the regions with the 

greatest coverage in the reference-quality streamgage dataset. 

For example, whereas the spatial coverage of streamgages in 

Souris-Red-Rainy (HUC region 9) was average for the complete dataset, the region has the highest spatial coverage for 

reference-quality streamgages (25 percent). In addition, whereas 

Alaska (HUC region 19) has one of the lowest percentages of 

areal coverage in the complete dataset, most of the streamgages 

are of reference quality, so the percentage of area covered by 

reference-quality streamgages is more in line with the rest of 

the country (fig. 6). The arid southwest is seen to have low 

spatial coverage of streamgages, with Rio Grande (HUC region 

13), Upper Colorado (HUC region 14), Lower Colorado (HUC 

region 15), and Great Basin (HUC region 16) all having spatial 

coverage of reference-quality streamgages less than 5 percent. 

Hawaii (HUC region 20) also shows very poor spatial coverage 

by streamgages in the reference-quality streamgage dataset at 

only 1 percent areal coverage. Table 1 lists, by basin size, the 

percentage of each HUC region that is covered by streamgages 

in the reference-quality streamgage dataset.

Differences in streamgage coverage by ecoregion are summarized in figure 7. Ecoregion 3.2 (Taiga Cordillera) does not 

include any streamgages from the complete dataset. There are 

no streamgages from the reference-quality streamgage dataset in 

the Brooks Range Tundra ecoregion (2.3), the Taiga Cordillera 

ecoregion (3.2), and the Everglades ecoregion (15.4). Because 

the ecoregions do not follow hydrologic divides, a streamgage 

Table 2. Cumulative percentage of level II ecoregions in the United States that are gaged.

[Level II ecoregions are from Commission for Environmental Cooperation (1997). DA, drainage area; ≤ , less than or equal to; mi2, square mile]

Level II ecoregion

Cumulative percentage gaged by all 

streamgages

Cumulative percentage gaged by reference 

gages

DA

≤500 mi2

DA

≤1,000 

mi2

DA

≤1,500 

mi2

DA

≤2,000 

mi2

DA

≤20,000 

mi2

DA

≤500 

mi2

DA

≤1,000 

mi2

DA

≤1,500 

mi2

DA

≤2,000 

mi2

DA

≤20,000 

mi2

2.2 Alaska Tundra 0 1 1 4 6 0 0 0 0 2

2.3 Brooks Range Tundra 0 1 1 4 21 0 0 0 3 21

3.1 Alaska Boreal Interior 0 0 0 0 5 0 0 0 0 5

3.2 Taiga Cordillera 0 0 0 0 0 0 0 0 0 0

5.2 Mixed Wood Shield 21 41 52 62 77 7 13 15 19 19

5.3 Atlantic Highlands 49 64 75 81 97 11 14 17 17 17

6.1 Boreal Cordillera 1 5 5 7 22 1 4 4 7 21

6.2 Western Cordillera 36 55 63 68 93 9 12 13 13 15

7.1 Marine West Coast Forest 9 12 13 14 18 5 6 6 7 10

8.1 Mixed Wood Plains 32 46 54 58 80 5 6 8 8 8

8.2 Central USA Plains 39 57 64 68 91 6 6 8 8 8

8.3 Southeastern USA Plains 26 39 47 51 82 6 9 10 10 10

8.4 Ozark and Ouachita-Appalachian Forests 39 55 63 67 87 11 15 18 18 19

8.5 Mississippi Alluvial and SE USA Coastal Plains 13 23 28 32 45 4 4 6 6 7

9.2 Temperate Prairies 21 38 47 55 82 6 9 12 13 14

9.3 West Central Semiarid Prairies 7 17 26 33 64 1 4 5 8 16

9.4 South Central Semiarid Prairies 12 23 33 39 82 3 5 6 7 10

9.5 Texas-Louisiana Coastal Plain 11 15 19 19 21 1 2 2 2 2

9.6 Tamaulipas-Texas Semiarid Plain 7 13 15 16 65 5 6 6 6 6

10.1 Cold Deserts 7 13 18 21 57 1 1 2 2 2

10.2 Warm Deserts 2 5 7 10 20 0 0 0 0 0

11.1 Mediterranean California 32 41 46 48 70 6 6 6 6 6

12.1 Western Sierra Madre Piedmont 13 18 31 38 87 5 5 5 5 5

13.1 Upper Gila Mountains 21 35 42 49 81 6 9 10 15 15

15.4 Everglades 1 2 2 2 11 0 0 0 0 0
10 A National Streamflow Network Gap Analysis

EXPLANATION

Gaged drainage less than  20,000 square miles

HUC boundary

Alaska Hawaii Puerto Rico

Figure 5. Map showing spatial coverage of reference-quality streamgage drainages. All streamgages have an upstream drainage area of less than 20,000 square miles.
Streamgage Gap Analysis for Gaged Locations 11

Percent

100

90

80

70

60

50

40

30

20

10

0

1 2 3 4 5 6 7 8 9 10A 10B 11 12 13 14 15 16 17 18 19 20 21

HUC region

Complete dataset 

Reference-quality streamgage dataset 

EXPLANATION

406

926

1,166

466

810

206

578

178

89

430

549

533

434

163

405

214

266

966

889

97

91

77

62

131

176

72

124

43

71

27

23

83

72

70

65

21

68

36

48

225

126

47

26

14

Figure 6. Graphs showing percentage of hydrologic unit code (HUC) regions gaged, complete dataset and reference-quality 

streamgage dataset. Each bar is labeled with the number of streamgages located in the HUC region. Figure 1 shows the 

location of each HUC region and table 1 lists the HUC regions.

may be located in one ecoregion, whereas the upstream drainage 

area can include area in another ecoregion. For example, whereas 

there are no reference-quality streamgages located within the 

Brooks Range Tundra, downstream streamgages outside of the 

ecoregion do measure flow from drainage areas that are partially 

contained in the ecoregion. The Everglades ecoregion includes 

a highly managed water system and has no reference-quality 

streamgages at all. Table 2 details the percentage of each ecoregion that is measured by streamgages in the reference-quality 

streamgage dataset, by varying drainage basin size.

Temporal Gap Analysis

Long-term streamflow records are essential to accurately 

calculate streamflow statistics. Long-term records are critical to tracking over time changes in flow due to land use 

changes, water management changes, or climate variability. 

Figure 8 shows the spatial coverage of streamgage drainages 

with more than 50 years of record. The spatial coverage of 

these long-term record streamgages is generally higher in 

the Eastern United States than in the Western United States. 

Alaska, Hawaii, and Puerto Rico are poorly covered by these 

long-term record streamgages. Overall, 47.9 percent of the 

conterminous United States is covered by streamgages with 

50 or more years of record. The percentage coverage declines 

sharply when only streamgages measuring flow in smaller 

drainages are considered (fig. 8B).

Tables 3 and 4 list the percentage of area in each HUC 

region or in each ecoregion, respectively, where at least 10 

years of continuous record are available in the two-decade 

period listed. The streamgage network grew rapidly in the 

early 1900s, and stabilized in the 1950s to 1960s. Since then, 

the number of streamgages and the area covered have been 

relatively stable, although many individual streamgages have 

been either discontinued or started since then.

Figure 9 shows the median number of years of record 

available at reference-quality streamgages in each of the HUC 

regions. This information should be considered in conjunction 

with the number of reference-quality streamgages and their 

spatial coverage (fig. 6). For example, although the median 

record length in Hawaii (HUC region 20) is quite long at 55 

years, the areal coverage of reference-quality streamgages in 

Hawaii is only about 1.3 percent. The arid Southwest has the 

shortest median record length, and was also observed to have 

poor spatial coverage in the spatial gap analysis.

Calculation of Flow Statistics

Most of the flow statistics that describe the long-term 

characteristics of flow (highlight 2 ) were calculated for the 

set of streamgages in the reference-quality streamgage dataset 

using code written in the Matlab programming environment. 

For the annual statistics, the water year is used as the basis of 

calculation. A water year is a 12-month period from October 1 
12 A National Streamflow Network Gap Analysis

Complete dataset 

Reference-quality streamgage dataset 

EXPLANATION

Percent

Level II ecoregion

100

90

80

70

60

50

40

30

20

10

0

2.2 2.3 3.1 3.2 5.2 5.3 6.1 6.2 7.1 8.1 8.3 8.4 8.5 9.2 9.3 9.4 9.5 9.6 10.1 10.2 11.1 12.1 13.1 15.4 8.2

9

2

6

0

180

300

15

1,449

323

807

477

1.740

1,013

443

468

272

703

64

23

709

123

526

26

75

2

2

0 

3

0

44

77

11

300

107

83

35

259

205

65

74

49

76

4

7

76

21

68

4

20

0

Figure 7. Graphs showing the percentages of ecoregions gaged for the complete dataset and the dataset that contains 

only reference-quality streamgages. Each bar is labeled with the number of streamgages in the ecoregion. A streamgage 

can measure flow in multiple ecoregions if part of its upstream drainage area is in another ecoregion. For example, about 20 

percent of ecoregion 2.3 is measured by streamgages in the reference-quality streamgage dataset, but these streamgages 

are in a downstream ecoregion. Figure 2 shows the extent of each ecoregion region and table 2 lists the ecoregions.

of the previous year through September 30 of the water year 

and is designated by the calendar year in which it ends. For 

example, the year ending September 30, 2011, is the 2011 

water year.

Statistics of peak flow frequency were obtained by querying the USGS National Streamflow Statistics (NSS) database, 

a national repository of streamflow statistics that are published 

in USGS reports. All peak flow statistics are based on the 

period of record that was used in the original report, as referenced in the NSS database. Statistics were not available for all 

the streamgages in the reference-quality streamgage dataset. 

Those streamgages that were not found in the NSS database 

are indicated in appendix 1.

Uncertainty of Estimated Statistics

The uncertainty of a statistic describes the potential 

difference between the estimated value of the statistic and 

the (unknown) true value of the statistic. The magnitude of 

the uncertainty of a flow statistic is affected by the length of 

the record, the variability of the streamflow, and anthropogenic effects within the basin. Generally, the uncertainty of a 

hydrologic statistic is greater when a short-term record is used 

to estimate its value. Conversely, a long-term record typically 

decreases the uncertainty. Uncertainty is also affected by the 

variability of flow. Statistics calculated for a highly variable 

time series will generally be subject to more uncertainty than 

statistics calculated from a stable time series. Knowing the 

uncertainty of statistics calculated from records of varying 

temporal extent can be useful in determining whether longer 

term records would be beneficial in a particular region for 

the purpose of reducing uncertainty in a statistic. Because of 

differences in the variability of streamflow across the Nation, 

records of different lengths are required to decrease the level of 

uncertainty by even amounts in different parts of the country.

All the analyses in this section of the report use only 

the reference-quality streamgages to maintain as consistent a 

record as possible over the period of record. Changes in flow 
Streamgage Gap Analysis for Gaged Locations 13

due to anthropogenic effects can confound estimates of variability in flow statistics. For example, as a result of urbanization, more impervious surfaces are created in a watershed, 

limiting infiltration and increasing surface runoff. Day-to-day 

variability in flow tends to increase. In addition, if flow tends 

to be lower before urbanization and greater after urbanization, 

this results in an increase in the range between the minimum 

and maximum observed flows. Using only the reference-quality streamgages minimizes these types of problems.

Mean Annual Flow

The mean annual flow is the average volume of water 

that flows past a streamgage or any selected point in a river 

reach in a year. The mean annual flow is equivalent to the 

mean daily flow multiplied by the number of days in a year. 

The annual flow past a continuous-record streamgage is 

computed for each year of record, producing an annual time 

series of streamflow. In this study, the mean annual flow is 

calculated as the mean of this annual time series. The mean is 

considered to be a sample mean because it is calculated from 

a sample of observations from the full population. Because of 

limited record lengths and natural variability in flow, there is 

uncertainty in how well this sample mean represents the true 

long-term population mean at a streamgage.

The standard error of the mean is a measure of the uncertainty in the estimate of the mean for the entire population 

when the mean of the population is calculated from a finite 

sample. The standard error of the mean (SE) can be calculated 

as follows:

SE s

n = , (1)

where

s is the standard deviation of the annual mean 

flow time series and

n is the number of years of record.

In equation 1, the standard error is calculated in the same 

units as the time series (for example, cubic feet per second). 

The standard error can instead be expressed as a fraction of 

the mean annual flow (SEfrac) by dividing by the mean annual 

flow:

SE SE

x

s

n x

CV

n

frac = = = 1 , (2)

where

x is the mean of the time series and

CV is the coefficient of variation ( s

x

), which 

quantifies the interannual variability 

observed in the time series.

When the actual length of observed record is used in 

equation 1 or equation 2, the standard error of the mean 

reflects the uncertainty in the mean for the observed record 

length. To calculate the standard error of the mean for a specified record length, different values of n can be inserted into 

equation 2. The coefficient of variation (fig. 10) is calculated 

using the full length of record to obtain the best possible estimate of the interannual variability in the time series.

Equation 2 can be rearranged to estimate the number of 

years of record needed to obtain a specified standard error, as 

follows:

n

SE

CV

frac

=

2

2 . (3)

The standard error of the mean is most appropriate as a 

measure of the uncertainty of the mean when the time series 

is a series of independent and identically distributed random 

variables where the year-to-year variability in the time series 

is random and uncorrelated. This is not strictly the case for 

hydrologic time series, which tend to exhibit some persistence, often causing a series of years to be wetter than normal 

and another series of years to be drier than normal. If the 

long-term mean is estimated from only a few years of record, 

the estimate will tend to be high if the years included in the 

sample were wetter than normal. Conversely, the estimate will 

Table 3. Percentage of hydrologic unit code regions with at least 

10 years of gaged record collected at streamgages draining less 

than or equal to 2,000 square miles.

[HUC, hydrologic unit code]

HUC region

Percentage of area gaged

1910–

1930

1931–

1950

1951–

1970

1971–

1990

1991–

2010

1 New England 26.5 52.2 55.3 53.6 48.9

2 Mid-Atlantic 24.0 51.0 56.4 56.3 56.6

3 South Atlantic-Gulf 3.6 31.7 38.1 38.8 42.0

4 Great Lakes 11.9 33.3 52.4 52.8 49.5

5 Ohio 16.1 53.2 58.9 57.9 52.5

6 Tennessee 37.7 52.1 52.9 49.9 39.5

7 Upper Mississippi 14.2 41.2 50.2 51.4 51.4

8 Lower Mississippi 0.0 24.2 34.3 33.1 29.3

9 Souris-Red-Rainy 0.0 29.9 51.5 51.0 45.8

10A Upper Missouri 4.4 21.2 41.8 38.8 29.8

10B Lower Missouri 3.4 8.8 27.3 25.8 22.7

11 Arkansas-White-Red 4.2 20.8 32.5 36.3 36.0

12 Texas-Gulf 0.0 22.6 31.0 35.5 28.5

13 Rio Grande 2.3 7.7 14.3 15.9 11.7

14 Upper Colorado 13.4 21.7 29.4 32.0 30.1

15 Lower Colorado 2.3 10.0 18.0 22.6 25.5

16 Great Basin 8.0 9.4 15.7 14.8 13.7

17 Pacific Northwest 16.1 33.2 40.1 40.5 37.3

18 California 19.0 30.7 38.4 39.1 34.7

19 Alaska 0.0 0.0 1.4 1.4 3.7

20 Hawaii 1.2 5.5 8.9 9.5 10.3

21 Caribbean 0.0 0.0 2.4 14.6 50.8
14 A National Streamflow Network Gap Analysis

Alaska Hawaii Puerto Rico

A

Percentage of conterminous

United States

605040

0

302010

<500 <1,000 <1,500 <2,000 <20,000

Drainage area, in mi2

B

Basins less than or equal to 2,000 mi2

EXPLANATION

HUC boundary

Figure 8. A, Map showing streamgage drainage basins less than or equal to 2,000 square miles (mi2) with at least 50 years of record collected between 1900 and 

2009 and B, graph showing percentages of conterminous United States with at least 50 years of record, by size of gaged drainage area. <, less than.
Streamgage Gap Analysis for Gaged Locations 15

43

48

39

44

49

50

28

55

10

Alaska Hawaii Puerto Rico

Water years

≤3031–3536–4040–4546–50>50

EXPLANATION

45 41

54

34

36

42

39

45

39

46

46 38

39

52

Figure 9. Map showing the median years of record for the reference-quality streamgages found in each hydrologic unit code (HUC) region. There is a limited number of reference-quality streamgages in all HUC regions. <, less than; >, greater than.
16 A National Streamflow Network Gap Analysis Mean annual flow CV 0.00 to 0.25 >0.25 to 0.50 >0.50 to 0.75 >0.75 to 1.00 >1.00 to 1.25 >1.25 to 1.50 >1.50 to 1.75 >1.75 to 2.00 >2.00 EXPLANATION HUC regions

Alaska Hawaii Puerto Rico

Figure 10. Map showing the coefficient of variation of the mean annual flow. CV, coefficient of variation; HUC, hydrologic unit code; >, more than.
Streamgage Gap Analysis for Gaged Locations 17

Table 4. Percentage of level II ecoregions with at least 10 years of gaged record collected at streamgages draining less than or equal 

to 2,000 square miles.

[Level II ecoregionas are from Commission for Environmental Cooperation (1997)]

Level II ecoregion Percentage of area gaged during specified time period

1910–1930 1931–1950 1951–1970 1971–1990 1991–2010

2.2 Alaska Tundra 0.0 0.0 0.0 0.0 3.8

2.3 Brooks Range Tundra 0.0 0.0 0.0 0.0 4.0

3.1 Alaska Boreal Interior 0.0 0.0 0.0 0.1 0.3

3.2 Taiga Cordillera 0.0 0.0 0.0 0.0 0.0

5.2 Mixed Wood Shield 16.5 34.6 50.6 51.9 46.6

5.3 Atlantic Highlands 43.2 71.8 77.8 74.8 71.2

6.1 Boreal Cordillera 0.0 0.0 3.8 4.2 7.4

6.2 Western Cordillera 28.8 49.9 59.1 58.9 55.3

7.1 Marine West Coast Forest 0.7 6.8 11.1 10.8 12.2

8.1 Mixed Wood Plains 15.9 44.7 51.8 51.1 49.7

8.2 Central USA Plains 14.1 47.5 61.6 61.9 62.6

8.3 Southeastern USA Plains 5.6 34.3 42.1 41.7 40.6

8.4 Ozark and Ouachita-Appalachian Forests 18.9 54.6 60.6 57.4 54.7

8.5 Mississippi Alluvial and SE USA Coastal Plains 0.0 13.5 19.8 23.3 24.9

9.2 Temperate Prairies 3.8 26.9 47.4 47.7 45.1

9.3 West-Central Semiarid Prairies 2.4 5.5 24.2 24.5 18.5

9.4 South Central Semiarid Prairies 2.9 16.5 30.0 34.0 27.4

9.5 Texas-Louisiana Coastal Plain 0.0 5.8 10.7 13.0 11.9

9.6 Tamaulipas-Texas Semiarid Plain 0.0 3.9 4.3 8.3 8.3

10.1 Cold Deserts 4.9 7.5 15.9 15.9 14.2

10.2 Warm Deserts 0.2 1.7 4.8 6.5 7.1

11.1 Mediterranean California 15.5 35.6 44.7 44.7 38.0

12.1 Western Sierra Madre Piedmont 6.7 21.8 24.5 28.1 31.3

13.1 Upper Gila Mountains 2.0 22.0 38.5 43.7 39.7

15.4 Everglades 0.0 0.0 0.0 1.1 1.1

tend to be low if the years included in the sample were drier 

than normal. With a longer period of record, the estimate of 

the mean tends to stabilize. In addition, a persistent trend in a 

time series can increase the standard deviation of a time series 

even if the variability around the trend line remains the same. 

This increase is because a persistent trend tends to increase the 

difference between the smallest and largest values in a time 

series. The effect of trends in increasing the standard error of 

the mean is not considered in this study.

To restate, the standard error of the mean characterizes the 

uncertainty of the sample mean, taking into account the length 

of record and the overall variability of the time series, but not 

persistence that results in periods of wetter or drier than average flows, nor trends in flow. Both of these factors will tend to 

increase the uncertainty, because the variability is not randomly 

distributed from year to year. Despite its limitations, the standard error of the mean can be considered a good estimate of the 

minimum level of uncertainty that can be expected when using 

finite record lengths to calculate a mean. The standard error 

of the mean is used in this analysis to facilitate comparison of 

uncertainty in flow statistics across the United States.

The coefficient of variation for the streamgages in the 

reference-quality streamgage dataset is shown in figure 10. 

The coefficient of variation of the mean annual flow is a 

measure of how much the flow varies from year to year and is 

calculated using the entire period of record available at each 

streamgage. Equation 2 is then used to calculate the standard 

error as a fraction of the mean annual flow at each streamgage. 

Results for an assumed record length of 10 years are mapped 

in figure 11. Figure 11A shows the standard error for individual stations, and figure 11B shows the median standard error 

for each HUC region. These are the standard errors that could 

be expected at these locations if only 10 years of record were 

available. Figure 12 is similar, but record lengths of 50 and 

100 years were used; figure 12A shows the standard error that 

could be expected if 50 years of record were available, and 

figure 12B shows the standard error that could be expected if 

100 years of record were available. In all cases, the coefficient 

of variation is calculated using the available length of record at 

each streamgage, to derive the best possible estimate of coefficient of variation at each streamgage.

When only 10 years of record are available, there is considerable variability in the standard error of the mean annual 

flow across the country, with the greatest standard errors in the 

Central and Southwestern United States, where the interannual 

variability in annual flow is highest. There is a considerable 
18 A National Streamflow Network Gap Analysis

decrease in the standard error when 100 years of record are 

available, with most areas showing fractional standard errors 

less than 0.2 (20 percent). Figure 13 shows the number of years 

of record that are needed in each HUC region to obtain a standard error of 0.10 (10 percent, calculated using equation 3).

Figure 13 also suggests that the number of years of record 

needed for a standard error of 10 percent is quite low in some 

HUC regions. The uncertainty calculation based on standard 

error of the mean does not include the effects of persistence 

in hydrologic records. The effect of persistence is to increase 

the uncertainty, so the number of years of record needed to 

achieve 10 percent uncertainty would be higher if the effects 

of persistence were included. Also, the number of years of 

record needed shown in figure 13 apply only to estimates of 

the mean annual flow. Other statistics related to more extreme 

events require considerably longer records. The map is 

intended to show differences across the country.

The number of years of record needed in some HUC 

regions to achieve an uncertainty of 10 percent is very large 

(fig. 13). The number of years of record needed declines 

sharply if a slightly higher level of uncertainty is acceptable 

(see for example Souris-Red-Rainy in fig. 14). For each HUC 

region, table 5 shows the median coefficient of variation of 

annual mean flow at streamgages in the HUC region. These 

median coefficients of variation can be used in equation 3 

to calculate the years of record needed for a desired level of 

uncertainty in estimating mean annual flow.

Table 5. Median coefficient of variation of annual 

mean flow of streamgages.

[HUC, hydrologic unit code; CV, coefficient of variation]

HUC region CV

1 New England 0.27

2 Mid-Atlantic 0.33

3 South Atlantic-Gulf 0.40

4 Great Lakes 0.25

5 Ohio 0.32

6 Tennessee 0.27

7 Upper Mississippi 0.56

8 Lower Mississippi 0.41

9 Souris-Red-Rainy 0.82

10A Upper Missouri 0.46

10B Lower Missouri 0.67

11 Arkansas-White-Red 0.52

12 Texas-Gulf 0.92

13 Rio Grande 0.56

14 Upper Colorado 0.36

15 Lower Colorado 0.97

16 Great Basin 0.56

17 Pacific Northwest 0.25

18 California 0.86

19 Alaska 0.17

20 Hawaii 0.35

21 Caribbean 0.36

The number of years of record needed varies with the 

desired level of uncertainty within each HUC region. For 

example, in New England (HUC region 1), to achieve a fractional standard error of 0.10 (10 percent) for the mean annual 

flow, a record of less than 10 years is needed. As a comparison, in the Upper Mississippi Basin (HUC region 7), a record 

of more than 30 years is needed to obtain the same standard 

error of the mean. In the Lower Colorado Basin (HUC region 

15), a record of 75 years is required to estimate the mean 

annual flow with an uncertainty of 10 percent. If the desired 

uncertainty were relaxed to 20 percent, then the number of 

years of record needed for Lower Colorado decreases to about 

19 years.

Monthly Flow Statistics

The uncertainty of mean monthly flows, maximum 

monthly flows, and minimum monthly flows are discussed in 

this section. Uncertainty is directly related to the coefficient 

of variation of statistics. The data in table 6 show how the 

median coefficient of variation varies seasonally for mean 

monthly flow, minimum monthly flow, and maximum monthly 

flow in each HUC region. The data in table 7 show how the 

median coefficient of variation varies seasonally by level II 

ecoregion. The coefficient of variation cannot be calculated 

when the mean monthly flow statistic is equal to zero, so stations where this occurs are omitted from the calculations. The 

larger the coefficient of variation is, the larger the uncertainty 

of the long-term monthly flow statistics. Note that only a small 

number of streamgages were available in some HUC regions 

and ecoregions for these calculations. Estimated values of the 

coefficient of variation are more likely to be representative of 

the entire HUC region or ecoregion when many streamgages 

were included in the analysis.

In general, the spatial pattern of the coefficient of variation for monthly flows mirrors that seen for mean annual flow. 

The coefficient of variation is lowest in the Eastern United 

States and the Pacific Northwest and highest in the Central and 

Southwestern United States where the greatest year-to-year 

variability in the maximum monthly flow (the maximum daily 

flow that is seen in a particular month) occurs. Consequently, 

more years of record are required to obtain a stable estimate 

of the maximum monthly flow statistic than for the minimum monthly flow or mean monthly flow statistic. Minimum 

monthly flow generally has the lowest coefficient of variation; in other words, it has the smallest amount of variability 

from year to year. However, in some parts of the country and 

for some months, the coefficient of variation for minimum 

monthly flow is of similar magnitude as the coefficient of 

variation for mean monthly flow.

Using equation 2, the standard error of any of the 

monthly flow statistics can be estimated by applying the coefficient of variation for a HUC region or ecoregion and specifying the record length. Equation 3 allows the calculation of the 

number of years of record needed to achieve a desired level of 

uncertainty.
Streamgage Gap Analysis for Gaged Locations 19

 0.0–0.1

>0.1–0.2

>0.2–0.3

>0.3–0.4

>0.4–0.5

>0.5–0.6

>0.6–0.7

>0.7–0.8

>0.8–0.9

>0.9–1.0

>1.0

Mean annual low

standard error

n=10 years

Alaska Hawaii Puerto Rico

HUC boundary

A

EXPLANATION

0.078

0.178

0.258

0.273

0.211

0.112

0.307

0.18

0.290

0.164

0.147

0.177

0.131

0.100

0.127

0.079

0.087

0.104

0.112

Alaska Hawaii Puerto Rico

0.053

0.113

Mean annual flow

standard error n=10

 0.000–0.100

>0.100–0.200

>0.200–0.300

>0.300–0.400

>0.400–0.500

0.085

0.079

B

EXPLANATION

Figure 11. Maps showing A, standard error of mean annual flow for 10 years for each streamgage in the reference-quality 

streamgage dataset and B, median standard error of the mean annual flow for stations in each hydrologic unit code (HUC) 

region. In all HUC regions, a limited number of streamgages was available. >, more than or equal to.
20 A National Streamflow Network Gap Analysis

 0.0–0.1

>0.1–0.2

>0.2–0.3

>0.3–0.4

>0.4–0.5

>0.5–0.6

>0.6–0.7

>0.7–0.8

>0.8–0.9

>0.9–1.0

>1.0

Mean annual flow

standard error 

n=50 years

Alaska Hawaii Puerto Rico

Alaska Hawaii Puerto Rico

 0.0–0.1

>0.1–0.2

>0.2–0.3

>0.3–0.4

>0.4–0.5

>0.5–0.6

>0.6–0.7

>0.7–0.8

>0.8–0.9

>0.9–1.0

>1.0

Mean annual flow

standard error

n=100 years

A

B

EXPLANATION

EXPLANATION

HUC boundary

HUC boundary

Figure 12. Maps showing standard error of mean annual flow for A, 50 and B, 100 years. If 100 years of record were 

available, the standard error would be reduced to less than 0.2 for all but a few streamgages.
Streamgage Gap Analysis for Gaged Locations 21 13 13

13

32

6

45

75

94

84

27

31

22

17

67

31

6

6

8

11

10

7

16

EXPLANATION

Alaska Hawaii Puerto Rico

Water years

3

Greater than 40

31 to 40

21 to 3011 to 206 to 10

Less than or equal to 5

(fractional) Map showing the number of years of record needed in each hydrologic unit code (HUC) region to estimate mean annual flow with a Figure 13.

standard error of 0.1 (10 percent). The number of years of record needed is calculated using the median coefficient of variation for each HUC region. The 

≤, less than or . Only a limited number of streamgages was available in each HUC region. number of years of record needed at an individual location will vary

≥, more than or equal to. equal to; 
22 A National Streamflow Network Gap Analysis Table 6. Median coefficient of variation for hydrologic unit code regions. [HUC, hydrologic unit code; CV, coefficient of variation] HUC region Statistic Median coefficient of variation October November December January February March April May June July August September 1 New England Minimum 0.85 0.75 0.55 0.45 0.48 0.45 0.41 0.44 0.63 0.63 0.70 0.68 Mean 1.06 0.65 0.63 0.63 0.67 0.55 0.40 0.47 0.70 0.84 1.04 1.06 Maximum 1.30 0.80 0.91 0.98 0.94 0.74 0.54 0.66 1.13 1.21 1.40 1.49 2 Mid-Atlantic Minimum 0.94 0.74 0.62 0.54 0.54 0.46 0.43 0.47 0.58 0.64 0.77 0.86 Mean 1.13 0.82 0.67 0.65 0.60 0.48 0.52 0.56 0.94 0.95 1.22 1.45 Maximum 1.53 1.14 1.01 1.04 0.96 0.77 0.80 0.96 1.63 1.40 1.81 2.07 3 South Atlantic-Gulf Minimum 0.79 0.66 0.60 0.51 0.47 0.43 0.49 0.58 0.67 0.76 0.82 0.76 Mean 1.11 1.10 0.81 0.66 0.60 0.60 0.72 0.90 1.01 1.00 0.94 1.14 Maximum 1.56 1.44 1.11 0.98 0.95 0.94 1.10 1.24 1.40 1.29 1.42 1.62 4 Great Lakes Minimum 0.57 0.47 0.38 0.38 0.35 0.42 0.43 0.43 0.51 0.45 0.42 0.51 Mean 0.73 0.53 0.45 0.46 0.49 0.50 0.37 0.54 0.60 0.68 0.73 0.79 Maximum 0.99 0.72 0.73 0.70 0.79 0.68 0.52 0.74 0.89 1.04 1.14 1.24

5 Ohio Minimum 1.11 1.00 0.82 0.64 0.54 0.44 0.44 0.60 0.76 0.86 1.00 1.09

Mean 1.44 1.00 0.78 0.65 0.58 0.53 0.53 0.76 1.03 1.11 1.22 1.55Maximum 1.72 1.24 0.92 0.85 0.80 0.78 0.82 1.00 1.31 1.38 1.48 1.83

6 Tennessee Minimum 0.47 0.47 0.52 0.46 0.39 0.31 0.32 0.33 0.37 0.41 0.40 0.42

Mean 0.74 0.80 0.62 0.53 0.46 0.47 0.44 0.50 0.58 0.63 0.66 0.84Maximum 1.26 1.21 0.94 0.89 0.77 0.83 0.81 1.04 1.16 1.17 1.31 1.54

7 Upper Mississippi Minimum 1.59 1.33 1.16 1.03 0.99 0.76 0.68 0.75 0.91 1.28 1.25 1.54

Mean 1.72 1.51 1.27 1.12 0.93 0.85 0.87 1.00 1.07 1.42 1.56 1.93Maximum 1.88 1.62 1.58 1.47 1.20 1.01 1.13 1.19 1.33 1.58 1.78 2.07

8 Lower Mississippi Minimum 0.34 0.44 0.60 0.53 0.51 0.46 0.51 0.50 0.51 0.50 0.39 0.39

Mean 1.47 1.23 0.93 0.83 0.72 0.67 0.88 1.14 1.05 1.17 1.17 1.66Maximum 2.20 1.69 1.22 1.11 0.99 0.99 1.25 1.45 1.83 2.06 1.79 2.33

9 Souris-Red-Rainy Minimum 1.35 1.40 1.15 1.27 1.17 1.80 1.44 1.10 1.26 1.58 1.86 1.63

Mean 1.49 1.53 1.26 1.15 1.74 1.41 1.01 1.25 1.39 1.49 2.00 1.75Maximum 2.03 1.72 1.36 1.09 2.89 1.57 1.14 1.44 1.59 1.96 2.23 1.96

10A Upper Missouri Minimum 0.56 0.48 0.59 0.68 0.55 0.61 0.63 0.79 0.75 0.66 0.56 0.64

Mean 0.58 0.44 0.45 0.61 0.67 0.67 0.90 0.82 0.96 0.88 0.83 0.80Maximum 0.70 0.61 0.54 0.69 1.18 1.21 1.21 1.27 1.24 1.17 1.02 1.09

10B Lower Missouri Minimum 1.51 1.16 1.06 1.06 1.02 0.86 0.81 0.92 1.08 1.34 1.27 1.46

Mean 1.80 1.43 1.23 1.21 1.06 1.11 0.99 1.10 1.22 1.80 1.70 1.81Maximum 2.21 1.59 1.54 1.62 1.45 1.33 1.29 1.26 1.35 1.72 1.89 1.90
Streamgage Gap Analysis for Gaged Locations 23

Table 6. Median coefficient of variation for hydrologic unit code regions.—Continued[HUC, hydrologic unit code; CV, coefficient of variation]

HUC region Statistic

Median coefficient of variation

October November December January February March April May June July August September

11 Arkansas-White-Red Minimum 1.45 1.23 0.90 0.75 0.66 0.63 0.67 0.80 0.94 1.23 1.43 1.70

Mean 1.85 1.32 1.07 0.92 0.81 0.80 0.86 0.98 1.27 1.39 1.65 1.81Maximum 2.13 1.78 1.52 1.40 1.35 1.23 1.29 1.25 1.61 1.74 2.17 2.23

12 Texas-Gulf Minimum 1.64 1.58 1.15 1.23 1.11 1.07 1.06 1.15 1.61 1.79 2.12 1.91

Mean 2.24 2.04 1.86 1.45 1.76 1.36 1.45 1.43 1.99 2.37 2.37 2.17Maximum 2.62 2.59 3.12 1.91 2.14 1.97 2.06 1.76 2.12 3.03 3.04 2.57

13 Rio Grande Minimum 0.43 0.46 0.40 0.36 0.31 0.35 0.51 0.62 0.76 0.56 0.56 0.48

Mean 0.67 0.57 0.37 0.32 0.35 0.54 0.81 0.92 0.92 0.72 0.80 0.70Maximum 1.08 0.84 0.55 0.47 0.54 0.69 0.88 0.98 0.94 0.84 0.93 1.02

14 Upper Colorado Minimum 0.50 0.42 0.37 0.36 0.34 0.38 0.60 0.66 0.61 0.68 0.53 0.44

Mean 0.50 0.38 0.37 0.36 0.36 0.44 0.54 0.45 0.58 0.71 0.56 0.45Maximum 0.59 0.42 0.40 0.39 0.49 0.67 0.70 0.48 0.59 0.77 0.65 0.70

15 Lower Colorado Minimum 0.70 0.98 0.93 1.05 1.30 1.13 1.29 1.23 1.36 0.89 0.88 0.67

Mean 2.61 1.83 1.87 2.05 1.56 1.15 1.38 1.34 1.63 1.64 1.40 1.75Maximum 3.08 2.41 2.36 2.26 1.91 1.73 1.49 1.57 1.51 2.02 1.79 2.54

16 Great Basin Minimum 0.47 0.41 0.42 0.45 0.46 0.43 0.54 0.71 0.85 0.77 0.59 0.51

Mean 0.43 0.37 0.46 0.50 0.43 0.47 0.57 0.72 0.83 0.77 0.66 0.54Maximum 0.53 0.54 0.69 0.66 0.76 0.72 0.66 0.80 0.91 0.93 0.75 0.66

17 Pacific Northwest Minimum 0.40 0.51 0.45 0.44 0.42 0.36 0.35 0.36 0.42 0.36 0.29 0.31

Mean 0.60 0.57 0.53 0.49 0.49 0.44 0.35 0.36 0.48 0.45 0.37 0.46Maximum 0.87 0.80 0.75 0.70 0.76 0.64 0.58 0.46 0.62 0.59 0.57 0.75

18 California Minimum 0.91 0.95 1.11 1.11 1.08 1.03 0.97 0.91 1.07 1.13 1.01 0.97

Mean 1.47 1.56 1.45 1.26 1.19 1.07 1.14 1.00 1.02 1.10 1.12 1.18Maximum 2.36 2.09 2.01 1.57 1.50 1.26 1.52 1.36 1.11 1.15 1.35 2.23

19 Alaska Minimum 0.39 0.41 0.37 0.42 0.40 0.41 0.39 0.65 0.38 0.34 0.34 0.40

Mean 0.41 0.45 0.53 0.44 0.51 0.43 0.39 0.41 0.31 0.30 0.36 0.42Maximum 0.56 0.56 0.60 0.64 0.64 0.58 0.68 0.45 0.38 0.42 0.55 0.57

20 Hawaii Minimum 0.63 0.62 0.58 0.56 0.61 0.61 0.56 0.56 0.64 0.53 0.64 0.67

Mean 0.67 0.73 0.70 0.82 0.87 0.89 0.75 0.73 0.68 0.62 0.70 0.72Maximum 0.94 0.95 0.99 1.08 1.07 0.99 0.97 1.01 0.94 0.89 0.99 1.00

21 Caribbean Minimum 0.48 0.46 0.41 0.39 0.33 0.34 0.40 0.44 0.48 0.50 0.62 0.58

Mean 0.70 0.77 0.65 0.58 0.52 0.51 0.69 0.80 0.65 0.61 0.66 0.85Maximum 1.10 1.23 1.30 1.54 1.22 0.99 1.14 0.94 0.90 1.02 0.95 1.45
24 A National Streamflow Network Gap Analysis Table 7. Median coefficient of variation for level II ecoregions in the United States. [Level II ecoregions are from Commission for Environmental Cooperation (1997). CV, coefficient of variation; HUC, hydrologic unit code; n/a, not available] HUC region Statistic Median coefficient of variation October November December January February March April May June July August September 2.2 Alaska Tundra Minimum 0.79 1.05 1.94 2.37 2.52 2.54 2.54 2.42 0.60 0.41 0.65 0.59 Mean 0.74 0.90 1.24 2.21 2.47 2.53 2.46 1.10 0.41 0.47 0.60 0.60 Maximum 0.99 0.81 1.10 1.99 2.41 2.52 2.55 1.04 0.50 0.74 1.02 0.80 2.3 Brooks Range Tundra Minimum n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Mean n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Maximum n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a 3.1 Alaska Boreal Interior Minimum 0.54 0.46 0.45 0.39 0.41 0.42 0.44 0.72 0.50 0.43 0.38 0.46 Mean 0.52 0.50 0.49 0.39 0.41 0.42 0.69 0.45 0.52 0.44 0.65 0.54 Maximum 0.78 0.55 0.49 0.44 0.41 0.42 1.07 0.55 0.61 0.71 1.53 0.73 3.2 Taiga Cordillera Minimum n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Mean n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Maximum n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a 5.2 Mixed Wood Shield Minimum 0.49 0.44 0.34 0.32 0.30 0.38 0.52 0.42 0.49 0.47 0.37 0.51 Mean 0.72 0.53 0.44 0.33 0.36 0.62 0.34 0.54 0.57 0.63 0.67 0.76

Maximum 0.99 0.66 0.63 0.47 0.57 0.81 0.47 0.67 0.76 0.91 1.04 1.03

5.3 Atlantic Highlands Minimum 0.85 0.71 0.51 0.48 0.50 0.47 0.41 0.45 0.59 0.59 0.72 0.70

Mean 1.05 0.63 0.60 0.64 0.65 0.50 0.41 0.49 0.76 0.90 1.10 1.17Maximum 1.34 0.86 0.96 1.01 0.96 0.73 0.55 0.75 1.22 1.29 1.52 1.59

6.1 Boreal Cordillera Minimum 0.39 0.34 0.34 0.31 0.28 0.28 0.30 0.75 0.37 0.23 0.27 0.40

Mean 0.37 0.37 0.34 0.33 0.29 0.29 0.37 0.43 0.33 0.22 0.25 0.41Maximum 0.52 0.43 0.38 0.35 0.34 0.31 0.60 0.47 0.39 0.27 0.43 0.58

6.2 Western Cordillera Minimum 0.37 0.44 0.43 0.41 0.38 0.37 0.42 0.49 0.53 0.47 0.36 0.34

Mean 0.50 0.53 0.50 0.47 0.48 0.44 0.40 0.40 0.53 0.54 0.43 0.42Maximum 0.79 0.75 0.75 0.68 0.74 0.65 0.58 0.45 0.59 0.66 0.57 0.68

7.1 Marine West Coast Forest Minimum 0.50 0.59 0.48 0.46 0.46 0.37 0.35 0.38 0.36 0.35 0.32 0.41

Mean 0.71 0.58 0.52 0.49 0.49 0.45 0.40 0.41 0.44 0.41 0.42 0.54Maximum 0.89 0.75 0.67 0.64 0.69 0.67 0.71 0.62 0.76 0.60 0.78 0.84

8.1 Mixed Wood Plains Minimum 0.85 0.73 0.53 0.51 0.48 0.48 0.40 0.51 0.60 0.59 0.67 0.74

Mean 1.02 0.66 0.58 0.59 0.60 0.44 0.47 0.53 0.86 0.89 1.05 1.20Maximum 1.36 0.86 0.86 0.92 0.87 0.68 0.63 0.84 1.35 1.32 1.43 1.65

8.2 Central USA Plains Minimum 1.33 1.21 0.84 0.80 0.66 0.60 0.49 0.56 0.76 0.96 0.97 1.30

Mean 1.69 1.31 0.94 1.03 0.79 0.67 0.64 0.88 1.06 1.30 1.57 1.97Maximum 1.98 1.37 1.21 1.18 1.09 0.91 0.87 1.18 1.42 1.51 2.03 2.11

8.3 Southeastern USA Plains Minimum 0.91 0.75 0.67 0.54 0.49 0.43 0.49 0.58 0.67 0.79 0.87 0.86

Mean 1.38 1.09 0.83 0.68 0.63 0.60 0.70 0.93 1.03 1.14 1.28 1.41Maximum 1.83 1.48 1.11 1.03 0.96 0.94 1.04 1.19 1.43 1.48 1.72 1.99

8.4 Ozark and Ouacguta-Appalachian 

Forests

Minimum 0.86 0.79 0.69 0.57 0.52 0.42 0.44 0.51 0.58 0.61 0.68 0.77Mean 1.21 0.97 0.76 0.65 0.57 0.53 0.54 0.65 0.94 0.94 1.05 1.42Maximum 1.66 1.36 1.02 0.98 0.90 0.83 0.89 1.02 1.41 1.37 1.56 2.02
Streamgage Gap Analysis for Gaged Locations 25

Table 7. Median coefficient of variation for level II ecoregions in the United States.—Continued[Level II ecoregions are from Commission for Environmental Cooperation (1997). CV, coefficient of variation; HUC, hydrologic unit code]

HUC region Statistic Median coefficient of variation October November December January February March April May June July August September

8.5 Mississippi Alluvial and SE USA 

Coastal Plains

Minimum 1.10 0.96 1.02 0.88 0.71 0.71 0.93 0.98 1.36 1.23 1.15 1.13Mean 1.31 1.29 1.26 0.91 0.89 0.90 1.07 1.28 1.34 1.13 1.14 1.30Maximum 1.46 1.53 1.49 1.03 1.14 1.01 1.23 1.47 1.51 1.26 1.31 1.47

9.2 Temperate Prairies Minimum 1.79 1.45 1.28 1.27 1.26 1.29 0.99 1.03 1.24 1.71 1.90 1.95

Mean 1.98 1.82 1.49 1.45 1.34 1.22 1.22 1.20 1.36 1.96 1.99 1.98Maximum 2.23 1.98 1.81 1.80 1.84 1.33 1.33 1.38 1.47 1.99 2.12 2.07

9.3 West Central Semiarid Prairies Minimum 0.76 0.64 0.71 0.82 1.03 0.87 0.81 0.93 0.86 0.90 0.96 0.83

Mean 1.24 0.66 0.62 0.93 1.27 1.01 0.99 1.25 1.12 1.27 1.21 1.19Maximum 1.49 0.87 0.72 1.20 1.80 1.33 1.39 1.50 1.34 1.58 1.54 1.86

9.4 South Central Semiarid Prairies Minimum 1.68 1.37 1.12 1.23 1.11 1.06 1.03 1.13 1.42 1.45 1.92 1.99

Mean 2.18 1.68 1.53 1.36 1.42 1.36 1.32 1.40 1.62 2.04 1.93 1.86Maximum 2.63 2.45 2.58 1.91 1.95 1.99 2.02 1.81 1.95 2.48 2.31 2.30

9.5 Texas-Louisiana Coastal Plain Minimum 1.33 1.16 1.30 1.15 1.29 0.97 1.03 1.31 1.51 1.95 1.40 1.31

Mean 2.10 2.42 2.10 1.54 2.03 2.12 2.20 1.59 2.01 2.62 2.34 2.57Maximum 2.53 2.69 2.69 1.53 2.03 2.00 2.15 1.62 1.95 2.97 3.09 2.58

9.6 Tamaulipas-Texas Semiarid Plain Minimum 3.36 2.36 3.03 3.32 3.88 3.37 3.35 2.68 4.93 3.50 4.67 3.83

Mean 3.04 3.50 4.22 4.00 3.92 3.22 2.87 2.41 2.74 3.15 3.81 2.91Maximum 3.44 4.01 4.98 4.69 4.88 3.23 3.76 3.34 3.16 3.65 3.96 3.50

10.1 Cold Deserts Minimum 0.43 0.41 0.49 0.51 0.47 0.56 0.60 0.72 0.77 0.70 0.59 0.50

Mean 0.50 0.47 0.56 0.62 0.55 0.60 0.65 0.74 0.80 0.76 0.66 0.55Maximum 0.63 0.64 0.91 0.89 0.88 0.75 0.85 0.86 0.89 0.80 0.77 0.71

10.2 Warm Deserts Minimum 2.51 2.09 1.97 1.69 1.71 1.86 1.85 2.47 2.68 2.72 2.70 1.95

Mean 2.95 3.12 2.38 2.59 2.55 1.91 1.67 2.11 2.77 2.39 2.33 2.66Maximum 2.97 3.67 2.77 2.88 2.54 2.64 2.65 2.07 3.02 2.68 2.69 3.00

11.1 Mediterranean California Minimum 1.34 0.99 1.24 1.30 1.38 1.24 1.25 1.15 1.35 1.49 1.56 1.55

Mean 1.86 2.20 1.76 1.44 1.48 1.37 1.44 1.17 1.18 1.39 1.54 1.49Maximum 2.63 2.64 2.20 1.80 1.73 1.76 1.90 1.55 1.22 1.45 1.74 2.87

12.1 Western Sierra Madre Piedmont Minimum 1.24 1.50 1.10 1.25 1.21 1.23 1.28 1.46 1.67 1.81 1.42 1.23

Mean 3.03 1.43 1.40 3.01 1.71 1.36 1.24 1.29 1.52 1.89 1.47 1.64Maximum 4.25 2.75 3.05 3.96 3.09 1.96 1.56 1.20 2.16 2.12 1.69 2.02

13.1 Upper Gila Mountains Minimum 0.65 0.97 0.82 0.99 1.17 1.01 1.20 1.19 0.98 0.57 0.76 0.54

Mean 2.39 1.65 1.78 1.80 1.44 1.06 1.31 1.19 1.23 0.83 1.08 1.48Maximum 3.01 2.31 2.28 2.13 1.80 1.56 1.13 1.36 1.22 1.82 1.70 2.54

15.4 Everglades Minimum 1.06 1.39 1.25 1.42 1.33 2.02 1.15 0.81 1.36 1.42 0.92 0.93

Mean 0.92 1.24 1.36 1.25 1.58 1.70 2.22 1.35 1.52 0.97 0.70 0.82Maximum 0.97 1.15 1.41 1.30 1.61 1.51 2.80 2.45 1.57 0.87 0.74 0.98
26 A National Streamflow Network Gap Analysis Needed years of record

Standard error (as fraction of flow)

90

80

70

60

50

40

30

20

10

0

0 0.2 0.4 0.6 0.8 1

Figure 14. Graph showing the number of years of streamflow record needed in hydrologic unit code region 9 

(Souris-Red-Rainy) to estimate mean annual flow with a specified standard error.

Peak Flow Statistics

In the United States, the frequency of peak flows is 

calculated according to guidelines specified in Guidelines for 

Determining Flood Flow Frequency (Bulletin 17B; U.S. Interagency Advisory Committee on Water Data, 1982). According 

to Bulletin 17B, annual time series of peak flows are fit to 

a log-Pearson type III (LPIII) distribution with adjustments 

for historical information and low outliers. Most peak flow 

frequency studies conducted by the USGS have been done 

on a State-by-State basis, in cooperation with local agencies. 

Results of these studies are entered into the USGS National 

Streamflow Statistics (NSS) database (Ries, 2007).

The LPIII statistics for 1,200 stations were obtained 

by querying the NSS database and retrieving LPIII statistics 

(mean, standard deviation, and skew) for all the stations in 

the reference-quality streamgage dataset where this information was available. Information was not available for all 

streamgages in the reference-quality streamgage dataset, and 

the streamgages that were not included in this analysis are 

noted in appendix 1.

The standard error of various flood quantiles were obtained 

by entering the LPIII statistics into the Weighted Independent 

Estimates (WIE) software that calculates the standard error 

of flood frequency quantiles (Cohn and others, 2012). WIE 

estimates the standard error assuming that the LPIII statistics 

pulled from NSS are valid for a systematic record with the 

specified record length. These estimates should be considered 

minimum uncertainties for these statistics, as they account for 

only one source of uncertainty.

Figure 15A shows the standard error of the 10 percent 

annual exceedance flood (10-year flood) for an assumed record 

length of 10 years where data were available from referencequality streamgage locations, and figure 15B shows the same 

for an assumed record length of 100 years. With the longer 

record length, uncertainty is considerably diminished, and 

nearly all the United States shows an uncertainty of less than 

20 percent. In general, the same spatial patterns of uncertainty 

that were observed for mean annual flows were also observed 

for peak flows. Areas with high interannual variability in 

flows, such as the Central and Southwestern United States, 

generally have the highest uncertainties. For peak flows, there 

is also a high uncertainty area in the Mid-Atlantic. Information 

on uncertainty of peak flows was not available for some States 

in the Mid-Atlantic.

Figure 16 shows the standard error of various exceedance 

level floods in all the HUC regions, all assuming that 10 years 

of record are available. The more extreme the flood event 

(lower exceedance probability), the greater the uncertainty in 

all regions of the country, although this is most pronounced in 

areas with large interannual variability in flood events.
Streamgage Gap Analysis for Gaged Locations 27

A

B

Alaska Hawaii Puerto Rico

 0.00–0.25

>0.25–0.50

>0.50–0.75

>0.75–1.00

>1.00–1.25

>1.25–1.50

>1.50–1.75

>1.75–2.00

>2.00–2.25

>2.25–2.50

>2.50

Standard error

peak flow

n = 10

Standard error

peak flow

n = 100

HUC region 

EXPLANATION

HUC region 

EXPLANATION

Alaska Hawaii Puerto Rico

 0.00–0.25

>0.25–0.50

>0.50–0.75

>0.75–1.00

>1.00–1.25

>1.25–1.50

>1.50–1.75

>1.75–2.00

>2.00–2.25

>2.25–2.50

>2.50

Figure 15. Maps showing standard error of 10 percent annual exceedance probability flood (10-year flood) for A, 

a record length of 10 years and B, for a record length of 100 years. >, more than.
28 A National Streamflow Network Gap Analysis A B

C D

0.21

0.44

0.45

0.52

0.41

0.24

0.55

0.38

0.51

0.36

0.39

0.27

0.30

0.22

0.25

0.31

0.19

0.25

0.33

0.27

Hawaii Alaska Puerto Rico

0.18

0.24

HUC regionMean SE

 0.0–0.2>0.2–0.4>0.4–0.6>0.6–0.8>0.8–1.0

0.26

0.57

0.55

0.67

0.53

0.30

0.71

0.47

0.63

0.44

0.49

0.33

0.37

0.28

0.32

0.39

0.23

0.32

0.44

0.34

Hawaii Alaska Puerto Rico

0.24

0.30

HUC regionMean SE

 0.0–0.2>0.2–0.4>0.4–0.6>0.6–0.8>0.8–1.0

0.30

0.71

0.64

0.81

0.65

0.35

0.87

0.56

0.74

0.52

0.59

0.38

0.43

0.33

0.37

0.47

0.27

0.39

0.54

0.40

Hawaii Alaska Puerto Rico

0.28

0.35

HUC regionMean SE

 0.0–0.2>0.2–0.4>0.4–0.6>0.6–0.8>0.8–1.0

0.36

0.77

0.78

1.04

0.81

0.37

1.08

0.79

0.91

0.62

0.67

0.43

0.48

0.38

0.43

0.54

0.31

0.44

0.69

0.47

Hawaii Alaska Puerto Rico

0.31

0.48

HUC regionMean SE

 0.0–0.2>0.2–0.4>0.4–0.6>0.6–0.8>0.8–1.0

D

Maps showing standard error of selected peak flow quantiles by hydrologic unit code (HUC) region, all assuming a record length of 10 years and the same log-

, 0.01 (100-year 

Figure 16.Pearson type III statistical distribution statistics. Annual exceedance probabilities equal A, 0.10 (10-year flood); B, 0.04 (25-year flood); C, 0.02 (50-year flood); and flood). These estimates are based on the limited number of streamgages available in each HUC region. >, more than.
Streamgage Gap Analysis for Ungaged Locations 29

Low-Flow Statistics

Similar to peak flow studies, studies designed to calculate 

low-flow frequency statistics have been conducted by the USGS 

primarily on a State-by-State basis, in cooperation with local 

agencies. The most commonly calculated low-flow frequency 

statistics are the annual minimum 7-day average flow expected 

to occur every 10 and 2 years (7Q10 and the 7Q2, respectively). 

Both are calculated by fitting a time series of annual minimum 

7-day average flows to a probability distribution. USGS studies 

most commonly use the LPIII distribution, as implemented in 

the Surface Water Statistics (SWSTAT) software.

Whereas it was possible to calculate the 7-day annual time 

series and estimate the 7Q10 and 7Q2 using estimated moments 

of the time series, a standard method for estimating the variance 

of the resulting estimate does not exist when a conditional probability adjustment is applied to account for zero flows. Nearly 

one-third of the reference-quality streamgages (530 of 1,630) 

experienced zero flow for at least one consecutive 7-day period 

during their period of record. Consequently, variance estimates 

were unavailable for nearly one-third of the reference-quality 

streamgages used in this study, particularly in the semiarid 

Central and arid Southwestern United States, but also sporadically throughout most of the country. As a result of the inability to 

calculate meaningful values of uncertainty for many streamgages, 

the uncertainty of low-flow statistics was omitted from this study.

Streamgage Gap Analysis for Ungaged 

Locations

At ungaged locations or locations with only limited data, 

it may not be possible to estimate statistics directly from the 

gaged record. At these locations, streamflow statistics can 

sometimes be calculated by transferring information from a 

continuous flow streamgage (index streamgage) with similar 

characteristics or by conducting a regional analysis of streamflow statistics using many streamgages. Factors that affect the 

use of these methods include the length of record available at 

continuous record streamgages in the region and the hydrologic similarity between the ungaged or limited-information 

watershed and other gaged watersheds in the region. This part 

of the study focuses on the following questions:

• Where has regional analysis been successful (Previous 

Regional Analyses section)?

• Are there long-term continuous record streamgages 

with sufficient record length and needed hydrologic 

similarity available (Availability of Index Streamgages 

section)?

Previous Regional Analyses

Regional regression equations to estimate statistics have 

been developed for many regions of the country, but they vary 

in terms of the flow statistics considered and the accuracy 

of the equations. The regression equations use more easily 

calculated basin characteristics to estimate the value of flow 

statistics. Table 8 lists the basin attributes that have been commonly used in previous regression studies.

The National Streamflow Statistics (NSS) database 

was queried in November 2010 to obtain regional regression equations that are applicable in rural locations for peak 

flows (1 percent and 10 percent annual exceedance probability flows), low flows (7Q10), and average flows (mean and 

median annual flows). Whereas peak flow equations were 

available in NSS for nearly all States in the United States 

(exceptions were Kansas, Oklahoma, and Louisiana), low and 

average flow equations were available for only about one-third 

of the States. The available equations were analyzed to summarize the most commonly used basin characteristics and the 

variability in equation accuracy across the country.

Drainage area was always included as an explanatory 

variable in the regression equations obtained from NSS, as was 

also found by Benson and Carter (1973). Measures of precipitation, elevation, and slope were also commonly included as 

significant variables for all types of flow. Measures of precipitation included mean annual precipitation as well as measures of 

seasonal precipitation or the intensity of precipitation events. 

Less commonly used but also appearing in many equations were 

variables describing the soils in the basin (soil permeability or 

soil type), land cover (impervious area, forest cover, or grass 

cover), and the amount of water storage available in the basin. 

In addition, information on temperature or snow was often used 

in colder climates. Other variables that were sometimes used 

included measures of the basin shape, indicators of geology, 

and flow indices (such as a recession index or variability index). 

Table 9 categorizes the frequency with which variables were 

used for regression of different types of statistics.

The accuracy of the regional regression equations varies 

by flow statistic and by region. Two different metrics were 

commonly reported in previous regression studies, the standard error of the estimate and the standard error of prediction. 

The standard error of the estimate is a measure of how well 

the regression model fits the observed data; it is a measure 

of the goodness of fit of the regression model. The standard 

error of prediction is a measure of how well the regression 

equation might be expected to predict future observations; it 

is calculated using both a measure of the goodness of fit of 

the regression model and a term representing uncertainty in 

the model coefficients. Whereas both metrics are a measure of 

the uncertainty in model results, the two measures cannot be 

directly compared and so are mapped separately.

Figures 17–20 show the standard error of prediction in 

parts A and the standard error of the estimate in parts B for 

previous regressions of mean annual flow (fig. 17), 1 percent 

annual exceedance probability (100-year flood; fig. 18), 10 

percent annual exceedance probability (10-year flood; fig. 19), 

and the 7-day average, 10-year minimum flow (7Q10; fig. 20). 

Uncertainties were generally lowest in the Eastern United 

States and highest in the Central and Southwestern United 
30 A National Streamflow Network Gap Analysis

Table 8. Basin attributes commonly used in regression studies.

Attribute Explanation

Drainage area The drainage area is the upstream watershed area that drains to a streamgage. Some studies use the contributing 

drainage area, which excludes any upstream areas that form a closed basin and so do not contribute flow to the 

streamgage.

Elevation Different studies may use maximum elevation in the basin, average elevation in the basin, or other similar variables.

Evapotranspiration Water withdrawn from a land area by evaporation from water surfaces and moist soil plus plant transpiration. Different 

studies may use mean annual evapotranspiration or seasonal evapotranspiration or other measures.

Flow index A numerical index calculated from streamflow records, such as an index of the rate of recession or variability in 

streamflow. A flow index must be estimated at an ungaged location.

Geology Typically, the percentage of the basin that is underlain by a particular geology.

Impervious area/

development index

A variable that is intended to characterize the extent of urbanization. Most commonly, this is the percentage of the 

basin that is covered by impervious surfaces but other measures of development are also used.

Land cover (natural) Typically, the percentage of the basin that is covered by a particular land cover type, such as forest or grassland. 

Latitude The latitude of the streamgage or basin centroid. 

Longitude The longitude of the streamgage or basin centroid.

Precipitation A measure of precipitation in the basin. Different studies may use annual maximum precipitation, average annual 

precipitation, different measures of seasonal precipitation, or an index of precipitation intensity.

Shape A measure of the shape of the basin, such as length divided by width.

Slope A measure of the slope, or steepness, of the basin. This may be the average slope, slope of the main channel, the percentage of the basin where slope exceeds a threshold, or other permutations.

Snow A measure of the amount of snowfall or the percentage of precipitation falling as snow.

Soils A variable that characterizes the soils or soil permeability. This may be the percentage of the basin with a specified soil 

type, the average soil permeability, or other similar measures.

Stream density A measure of the stream density, such as the total length of streams in a basin divided by the basin area.

Water storage A measure of the upstream water storage in the basin. This may include the percentage of the basin covered by lakes, 

wetlands, or other water bodies.

Winter temperature Average minimum temperature, average January temperature, or similar. It is used to characterize whether snow and 

ice are a factor in the basin.

Table 9. Basin attributes appearing in regression equations developed by the USGS and included in the National Streamflow Statistics 

(NSS) database.

Frequency Peak flow equations Low flow equations Average (mean and median) flow equations

Frequently used Drainage area1 Drainage area1 Drainage area1

Precipitation Precipitation Precipitation

Slope Elevation

Moderately used Elevation Slope Soils

Impervious area/development index Elevation Slope

Water storage Soils Land cover (natural)

Other Latitude

Occasionally used 

or rarely used 

Shape Winter temperature Flow Index

Soils Geology Winter temperature

Geology Flow index Water storage

Land cover (natural) Land cover (natural) Impervious area/development index

Snow Impervious area/development index Shape

Winter temperature Stream density Longitude

Evapotranspiration Water storage Geology

Latitude Shape Stream density

Longitude Longitude Other

Other

1

Drainage area was used in all regression equations.
Streamgage Gap Analysis for Ungaged Locations 31

States. Differences in the available data when the studies were 

completed, the methods used, and other factors are likely to 

have contributed to differences in the accuracy of the regression equation. In general, the results of peak flow equations 

had the lowest uncertainty, followed by mean annual flow 

statistics. Low-flow statistics generally had the largest uncertainties and were sometimes extremely large. For example, 

the standard error of prediction of the low-flow regression 

equations in Colorado and Arkansas exceeded 200 percent 

(fig. 20A).

Availability of Index Streamgages

At locations where measured streamflow information 

is limited or nonexistent, estimates of streamflow statistics 

can sometimes be made by transferring information from 

streamgages with a long-term record. The watershed upstream 

of the long-term streamgage, however, must exhibit similar 

hydrologic behavior to the watershed upstream of the location 

of interest.

Selection of an appropriate index streamgage is a key to 

the success of information transfer techniques. One method of 

selecting an index streamgage relies on finding streamgages 

where the streamflow is highly correlated with flow at the 

location of interest. If there is a short streamflow record 

available, the short time series can be used to estimate correlations between the short record site and nearby long-term 

sites. When the location of interest is ungaged, Archfield and 

Vogel (2010) showed that correlation maps can be effective 

in identifying possible index streamgages. Correlation maps 

have been developed for all the United States and can indicate 

which streamgages are the least correlated to others in the 

streamgage network. Because the least correlated streamgages 

are most unlike the others, these streamgages are important for 

the independent information they provide. Locations where the 

analysis shows that there are no highly correlated streamgages 

could be considered for addition of new streamgages, should 

resources become available.

Another method for selecting index streamgages is the 

hydrologic similarity between the watershed of interest and 

nearby gaged watersheds. The more similar they are in terms 

of basin attributes—such as drainage area size, mean annual 

precipitation, elevation, geology, or land use—the more likely 

they are to be useful as an index site. Regionalization of 

statistics is typically accomplished by relating values of easily measurable basin attributes to the values of flow statistics 

of interest and then assessing the range of basin attributes 

covered by the streamgage network. Ideally, the streamgage 

network would cover the full range of known basin attributes.

Correlation Analysis

Streamflow is the expression of the complex interaction 

between climate, geology, and land surface conditions in its 

contributing catchment. Correlation between two streamflow 

time series could be interpreted as a measure of how similarly 

two catchments (pair of streamgages) respond to these interactions and therefore can be used to understand similarities and 

uniqueness in the hydrologic response of the network. Furthermore, methods to estimate daily streamflow at ungaged locations commonly require transferring the timing of streamflows 

from an index streamgage to an ungaged location, making correlation an important factor in deciding which index streamgage 

to select. For ungaged locations, Archfield and Vogel (2010) 

introduced the map-correlation method, which can be used to 

select the index streamgage estimated to have the highest correlated daily streamflows with the ungaged location.

Correlations between streamflow time series at referencequality streamgage locations within each major HUC region 

(fig. 1B) were evaluated to answer the following questions:

• What is the distribution of correlation across the 

streamgage network for daily streamflow and high- and 

low-flow events (Estimation of Correlation section)?

• Can the streamgage network provide highly correlated index streamgages suitable for estimating daily 

streamflow and high- and low-flow events across the 

entire network (Distribution of Correlations Across the 

United States section)?

• Are there regions of the United States where distance 

can be used as a surrogate for the selection of the highest correlated streamgage (Relation Between Distance 

and Correlation section)?

• If distance is not a good surrogate for correlation, how 

well is the map-correlation method able to estimate 

correlation between a gaged and ungaged location 

(Map Correlation Across the United States section)?

Estimation of Correlation

The correlation of daily streamflow between each possible pairing of the 1,630 study streamgages was estimated by 

HUC region. Correlations were estimated using the coincident, 

observed streamflow at each pair of streamgages. The mapcorrelation method was then applied to determine the utility of 

the method to estimate correlations at ungaged locations. To 

examine the availability of highly correlated index streamgages 

so that daily streamflow in sparsely measured locations could 

be estimated, correlations were computed for three coincident 

periods—the entire coincident daily streamflow record, the 

daily streamflow record for a high-flow period (the period 

when streamflows at both streamgages were greater than the 

0.1 exceedance probability), and the daily streamflow record 

for a low-flow period (the period when streamflows at both 

streamgages were less than the 0.9 exceedance probability).

Estimation of Correlation Using Observed Streamflow

For each HUC region in the United States, correlations 

between coincident streamflows at each pair of streamgages 
32 A National Streamflow Network Gap Analysis

Alaska Hawaii Puerto Rico

Alaska Hawaii Puerto Rico

A

B

SE of prediction (%)

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

68.4

29.8

13.7

12

17.6

7.6

54.6

47.9

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

SE of estimate (%)

30

44.3

33.9

52.8

41.3

25.3

12.7

17.3

15.3

Figure 17. Maps showing 

the standard error (SE) of A, 

prediction and B, the estimate 

for regression equations used 

to predict mean annual flow. %, 

percent; >, more than.
Streamgage Gap Analysis for Ungaged Locations 33

Alaska Hawaii Puerto Rico

Alaska Hawaii Puerto Rico

A

B

67.2

33.2

81.5

71.8

53

88.1 70.3

59.1

68.7

55

77.8

54.3 62.7

25.9

35.1

39.3

30

49.2

39.3

28.6 31.7

67.3

55.6

50.3

44.3

53.1

40.8

38.2

41

38.6

38.8

47.2

35.3

37

29.4

39.2

59.5

44.2

65.4

26.3

66

45.6

22

25

52.8

19

72

36.3

32.7

48.6

46

36.7

57.1

37.2

61.9

43.4

33.8

37

25.1

47.3

44.7

64.3

55.7

79.2

50

106.3 45

70.5

55

57

SE of prediction (%)

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

SE of estimate (%)

Figure 18. Maps showing 

the standard error (SE) of A, 

prediction and B, the estimate 

for regression equations used 

to predict the 1 percent annual 

exceedance probability flood 

(100-year flood). %, percent; >, 

more than.
34 A National Streamflow Network Gap Analysis

Alaska Hawaii Puerto Rico

Alaska Hawaii Puerto Rico

A

B

65

45.7

27.3

68.3 36.6

54 65.5

67.2

34.6

31.8

57.4

72.9

26

34.2

77.3

52.8

65.3

41.1

30.4

30

28

72.5 32.2

52

48.9

47.5

37.9

26.8

44.5

60.1

54

83.5

67.4

59.3 53.7

32.4

38.3 38.8

52.2

27.7

42

34.9

34.8

37.5

58.4

50

41.2

35.3

45.1

60.3

68.3

25.3

30.3

50

42

39.5

50.5

34.6

35.4

24

31

50.3

35

33

20.5

31.2

32.3

40.6 31.1

23.8

SE of prediction (%)

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

SE of estimate (%)

Figure 19. Maps showing 

the standard error (SE) of A, 

prediction and B, the estimate 

for regression equations used 

to predict the 10 percent 

annual exceedance probability 

flood (10-year flood). %, 

percent; >, more than.
Streamgage Gap Analysis for Ungaged Locations 35

Alaska Hawaii Puerto Rico

Alaska Hawaii Puerto Rico

A

B

79.4

70.8

55.8

29

78.5

112.8

219.3

238.6

44.3

183

83.1

51

67.7

28

82.9

115.6

90

27.5 65.7

62.5

SE of prediction (%)

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

 No information

 0–25

>25–50

>50–75

>75–100

>100–110

SE of estimate (%)

Figure 20. Graphs showing 

the standard error (SE) of A, 

prediction and B, the estimate 

for regression equations used 

to predict the 7-day average, 

10-year minimum flow (7Q10). 

%, percent; >, more than.
36 A National Streamflow Network Gap Analysis

were estimated using Pearson’s correlation coefficient (r), 

which measures the linear correlation between two variables 

(Helsel and Hirsch, 1992); the correlation coefficient was 

selected because of its common use in the selection of index 

streamgages for record extension and patching. With this 

method, the natural logarithms of the coincident streamflows 

are computed to linearize the relation between the two time 

series before the correlation was estimated.

Pearson r values can range from -1 to 1, with a value of 

1 indicating perfect correlation and a value of -1 indicating 

perfect negative correlation. A value of zero indicates that 

the two variables exhibit no correlation. There are limitations 

to the use of r to estimate correlation, most notably that the 

natural logarithm cannot be computed if streamflow is zero. 

For this analysis, zero-valued observed streamflows were 

removed from the record before the correlation was estimated. 

As a result, for some pairs of streamgages, the number of 

coincident streamflows may be too small to result in a reliable 

estimate of r. For this reason, only r values statistically significant at the 90 percent confidence level were reported.

To estimate the coincident period between streamflows 

for the high- and low-flow periods, the streamflows at the 

0.1 and 0.9 exceedance probability were first estimated at 

each streamgage using the Weibull plotting position and a 

single-order statistic (as presented in Vogel and Fennessey, 

1994, equation 2). The streamflow record was then truncated 

to contain only the periods of high or low flow. The dates for 

which each pair of streamgages were in a high- or low-flow 

period were recorded, and only the corresponding streamflows 

on those dates were used to compute the r value between the 

high- and low-flow periods, respectively.

Mapping of Correlation for Ungaged Locations

Using the methods described in Archfield and Vogel 

(2010), the correlation between a streamgage and an ungaged 

location was estimated using map correlation for each HUC 

region in the United States. Map correlation has been applied 

previously to regions in the Eastern United States (Archfield 

and Vogel, 2010); however, the utility of the method for estimating correlations at ungaged sites across the United States is 

unknown.

Map correlation is an application of ordinary kriging and 

is summarized here from Archfield and Vogel (2010). A spatial 

model, termed a variogram, is fit to the correlation values 

between each streamgage and the other streamgages in the 

study area, resulting in one spatial model per streamgage in 

the study area. This spatial model can then be used to estimate 

the correlation between the streamgage and an ungaged location. When there is more than one potential index streamgage, 

the spatial models can be used to discern which index 

streamgage results in the highest estimated correlation with 

the ungaged location.

To evaluate the utility of map correlation to estimate 

the correlation between an ungaged location and a particular 

streamgage, a leave-one-out cross-validation experiment was 

used. The streamgages used to develop the spatial model were 

removed—one at a time—and the parameters of the spatial 

model were estimated again without the removed site. The 

spatial model was then used to estimate the correlation at the 

removed site. Estimated correlations were then compared with 

the observed correlations using the root mean square error 

(RMSE) to determine the goodness-of-fit of the spatial model.

Distribution of Correlations Across the United 

States

Correlations were computed between each streamgage 

and all other streamgages in the same HUC region, resulting in 

a set of r values for each streamgage in the HUC region for all 

coincident streamflows (fig. 21), coincident high-flow events 

(fig. 22), and coincident low-flow events (fig. 23). The figures 

show box plots for the correlation between each streamgage 

and all other streamgages in the HUC region. The streamgages 

are shown in order of ascending station ID (not labeled on 

figs. 21–23). For all coincident streamflows, the distribution 

of correlations tend to be higher and less variable for HUC 

regions located in the Eastern United States, with the exception of the Southeastern United States (HUC region 3; fig. 21). 

By contrast, HUC regions in the Central United States (HUC 

regions 10 and 11) show substantially lower correlations 

between streamgages (fig. 21). Differences in the distribution 

of correlations across HUC regions do not appear to be dependent upon streamgage density.

Correlations between streamflows for coincident highflow (fig. 22) and low-flow (fig. 23) periods tended to be lower 

and more variable than correlations for all coincident streamflows. For streamgages shown as a discontinuous line on 

figures 22 and 23, coincident high- or low-flow periods were 

not experienced at all or not frequently enough to produce 

a significant correlation. This finding suggests that there are 

streamgages in the network that respond uniquely to high- or 

low-flow conditions. This situation occurs more frequently 

for low flows (fig. 23) than for high flows (fig. 22), potentially 

suggesting that streamgage pairs may respond similarly to a 

high-flow event but not a low-flow event.

The maximum correlation at each streamgage was also 

mapped (fig. 24). Mapping the maximum correlation is the 

equivalent to selecting the highest correlation in each box 

plot and mapping that value. For correlations computed from 

coincident daily streamflow, most streamgages have streamflows highly correlated with at least one other streamgage; 

this is particularly true for streamgages located in the Eastern and Western United States with the exception of coastal 

locations in the Southeastern United States. For the Central 

and Southwestern United States, particularly the Midwest and 

Texas, there are very few highly correlated streamgages. For 

this region of the United States, the use of an index to transfer 

timing to an ungaged location may not yield reliable timeseries estimates. Areas of high maximum correlations appear 

to follow a pattern closely related to mountainous regions of 
Streamgage Gap Analysis for Ungaged Locations 37

the United States, whereas regions with lower elevations tend 

to have lower maximum correlations (fig. 24).

For each streamgage, the number of other streamgages 

with a correlation value greater than 0.8 was examined (fig. 

25). If a streamgage was highly correlated with many other 

streamgages, then several streamgages would be appropriate 

for use as an index streamgage for that particular streamgage. 

Mountainous regions of the United States and southern Alaska 

appear to have many more streamgages that correlate well 

with other streamgages in their respective HUC regions. In 

contrast a large part of the Central United States, coastal 

areas in the Southeastern United States, Hawaii, and Puerto 

Rico have at least one highly correlated streamgage (fig. 24) 

but few other streamgages considered suitable as an index 

streamgage (fig. 25). For these regions, methods to select the 

index streamgage need to be precise because there is a greater 

chance of not choosing a highly correlated index streamgage.

For correlations between coincident streamflows for highand low-flow periods, higher maximum correlation values are 

observed for high-flow periods compared with low-flow periods (figs. 26 and 27, respectively). Correlations for coincident 

high-flow periods behave similarly to correlations computed 

from all coincident streamflow values, with higher maximum 

correlations along the Eastern (excluding Southeastern) and 

Western United States and lower maximum correlations in 

the Interior and Southeastern United States. Correlations 

estimated from coincident low-flow periods suggest that there 

is more unique behavior in the response of the streamgage 

network to low-flow periods than to high-flow periods.

Relation Between Distance and Correlation

Given that most areas of the United States have at least 

one and sometimes many suitable streamgages for information transfer, the relation between distance and correlation is 

examined. If there are areas of the country where the nearest 

streamgage can provide a surrogate for the highest correlated 

index streamgage, then more sophisticated and data-intensive 

techniques to select the index streamgage need not be applied.

To determine if distance between streamgages could be 

used to predict correlation, a linear regression equation was fit 

between the distances, and r values computed between each 

pair of streamgages by HUC region. For example, there are 

131 streamgages in New England (HUC region 1). Assuming 

that each of the other 130 streamgages has enough coincident 

record to yield a statistically significant r value, there are 130 

other streamgages for each streamgage in New England to 

measure the distance between paired streamgage outlets and 

the correlation between coincident streamflow time series. The 

coefficient of determination (r2) of the regression between distance and r was determined for all coincident streamflows (fig. 

28), coincident high-flow events (fig. 29), and coincident lowflow events (fig. 30). A subset of relations between distance 

and r was selected and plotted to verify that the assumptions 

of linear regression were met, most notably that the relation 

between distance and r was linear.

Whereas distance and correlation are highly related 

for some streamgages, in general, distance was seen to be a 

poor predictor of correlation. The relatively weak ability of 

distance to act as a surrogate for correlation seen nationally 

confirms the findings of Archfield and Vogel (2010), which 

applied only to New England. For correlations determined 

from all coincident streamflows, areas with high r2 values are 

located primarily in the Northeastern United States and along 

the southwestern part of the Mississippi River Basin (fig. 28). 

These geographic patterns do not appear related to streamgage 

density or to the number of highly correlated sites at the 

streamgage; if the geographic patterns adhered to these two 

criteria, then the Western United States also would have high 

r2 values. For correlations determined from coincident high 

and low flows (figs. 29 and 30, respectively), there are either 

weak or no significant relations between distance and correlation, with the exception of a few streamgages in scattered 

locations across the country.

Map Correlation Across the United States

Distance, although sometimes highly related to correlation, does not appear to be a reliable way to select the most 

correlated index streamgage. Therefore, the utility of the 

map-correlation method was investigated to determine how 

well the correlation between a gaged and ungaged location 

could be estimated. Using the methods described in Archfield 

and Vogel (2010) and cross validation described in this report, 

RMSEs were determined from observed and map-correlationestimated correlation values for coincident daily streamflows 

at each streamgage, coincident streamflows for high-flow 

periods, and coincident streamflows for low-flow periods. 

The RMSEs between observed and estimated correlations 

determined for the coincident daily streamflows show that the 

map-correlation method is able to provide good estimates of 

correlation at ungaged locations in the Northeastern and MidAtlantic United States and Puerto Rico and to a lesser extent 

in the Southeastern United States and the Great Lakes region 

(fig. 31). For other regions of the United States, the RMSEs 

are much larger, making the estimates unreliable for estimating correlation at ungaged locations (fig. 31). High RMSEs are 

also found nationwide for correlations determined for highand low-flow periods (figs. 32 and 33, respectively).

There may be several reasons for the poor performance of 

the map-correlation method across much of the United States. 

The map-correlation method, as applied in this study, uses 

the variogram model form and binning strategy developed 

for applications of the map-correlation method to areas in the 

Eastern and Mid-Atlantic United States. Another spatial model 

form may be appropriate for streamgages in the Central and 

Western United States and in Alaska and Hawaii. Furthermore, 

map correlation has not been applied previously to correlations 

determined for only high- and low-flow periods, and other 

spatial model forms may be appropriate for this reason.
38 A National Streamflow Network Gap Analysis

Correlation coefficient

HUC region 01

HUC region 02

HUC region 03

HUC region 04

HUC region 05

HUC region 06

HUC region 07

HUC region 08

HUC region 09

HUC region 10

HUC region 11

HUC region 12

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

StreamgagesStreamgages

Streamgages Streamgages

Streamgages Streamgages

Streamgages

Streamgages Streamgages

Streamgages

Streamgages

Streamgages

Correlation coefficient

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Figure 21. Graphs showing the distribution of Pearson’s correlation coefficient between coincident daily streamflows at each 

streamgage and all other streamgages in each hydrologic code (HUC) region. The streamgages within each HUC are plotted in 

ascending order by streamgage identification number (appendix 1).
Streamgage Gap Analysis for Ungaged Locations 39

Figure 21. Continued.

EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 × 

 (75th percentile–25th percentile))

Lower limit (25th percentile + 1.5 × 

 (75th percentile–25th percentile))

Values above the upper limit 

 or below the lower limit Streamgages

HUC region 13

HUC region 14

HUC region 15

HUC region 16

HUC region 17

HUC region 18

HUC region 19

HUC region 20

HUC region 21

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages Streamgages

Streamgages

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0
40 A National Streamflow Network Gap Analysis

Correlation coefficient

HUC region 01

HUC region 02

HUC region 03

HUC region 04

HUC region 05

HUC region 06

HUC region 07

HUC region 08

HUC region 09

HUC region 10

HUC region 11

HUC region 12

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

StreamgagesStreamgages

Streamgages Streamgages

Streamgages Streamgages

Streamgages

Streamgages Streamgages

Streamgages

Streamgages

Streamgages

Correlation coefficient

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Figure 22. Graphs showing the distribution of Pearson’s correlation coefficient between coincident streamflows greater than the 

0.1 exceedance probability (high flows) at each streamgage and all other streamgages in each hydrologic code (HUC) region. The 

streamgages within each HUC are plotted in ascending order by streamgage identification number (appendix 1). Discontinuous lines 

indicate periods where coincident flows were experienced either not at all or not frequently enough to produce a significant correlation.
Streamgage Gap Analysis for Ungaged Locations 41

EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 × 

 (75th percentile–25th percentile))

Lower limit (25th percentile + 1.5 × 

 (75th percentile–25th percentile))

Values above the upper limit 

 or below the lower limit

Streamgages

HUC region 13

HUC region 14

HUC region 15

HUC region 16

HUC region 17

HUC region 18

HUC region 19

HUC region 20

HUC region 21

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages Streamgages

Streamgages

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Figure 22. Continued.
42 A National Streamflow Network Gap Analysis

Correlation coefficient

HUC region 01

HUC region 02

HUC region 03

HUC region 04

HUC region 05

HUC region 06

HUC region 07

HUC region 08

HUC region 09

HUC region 10

HUC region 11

HUC region 12

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Correlation coefficient

StreamgagesStreamgages

Streamgages Streamgages

Streamgages Streamgages

Streamgages

Streamgages Streamgages

Streamgages

Streamgages

Streamgages

Correlation coefficient

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Figure 23. Graphs showing the distribution of Pearson’s correlation coefficient between coincident streamflows less than the 

0.9 exceedance probability (low flows) at each streamgage and all other streamgages in each hydrologic code (HUC) region. The 

streamgages within each HUC are plotted in ascending order by streamgage identification number (appendix 1). Discontinuous lines 

indicate periods where coincident flows were experienced either not at all or not frequently enough to produce a significant correlation.
Streamgage Gap Analysis for Ungaged Locations 43

EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 × 

 (75th percentile–25th percentile))

Lower limit (25th percentile + 1.5 × 

 (75th percentile–25th percentile))

Values above the upper limit 

 or below the lower limit Streamgages

HUC region 13

HUC region 14

HUC region 15

HUC region 16

HUC region 17

HUC region 18

HUC region 19

HUC region 20

HUC region 21

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient Correlation coefficient Correlation coefficient

Correlation coefficient

Correlation coefficientCorrelation coefficient

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages

Streamgages Streamgages

Streamgages

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Figure 23. Continued.
44 A National Streamflow Network Gap Analysis

Maximum correlation value 

between streamflows 

at the streamgage

 0.5

>0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

HUC region and number

EXPLANATION

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

20

21

Figure 24. Map showing the maximum values of Pearson’s correlation coefficient for each hydrologic unit code (HUC) region 

between coincident daily streamflows at each streamgage and all other streamgages. <, less than; >, more than.
Streamgage Gap Analysis for Ungaged Locations 45

HUC region and number

Number of streamgages with 

correlations greater than 0.8

 0

>0–5

>5–10

>10–25

>25

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20 21

Figure 25. Map showing number of streamgages with correlated daily streamflows greater than 0.8 (where 1.0 is the highest 

correlation possible) in each hydrologic unit code region. <, less than; >, more than.
46 A National Streamflow Network Gap Analysis

HUC region and number

Maximum correlation value between streamflows 

at the streamgage

< 0.5

 0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 26. Map showing the maximum values of Pearson’s correlation coefficient between coincident streamflows greater 

than the 0.1 exceedance probability (high flows) at each streamgage and all other streamgages in each hydrologic unit code 

region. <, less than; >, more than.
Streamgage Gap Analysis for Ungaged Locations 47

HUC region and number

Maximum correlation value between streamflows 

at the streamgage

< 0.5

 0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 27. Map showing the maximum values of Pearson’s correlation coefficient between coincident streamflows less than 

the 0.9 exceedance probability (low flows) at each streamgage and all other streamgages in each hydrologic unit code region. 

<, less than; >, more than.
48 A National Streamflow Network Gap Analysis

HUC region and number

R-squared value obtained by fitting a regression between 

distance and correlation at 

the streamgage

Regression not significant

< 0.5

 0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 28. Map showing coefficient of determination (R-squared value) obtained by regressing distance against correlation 

between distance and correlation between coincident daily streamflows at each streamgage and all other streamgages in 

each hydrologic code unit region. Regression not significant means that a statistically significant equation relating distance to 

correlation could not be determined at the 90-percent confidence level for that streamgage. <, less than; >, more than.
Streamgage Gap Analysis for Ungaged Locations 49

HUC region and number

R-squared value obtained by fitting a regression between 

distance and correlation at 

the streamgage

Regression not significant

< 0.5

 0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 29. Map showing coefficient of determination (R-squared value) obtained by regressing distance against correlation 

between coincident streamflows greater than the 10-percent exceedence probability (high flows) at each streamgage and all 

other streamgages in each hydrologic code unit region. Regression not significant means that a statistically significant equation 

relating distance to correlation could not be determined at the 90-percent confidence level for that streamgauge. <, less than;

>, more than.
50 A National Streamflow Network Gap Analysis

HUC region and number

R-squared value obtained by fitting a regression between 

distance and correlation at 

the streamgage

Regression not significant

< 0.5

 0.5–0.7

>0.7–0.8

>0.8–0.9

>0.9

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 30. Map showing coefficient of determination (R-squared value) obtained by regressing distance against correlation 

between coincident streamflows less than the 90-percent exceedence probability (low flows) at each streamgage and all other 

streamgages in each hydrologic code unit region. Regression not significant means that a statistically significant equation 

relating distance to correlation could not be determined at the 90-percent confidence level for that streamgage. <, less than; 

>, more than.
Streamgage Gap Analysis for Ungaged Locations 51

HUC region and number

Alaska Hawaii Puerto Rico

Root-mean-square error 

between observed and 

estimated correlations

Not enough data for 

 fit variogram

<0.025

 0.025–0.05

>0.05–0.1

>0.1

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 31. Map showing root mean square error computed from observed and map-correlation-estimated correlation between 

coincident daily streamflows at each streamgage and all other streamgages in each hydrologic code unit region. <, less than; 

>, more than.
52 A National Streamflow Network Gap Analysis

HUC region and number

Root-mean-square error 

between observed and 

estimated correlations

Not enough data for 

 fit variogram

<0.025

 0.025–0.05

>0.05–0.1

>0.1

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 32. Map showing root mean square error computed from observed and map-correlation-estimated correlation between 

coincident streamflows greater than the 10-percent exceedence probability (high flows) at each streamgage and all other 

streamgages in each hydrologic code unit region. <, less than; >, more than.
Streamgage Gap Analysis for Ungaged Locations 53

2-digit hydrologic unit boundary, and number

Root-mean-square error 

between observed and 

estimated correlations

Not enough data for 

 fit variogram

<0.025

>0.025–0.05

>0.05–0.1

>0.1

Alaska Hawaii Puerto Rico

EXPLANATION

20

01

02

03

04

06

05

08

09

07

10A

10B

11

12

13

14

15

16

17

18

19

20

21

Figure 33. Map showing root mean square error computed from observed and map-correlation-estimated correlation 

between coincident streamflows less than the 90-percent exceedence probability (low flows) at each streamgage and all other 

streamgages in each hydrologic code unit region. <, less than; >, more than.
54 A National Streamflow Network Gap Analysis

Basin Attribute Coverage

Basin attribute similarity is another commonly used 

method for selecting an index streamgage. Basin attributes 

are also used to develop regional regression equations for 

estimating streamflow statistics at ungaged locations. In both 

cases, a streamgage network that covers the full range of basin 

attributes that is observed at ungaged locations is desirable. 

This part of the analysis assesses how well the streamgages in 

the reference-quality streamgage dataset cover the full range 

of basin attributes observed at ungaged locations in the continental United States. Alaska, Hawaii, and Puerto Rico were 

not included because the GIS layers used to calculate basin 

attributes within the continental United States were not available for Alaska, Hawaii, and Puerto Rico.

Basin attributes commonly used in regional regression 

studies are listed in table 9 in this report. With the exception of 

latitude, those attributes that were noted as “frequently used” 

and “moderately used” were used in this analysis of basin 

similarity, as listed below:

• drainage area

• average basin elevation

• average basin slope

• forest cover

• water storage

• impervious area

• average annual precipitation

• soil permeability

• snow, as a percentage of annual precipitation

• average annual temperature

The first eight attributes listed are the list of “frequently 

used” and “moderately used” attributes from published 

regional regression equations. Although latitude was also 

“moderately used” in low-flow studies, it was not included in 

this analysis of basin similarity. Snow and average annual temperature are included because they are important in cold and 

high elevation areas.

The analysis also includes annual average temperature 

and the percentage of precipitation that falls as snow, two 

variables that were often used in colder climates. Values for 

these variables were calculated by Falcone and others (2010) 

for reference-quality streamgages in GAGES–II-prelim.

The same underlying GIS layers were used to calculate 

values of the basin attributes in “gageable watersheds”. The 

gageable watersheds are defined in this study as HUC 10-digit 

watersheds (level-5 HUCs) that are also headwater basins. 

Ideally, additional gageable watersheds would have been 

defined that were smaller than the headwaters of HUC 10-digit 

watersheds, but additional GIS processing beyond the scope 

of this study was needed to achieve this result. The gageable 

watersheds have a mean drainage area of about 180 mi2.

The distribution of the attribute values in gaged watersheds is compared with the distribution of these attribute 

values in the gageable watersheds to assess whether the full 

range of basin characteristics observed at gageable watersheds 

is being covered by streamgages (appendix 2). Where the full 

range in values for gageable watersheds is covered by the 

gaged watersheds (reference quality), the streamgage network 

is doing a good job representing the range of basin characteristics that are actually observed.

The drainage area at the reference-quality streamgages is 

the NWIS reported value; if there is no NWIS value reported, 

then the GIS-derived drainage area is used. Generally, there 

is fairly good coverage of the full range of drainage area 

observed at gageable watersheds by the reference-quality 

streamgages.

The streamgages in the reference-quality streamgage 

network appear to be doing a fairly good job of representing 

the range of basin characteristics for most of the attributes 

listed above. In part, this may be because the average size of 

the gageable watersheds is fairly large and characteristics are 

averaged over these large areas. More extreme values of basin 

attributes that may occur over limited spatial areas are not 

seen in attributes calculated for the gageable watersheds based 

on HUC 10-digit watersheds. Using smaller basins would give 

a more complete picture of whether the full range of basin 

attributes observed at ungaged locations is being covered by 

the streamgage network.

Overall, the reference-quality streamgages cover the 

range of attributes observed at gageable watersheds fairly 

well, but there are some exceptions. Analysis indicated that 

the streamgage network does not adequately represent areas 

with low forest cover or high impervious cover. This finding is expected because the reference-quality streamgages 

were selected so that they do not measure flow at basins 

with substantial land-cover changes, such as deforestation or 

urbanization. The streamgages in the complete dataset (not 

just the reference-quality streamgage dataset) are likely to 

cover these types of attributes more fully. Reference-quality 

streamgages were the focus of this analysis because these are 

the streamgages that are most likely to be of value in estimating statistics at ungaged locations using existing regression 

and index site transfer methods.

There are also instances where specific basin attributes 

are not covered well in some HUC regions. For example, the 

highest elevations are not covered well in Souris-Red-Rainy 

(HUC region 9), Arkansas-White-Red (HUC region 11), or 

Texas-Gulf (HUC region 12). Conversely, the lowest elevations are not being covered well in the Rio Grande (HUC 

region 13), Lower Colorado (HUC region 15), or Great Basin 

(HUC region 16). These arid and semiarid HUC regions seem 
Summary and Conclusions 55

to have a variety of mismatches in gageable and gaged basin 

attributes. For example, very low precipitation values are seen 

at the gageable watersheds but not in the watersheds draining 

to reference-quality streamgages. Permeability, snow, temperature, and water cover are other variables that have gaps in their 

coverages in these regions.

Summary and Conclusions

The U.S. Geological Survey (USGS) conducted a gap 

analysis to evaluate how well the USGS streamgage network 

meets a variety of needs, focusing on the ability to calculate 

various statistics at locations that have streamgages (gaged) 

and that do not have streamgages (ungaged), and to determine 

where there are gaps in the network of gaged locations, how 

accurately desired statistics can be calculated with a given 

length of record, and if the current network allows for estimation of these statistics at ungaged locations. The results of this 

analysis are summarized in table 10.

Spatial Gap Analysis

USGS streamgages in the complete dataset measure flow 

at drainage areas of 20,000 square miles (mi2) or less. Flow is 

measured for about 72 percent of the land area in the conterminous United States. Alaska and Hawaii have the lowest 

density of streamgages in the United States, with large parts 

of these States containing no USGS streamgages. The spatial 

distribution of streamgages in the complete dataset is uneven 

within the conterminous United States as well, with the most 

streamgages concentrated in the most populated areas of the 

country. The density of USGS streamgages tends to be low 

in much of the arid Southwest. Regional differences in the 

spatial coverage of streamgages are especially pronounced for 

streamgages that measure flow at drainage areas smaller than 

1,000 mi2.

The overall spatial coverage of streamgages in the 

reference-quality streamgage dataset is much lower, at 8.6 

percent for the conterminous United States. The spatial coverage of reference-quality streamgages in Alaska is similar (8.9 

percent). The lowest reference-quality streamgage coverage 

is observed in the Southwestern United States, Hawaii, and 

Puerto Rico.

Temporal Gap Analysis

The USGS streamgage network has been fairly stable in 

terms of number of streamgages since the 1950s and 1960s. 

The median record length for all streamgages in the complete dataset is 42 years, The median record length for all 

streamgages within a hydrologic unit code (HUC) region is 

lowest for Alaska (HUC region 19) and Puerto Rico (HUC 

region 21). In an effort to consider record length in conjunction with spatial coverage, the areal coverage of streamgages 

with record lengths of 50 years or greater was determined. The 

spatial coverage of these long-term record streamgages is lowest outside the conterminous United States (Alaska, Hawaii, 

and Puerto Rico) and in arid and semiarid areas of the Central 

and Southwestern United States.

Uncertainty Analysis

A minimum level of uncertainty in various streamflow 

statistics was estimated based on the interannual variability 

in the streamflow time series used to calculate the statistics. 

As calculated in this study, differences in uncertainty of flow 

statistics across the country are the result of differences in the 

interannual variability of flow. For each of the statistics used 

in this analysis, the greatest variability is generally observed in 

the arid and semiarid Central and Southwestern United States. 

A greater number of years of record are required in these areas 

to achieve comparable levels of uncertainty throughout the 

country for most statistics.

This analysis is limited by the use of some simplifying 

assumptions that cause the estimated uncertainty to be lower 

than would be expected if all sources of uncertainty were considered. In particular, persistence in hydrologic records was 

not considered in this study. The estimates of uncertainty may 

or may not apply in areas that are ungaged. If the interannual 

variability at ungaged sites is similar to that for gaged areas, 

the uncertainty will be similar. However, if the interannual 

variability is different, then the uncertainty may also be quite 

different.

Previous Regression Studies

Regional regression equations developed in previous 

studies to estimate peak flows, low flows, and annual flows 

use many of the same basin attributes as explanatory variables. 

Drainage area, precipitation, elevation, and slope were the 

most commonly used basin attributes in previous USGS studies. Peak flow equations were the most widely available across 

the country and are generally the most accurate. Equations to 

estimate low-flow frequency statistics are the least accurate. 

Equations were generally most accurate in the Eastern United 

States and lowest in the Central and Southwestern United 

States, but exceptions abound. However, due to the different 

times when the studies were completed and the methods used, 

not all the differences in regression equation accuracy may 

be directly attributable to differences in hydrology or data 

availability.
56 A National Streamflow Network Gap Analysis

Correlation

Correlations between reference-quality streamgages for 

all coincident streamflow and high- and low-flow periods 

were evaluated to determine similarities and uniqueness in the 

streamgage network as well as to understand the suitability 

of the network to provide index streamgages for information transfer to an ungaged location. Most highly correlated 

streamgages are in the Eastern and Western United States and 

appear to coincide with mountainous regions of the United 

States. Areas with highly correlated streamgages provide index 

streamgages with the potential for good transfer of information 

to an ungaged location.

Lower correlations are found in the Central United States 

and coastal areas in the Southeastern United States, suggesting 

that few or no streamgages in these areas would yield index 

streamgages suitable for information transfer, regardless of the 

index streamgage selection method used. The use of distance 

as a surrogate to select a highly correlated index streamgage 

appears to work in some areas although not reliably. The use 

of the map-correlation method to estimate correlation between 

a streamgage and ungaged location showed promise for the 

Eastern United States but less so for other areas of the Nation. 

Correlations estimated between coincident high- and low-flow 

periods were lower than correlations estimated from the entire 

coincident periods at each streamgage, and there appears to be 

more similarity among streamgages for coincident high-flow 

periods than for coincident low-flow periods, suggesting there 

is more dissimilarity amongst streamgages during low-flow 

periods than high-flow periods.

Basin Attribute Similarity

The USGS streamgages in the reference-quality 

streamgage dataset were evaluated to determine if the basin 

attributes observed at upstream watersheds covered the range 

observed at gageable watersheds. The gageable watersheds are 

defined in this study as watershed-level HUC (10-digit) codes 

that are headwater basins. Any gaps in the coverage of the full 

range of basin attributes is a potential problem for transferring 

streamflow information from gaged to ungaged areas. Basin 

attributes that were commonly used in previous USGS studies 

to develop regional regression equations were included in this 

analysis.

The USGS streamgage network of reference-quality 

streamgages defined for this study covers the range of basin 

attributes observed at gageable watersheds in most parts of the 

country fairly well, for most attributes. Some notable exceptions include often remote areas such as those with very high 

elevation or extreme aridity. In some cases areas with very 

low elevations were also poorly covered. The analysis also 

indicates that the streamgage network does not adequately 

represent areas with low forest cover or high impervious 

cover. The streamgages in the complete dataset, not only 

those in the reference-quality streamgage dataset, are likely to 

cover these types of attributes more fully. Reference-quality 

streamgages were the focus of this analysis because these are 

the streamgages that are most likely to be of value in estimating statistics at ungaged locations when using existing regression and index site transfer methods.

This analysis is limited by the use of only the set of gageable watersheds. A more complete analysis of basin attribute 

similarity would require the definition of additional gageable 

watersheds at finer scales than were available for use in this 

study.

Further Work

Further work to expand parts of this network gap analysis 

would increase the usefulness and confidence in these results. 

The uncertainty analysis included in this report calculates a 

minimum level of uncertainty and does not consider the effects 

of persistence in hydrologic time series, which is expected 

to increase uncertainty above the estimates reported here. To 

better understand the full uncertainty of streamflow statistics, 

additional time-series analysis could be undertaken to estimate 

the effects of persistence on uncertainty. The uncertainty of 

low-flow frequency statistics was not undertaken in this report 

because of issues in estimating the variance of the frequency 

statistics when the conditional probability adjustment is used 

to accommodate zero flow conditions. Additional work to 

develop, test, and implement an estimator could provide these 

estimates of low-flow uncertainty.

Alaska, Hawaii, and Puerto Rico were omitted from the 

basin similarity analysis because the GIS layers used in the 

conterminous United States were not available. To complete 

a basin similarity analysis outside the conterminous United 

States, alternative datasets would need to be identified or 

developed. Headwater basins at the smaller scale of subwatersheds (HUC 12-digit codes) could be added to the set of gageable watersheds to broaden the view of what basin characteristics need to be covered by the streamgage network. In addition 

to subwatersheds, other watersheds could be defined at every 

outlet of basins as defined in the U.S. Department of Agriculture Natural Resources Conservation Service (2012) Watershed Boundary Dataset to develop an even more complete set 

of gageable watersheds.
Further Work 57

Table 10. Summary of key findings by hydrologic unit code (HUC) region.

[HUC, hydrologic unit code]

HUC 

region HUC region name

Spatial coverage, 

 percentage of area 

that is measured 

by streamgages

Temporal 

coverage, 

median 

years of record

Uncertainty of 

statistics, 

qualitative 

assessment

Maximum correlation 

between reference dataset streamgages, median 

for all flows

1 New England Complete dataset: 74 percent 50 years Low 0.95

Reference dataset: 13 percent

2 Mid-Atlantic Complete dataset: 78 percent 52 years Low to moderate 0.95

Reference dataset: 12 percent

3 South Atlantic-Gulf Complete dataset: 79 percent 38 years Low to moderate 0.89

Reference dataset: 11 percent

4 Great Lakes Complete dataset: 73 percent 39 years Low 0.91

Reference dataset: 13 percent

5 Ohio Complete dataset: 86 percent 44 years Low 0.91

Reference dataset: 11 percent

6 Tennessee Complete dataset: 69 percent 49 years Low 0.93

Reference dataset: 13 percent

7 Upper Mississippi Complete dataset: 88 percent 45 years Moderate 0.86

Reference dataset: 11 percent

8 Lower Mississippi Complete dataset: 63 percent 48 years Low to moderate 0.84

Reference dataset: 6 percent

9 Souris-Red-Rainy Complete dataset: 65 percent 54 years High 0.82

Reference dataset: 25 percent

10A Upper Missouri Complete dataset: 70 percent 39 years Moderate 0.85*

Reference dataset: 11 percent

10B Lower Missouri Complete dataset: 84 percent 41 years Moderate 0.85*

Reference dataset: 16 percent

11 Arkansas-White-Red Complete dataset: 79 percent 46 years Moderate 0.83

Reference dataset: 10 percent

12 Texas-Gulf Complete dataset: 79 percent 43 years High 0.79

Reference dataset: 10 percent

13 Rio Grande Complete dataset: 40 percent 46 years Moderate 0.90

Reference dataset: 3 percent

14 Upper Colorado Complete dataset: 77 percent 36 years Low to moderate 0.94

Reference dataset: 4 percent

15 Lower Colorado Complete dataset: 66 percent 39 years High 0.83

Reference dataset: 5 percent

16 Great Basin Complete dataset: 31 percent 34 years Moderate 0.89

Reference dataset: 1 percent

17 Pacific Northwest Complete dataset: 76 percent 45 years Low 0.97

Reference dataset: 13 percent

18 California Complete dataset: 62 percent 42 years High 0.94

Reference dataset: 8 percent

19 Alaska Complete dataset: 10 percent 28 years Low 0.93

Reference dataset: 9 percent

20 Hawaii Complete dataset: 10 percent 55 years Low to moderate 0.86

Reference dataset: 1 percent

21 Caribbean Complete dataset: 51 percent 29 years Low to moderate 0.81

Reference dataset: 4 percent

*

Separate values were not calculated for the Upper and Lower Missouri River Basin. This value represents the median for the entire Missouri region (HUC 

region 10).
58 A National Streamflow Network Gap Analysis

References Cited

Archfield, S.A., and Vogel, R.M., 2010, Map correlation 

method—Selection of a reference streamgage to estimate 

daily streamflow at ungaged catchments: Water Resources 

Research, v. 46, W10513, 15 p., accessed [date], at 

http://www.agu.org/pubs/crossref/2010/

2009WR008481.shtml.

Benson, M.A., and Carter, R.W., 1973, A national study of 

the streamflow data-collection program: U.S. Geological 

Survey Water Supply Paper 2028, 44 p.

Cohn, T.A., Berenbrock, Charles, Kiang, J.E., and Mason, 

R.R., Jr., 2012, Calculating weighted estimates of peak 

streamflow statistics: U.S. Geological Survey Fact Sheet 

2012–3038, 4 p., available at http://pubs.usgs.gov/

fs/2012/3038/.

Commission for Environmental Cooperation, 1997, Ecological 

regions of North America—Toward a common perspective: 

Montreal, Canada, Commission for Environmental Cooperation, 71 p. (Accessed September 24, 2012, at 

http://www.cec.org/Storage/42/3484_eco-eng_EN.pdf.)

Falcone, J.A., Carlisle, D.M., Wolock, D.M., and Meador, 

M.R., 2010, GAGES—A streamgage database for evaluating natural and altered flow conditions in the conterminous 

United States: Ecology, v. 91, p. 621.

Falcone, J.A., 2011, GAGES–II—Geospatial attributes of 

gages for evaluating streamflow: U.S. Geological Survey, 

accessed September 24, 2012, at http://water.usgs.gov/GIS/

metadata/usgswrd/XML/gagesII_Sept2011.xml.

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

water resources: Amsterdam, Elsevier Studies in Environmental Science 49, 522 p.

Natural Resources Conservation Service, 2012, Watershed 

boundary dataset: U.S. Department of Agriculture Nature 

Resources Conservation Service, accessed October 10, 

2012, at http://www.nrcs.usda.gov/wps/portal/nrcs/main/

national/water/watersheds/dataset.

Ries, K.G., III, 2007, The national streamflow statistics 

program—A computer program for estimating streamflow 

statistics for ungaged sites: U.S. Geological Survey Techniques and Methods, book 4, chap. A6, 37 p. (Also available 

at http://pubs.usgs.gov/tm/2006/tm4a6/.)

U.S. Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood flow frequency: U.S. Geological Survey Bulletin 17B, 28 p., 14 appendixes. (Also 

available at http://water.usgs.gov/osw/bulletin17b/

dl_flow.pdf.)

Vogel, R.M., and Fennessey, N.M., 1994, Flow duration 

curves I—A new interpretation and confidence intervals: 

Journal of Water Resources Planning and Management, v. 

120, no. 4, p. 485–504.

Wieczorek, Michael, 2011, USGS streamgage NHDPlus 

version 1 basins 2011: U.S. Geological Survey, accessed 

November 29, 2012, at http://water.usgs.gov/GIS/metadata/

usgswrd/XML/streamgagebasins.xml
Appendix 1. Gages Used in the ReferenceQuality Streamgage Dataset

Reference-quality gages used in a national streamflow gap analysis study are available as a 

separate Microsoft Excel file (click here to download).

Appendix 2. Basin Attributes at Gageable 

Watersheds and Gaged Basins for Each 

Hydrologic Unit Code Region
62 A National Streamflow Network Gap Analysis

Figure 2–1. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in New England (hydrologic unit code (HUC) region 1). m, meter; mi2

, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.

HUC Region 1: New England

0 500 1000 0

50

100

150

Avg elev [m]

Number of basins

Gageable basins

Gaged basins

0 1,000 2,000 0

50

100

150

200

Drainage area [mi2]

Number of basins

0 10 20 30 0

20

40

60

80

100

Slope [%]

Number of basins

0 20 40 60 80 100 0

20

40

60

80

Forest [%]

Number of basins

0 20 40 60 0

50

100

150

200

250

Water [% of area]

Number of basins

0 20 40 60 80 0

50

100

150

200

250

300

Impervious area [%]

Number of basins

0 500 1,000 1,500 0

50

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Precip [mm]

Nnumber of basins

0 5 10 15 0

20

40

60

80

100

Permeability [inches per hr]

Number of basins

0 10 20 30 40 0

20

40

60

80

Snow [% of precip]

Number of basins

−2 0 2 4 6 0

10

20

30

40

50

60

Min T [ °C]

Number of basins

EXPLANATION
Appendix 2 63

Figure 2–2. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage dataset) in 

the Mid-Atlantic (hydrologic unit code (HUC) region 2). m, meter; mi2, square mile; mm, millimeter; in/hr, inches per hour; %, percent; 

°C, degrees Celsius.

HUC Region 2: Mid-Atlantic

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1000 0

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64 A National Streamflow Network Gap Analysis

HUC Region 3: Southeast

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1,000 0

100

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400

0 1,000 2,000 0

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400

0 5 10 0

100

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500

0 20 40 60 80 0

100

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500

600

700

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Figure 2–3. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Southeast (hydrologic unit code (HUC) region 3). m, meter; mi2, square mile; mm, millimeter; in/hr, 

inches per hour; %, percent; °C, degrees Celsius.
Appendix 2 65

HUC Region 4: Great Lakes

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 200 400 600 0

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0 20 40 0

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5 15 25 35 45 55 65 75 85 95 0

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Figure 2–4. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Great Lakes (hydrologic unit code (HUC) region 4). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
66 A National Streamflow Network Gap Analysis

HUC Region 5: Ohio

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1000 0

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Figure 2–5. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Ohio (hydrologic unit code (HUC) region 5). m, meter; mi2, square mile; mm, millimeter; in/hr, inches per hour; %, 

percent; °C, degrees Celsius.
Appendix 2 67

HUC Region 6: Tennessee

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1,000 0

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100

5

Figure 2–6. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Tennessee (hydrologic unit code (HUC) region 6). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
68 A National Streamflow Network Gap Analysis

HUC Region 7: Upper Mississippi

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 200 400 0

20

40

60

80

100

120

0 1,000 2,000 0

50

100

150

200

0 20 40 60 80 0

50

100

150

200

250

300

0 20 40 0

100

200

300

400

500

600

−2 0 2 4 6 8 0

20

40

60

80

100

120

0 5 10 0

50

100

150

200

250

300

0 500 1,000 0

50

100

150

200

0 5 10 0

50

100

150

200

250

300

350

0 10 20 0

50

100

150

0 20 40 0

100

200

300

400

500

600

15

Figure 2–7. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Upper Mississippi (hydrologic unit code (HUC) region 7). m, meter; mi2, square mile; mm, millimeter; in/hr, 

inches per hour; %, percent; °C, degrees Celsius.
Appendix 2 69

HUC Region 8: Lower Mississippi

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 100 200 300 0

10

20

30

40

50

60

70

0 500 1,000 1,500 2,000 0

10

20

30

40

50

60

0 20 40 60 80 0

20

40

60

80

0 10 20 30 0

50

100

150

200

250

0 5 10 15 0

10

20

30

40

50

60

0 5 10 0

20

40

60

80

100

120

0 500 1,000 1,500 0

10

20

30

40

50

0 10 20 0

20

40

60

80

100

0 5 10 0

20

40

60

80

100

120

0 20 40 0

50

100

150

200

250

400 100

Figure 2–8. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Lower Mississippi (hydrologic unit code (HUC) region 8). m, meter; mi2, square mile; mm, millimeter; in/hr, 

inches per hour; %, percent; °C, degrees Celsius.
70 A National Streamflow Network Gap Analysis

HUC Region 9: Souris-Red-Rainy

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1,000 1,500 0

20

40

60

80

100

120

0 500 1,000 1,500 2,000 0

10

20

30

40

50

60

0 20 40 60 80 0

20

40

60

80

100

0 2 4 0

50

100

150

−4 −3 −2 −1 0

10

20

30

40

0 2 4 6 8 0

10

20

30

40

0 500 1,000 1,500 0

20

40

60

80

100

0 20 40 0

50

100

150

200

0 20 40 60 0

50

100

150

0 10 20 0

20

40

60

80

100

120

0

Figure 2–9. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Souris-Red-Rainy (hydrologic unit code (HUC) region 9). m, meter; mi2, square mile; mm, millimeter; in/hr, 

inches per hour; %, percent; °C, degrees Celsius.
Appendix 2 71

HUC Region 10: Missouri

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 3,000 0

50

100

150

200

250

300

350

0 1,000 2,000 0

100

200

300

400

500

0 20 40 60 80 0

200

400

600

800

1,000

0 20 40 0

200

400

600

800

1,000

1,200

−5 0 5 0

100

200

300

400

0 5 10 0

100

200

300

400

500

600

0 500 1,000 0

50

100

150

200

250

300

350

0 20 40 0

200

400

600

800

1,000

0 20 40 60 0

100

200

300

400

500

600

700

0 10 20 0

200

400

600

800

1,000

1,200

80 100

Figure 2–10. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Missouri (hydrologic unit code (HUC) region 10). m, meter; mi2, square mile; mm, millimeter; in/hr, inches per 

hour; %, percent; °C, degrees Celsius.
72 A National Streamflow Network Gap Analysis

HUC Region 11: Arkansas-White-Red

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 3,000 0

50

100

150

200

0 500 1,000 1,500 2,000 0

20

40

60

80

0 20 40 60 80 0

50

100

150

200

0 20 40 0

50

100

150

200

250

300

350

−5 0 5 10 0

20

40

60

80

100

120

0 5 10 0

50

100

150

200

0 500 1,000 1,500 0

20

40

60

80

0 20 40 0

50

100

150

200

250

0 20 40 60 0

50

100

150

200

250

300

0 5 10 0

50

100

150

200

250

300

350

100

15

Figure 2–11. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Arkansas-White-Red Basin (hydrologic unit code (HUC) region 11). m, meter; mi2, square mile; mm, 

millimeter; in/hr, inches per hour; %, percent; °C, degrees Celsius.
Appendix 2 73

HUC Region 12: Texas-Gulf

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 500 1,000 0

20

40

60

80

100

0 1,000 2,000 3,000 0

50

100

150

200

250

0 20 40 60 0

20

40

60

80

100

120

140

0 20 40 0

50

100

150

200

250

0 5 10 15 0

20

40

60

80

0 2 4 6 8 0

20

40

60

80

100

120

0 500 1,000 1,500 0

10

20

30

40

50

0 5 10 0

20

40

60

80

100

0 1 2 3 0

50

100

150

0 20 40 60 0

50

100

150

200

250

300

20

20

Figure 2–12. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Texas-Gulf Basin (hydrologic unit code (HUC) region 12). m, meter; mi2, square mile; mm, millimeter; in/hr, 

inches per hour; %, percent; °C, degrees Celsius.
74 A National Streamflow Network Gap Analysis

HUC Region 13: Rio Grande

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 3,000 100 0

20

40

60

80

0 1,000 2,000 3,000 0

20

40

60

80

0 20 40 60 80 0

50

100

150

200

−5 0 5 10 15 0

10

20

30

40

50

60

0 5 10 0

20

40

60

80

100

120

140

0 500 1,000

0

20

40

60

80

100

0 20 40 0

20

40

60

80

100

0 20 40 60 0

50

100

150

200

0 2 4

0

50

100

150

200

250

300

0 1 2

0

100

200

300

Figure 2–13. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Rio Grande (hydrologic unit code (HUC) region 13). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
Appendix 2 75

HUC Region 14: Upper Colorado

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 3,000 0

10

20

30

40

50

60

0 500 1,000 1,500 2,000 0

10

20

30

40

50

60

0 20 40 60 80 0

20

40

60

80

100

0 0.5 1 0

20

40

60

80

100

120

−5 0 5 0

10

20

30

40

50

0 2 4 6 8 0

10

20

30

40

50

60

70

0 500 1,000 0

10

20

30

40

50

60

70

0 20 40 0

10

20

30

40

50

60

0 20 40 60 0

10

20

30

40

50

60

70

0 20 40 60 0

10

20

30

40

50

60

70

100

80

Figure 2–14. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Upper Colorado (hydrologic unit code (HUC) region 14). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
76 A National Streamflow Network Gap Analysis

HUC Region 15: Lower Colorado

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 100 0

10

20

30

40

50

0 500 1,000 1,500 0

10

20

30

40

50

0 20 40 60 80 0

20

40

60

80

100

120

0 10 20 30 0

50

100

150

200

250

0 5 10 15 0

10

20

30

40

50

0 2 4 6 8 0

20

40

60

80

0 200 400 600 800 0

10

20

30

40

50

0 10 20 30 40 0

20

40

60

80

0 20 40 0

20

40

60

80

100

120

0 0.5 1 1.5 0

50

100

150

200

250

40

Figure 2–15. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in Lower Colorado (hydrologic unit code (HUC) region 15). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
Appendix 2 77

HUC Region 16: Great Basin

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

70

0 1,000 2,000 3,000 0

20

40

60

80

0 1,000 2,000 0

20

40

60

80

100

0 20 40 60 80 0

50

100

150

200

0 10 20 0

50

100

150

200

250

300

350

−5 0 5 10 0

20

40

60

80

100

120

0 5 10 0

20

40

60

80

100

120

0 500 1,000 1,500 0

50

100

150

200

0 500 1,000 1,500 0

50

100

150

200

0 20 40 60 0

20

40

60

80

100

120

0 10 20 30 0

50

100

150

200

250

300

350

40

Figure 2–16. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Great Basin (hydrologic unit code (HUC) region 16). m, meter; mi2

, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.
78 A National Streamflow Network Gap Analysis

Figure 2–17. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in the Pacific Northwest (hydrologic unit code (HUC) region 17). m, meter; mi2, square mile; mm, millimeter; 

in/hr, inches per hour; %, percent; °C, degrees Celsius.

HUC Region 17: Pacific Northwest

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 100

0

50

100

150

200

250

300

0 1,000 2,000 0

50

100

150

200

250

0 20 40 60 80 0

50

100

150

200

250

300

0 20 40 60 80 0

200

400

600

800

1,000

−5 0 5 0

50

100

150

200

250

0 5 10 0

50

100

150

200

250

300

350

0 2,000 4,000 0

50

100

150

200

250

300

350

0 20 40 60 0

50

100

150

200

0 20 40 60 80 0

100

200

300

400

500

0 20 40 60 80 0

200

400

600

800

1,000

100
Appendix 2 79

HUC Region 18: California

Avg elev [m]

Number of basins

Drainage area [mi2]

Number of basins

Slope [%]

Number of basins

Forest [%]

Number of basins

Water [% of area]

Number of basins

Impervious area [%]

Number of basins

Precip [mm]

Nnumber of basins

Permeability [inches per hr]

Number of basins

Snow [% of precip]

Number of basins

Min T [°C]

Number of basins

Gageable basins

Gaged basins

EXPLANATION

0 1,000 2,000 3,000 100 0

50

100

150

200

0 1,000 2,000 0

50

100

150

200

250

300

0 20 40 60 80 0

50

100

150

200

250

300

0 20 40 60 0

100

200

300

400

500

600

−5 0 5 10 15 0

50

100

150

200

0 5 10 15 0

50

100

150

200

250

0 1,000 2,000 3,000 0

50

100

150

200

250

0 20 40 60 0

20

40

60

80

100

120

140

0 20 40 60 80 0

100

200

300

400

500

0 5 10 15 0

100

200

300

400

500

600

Figure 2–18. Histograms of basin attributes at gageable watersheds and gaged basins (reference-quality streamgage 

dataset) in California (hydrologic unit code (HUC) region 18). m, meter; mi2, square mile; mm, millimeter; in/hr, inches 

per hour; %, percent; °C, degrees Celsius.

For more information concerning this publication, contact:

Office of Surface Water

U.S. Geological Survey

12201 Sunrise Valley Drive, Mail Stop 415

Reston, VA 20192

(703) 648–5301

Publishing support provided by:

Reston and Pembroke Publishing Service Centers

Edited by Anna Glover

Original graphics by Mark Bonito

Original tables by Mary (Pat) Lee

Final graphics and layout by Jeannette Foltz
Kiang and others—A National Streamflow Network Gap Analysis—Scientific Investigations Report 2013–5013