U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5232

Prepared in cooperation with the Iowa Department of Natural Resources

Computing Daily Mean Streamflow at Ungaged Locations in 

Iowa by using the Flow Anywhere and Flow Duration Curve 

Transfer Statistical Methods
Cover. Turkey River near Eldorado, Iowa. Photograph by Jon Nania, U.S. Geological Survey.
Computing Daily Mean Streamflow at 

Ungaged Locations in Iowa by using the 

Flow Anywhere and Flow Duration Curve 

Transfer Statistical Methods

By S. Mike Linhart, Jon F. Nania, Curtis L. Sanders, Jr., and Stacey A. Archfield

Prepared in cooperation with the Iowa Department of Natural Resources

Scientific Investigations Report 2012–5232

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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Suggested citation:

Linhart, S.M., Nania, J.F., Sanders, C.L., Jr., and Archfield, S.A., 2012, Computing daily mean streamflow at ungaged 

locations in Iowa by using the Flow Anywhere and Flow Duration Curve Transfer statistical methods: U.S. Geological 

Survey Scientific Investigations Report 2012–5232, 50 p.
iii

Contents

Acknowledgments........................................................................................................................................vi

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

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

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

Description of Study Area ...................................................................................................................3

Previous Studies ...................................................................................................................................3

Trend Analysis ................................................................................................................................................3

Flow Anywhere Method Analytical Procedures ....................................................................................13

Identification of Local Regions.........................................................................................................13

Regression Methods ..........................................................................................................................14

Determination of Reference Streamgages............................................................................14

Determination of Aggregated Regions...................................................................................14

Development of Regional Regression Equations ..........................................................................20

Left-Censored Regression...............................................................................................23

Ordinary-Least-Squares Regression.............................................................................24

Accuracy and Limitations of Regression Estimates .....................................................................24

Comparison of Observed and Estimated Streamflows........................................................24

Uncertainty of Estimated Streamflows ..................................................................................27

Limitations of Methods .............................................................................................................29

Flow Duration Curve Transfer Analytical Procedures ...........................................................................32

Regression Methods ..........................................................................................................................32

Determination of Reference Streamgages.....................................................................................36

Comparison of Observed and Estimated Streamflows.................................................................37

Uncertainty of Estimated Streamflows ...........................................................................................42

Limitations of Methods.......................................................................................................................42

Summary........................................................................................................................................................45

References Cited..........................................................................................................................................48

Figures

1. Map showing locations of U.S. Geological Survey streamgages in Iowa considered

for development of the Flow Anywhere and Flow Duration Curve Transfer methods ......4

2. Graphs showing translation of a flow-duration curve to a time series of estimated

streamflow by using the Flow Duration Curve Transfer method showing the

observed time series, flow-duration curve, exceedance probability, and estimated

time series at the ungaged site ................................................................................................11

3. Graphs showing the 90-percent exceedance probability of daily mean streamflow

by water year for U.S. Geological Survey streamgages 05412500, Turkey River at

Garber, Iowa; 05452200, Walnut Creek near Hartwick, Iowa; and 06483500, Rock

River near Rock Valley, Iowa ....................................................................................................12
iv

4. Map showing Pearson’s r correlations with the logarithm (base 10) of daily

streamflows at the U.S. Geological Survey streamgages 05388250, Upper Iowa

River near Dorchester, Iowa; 05453000, Big Bear Creek at Ladora, Iowa; and

06605850, Little Sioux River at Linn Grove, Iowa....................................................................15

5. Map showing local and aggregated region boundaries in Iowa for the Flow

Anywhere method ......................................................................................................................18

6. Map showing landforms, aggregated region boundaries, and local region

boundaries in Iowa.....................................................................................................................19

7. Graphs showing correlation between residual (e

i

) and predicted streamflow, time,

and lagged residual (e(i-1)) for aggregated region 1 in the Flow Anywhere method

determined by using the entire dataset and by using one value every 2 months............25

8. Graphs showing observed and estimated daily mean streamflows relative to the 

1:1 line for aggregated region 1, aggregated region 2, and aggregated region 3, 

Iowa ..............................................................................................................................................27

9. Graphs showing observed and estimated daily mean streamflow relative to the 

1:1 line for U.S. Geological Survey streamgages 05387440, Upper Iowa River at

Bluffton, Iowa; and 05416900, Maquoketa River at Manchester, Iowa, showing the

closest and poorest agreement between unregulated observed and estimated

mean daily streamflow, October 1, 2004, to September 30, 2009, determined by

using the Flow Anywhere method ...........................................................................................29

10. Hydrographs showing observed and estimated hydrographs for U.S. Geological

Survey streamgages 05387440, Upper Iowa River at Bluffton, Iowa; and 05416900,

Maquoketa River at Manchester, Iowa, showing the closest and poorest

agreement between unregulated observed and estimated, daily mean streamflows,

October 1, 2004, to September 30, 2009, determined by using the Flow Anywhere

method..........................................................................................................................................30

11. Graphs showing observed and estimated cumulative daily mean streamflows for

U.S. Geological Survey streamgages 05387440, Upper Iowa River at Bluffton, Iowa,

and 05416900, Maquoketa River at Manchester, Iowa, October 1, 2004, to

September 30, 2009.....................................................................................................................31

12. Maps showing estimated Pearson’s r correlations of the logarithm of daily

streamflows at the U.S. Geological Survey streamgages 05412500, Turkey River at

Garber, Iowa, 05452200, Walnut Creek near Hartwick, Iowa, and 06483500, Rock

River near Rock Valley, Iowa ....................................................................................................38

13. Graphs showing observed and estimated daily mean streamflows for U.S.

Geological Survey streamgages 05387440, Upper Iowa River at Bluffton, Iowa; and

05416900, Maquoketa River at Manchester, Iowa, showing the closest and poorest

agreement between unregulated observed and estimated daily mean streamflow,

October 1, 2004, to September 30, 2009, determined by using the Flow Duration

Curve Transfer method...............................................................................................................41

14. Hydrogaphs showing observed and estimated hydrographs for U.S. Geological

Survey streamgages 05387440, Upper Iowa River at Bluffton, Iowa, and 05416900,

Maquoketa River at Manchester, Iowa, showing the closest and poorest

agreement between unregulated observed and estimated, daily mean streamflow,

October 1, 2004, to September 30, 2009, determined by using the Flow Duration

Curve Transfer method...............................................................................................................43

15. Graphs showing observed and estimated flow duration exceedance probabilities

for selected streamgages in Iowa ...........................................................................................44
v

Tables

1. Description of streamgages used to estimate streamflow at ungaged locations in

Iowa by using the Flow Anywhere and Flow Duration Curve Transfer methods...............5

2. Streamgages removed from the Flow Anywhere regression analyses ............................20

3. Streamgages used to develop regression equations for the Flow Anywhere

method, Iowa...............................................................................................................................21

4. Regression equations for estimating streamflow at ungaged locations in Iowa by

using the Flow Anywhere method ...........................................................................................26

5. Results of validation study for the Flow Anywhere and Flow Duration Curve

Transfer methods........................................................................................................................28

6. Statistical summary of drainage areas used to develop regional regression

equations in Iowa .......................................................................................................................32

7. Basin, climate, and land-use characteristics at three U.S. Geological streamgages,

tested for use in the estimation of streamflow at ungaged sites .......................................33

8. Regression equations for estimating flow-duration statistics for unregulated

streams in Iowa...........................................................................................................................35

9. Range of basin characteristics used for final regression equations for estimating

flow-duration statistics for unregulated streams in Iowa ...................................................45

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

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

A water year is the 12-month period October 1 through September 30 designated by the year in 

which it ends.
vi

Acknowledgments

The authors express their gratitude to the personnel of the Iowa Department of Natural 

Resources, Water Monitoring Division, for their assistance in project planning. 

The authors also thank the following USGS personnel: David Eash, for overall project guidance 

and regression technical assistance; Ken Eng, for assistance with initial project development; 

Julie Kiang, for technical assistance with the regression analysis; and Kris Lund, for work to 

prepare the maps. The authors also express their appreciation to the many other USGS personnel who assisted with the collection and analysis of streamflow data used in this study. 
Computing Daily Mean Streamflow at Ungaged Locations 

in Iowa by using the Flow Anywhere and Flow Duration 

Curve Transfer Statistical Methods

By S. Mike Linhart, Jon F. Nania, Curtis L. Sanders, Jr., and Stacey A. Archfield

Abstract

The U.S. Geological Survey (USGS) maintains approximately 148 real-time streamgages in Iowa for which daily 

mean streamflow information is available, but daily mean 

streamflow data commonly are needed at locations where 

no streamgages are present. Therefore, the USGS conducted 

a study as part of a larger project in cooperation with the 

Iowa Department of Natural Resources to develop methods 

to estimate daily mean streamflow at locations in ungaged 

watersheds in Iowa by using two regression-based statistical 

methods. The regression equations for the statistical methods 

were developed from historical daily mean streamflow and 

basin characteristics from streamgages within the study area, 

which includes the entire State of Iowa and adjacent areas 

within a 50-mile buffer of Iowa in neighboring states. Results 

of this study can be used with other techniques to determine 

the best method for application in Iowa and can be used to 

produce a Web-based geographic information system tool to 

compute streamflow estimates automatically. 

The Flow Anywhere statistical method is a variation 

of the drainage-area-ratio method, which transfers sameday streamflow information from a reference streamgage to 

another location by using the daily mean streamflow at the reference streamgage and the drainage-area ratio of the two locations. The Flow Anywhere method modifies the drainage-arearatio method in order to regionalize the equations for Iowa 

and determine the best reference streamgage from which to 

transfer same-day streamflow information to an ungaged location. Data used for the Flow Anywhere method were retrieved 

for 123 continuous-record streamgages located in Iowa and 

within a 50-mile buffer of Iowa. The final regression equations were computed by using either left-censored regression 

techniques with a low limit threshold set at 0.1 cubic feet per 

second (ft3/s) and the daily mean streamflow for the 15th day 

of every other month, or by using an ordinary-least-squares 

multiple linear regression method and the daily mean streamflow for the 15th day of every other month.

The Flow Duration Curve Transfer method was used to 

estimate unregulated daily mean streamflow from the physical 

and climatic characteristics of gaged basins. For the Flow 

Duration Curve Transfer method, daily mean streamflow quantiles at the ungaged site were estimated with the parameterbased regression model, which results in a continuous daily 

flow-duration curve (the relation between exceedance probability and streamflow for each day of observed streamflow) 

at the ungaged site. By the use of a reference streamgage, the 

Flow Duration Curve Transfer is converted to a time series. 

Data used in the Flow Duration Curve Transfer method were 

retrieved for 113 continuous-record streamgages in Iowa and 

within a 50-mile buffer of Iowa. The final statewide regression 

equations for Iowa were computed by using a weighted-leastsquares multiple linear regression method and were computed 

for the 0.01-, 0.05-, 0.10-, 0.15-, 0.20-, 0.30-, 0.40-, 0.50-, 

0.60-, 0.70-, 0.80-, 0.85-, 0.90-, and 0.95-exceedance probability statistics determined from the daily mean streamflow with 

a reporting limit set at 0.1 ft3/s. The final statewide regression 

equation for Iowa computed by using left-censored regression 

techniques was computed for the 0.99-exceedance probability 

statistic determined from the daily mean streamflow with a 

low limit threshold and a reporting limit set at 0.1 ft3/s. 

For the Flow Anywhere method, results of the validation 

study conducted by using six streamgages show that differences between the root-mean-square error and the mean absolute error ranged from 1,016 to 138 ft3

/s, with the larger value 

signifying a greater occurrence of outliers between observed 

and estimated streamflows. Root-mean-square-error values 

ranged from 1,690 to 237 ft3/s. Values of the percent rootmean-square error ranged from 115 percent to 26.2 percent. 

The logarithm (base 10) streamflow percent root-mean-square 

error ranged from 13.0 to 5.3 percent. Root-mean-square-error 

observations standard-deviation-ratio values ranged from 0.80 

to 0.40. Percent-bias values ranged from 25.4 to 4.0 percent. 

Untransformed streamflow Nash-Sutcliffe efficiency values 

ranged from 0.84 to 0.35. The logarithm (base 10) streamflow 

Nash-Sutcliffe efficiency values ranged from 0.86 to 0.56. 

For the streamgage with the best agreement between observed 

and estimated streamflow, higher streamflows appear to be 

underestimated. For the streamgage with the worst agreement between observed and estimated streamflow, low flows 

appear to be overestimated whereas higher flows seem to be 
2 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

underestimated. Estimated cumulative streamflows for the 

period October 1, 2004, to September 30, 2009, are underestimated by -25.8 and -7.4 percent for the closest and poorest 

comparisons, respectively.

For the Flow Duration Curve Transfer method, results 

of the validation study conducted by using the same six 

streamgages show that differences between the root-meansquare error and the mean absolute error ranged from 437 to 

93.9 ft3/s, with the larger value signifying a greater occurrence of outliers between observed and estimated streamflows. 

Root-mean-square-error values ranged from 906 to 169 ft3/s. 

Values of the percent root-mean-square-error ranged from 67.0 

to 25.6 percent. The logarithm (base 10) streamflow percent 

root-mean-square error ranged from 12.5 to 4.4 percent. 

Root-mean-square-error observations standard-deviation-ratio 

values ranged from 0.79 to 0.40. Percent-bias values ranged 

from 22.7 to 0.94 percent. Untransformed streamflow NashSutcliffe efficiency values ranged from 0.84 to 0.38. The logarithm (base 10) streamflow Nash-Sutcliffe efficiency values 

ranged from 0.89 to 0.48. For the streamgage with the closest 

agreement between observed and estimated streamflow, there 

is relatively good agreement between observed and estimated 

streamflows. For the streamgage with the poorest agreement 

between observed and estimated streamflow, streamflows 

appear to be substantially underestimated for much of the 

time period. Estimated cumulative streamflow for the period 

October 1, 2004, to September 30, 2009, are underestimated 

by -9.3 and -22.7 percent for the closest and poorest comparisons, respectively.

Introduction

Streamflow data are used by a variety of individuals 

including water resource managers and recreationists. The 

U.S. Geological Survey (USGS) provides daily mean streamflow information at many streamgage locations in Iowa and 

surrounding states (fig. 1). Commonly, however, daily mean 

streamflow data are needed at locations where no streamgages 

are present. Therefore, the USGS conducted a study as part of 

a larger project in cooperation with the Iowa Department of 

Natural Resources to develop methods to estimate daily mean 

streamflow at locations in ungaged watersheds in Iowa by 

using two regression-based statistical methods. Two statistical 

methods were used to estimate streamflow: a variation of the 

drainage-area-ratio method (Flow Anywhere method) and a 

quantile-based regression model referred to here as the Flow 

Duration Curve Transfer method. 

The drainage-area-ratio method is a commonly used 

technique for computing flow in ungaged watersheds. In this 

method, same-day streamflow information is transferred from 

a reference streamgage to another location on the basis of the 

ratio of the drainage areas of the two locations (Asquith and 

others, 2006). The drainage-area-ratio equation (Emerson and 

others, 2006) is 

Q A

A u Qu

r

= r , (1)

where

Qu is the streamflow at the ungaged location,

Au is the drainage area at the ungaged location,

Ar is the drainage area at the reference 

streamgage, and

Qr is the streamflow at the reference streamgage.

In the Flow Anywhere method, the drainage-area-ratio 

method is modified in order to regionalize the equation for 

Iowa and determine the most appropriate reference streamgage 

to use for the transfer of same-day streamflow information from that reference streamgage to an ungaged location. 

First, the correlation of historical streamflow data between 

streamgages in the study area is examined to determine local 

region boundaries. A local region is an area in which the 

streamflows measured at all the streamgages are highly correlated. Within each local region, an appropriate reference 

streamgage is selected that most closely represents historical 

streamflow in the local region. Local regions are sized so that 

any storm system that passes through the region is likely to 

affect the entire area equally, as confirmed by the high correlation exhibited between streamflows measured at streamgages 

in a local area. In addition, the local regions are defined so that 

the basins within the regions are physiographically similar. 

After establishment of local regions, regression techniques are 

used to identify local regions that exhibit similar hydrologic 

properties and, therefore, can be aggregated for analysis. Historical streamflow data from each aggregated region are then 

used to develop regression equations that modify the drainagearea ratio equation as follows:

Q C A

A u Q u

r

= r





 





β

γ , (2)

where

C is the intercept (which is a constant),

β is the drainage-area-ratio exponent, and

γ is the reference streamgage exponent.

The regression intercept and exponents in equation 2 

were used to calibrate equation 1 for Iowa. The drainage-arearatio exponent has the effect of adjusting the predicted 

streamflow hydrograph higher or lower by means of the 

drainage-area ratio. The exponent for streamflow at the reference streamgage has the effect of increasing or decreasing the 

variability of streamflows at the reference streamgage for the 

predicted streamflow hydrograph.

The Flow Duration Curve Transfer method, a quantileand parameter-based regression model, was used to estimate 

unregulated daily mean streamflow statistics from the physical and climatic characteristics of gaged basins. This method 

was initially introduced by Fennessey (1994) and also was 
Trend Analysis 3

published by Hughes and Smakhtin (1996), Smakhtin (1999), 

Smakhtin and Masse (2000), Mahamoud (2008), and Archfield 

and others (2009). With use of the regression model together 

with streamflows at a reference streamgage, estimates of 

unregulated, daily mean streamflow time series at ungaged 

sites can be made. For the Flow Duration Curve Transfer 

method, daily mean streamflow quantiles at the ungaged 

site are estimated by using the parameter-based regression 

model, resulting in a continuous daily flow-duration curve 

(the relation between exceedance probability and streamflow 

for each day of observed streamflow) at the ungaged site. By 

the use of a reference streamgage, the flow-duration curve 

is converted to a time series. As explained in Waldron and 

Archfield (2006), the observed time series of streamflow at the 

reference gage (Q) (fig. 2A) is used to develop a flow-duration 

curve (fig. 2B), which represents the probability of exceedance (P) for each streamflow value in the record. The assumption is then made that the probability of exceeding a flow at 

the reference streamgage is equivalent to the probability of 

exceeding a flow at the ungaged site (P) (fig. 2C). Then, by 

equating the exceedance probabilities at the ungaged site and 

the reference streamgage, the dates of streamflow associated 

with each exceedance probability at the reference streamgage 

are transferred to the ungaged site to construct a time series of 

streamflow at the ungaged site (Q) (fig. 2D). 

The methods developed in this study can be compared 

with other methods for estimating streamflows at ungaged 

locations to determine the best method for use in Iowa. In 

addition, the results of this study can be used to produce 

a Web-based Geographic Information System (GIS) tool, 

similar to the USGS Streamstats interface (Ries and others, 

2009), to compute streamflow at ungaged locations in Iowa 

automatically.

Purpose and Scope

Regression equations developed for estimating daily 

mean streamflow at ungaged locations in Iowa by using the 

Flow Anywhere and Flow Duration Curve Transfer methods 

are described. The period of record from which the regression 

equations were developed is based on a trend analysis that is 

discussed in the report. Methods for selecting the streamgages 

to be used in developing the regression equations are presented. The types of regression analysis used, along with the 

accuracies and limitations of both methods, also are included. 

Description of Study Area

The regression equations for estimating mean daily 

streamflow in ungaged watersheds with the Flow Anywhere 

and Flow Duration Curve Transfer methods were developed 

for use only in Iowa. The equations were developed from 

recorded daily mean streamflow and basin characteristics for 

streamgages within the study area (fig. 1), which includes the 

entire State of Iowa and adjacent areas within a 50-mile (mi) 

buffer of Iowa in the neighboring States of Illinois, Minnesota, 

Missouri, Nebraska, and Wisconsin. No streamgages within 

the buffer area in South Dakota were used because of either 

upstream diversions or regulation. There are 10 landform 

regions in Iowa with distinct characteristics (Prior, 1991; Prior 

and others, 2009) and are used to help develop regions for the 

Flow Anywhere method. 

Previous Studies

 Studies have been completed to compute streamflow 

at ungaged locations outside Iowa by using variations of the 

drainage-area-ratio method. Asquith and others (2006) evaluate the effects of computing the drainage-area-ratio exponent 

for selected streams in Texas and describe similar, previously 

published studies. Sanders (2002) uses similar referencestreamgage selection techniques to compare hydrographs of 

observed streamflows. Archfield and others (2009) evaluate 

the Flow Duration Curve Transfer method for use in an interactive decision-support tool referred to as the Massachusetts 

Sustainable-Yield Estimator (MA SYE). Esralew and Smith 

(2010) use the Flow Duration method for estimating flowduration and annual mean-flow statistics for ungaged streams 

in Oklahoma. Risley and others (2008) estimate flow-duration 

and low-flow-frequency statistics for unregulated stream in 

Oregon to provide decision makers with surface-water information needed for activities such as water-quality regulation, 

water-rights adjudication, biological habitat assessment, infrastructure design, water-supply planning, and management. 

Trend Analysis

Stationarity is assumed in both the Flow Anywhere and 

Flow Duration Curve Transfer methods; therefore, a trend 

analysis was conducted to determine whether this assumption 

was met. Trend analyses were performed for the 90-percent, 

50-percent, and 10-percent exceedance probabilities by using 

annual mean streamflow (mean of daily mean streamflows for 

each water year; a water year is the 12-month period October 1 through September 30 designated by the year in which 

it ends). Prior to the final selection of the streamgages used 

in the Flow Anywhere and Flow Duration Curve Transfer 

methods, 102 streamgages in Iowa with periods of record 

greater than 10 years were tested by using Kendall’s tau

hypothesis test. Positive trends were found in the annual mean 

streamflow quantiles at the 90-percent exceedance probability statistic for 61 of those streamgages. Trends in these data 

could introduce a bias into the Flow Duration Curve Transfer 

analyses, violating the assumption that flow-duration statistics 

are independent and stationary over time. Positive trends were 

found for the annual 90-percent streamflow quantiles at 3 of 

those 61 streamgages (fig. 3): 05412500, Turkey River at Garber, Iowa, (fig. 1, map no. 13, and table 1); 05452200, Walnut 

Creek near Hartwick, Iowa (fig. 1, map no. 32, and table 1); 
98° 96° 94° 92° 90° 

44° 42° 40° 9 3 2 1 8 6 5 91 90 87 8653 51 2

99 9897 96 95 94 93 92 89 88 85 84 83 81 80 77 76 7574 73 72 71 70 6968 66 65 63 62 61 59 57 55 54 52 50 49 47 45 42 40 39 37 34 32 29 27 26 23 22 21 20 19 18 16 15 14 13 10 114 108 105 123 121 120 119 118117 115 113 112 111 110 109 103 100 7 4 82 79 78 67 64 60 58 56 48 464443 41 3836 35 33 31 30 28 17 12 11 107 106 104 122 116 102 101 25 IOWA 

MISSOURI MINNESOTA NEBRASKA 

SOUTH DAKOTA KANSAS

Base from U.S. Geological Survey digital data, 2005, 1:24,000Universal Transverse Mercator projection, Zone 15

EXPLANAT

Study area boundary

Streamgage considered for us

Flow Duration Curve Trans

86

Streamgage considered for us

method and map number

52

0 50 100 MILES0 50 100 KILOMETERS

Figure 1. Locations of U.S. Geological Survey streamgages in Iowa considered for development of the Flow Anywhere and Flow Duration Curve Transfer methods (streamgages are listed and identified by map number in table 1).
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration Curv[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; WMissouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method]

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS 

drainage 

area 

(mi2)

Published 

drainage 

area1

(mi2)

Entire period of record

Number 

of years of 

record used

Latitude, N

(decimal de

1 05319500 Watonwan River near Garden City, MN 873 851 03/01/1940–09/30/1945, 

09/01/1976–09/30/2009

32 44.046

2 05320500 Le Sueur River near Rapidan, MN 1,128 1,110 10/01/1939–09/30/1945,

08/01/1949–09/30/2009

32 44.111

3 05383950 Root River near Pilot Mound, MN2 565 565 08/09/2002–09/30/2009 7 43.7844 05387440 Upper Iowa River at Bluffton, IA2 367 367 10/01/2002–09/30/2009 7 43.4065 05387500 Upper Iowa River at Decorah, IA 511 511 10/01/1951–11/01/1983,

10/01/2002–09/30/2009

13 43.304

6 05388250 Upper Iowa River near Dorchester, IA 768 770 10/01/1938–09/30/1939, 

07/01/1975–09/30/2009

32 43.421

7 05389000 Yellow River at Ion, IA2 219 221 10/01/1934–09/30/1951, 

09/21/2004–09/30/2009

5 43.111

8 05389400 Bloody Run Creek near Marquette, IA 34.3 34.1 10/01/1991–09/30/2009 18 43.0409 05410490 Kickapoo River at Steuben, WI 700 687 05/23/1933–09/30/2009 32 43.182

10 05411850 Turkey River near Eldorado, IA2 642 641 09/28/2000–09/30/2009 9 43.054

11 05412020 Turkey River above French Hollow 

Creek at Elkader, IA2

905 903 09/06/2001–09/30/2009 8 42.843

12 05412400 Volga River at Littleport, IA 350 348 09/16/1999–09/30/2009 10 42.75313 05412500 Turkey River at Garber, IA 1,553 1,545 08/08/1913–11/30/1916, 

05/14/1919–09/30/1927, 04/24/1929–09/30/1930, 10/01/1932–09/30/2009

32 42.740

14 05413500 Grant River at Burton, WI 269 269 10/01/1934–09/30/2009 32 42.72015 05414820 Sinsinawa River near Menominee, IL 40.0 39.6 10/01/1967–09/30/2009 32 42.47816 05416900 Maquoketa River at Manchester, IA2 279 275 04/26/2000–12/16/2002, 

06/23/2003–09/30/2009

7 42.470

17 05418400 North Fork Maquoketa River near 

Fulton, IA

503 505 10/01/1998–09/30/2009 11 42.164

18 05418500 Maquoketa River near Maquoketa, IA 1,551 1,553 09/01/1913–09/30/2009 32 42.08319 05419000 Apple River near Hanover, IL 247 247 10/01/1934–09/30/2009 32 42.25220 05421000 Wapsipinicon River at Independence, IA 1,053 1,048 07/01/1933–09/30/2009 32 42.463
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration CurvContinued [no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; W

Missouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method] Map no. USGS streamgage number Streamgage name GIS drainage area (mi2) Published drainage area1 (mi2) Entire period of record Number of years of record used Latitude, N

(decimal de

21 05421740 Wapsipinicon River near Anamosa, IA2 1,581 1,575 07/10/2002–09/30/2009 7 42.083

22 05422000 Wapsipinicon River near De Witt, IA 2,336 2,336 07/27/1934–09/30/2009 32 41.767

23 05422560 Duck Creek at 110th Ave at Davenport, IA 15.5 16.1 03/29/1994–09/30/2009 15 41.556

24 05435500 Pecatonica River at Freeport, IL 1,337 1,326 09/11/1914–09/30/2009 32 42.302

25 05444000 Elkhorn Creek near Penrose, IL 147 146 10/01/1939–9/30/2009 32 41.902

26 05449500 Iowa River near Rowan, IA 427 418 10/01/1940–09/30/2009 32 42.759

27 05451210 South Fork Iowa River northeast of New Providence, IA 224 224 10/25/1995–09/30/2009 13 42.315

28 05451500 Iowa River at Marshalltown, IA 1,534 1,532 10/01/1902–09/30/1903, 10/01/1914–09/30/1927, 10/01/1932–09/30/2009 32 42.065

29 05451700 Timber Creek near Marshalltown, IA 120 118 10/01/1949–09/30/2009 32 42.008

30 05451900 Richland Creek near Haven, IA 56.1 56.1 10/01/1949–09/30/2009 32 41.899

31 05452000 Salt Creek near Elberon, IA 199 201 10/01/1945–9/30/2009 32 41.964

32 05452200 Walnut Creek near Hartwick, IA 70.5 70.9 10/01/1949–09/30/2009 32 41.835

33 05453000 Big Bear Creek at Ladora, IA 187 189 10/01/1945–09/30/2009 32 41.749

34 05453100 Iowa River at Marengo, IA 2,793 2,794 10/01/1956–09/30/2009 32 41.812

35 05454000 Rapid Creek near Iowa City, IA 25.3 25.3 10/01/1937–09/30/2009 32 41.700

36 05454220 Clear Creek near Oxford, IA 60.8 58.4 11/04/1993–09/30/2009 15 41.718

37 05454300 Clear Creek near Coralville, IA 98.1 98.1 10/01/1952–09/30/2009 32 41.676

38 05455100 Old Mans Creek near Iowa City, IA 201 201 10/01/1950–09/30/1964, 10/01/1984–09/30/2009 25 41.606

39 05455500 English River at Kalona, IA 574 574 09/13/1939–09/30/2009 32 41.469

40 05457000 Cedar River near Austin, MN 398 399 06/01/1909–09/30/1914, 

10/01/1944–09/30/2009

32 43.637

41 05457700 Cedar River at Charles City, IA 1,075 1,054 10/01/1964–09/30/1995, 

10/01/2000–09/30/2009

27 43.062

42 05458000 Little Cedar River near Ionia, IA 295 306 10/01/1954–09/30/2009 32 43.033
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration CurvContinued[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; W

Missouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method]

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS 

drainage 

area 

(mi2)

Published 

drainage 

area1

(mi2)

Entire period of record

Number 

of years of 

record used

Latitude, N

(decimal de

43 05458500 Cedar River at Janesville, IA 1,671 1,661 10/01/1904–09/30/1906, 

10/01/1914–09/30/1927, 10/01/1932–09/30/1942, 10/01/1945–09/30/2009

32 42.648

44 05458900 West Fork Cedar River at Finchford, IA 851 846 10/01/1945–09/30/2009 32 42.629

45 05459500 Winnebago River at Mason City, IA 517 526 10/01/1932–09/30/2009 32 43.165

46 05462000 Shell Rock River at Shell Rock, IA 1,731 1,746 06/11/1953–09/30/2009 32 42.711

47 05463000 Beaver Creek at New Hartford, IA 351 347 10/01/1945–09/30/2009 32 42.572

48 05463500 Black Hawk Creek at Hudson IA 298 303 04/01/1952–09/30/1995, 

09/07/2001–09/30/2009

26 42.407

49 05464000 Cedar River at Waterloo, IA 5,149 5,146 10/1/1940–9/30/2009 32 42.495

50 05464220 Wolf Creek near Dysart, IA 298 299 10/24/1995–09/30/1998, 

05/16/2001–09/30/2009

10 42.251

51 05464500 Cedar River at Cedar Rapids, IA 6,506 6,510 10/1/1902–9/30/2009 32 41.971

52 05464942 Hoover Creek at Hoover Nat Hist Site, 

West Branch, IA2

2.60 2.58 04/27/2000–09/30/2009 9 41.669

53 05465000 Cedar River near Conesville, IA 7,783 7,787 09/16/1939–09/30/2009 32 41.409

54 05466000 Edwards River near Orion, IL 156 155 10/01/1940–09/30/2009 32 41.272

55 05466500 Edwards River near New Boston, IL 442 445 10/01/1934–09/30/2009 32 41.187

56 05467000 Pope Creek near Keithsburg, IL 172 174 10/01/1934–09/30/1986, 

03/01/1987–09/30/1987, 03/01/1988–09/30/1988, 03/01/1989–09/30/1989, 03/01/1990–09/30/1996, 10/01/1997–09/30/2009

27 41.128

57 05469000 Henderson Creek near Oquawka, IL 436 432 10/01/1934–09/30/1996, 

10/01/1997–09/30/2009

31 41.001

58 05470000 South Skunk River near Ames, IA 317 315 07/28/1920–09/30/1927, 

10/01/1932–10/03/1995, 09/28/1996–09/30/2009

30 42.066

59 05470500 Squaw Creek at Ames, IA 210 204 05/24/1919–09/30/1927, 

05/24/1965–09/30/2009

32 42.023
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration CurvContinued [no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; W

Missouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method] Map no. USGS streamgage number Streamgage name GIS drainage area (mi2) Published drainage area1 (mi2) Entire period of record Number of years of record used Latitude, N

(decimal de

60 05471050 South Skunk River at Colfax, IA 806 803 10/01/1985–09/30/2009 24 41.681

61 05471200 Indian Creek near Mingo, IA 277 276 05/22/1958–09/30/1975, 10/01/1985–09/30/2009 24 41.805

62 05471500 South Skunk River near Oskaloosa, IA 1,640 1,635 10/01/1945–09/30/2009 32 41.355

63 05472500 North Skunk River near Sigourney, IA 734 730 10/01/1945–09/30/2009 32 41.300

64 05473400 Cedar Creek near Oakland Mills, IA 533 533 07/01/1977–09/30/2009 32 40.925

65 05473450 Big Creek north of Mount Pleasant, IA 60.9 58.0 10/01/1997–09/30/2009 12 41.007

66 05474000 Skunk River at Augusta, IA 4,310 4,312 09/30/1913–11/15/1913, 10/01/1914–09/30/2009 32 40.753

67 05476750 Des Moines River at Humboldt, IA 2,270 2,256 10/01/1964–09/30/2009 32 42.719

68 05479000 East Fork Des Moines River at Dakota City, IA 1,306 1,308 03/01/1940–09/30/2009 32 42.723

69 05480500 Des Moines River at Fort Dodge, IA 4,202 4,190 04/23/1905–07/19/1906, 10/01/1913–09/30/1927, 10/01/1946–09/30/2009 32 42.508

70 05481000 Boone River near Webster City, IA 846 844 03/09/1940–09/30/2009 32 42.432

71 05481300 Des Moines River near Stratford, IA 5,464 5,452 10/01/1967–09/30/2009 32 42.251

72 05481950 Beaver Creek near Grimes, IA 370 358 04/20/1960–09/30/2009 32 41.688

73 05482300 North Raccoon River near Sac City, IA 697 700 06/01/1958–09/30/2009 32 42.354

74 05482500 North Raccoon River near Jefferson, IA 1,609 1,619 03/01/1940–09/30/2009 32 41.988

75 05483450 Middle Raccoon River near Bayard, IA 382 375 03/23/1979–09/30/2009 30 41.778

76 05484000 South Raccoon River at Redfield, IA 987 994 03/04/1940–09/30/2009 32 41.589

77 05484500 Raccoon River at Van Meter, IA 3,425 3,441 04/25/1915–09/30/2009 32 41.533

78 05486000 North River near Norwalk, IA 349 349 02/28/1940–09/30/2009 32 41.457

79 05486490 Middle River near Indianola, IA 489 503 03/01/1940–09/30/2009 32 41.424

80 05487470 South River near Ackworth, IA 458 460 03/01/1940–09/30/2009 32 41.337

81 05487980 White Breast Creek near Dallas, IA 340 342 10/01/1962–09/30/2009 32 41.246

82 05488200 English Creek near Knoxville, IA 90.7 90.1 07/01/1985–09/30/2009 24 41.300

83 05489000 Cedar Creek near Bussey, IA 372 374 10/01/1947–09/30/2009 32 41.219
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration CurvContinued[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; W

Missouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method]

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS 

drainage 

area 

(mi2)

Published 

drainage 

area1

(mi2)

Entire period of record

Number 

of years of 

record used

Latitude, N

(decimal de

84 05494300 Fox River at Bloomfield, IA 87.3 87.7 10/01/1957–10/02/1973, 

05/27/1997–09/30/2009

12 40.769

85 05495000 Fox River at Wayland, MO 396 400 03/01/1922–09/30/2009 32 40.392

86 05495500 Bear Creek near Marcelline, IL 349 349 03/01/1944–09/30/2009 32 40.142

87 05496000 Wyaconda River above Canton, MO 398 393 10/01/1932–

09/30/1972,10/01/1979–09/30/2009

30 40.142

88 05568800 Indian Creek near Wyoming, IL 63.2 62.7 10/01/1959–09/30/2009 32 41.018

89 05570000 Spoon River at Seville, IL 1,638 1,636 07/24/1914–09/30/2009 32 40.490

90 05584500 La Moine River at Colmar, IL 663 655 10/01/1944–09/30/2009 32 40.330

91 05585000 La Moine River at Ripley, IL 1,312 1,293 03/12/1921–09/30/2009 32 40.024

92 06483290 Rock River below Tom Creek at Rock 

Rapids, IA2

851 853 05/01/2001–09/30/2009 8 43.423

93 06483500 Rock River near Rock Valley, IA 1,584 1,592 06/11/1948–09/30/2009 32 43.214

94 06600100 Floyd River at Alton, IA 267 268 10/01/1955–09/30/2009 32 42.981

95 06600500 Floyd River at James, IA 886 886 12/08/1934–09/30/2009 32 42.576

96 06602400 Monona-Harrison Ditch near Turin, IA 929 900 05/07/1942–09/30/2009 32 41.964

97 06605000 Ocheyedan River near Spencer, IA 440 426 10/01/1977–09/30/2009 32 43.128

98 06605850 Little Sioux River at Linn Grove, IA 1,567 1,548 10/01/1972–09/30/2009 32 42.895

99 06606600 Little Sioux River at Correctionville, IA 2,520 2,500 05/28/1918–09/30/2009 32 42.482

100 06607200 Maple River at Mapleton, IA 670 669 10/01/1941–09/30/2009 32 42.156

101 06607500 Little Sioux River near Turin, IA 3,553 3,526 10/01/1977–09/30/2009 32 41.964

102 06608500 Soldier River at Pisgah, IA 409 407 03/05/1940–09/30/2009 32 41.830

103 06609500 Boyer River at Logan, IA 870 871 05/24/1918–11/30/1924, 

02/01/1925–07/01/1925, 11/04/1937–09/30/2009

32 41.642

104 06803510 Little Salt Creek near Lincoln, NE 43.1 43.6 10/01/1969–09/30/2009 32 40.893

105 06803520 Stevens Creek near Lincoln, NE2 50.0 47.8 10/01/1968–09/30/2009 32 40.856

106 06803530 Rock Creek near Ceresco, NE 120 120 04/01/1970–09/30/2009 32 41.015

107 06804000 Wahoo Creek at Ithaca, NE 272 273 10/01/1949–09/30/2009 32 41.147
Table 1. Description of streamgages used to estimate streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration CurvContinued [no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; NAD 83, North American Datum of 1983; MN, Minnesota; IA, Iowa; W

Missouri; NE, Nebraska; shaded rows, streamgages used in the Flow Anywhere method but not used in the Flow Duration Curve Transfer method] Map no. USGS streamgage number Streamgage name GIS drainage area (mi2) Published drainage area1 (mi2) Entire period of record Number of years of record used Latitude, N

(decimal de

108 06804900 Johnson Creek near Memphis, NE 23.4 21.5 08/28/1990–09/30/2009 19 41.146

109 06807410 West Nishnabotna River at Hancock, IA 611 609 10/02/1959–09/30/2009 32 41.390

110 06808500 West Nishnabotna River at Randolph, IA 1,329 1,326 06/01/1948–09/30/2009 32 40.873

111 06809210 East Nishnabotna River near Atlantic, IA 440 436 10/01/1960–09/30/2009 32 41.346

112 06809500 East Nishnabotna River at Red Oak, IA 895 894 05/22/1918–11/30/1924, 02/08/1925–07/04/1925, 05/29/1936–09/30/2009 32 41.008

113 06810000 Nishnabotna River above Hamburg, IA 2,809 2,806 03/01/1922–09/30/1923, 10/01/1928–09/30/2009 32 40.601

114 06811500 Little Nemaha River at Auburn, NE 793 792 09/01/1949–09/30/2009 32 40.392

115 06817000 Nodaway River at Clarinda, IA 761 762 05/17/1918–07/04/1925, 05/14/1936–09/30/2009 32 40.743

116 06817700 Nodaway River near Graham, MO 1,516 1,380 10/22/1982–09/30/2009 27 40.202

117 06819185 East Fork 102 River at Bedford, IA 85.8 85.4 10/01/1983–09/30/2009 27 40.660

118 06819500 102 River at Maryville, MO 491 500 10/01/1932–12/31/1990, 03/22/2001–09/30/2009 21 40.345

119 06897000 East Fork Big Creek near Bethany, MO 90.8 95.0 04/01/1934–09/30/1972, 10/01/1996–09/30/1999, 10/01/2000–9/30/2009 12 40.297

120 06897500 Grand River near Gallatin, MO 2,246 2,250 10/01/1920–09/30/2009 32 39.927

121 06898000 Thompson River at Davis City, IA 695 701 05/14/1918–07/02/1925, 07/14/1941–09/30/2009 32 40.640

122 06903400 Chariton River near Chariton, IA 186 182 10/01/1965–09/30/2009 32 40.951

123 06903700 South Fork Chariton River near Promise City, IA 170 168 10/01/1967–09/30/2009 32 40.800

1Published in National Water Information System (NWIS).2Data from this streamgage were used in the Flow Anywhere method but not in the Flow Duration Curve Transfer method.
Trend Analysis 11

Figure 2. Translation of a flow-duration curve to a time series of estimated streamflow by using the Flow Duration Curve Transfer 

method showing (A) the observed time series, (B) flow-duration curve, (C) exceedance probability, and (D) estimated time series at 

the ungaged site (from Archfield, 2009).

Time

Flow-duration curve

estimated by the

parameter-based

regression method 

at the ungaged site

D

Exceedence probability

Gaged streamflows Ungaged streamflows

Flow-duration curve 

at the reference 

streamflow-gaging 

station

A B

C

Streamflow

quantile for

gaged site

Estimated

streamflow

quantile for

ungaged site

and 06483500, Rock River near Rock Valley, Iowa (fig. 1, 

map no. 93, and table 1). Positive trends also were seen in the 

data from 2 of the 34 out-of-state streamgages tested. Tests for 

trends also were completed for the 50-percent and 10-percent 

exceedance probabilities; however, the number of streamgages 

that showed trends in streamflow decreased with decreasing 

percent exceedances (higher streamflows). At the 90-percent 

exceedance probability, one streamgage in Iowa had a negative 

trend in streamflow and no out-of-state streamgages had negative trends in streamflow. Testing for Kendall’s tau hypothesis 

test was done with the SWSTAT statistical program (Lumb 

and others, 1990). A P-value threshold of 5 percent (α=0.05) 

was used for this method and values less than or equal to 

5 percent were flagged as having statistically significant trends 

(positive or negative). 

Possible reasons for the trends in low-flow statistics 

have been examined in several previous studies. Positive 

trends in low-flow statistics were found at 133 of the 208 

Iowa and out-of-state streamgages tested for a low-flow study 

(Eash and Barnes, 2012). For some areas of the state and for 

some periods of record, trends in precipitation were found to 

be statistically significant but the precipitation data did not 

appear to fully explain low-flow trends (Eash and Barnes, 

2012). Changes in agricultural practices are thought to be the 

main cause of positive low-flow trends in Iowa (Shilling and 

Libra, 2003: Shilling, 2005). For the mean annual streamflow 

90-percent exceedance probability statistic, 1978 was found 

to be the latest date beyond which no data exhibit a trend as 

determined by using the trend analysis test.
12 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Figure 3. The 90-percent exceedance probability of daily mean streamflow by water year for U.S. Geological Survey streamgages 

(A) 05412500, Turkey River at Garber, Iowa; (B) 05452200, Walnut Creek near Hartwick, Iowa; and (C) 06483500, Rock River near Rock 

Valley, Iowa.

1940 1950 1960 1970 1980 1990 2000 2010

0

100

200

300

50

150

250

Trend line

1950 1960 1970 1980 1990 2000 2010

0

10

20

30

5

15

25

Trend line

1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

0

200

400

600

100

300

500

700

Streamflow, in cubic feet per second Streamflow, in cubic feet per second Streamflow, in cubic feet per second

A 05412500, Turkey River at Garber, Iowa

P = 0.001

Kendall’s tau = 0.247

Trend line

B 05452200, Walnut Creek near Hartwick, Iowa

P = 0.000

Kendall’s tau = 0.333

C 06483500, Rock River near Rock Valley, Iowa

P = 0.000

Kendall’s tau = 0.432

Year

Year

Year
Flow Anywhere Method Analytical Procedures 13

Flow Anywhere Method Analytical 

Procedures

Data used in the Flow Anywhere method were retrieved 

for 123 continuous-record streamgages located in Iowa and 

within a 50-mi buffer of Iowa in the neighboring States of 

Illinois, Minnesota, Missouri, Nebraska, and Wisconsin (fig. 1, 

table 1). A continuous-record streamgage is a gage at which 

stage is recorded continuously; streamflow is then computed 

from the stage data (Nalley and others, 2002). Streamgages 

with at least 5 complete years of daily mean streamflow 

through the 2009 water year (October 1, 2004, to September 30, 2009) and that are minimally affected by regulation or 

diversion were initially selected for evaluation in the study; 

these included 92 streamgages in Iowa and 31 streamgages in 

adjacent states. A period of record encompassing 5 complete 

years of data was used so that the number of streamgages 

in the local regions was adequate to perform the analysis. 

Because 10 complete years of daily mean streamflow data 

were used in the Flow Duration Curve Transfer method, the 

set of streamgages used was slightly different than the set 

used in the Flow Anywhere method. In another flow-duration 

study (Risley and others, 2008), a period of 10 complete years 

of record also was used because estimates of the extremes of 

the daily mean flows are more accurate the longer the period 

of record used. Streamgages in adjacent states were included 

in the study to improve the representation of streamflow 

characteristics near the Iowa border and improve the results 

of the regression analysis for locations near the state border. 

Daily mean streamflow values prior to the beginning of the 

1978 water year (October 1, 1977) were not used in the final 

analyses because trends were found in the entire record for 

some streamgages. As noted in the Trend Analysis section, 

this is the latest date beyond which no data exhibit a trend 

as determined by using the trend-analysis test. Daily mean 

streamflow data for the 123 streamgages were retrieved from 

the USGS National Water Information System (NWIS) database (U.S. Geological Survey, 2011). The drainage areas of the 

123 streamgages were measured by using a GIS. The drainage areas were measured by following procedures used by 

Eash and Barnes (2012). Drainage-area values from the GIS 

were compared to the published values in the NWIS database 

(table 1). The GIS drainage-area value is used in this study to 

develop the regression equations in order to remain consistent with the measurement techniques that would be used in a 

Web-based tool.

Identification of Local Regions

Areas of highly correlated streamflows are determined as 

part of the Flow Anywhere method. The Pearson’s r correlation value of 0.866 was used to represent high correlation, 

as this value results in a concentrated area of correlation for 

most areas of the study area. The areas, referred to as local 

regions, contain streamgages at which streamflows historically 

are highly correlated to streamflows at other streamgages in 

the local region. Local regions are used to limit the selection 

area for reference streamgages to areas of similar streamflow characteristics. The correlation of streamflows between 

streamgages was quantified by using the Pearson’s r correlation coefficient (Helsel and Hirsch, 2002), and is determined 

as 

r

n

x y x y

i

n

i

sx

i

sy

= −

 −



 





 −













 =

∑ 1

1 1 ( ) , (3)

where

r is the Pearson’s r correlation coefficient,

n is the number of pairs of observations,

xi is the ith value of the x parameter,

x is the mean value of the x parameter,

y is the mean value of the y parameter,

yi is the ith value of the y parameter,

sx is the standard deviation of the x parameter, 

 and

sy is the standard deviation of the y parameter.

The computation for the Pearson’s r correlation coefficient requires that the number of observations between the two 

datasets being compared be the same. Because record lengths 

vary between streamgages, the number of observations used 

when comparing two streamgages was limited by the shorter 

record length of the two streamgages being compared. For 

example, when the Pearson’s r correlation coefficient between 

streamgages 05388250, Upper Iowa River near Dorchester, 

Iowa (fig. 1, map no. 6, and table 1), and 05411850, Turkey 

River near Eldorado, Iowa (fig. 1, map no. 10, table 1), was 

computed, 9 years of observations were used because station 

05411850, Turkey River near Eldorado, Iowa, has the shorter 

of the two record lengths at 9 years. 

An absolute value of the Pearson’s r correlation coefficient equal to 1.0 represents a perfect correlation between two 

streamgages and 0.0 represents no correlation. The Pearson’s r

correlation coefficient was computed for the relation between 

the logarithm (base 10) of the streamflow at each streamgage 

and every other streamgage in the study area. The use of the 

logarithm (base 10) streamflow value creates a more constant variance among the data (Helsel and Hirsch, 2002). The 

results were examined geographically by developing a map for 

each streamgage showing its Pearson’s r correlation value with 

every other streamgage in the study area (figs. 4A, 4B, and 4C

show results for three selected gages). Streamgages with high 

correlation—Pearson’s r correlation values greater than or 

equal to 0.800—are shown as green, blue, or red symbols. A 

polygon that follows the basin boundaries of the most highly 

correlated streamgages—those with a Pearson’s r correlation value greater than 0.866—was drawn on each correlation map for the study area. These polygons showed common 
14 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

areas of high correlation throughout the study area. These 

common areas were determined to be local regions of high 

correlation where streamflow data historically are generally 

closely related to those at other locations. In some instances, a 

streamgage did not have a Pearson’s r correlation coefficient 

of 0.87 or higher with respect to any other streamgage in 

the study area. In such instances, the streamgage was placed 

in the same local region as nearby streamgages. Final local 

region boundaries were determined by using Iowa landform 

regions (Prior, 1991; Prior and others, 2009) and the 12-digit 

hydrologic-unit-code boundaries as a guide (figs. 5 and 6). 

Streamflow data from some streamgages in the neighboring 

states were found to be poorly correlated to those from any 

streamgages in Iowa. These streamgages were removed from 

the study with the assumption that they likely lie in a local 

region not characteristic of Iowa, and therefore are not relevant to this study (table 2). This process left 107 streamgages 

for the development of the Flow Anywhere method. Each 

remaining streamgage used in the study was classified for 

inclusion in a specific local region (table 3). 

Regression Methods

Regression techniques are used in the Flow Anywhere 

method to determine the reference streamgage in each local 

region and also to group together local regions that have 

similar hydrologic properties. Regression methods also are 

used to develop final regional regression equations to compute 

streamflows at ungaged locations. Logarithmic (base 10) transformations of streamflows and drainage areas were performed. 

The transformations were used to achieve homoscedacity of 

the residuals about the regression line between variables and 

to linearize the relations (Eash, 2001). The statistical software 

package R was used for computations and to develop regression equations (R Development Core Team, 2010). Ordinaryleast-squares and left-censored regression techniques were 

used. Weighting methods, such as a weighted-least-squares 

(WLS) analysis, were not applied in this study. Even though 

the streamgages in the study area have records of varying 

lengths, the quality of individual daily mean streamflow values 

does not depend on the length of record at a streamgage.

Determination of Reference Streamgages

The Flow Anywhere method relies on the selection of 

an appropriate continuous-record streamgage from which to 

transfer streamflow characteristics to the ungaged location. 

Within each local region, a reference streamgage is selected 

that is determined to best represent streamflows for that area. 

The reference streamgage for each local region was selected 

by comparing hydrographs and results of ordinary-leastsquares regressions. An ordinary-least-squares regression 

analysis was completed for each streamgage in a local region 

by using it as a potential reference streamgage, a process similar to that described by equation 2. The independent variables, 

also known as the explanatory variables, were the daily mean 

streamflows at the candidate reference streamgage and the 

drainage-area ratio between the nonreference streamgage and 

the candidate reference streamgage. The dependent variable, 

also known as the response variable, was the same-day streamflow at the nonreference streamgage in the local region. This 

process was repeated for each streamgage in the local region 

by using it as a candidate reference streamgage. The candidate 

reference streamgage that resulted in the regression equation having the highest coefficient of determination (R2

) was 

selected as the reference streamgage for that local region. R2

is a measure of the percent of the variation in the response (y) 

variable that is accounted for by the variation in the explanatory variables (Helsel and Hirsch, 2002). Additional visual 

analysis of observed and estimated hydrographs for goodness 

of fit was used to verify the selection of the appropriate reference streamgage. This analysis was completed for all of the 

local regions to determine a unique reference streamgage for 

each region (table 3). The selected reference streamgage in 

each local region was used to relate known streamflow measurements made at a streamgage to an ungaged location within 

the same local region.

Determination of Aggregated Regions

The previously determined local regions contain an insufficient number of streamgages from which to compute reliable 

regional regression equations. The number of streamgages 

in each local region ranges from 3 to 13 (table 3). In order to 

achieve an adequate number of streamgages for regression 

analyses, local regions of similar hydrologic properties were 

grouped together. To develop these groupings, an ordinaryleast-squares regression initially was computed by using all 

the streamgages in the study area except those that had been 

removed as a result of low correlation to other streamgages in 

Iowa, as noted in the section Identification of Local Regions. 

The independent variables of the regression were the streamflow at the reference streamgage and the ratio of the drainage 

area of the nonreference streamgage to that of the associated 

reference streamgage. The dependent variable was the sameday streamflow at the nonreference streamgage, as noted in 

equations 1 and 2. Residual values at each streamgage from 

the preliminary regression analysis were examined geographically to identify spatial trends in the results. Residual values 

indicate the differences between observed streamflows and 

estimated streamflows from the regression equations. Three 

general groupings of residual values from local regions were 

observed: consistently positive, consistently negative, and 

evenly distributed about zero. These groupings were used to 

define three areas of aggregated local regions. An ordinaryleast-squares regression was computed again, as noted above, 

on each aggregated local region to determine whether an 

individual local region demonstrated a consistent residual 

value rather than being distributed about zero. Local regions 

found to have consistent residual values in the positive or 

negative direction were moved to a different aggregated region 
98° 96° 94° 92° 90° 

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Figure 4. Pearson’s r correlations with the logarithm (base 10) of daily streamflows at the U.S. Geological Survey streamgages(A) 05388250, Upper Iowa River near Dorchester, Iowa; (B) 05453000, Big Bear Creek at Ladora, Iowa; and (C) 06605850, Little Sioux River at Linn Grove, Iowa (streamgages are listed and identified by map number in table 1).
98° 96° 94° 92° 90° 

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Figure 4. Pearson’s r correlations with the logarithm (base 10) of daily streamflows at the U.S. Geological Survey streamgages (A) 05388250, Upper Iowa River near Dorchester, Iowa; (B) 05453000, Big Bear Creek at Ladora, Iowa; and (C) 06605850, Little Sioux River at Linn Grove, Iowa (streamgages are listed and identified by map number in table 1).—Continued
98° 96° 94° 92° 90° 

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Figure 4. Pearson’s r correlations with the logarithm (base 10) of daily streamflows at the U.S. Geological Survey streamgages (A) 05388250, Upper Iowa River near Dorchester, Iowa; (B) 05453000, Big Bear Creek at Ladora, Iowa; and (C) 06605850, Little Sioux River at Linn Grove, Iowa (streamgages are listed and identified by map number in table 1).—Continued
J I E A C O K L B H G D M F P

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EXPLANAT

8

0 50 100 MILES0 50 100 KILOMETERS Aggregated Region 1

Aggregated Region 2Aggregated Region 3Letter designation of local region Figure 5. Local and aggregated region boundaries in Iowa for the Flow Anywhere method.
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Landform region data from Prior, Kohrt, and Quade,

Iowa Geological Survey, 2009

Figure 6. Landforms, aggregated region boundaries, and local region boundaries in Iowa (streamgages are listed and identified by map number in table 1).
20 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Table 2. Streamgages removed from the Flow Anywhere regression analyses.

[no., number; USGS, U.S. Geological Survey; MN, Minnesota; WI, Wisconsin; IL, Illinois; IA, Iowa; GIS, Geographic Information System; 

mi2, square miles MO, Missouri, NE, Nebraska]

Map 

no.

USGS 

streamgage 

number

Streamgage name Reason for removal of streamgage from regression 

analyses

1 05319500 Watonwan River near Garden City, MN Located in local region completely outside Iowa border.

2 05320500 Le Sueur River near Rapidan, MN Located in local region completely outside Iowa border.

3 05383950 Root River near Pilot Mound, MN Located in local region completely outside Iowa border.

9 05410490 Kickapoo River at Steuben, WI Located in local region completely outside Iowa border.

24 05435500 Pecatonica River at Freeport, IL Located in local region completely outside Iowa border.

25 05444000 Elkhorn Creek near Penrose, IL Located in local region completely outside Iowa border.

51 05464500 Cedar River at Cedar Rapids, IA GIS drainage area larger than 5,500 mi2.

53 05465000 Cedar River at Conesville, IA GIS drainage area larger than 5,500 mi2.

86 05495500 Bear Creek near Marcelline, IL Located in local region completely outside Iowa border.

87 05496000 Wyaconda River above Canton, MO Located in local region completely outside Iowa border.

90 05584500 La Moine River at Colmar, IL Located in local region completely outside Iowa border.

91 05585000 La Moine River at Ripley, IL Located in local region completely outside Iowa border.

104 06803510 Little Salt Creek near Lincoln, NE Located in local region completely outside Iowa border.

105 06803520 Stevens Creek near Lincoln, NE Located in local region completely outside Iowa border.

106 06803530 Rock Creek near Ceresco, NE Located in local region completely outside Iowa border.

107 06804000 Wahoo Creek at Ithaca, NE Located in local region completely outside Iowa border.

108 06804900 Johnson Creek near Memphis, NE Located in local region completely outside Iowa border.

114 06811500 Little Nemaha River at Auburn, NE Located in local region completely outside Iowa border.

and the ordinary-least-squares regression was recomputed. 

This process was repeated until local regions did not indicate 

an obvious positive or negative residual value and were evenly 

distributed about zero. 

Streamgages with large drainage areas, greater than 

5,500 square miles (mi2), greatly influenced the results for the 

local region to which they were assigned. The drainage basins 

of two streamgages in the study area are larger than 5,500 mi2

(table 2). These streamgages were removed from the study 

and the ordinary-least-squares regression was recomputed. 

Removing the two largest basins restricts the application 

slightly because it is not appropriate to use the method outside 

the range of values of the explanatory variables. The application therefore is restricted to basins smaller than 5,500 mi2

.

The results of the final ordinary-least-squares regression 

determined the association of each local region to one of three 

aggregated regions for the study area (table 3; fig. 5).

Development of Regional Regression Equations

After the aggregated regions were finalized, regional 

regression equations were solved to compute streamflow 

for ungaged locations. As in the preliminary ordinary-leastsquares regression analyses to determine the reference 

streamgages and aggregated regions, the independent variables were the ratio of the drainage area of the nonreference 

streamgages to those of the associated reference streamgages, 

and the streamflow at the reference streamgages. The dependent variable was the same-day streamflow at the nonreference streamgage as in equation 2. Because the records of a 

number of streamgages in the study area include observed 

zero streamflows, two types of regression analyses were performed to develop the final equations for the three aggregated 

regions. Left-censored regression analyses were performed in 

aggregated regions where zero streamflows were observed. 

Ordinary-least-squares regression analyses were used in aggregated regions where zero flows were not observed. 
Flow Anywhere Method Analytical Procedures 21

Table 3. Streamgages used to develop regression equations for the Flow Anywhere method, Iowa.

[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; IA, Iowa; MO, Missouri; IL, Illinois; MN, Minnesota; 

WI, Wisconsin. Locations of aggregated and local regions for the Flow Anywhere method are shown in fig. 5]

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS drainage 

area 

(mi2)

Aggregated 

region Local region Reference streamgage

60 05471050 South Skunk River at Colfax, IA 806 1 A Yes.

27 05451210 South Fork Iowa River northeast of New Providence, IA 224 1 A No.

28 05451500 Iowa River at Marshalltown, IA 1,534 1 A No.

58 05470000 South Skunk River near Ames, IA 317 1 A No.

59 05470500 Squaw Creek at Ames, IA 210 1 A No.

61 05471200 Indian Creek near Mingo, IA 277 1 A No.

62 05471500 South Skunk River near Oskaloosa, IA 1,640 1 A No.

63 05472500 North Skunk River near Sigourney, IA 734 1 A No.

72 05481950 Beaver Creek near Grimes, IA 370 1 A No.

83 05489000 Cedar Creek near Bussey, IA 372 1 G Yes.

80 05487470 South River near Ackworth, IA 458 1 G No.

81 05487980 White Breast Creek near Dallas, IA 340 1 G No.

82 05488200 English Creek near Knoxville, IA 90.7 1 G No.

122 06903400 Chariton River near Chariton, IA 186 1 G No.

123 06903700 South Fork Chariton River near Promise City, IA 170 1 G No.

6 05388250 Upper Iowa River near Dorchester, IA 768 1 H Yes.

4 05387440 Upper Iowa River at Bluffton, IA 367 1 H No.

5 05387500 Upper Iowa River at Decorah, IA 511 1 H No.

7 05389000 Yellow River at Ion, IA 219 1 H No.

8 05389400 Bloody Run Creek near Marquette, IA 34.3 1 H No.

10 05411850 Turkey River near Eldorado, IA 642 1 H No.

11 05412020 Turkey River above French Hollow Creek at Elkader, IA 905 1 H No.

12 05412400 Volga River at Littleport, IA 350 1 H No.

13 05412500 Turkey River at Garber, IA 1,553 1 H No.

85 05495000 Fox River at Wayland, MO 396 1 O Yes.

64 05473400 Cedar Creek near Oakland Mills, IA 533 1 O No.

65 05473450 Big Creek north of Mount Pleasant, IA 60.9 1 O No.

66 05474000 Skunk River at Augusta, IA 4,310 1 O No.

84 05494300 Fox River at Bloomfield, IA 87.3 1 O No.

120 06897500 Grand River near Gallatin, MO 2,246 1 P Yes.

117 06819185 East Fork 102 River at Bedford, IA 85.8 1 P No.

118 06819500 102 River at Maryville, MO 491 1 P No.

119 06897000 East Fork Big Creek near Bethany, MO 90.8 1 P No.

112 06809500 East Nishnabotna River at Red Oak, IA 895 2 B Yes.

109 06807410 West Nishnabotna River at Hancock, IA 611 2 B No.

110 06808500 West Nishnabotna River at Randolph, IA 1,329 2 B No.

111 06809210 East Nishnabotna River near Atlantic, IA 440 2 B No.

113 06810000 Nishnabotna River above Hamburg, IA 2,809 2 B No.

103 06609500 Boyer River at Logan, IA 870 2 C Yes.

75 05483450 Middle Raccoon River near Bayard, IA 382 2 C No.

76 05484000 South Raccoon River at Redfield, IA 987 2 C No.
22 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS drainage 

area 

(mi2)

Aggregated 

region Local region Reference streamgage

96 06602400 Monona-Harrison Ditch near Turin, IA 929 2 C No.

100 06607200 Maple River at Mapleton, IA 670 2 C No.

101 06607500 Little Sioux River near Turin, IA 3,553 2 C No.

102 06608500 Soldier River at Pisgah, IA 409 2 C No.

74 05482500 North Raccoon River near Jefferson, IA 1,609 2 D Yes.

73 05482300 North Raccoon River near Sac City, IA 697 2 D No.

77 05484500 Raccoon River at Van Meter, IA 3,425 2 D No.

33 05453000 Big Bear Creek at Ladora, IA 187 2 F Yes.

29 05451700 Timber Creek near Marshalltown, IA 120 2 F No.

30 05451900 Richland Creek near Haven, IA 56.1 2 F No.

31 05452000 Salt Creek near Elberon, IA 199 2 F No.

32 05452200 Walnut Creek near Hartwick, IA 70.5 2 F No.

34 05453100 Iowa River at Marengo, IA 2,793 2 F No.

57 05469000 Henderson Creek near Oquawka, IL 436 2 N Yes.

54 05466000 Edwards River near Orion, IL 156 2 N No.

55 05466500 Edwards River near New Boston, IL 442 2 N No.

56 05467000 Pope Creek near Keithsburg, IL 172 2 N No.

88 05568800 Indian Creek near Wyoming, IL 63.2 2 N No.

89 05570000 Spoon River at Seville, IL 1,638 2 N No.

68 05479000 East Fork Des Moines River at Dakota City, IA 1,306 3 E Yes.

26 05449500 Iowa River near Rowan, IA 427 3 E No.

45 05459500 Winnebago River at Mason City, IA 517 3 E No.

67 05476750 Des Moines River at Humboldt, IA 2,270 3 E No.

69 05480500 Des Moines River at Fort Dodge, IA 4,202 3 E No.

70 05481000 Boone River near Webster City, IA 846 3 E No.

71 05481300 Des Moines River near Stratford, IA 5,464 3 E No.

98 06605850 Little Sioux River at Linn Grove, IA 1,567 3 I Yes.

92 06483290 Rock River below Tom Creek at Rock Rapids, IA 851 3 I No.

93 06483500 Rock River near Rock Valley, IA 1,584 3 I No.

94 06600100 Floyd River at Alton, IA 267 3 I No.

95 06600500 Floyd River at James, IA 886 3 I No.

97 06605000 Ocheyedan River near Spencer, IA 440 3 I No.

99 06606600 Little Sioux River at Correctionville, IA 2,520 3 I No.

44 05458900 West Fork Cedar River at Finchford, IA 851 3 J Yes.

20 05421000 Wapsipinicon River at Independence, IA 1,053 3 J No.

21 05421740 Wapsipinicon River near Anamosa, IA 1,581 3 J No.

22 05422000 Wapsipinicon River near De Witt, IA 2,336 3 J No.

40 05457000 Cedar River near Austin, MN 398 3 J No.

41 05457700 Cedar River at Charles City, IA 1,075 3 J No.

42 05458000 Little Cedar River near Ionia, IA 295 3 J No.

43 05458500 Cedar River at Janesville, IA 1,671 3 J No.

Table 3. Streamgages used to develop regression equations for the Flow Anywhere method, Iowa.—Continued

[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; IA, Iowa; MO, Missouri; IL, Illinois; MN, Minnesota; 

WI, Wisconsin. Locations of aggregated and local regions for the Flow Anywhere method are shown in fig. 5]
Flow Anywhere Method Analytical Procedures 23

Map 

no.

USGS 

streamgage 

number

Streamgage name

GIS drainage 

area 

(mi2)

Aggregated 

region Local region Reference streamgage

46 05462000 Shell Rock River at Shell Rock, IA 1,731 3 J No.

47 05463000 Beaver Creek at New Hartford, IA 351 3 J No.

48 05463500 Black Hawk Creek at Hudson IA 298 3 J No.

49 05464000 Cedar River at Waterloo, IA 5,149 3 J No.

50 05464220 Wolf Creek near Dysart, IA 298 3 J No.

121 06898000 Thompson River at Davis City, IA 695 3 K Yes.

78 05486000 North River near Norwalk, IA 349 3 K No.

79 05486490 Middle River near Indianola, IA 489 3 K No.

115 06817000 Nodaway River at Clarinda, IA 761 3 K No.

116 06817700 Nodaway River near Graham, MO 1,516 3 K No.

38 05455100 Old Mans Creek near Iowa City, IA 201 3 L Yes.

23 05422560 Duck Creek at 110th Ave at Davenport, IA 15.5 3 L No.

35 05454000 Rapid Creek near Iowa City, IA 25.3 3 L No.

36 05454220 Clear Creek near Oxford, IA 60.8 3 L No.

37 05454300 Clear Creek near Coralville, IA 98.2 3 L No.

39 05455500 English River at Kalona, IA 574 3 L No.

52 05464942 Hoover Creek at Hoover Nat Hist Site, West Branch, IA 2.6 3 L No.

19 05419000 Apple River near Hanover, IL 247 3 M Yes.

14 05413500 Grant River at Burton, WI 269 3 M No.

15 05414820 Sinsinawa River near Menominee, IL 40.0 3 M No.

16 05416900 Maquoketa River at Manchester, IA 279 3 M No.

17 05418400 North Fork Maquoketa River near Fulton, IA 503 3 M No.

18 05418500 Maquoketa River near Maquoketa, IA 1,551 3 M No.

Table 3. Streamgages used to develop regression equations for the Flow Anywhere method, Iowa.—Continued

[no., number; USGS, U.S. Geological Survey; GIS, Geographic Information System; mi2, square miles; IA, Iowa; MO, Missouri; IL, Illinois; MN, Minnesota; 

WI, Wisconsin. Locations of aggregated and local regions for the Flow Anywhere method are shown in fig. 5]

Left-Censored Regression

Left-censored regression, also referred to as “Tobit 

regression,” is used when less than 20 percent of the dataset is 

censored (Helsel and Hirsch, 2002). The datasets for aggregated regions 1 and 2 contain a small number of zero streamflow values (less than 20 percent); therefore, a left-censored 

regression was used for these areas. Left-censored regression 

analyses allow the use of a censoring threshold in the development of the equations to estimate flow at ungaged locations 

within those regions. A censoring threshold of 0.10 ft3/s was 

used to censor small dependent-variable streamflows and zero 

flows because of the uncertainty inherent in measuring daily 

mean streamflow values below 0.1 ft3/s. Daily mean streamflow values as low as 0.01 ft3

/s are recorded at streamgages; 

therefore, in addition to the zero flows, streamflows less 

than or equal to 0.1 ft3/s were censored in the regression 

analyses. Censored regression is similar to multiple linear 

regression except that the regression coefficients are fit by 

maximum-likelihood estimation (MLE) (Helsel and Hirsch, 

2002). Additional information on MLE is presented in Helsel 

and Hirsch (2002) and in Runkel and others (2004). Cohn 

(1988) has shown that censored regression estimates are 

slightly biased, and an adjustment for first-order bias in these 

estimates is made by an adjusted maximum-likelihood estimation (AMLE) computation. 

In regression analysis, an assumption is made that 

residual values are not correlated to one another or do not 

exhibit a trend (Helsel and Hirsch, 2002). To test for correlation or trends in the residual values, graphical representations 

of the residual values for each aggregated region were examined with respect to their relation to the estimated streamflow, time, and lagged residuals (fig. 7). Residual values as a 

function of the estimated value were examined for curvature 

and heteroscedasticity, with none being noted (fig. 7A). The 

“slice” feature at the low flows is attributed to censoring the 

data below 0.1 ft3/s. Residual values as a function of time 
24 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

also were examined for trends or patterns through time, with 

none being noted (fig. 7C). Residual values as a function of 

the 1-day lagged residuals also were examined, and a linear 

trend was noted by visual observation (fig. 7E). To remedy 

this issue, samples from the dataset were discarded from the 

left-censored regression in a regular pattern until the residuals 

were found not to be serially correlated. Using the daily mean 

streamflow from the 15th day of every other month resulted 

in the removal of visual serial correlation from the residuals 

(figs. 7B, 7D, and 7F). It is believed that this process does 

not affect the results or accuracy of the regression because the 

correlation that existed indicated the presence of a considerable amount of redundant information in the dataset (Helsel 

and Hirsch, 2002). Using any day of every other month would 

achieve the same results as there is nothing significant about 

the 15th day of every other month—for example, the 1st day 

of every other month or the 28th day of every other month is 

assumed to work just as well. The final regression equations 

for aggregated regions 1 and 2 were computed by using leftcensored regression techniques with a low limit threshold set 

at 0.1 ft3/s and the daily mean streamflow from the 15th day of 

every other month (table 4).

Ordinary-Least-Squares Regression

The dataset for aggregated region 3 did not contain any 

zero streamflow values; therefore, a censored regression was 

not needed. An ordinary-least-squares regression was used 

for aggregated region 3. As in the left-censored regression 

analysis of aggregated regions 1 and 2, the initial ordinaryleast-squares regression results were examined for correlation 

between residual values. Results of the analysis of residuals 

and their relation to the estimated streamflow, time, and lagged 

residuals for the ordinary-least-squares regression were similar 

to those found for the left-centered regression. The correlation 

between residuals and lagged residuals again was observed by 

using the entire dataset. The dataset for aggregated region 3 

also was sampled until no correlation was observed. This 

process also resulted in a dataset of daily mean streamflows 

from the 15th day of every other month. The final regression 

equation for aggregated region 3 was computed by using an 

ordinary-least-squares multiple linear regression method and 

the daily mean streamflow from the 15th day of every other 

month (table 4).

Accuracy and Limitations of Regression 

Estimates

The accuracies of the final regression equations for aggregated regions 1, 2, and 3 were analyzed and quantified. The 

final equations are presented in table 4, along with the associated standard errors of the model. The average standard error 

of estimate (SEE) measures how well the regression model fits 

the data that were used to develop it. The values of standard 

error were determined by using equations presented in Riggs 

(1968). The standard error values in logarithm (base 10) 

format represent the errors of equations developed by using 

the logarithm (base 10) transformed data. The range of percent 

error represents the errors for the final untransformed equations (Hortness, 2006). The standard error of prediction (SEP) 

also was computed for the ordinary-least-squares regression 

(table 4). The SEP is a measure of the accuracy with which 

the regression model can estimate daily mean streamflows at 

ungaged sites. The SEP accounts for model error, SEE, and 

the sampling error (error that results from estimating model 

parameters from limited data) in estimating the accuracy of 

the equations. Compared to the SEE, the SEP provides a better 

overall measure of the predictive ability of a model (Eash, 

2001). The SEP is not applicable to a left-censored regression 

analysis. 

Comparison of Observed and Estimated 

Streamflows

The time series of unregulated, daily mean streamflow at ungaged locations is created by the following steps: 

(1) determine which local region contains the ungaged location, (2) select the appropriate reference streamgage within 

the same local region, (3) determine the drainage areas at the 

ungaged location and the reference streamgage, (4) determine 

which aggregated region contains the local region, (5) obtain 

the daily mean streamflow at the reference streamgage for the 

desired dates of computation, and (6) compute the estimated 

streamflow at the ungaged location from the appropriate 

aggregated-region equation. The performance of the Flow 

Anywhere method in each aggregated region was examined by comparing the observed and estimated streamflows 

throughout the aggregated region (fig. 8). The comparisons 

did not demonstrate an obvious range of streamflows that were 

consistently over- or underestimated, with the exception of the 

extreme low streamflows, as shown in figure 8. These streamflows generally appear to be slightly overestimated. Tests 

were completed by removing or adding local regions within 

the study area from or to different aggregated regions. These 

changes did not improve the estimation for the lower streamflows; therefore, the results presented in table 4 are believed 

to produce the best possible agreement with the dataset. 

Hydrographs of observed and estimated streamflows for nonreference streamgages in the dataset also were analyzed. Any 

consistencies of over- or underestimation of streamflows that 

were observed in a local region were removed by moving local 

regions to a different aggregated region to determine whether 

regression errors could be improved. As noted above for the 

comparison of observed and estimated streamflows, tests were 

completed by removing or adding local regions from or to 

different aggregated regions to determine whether regression 

errors could be improved. 

To evaluate the Flow Anywhere method for estimating streamflow at ungaged locations, a validation procedure 

was completed for six streamgages in the dataset (table 5). 

These six streamgages were selected because they were not 
Flow Anywhere Method Analytical Procedures 25

4

2

0

-2

-4

1977 1980 1985 1990 1995 2005 2010

C

Year

Residual (e ) in logarithm, base 10

i

2000

Aggregated region 1, entire dataset

4

2

0

-2

-4

0.1 1 10 100 1,000 10,000 100,000 1,000,000

A

Predicted streamflow, in cubic feet per second

Residual (e ) in logarithm, base 10

i

4

2

0

-2

-4

0.1 1 10 100 1,000 10,000 100,000 1,000,000

B

Predicted streamflow, in cubic feet per second

Residual (e ) in logarithm, base 10

i

Aggregated region 1, one value every 2 months

4

2

0

-2

-4

1977 1980 1985 1990 1995 2005 2010

D

Year

Residual (e ) in logarithm, base 10

i

2000

4

2

0

-2

-4

-4 -2 0 2 4

F

Lagged residual (e(i-1)) in logarithm, base 10

Residual (e ) in logarithm, base 10

i

Kendall’s tau = 0.22

4

2

0

-2

-4

-4 -2 0 2 4

E

Lagged residual (e(i-1)) in logarithm, base 10

Residual (e ) in logarithm, base 10

i

Kendall’s tau = 0.77

Figure 7. Correlation between residual (ei) and (A, B) predicted streamflow, (C, D) time, and (E, F ) lagged residual (e(i-1)) for aggregated 

region 1 in the Flow Anywhere method determined by using the entire dataset (left column) and by using one value every 2 months (right 

column).
26 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Table 4. Regression equations for estimating streamflow at ungaged locations in Iowa by using the Flow Anywhere method.

[SEE, average standard error of estimate; SEP, average standard error of prediction; DAu, Geographic Information System (GIS) drainage area at ungaged 

location in the ungaged watershed; DAr, GIS drainage area at the reference streamgage; Qu, streamflow at the ungaged location; Qr, streamflow at the reference 

streamgage; NA, not applicable. Aggregated regions are shown in fig. 5]

Aggregated 

region Equation

Number of 

streamgages used to 

develop equation

Number of 

left-censored 

values

Standard error of model

SEE 

(percent)

SEP 

Log (percent) 10 Percent

1 Qu = 1.06(DAu/DAr)

1.20Qr0.979 33 30 0.377 +138 to -58.0 98.2 NA

2 Qu = 1.52(DAu/DAr)1.05Qr

0.922 27 21 0.229 +69.4 to -41.0 55.2 NA

3 Qu = 3.30(DAu/DAr)1.07Qr

0.800 45 NA 0.256 +80.1 to -44.8 62.3 64.3

used for the Flow Duration Curve Transfer method. A validation study for the Flow Duration Curve Transfer method in 

which one streamgage at a time would be removed would be a 

more robust validation, but is beyond the scope of this report, 

as manually regenerating regression equations for the Flow 

Duration Curve Transfer method after a streamgage has been 

removed is a lengthy process. For each of the six streamgages 

used to evaluate the Flow Anywhere method, the regional 

regression equations were redeveloped without that particular 

streamgage in the dataset. Using this method to evaluate the 

estimates of daily mean streamflow at a streamgage that was 

not used in the development of the Flow Anywhere method 

resembles the scenario of computing daily mean streamflow 

at an ungaged location. Observed and estimated flows at 

the six streamgages were compared for goodness of fit. To 

quantify the goodness of fit, the mean absolute error (MAE), 

root-mean-square error (RMSE), percent root-mean-square 

error (PRMSE), RMSE-observations standard deviation 

ratio (RSR), percent bias (PBIAS), and Nash-Sutcliffe (NS) 

efficiency value (Nash and Sutcliffe, 1970) were computed for 

each of the six streamgages. The percent RMSE is an indication of how well the estimated values match the observed 

values. A percent RMSE value of 0.0 indicates a perfect fit 

between observed and estimated flows; the larger the value, 

the poorer the fit between observed and estimated flows. In 

general, the RMSE exceeds the MAE, and the degree to which 

this occurs is an indicator of the extent to which outliers (or 

variance in the differences between modeled and observed values) exist in the data (Legates and McCabe, 1999). The RSR 

is an indicator of model-simulation performance and is the 

RMSE divided by the standard deviation of the observed data. 

A value of 0.0 would indicate zero RMSE or residual variation and, therefore, perfect model simulation (Moriasi and 

others, 2007). The PBIAS measures the average tendency of 

the estimated data to be larger or smaller than their observed 

counterparts, with an optimal value of 0.0. Positive values 

indicate model underestimation bias, and negative values 

indicate model overestimation bias (Gupta and others, 1999). 

The NS value is a measure of how well the estimated values 

match the observed values. NS values range from -∞ to 1. Values of 0.0 or less indicate that the mean measured streamflow 

is a better predictor than simulated streamflows; a value of 1 

indicates a perfect fit between observed and estimated values 

(Moriasi and others, 2007). The NS and percent PRMSE were 

computed for both the logarithm (base 10) and untransformed 

streamflows. The logarithmic transformation helps to overcome the sensitivity that extreme values can have as a result of 

squaring of differences. Streamflow-model simulations can be 

considered satisfactory if NS is greater than 0.50, RSR is less 

than 0.70, and PBIAS is plus or minus 25 percent (Moriasi 

and others, 2007). Results of the validation studies for the 

Flow Anywhere and Flow Duration Curve Transfer methods 

are compiled in table 5. For the Flow Anywhere method, differences between the RMSE and the MAE (differences not 

shown in table 5) ranged from 1,016 ft3/s at 05421740, Wapsipinicon River near Anamosa, Iowa, to 138 ft3

/s at 05387440, 

Upper Iowa River at Bluffton, Iowa, signifying a greater 

occurrence of outliers between observed and estimated streamflows at 05421740, Wapsipinicon River near Anamosa, Iowa. 

RMSE values ranged from 1,690 ft3/s at 05421740, Wapsipinicon River near Anamosa, Iowa, to 237 ft3

/s at 05387440, 

Upper Iowa River at Bluffton, Iowa. PRMSE values ranged 

from 115 percent at 06483290, Rock River below Tom Creek 

at Rock Rapids, Iowa, to 26.2 percent at 05387440, Upper 

Iowa River at Bluffton, Iowa. The logarithm (base 10) streamflow PRMSE ranged from 13.0 percent at 06483290, Rock 

River below Tom Creek at Rock Rapids, Iowa, to 5.3 percent at 05387440, Upper Iowa River at Bluffton, Iowa. RSR 

values ranged from 0.80 at 05416900, Maquoketa River at 

Manchester, Iowa, to 0.40 at 05387440, Upper Iowa River 

at Bluffton, Iowa. PBIAS values ranged from 25.4 percent at 

05387440, Upper Iowa River at Bluffton, Iowa, to 4.0 percent 

at both 05412020, Turkey River above French Hollow Creek 

at Elkader, Iowa, and 06483290, Rock River below Tom Creek 

at Rock Rapids, Iowa. Untransformed streamflow NS values 

ranged from 0.84 at 05387440, Upper Iowa River at Bluffton, 

Iowa, to 0.35 at 05416900, Maquoketa River at Manchester, 

Iowa. The logarithm (base 10) streamflow NS values ranged 
Flow Anywhere Method Analytical Procedures 27

Figure 8. Observed and estimated daily mean streamflows 

relative to the 1:1 line for (A) aggregated region 1, (B) aggregated 

region 2, and (C) aggregated region 3, Iowa.

0.1

1

10

100

1,000

10,000

100,000

A Aggregated region 1

1:1 line

0.1

1

10

100

1,000

10,000

100,000

B Aggregated region 2

0.1 1 10 100 1,000 10,000 100,000

Observed streamflow, in cubic feet per second

0.1 1 10 100 1,000 10,000 100,000

Observed streamflow, in cubic feet per second

0.1

1

10

100

1,000

10,000

100,000

C Aggregated region 3

1:1 line

1:1 line

Estimated streamflow, in cubic feet per second Estimated streamflow, in cubic feet per second Estimated streamflow, in cubic feet per second

0.1 1 10 100 1,000 10,000 100,000

Observed streamflow, in cubic feet per second

from 0.86 to 0.56 for the same two sites, respectively. On the 

basis of all the ranges of statistics reported above, including 

the difference between the RMSE and MAE, the observed and 

estimated daily mean streamflows for the streamgages with 

the closest (05387440, Upper Iowa River at Bluffton, Iowa, 

map no. 4) and poorest (05416900, Maquoketa River at Manchester, Iowa, map no. 16) agreements were analyzed further 

(fig. 9). A comparison of observed and estimated hydrographs 

for the same streamgages also was completed (fig. 10). For 

05387440, Upper Iowa River at Bluffton, Iowa, the higher 

flows appear to be underestimated. For 05416900, Maquoketa 

River at Manchester, Iowa, low flows appear to be overestimated whereas higher flows seem to be underestimated. Estimated cumulative streamflows for the period October 1, 2004, 

to September 30, 2009, are underestimated for 05387440, 

Upper Iowa River at Bluffton, Iowa, and 05416900, Maquoketa River at Manchester, Iowa, by -25.8 and -7.4 percent, 

respectively (fig. 11). Cumulative daily mean streamflows 

for the observed, Flow Anywhere, and Flow Duration Curve 

Transfer methods shown in figure 11 are limited to those days 

when estimated streamflows could be computed for streamflows greater than the 0.99-percent exceedance probability (or 

less than the 0.01-percent exceedance probability) with the 

Flow Duration Curve Transfer method. As discussed in the 

Flow Duration Curve Transfer Analytical Procedures section (farther on in this report), one of the limitations of the 

Flow Duration Curve Transfer method is that streamflows 

outside the bounds of the 0.99- to 0.01- percent exceedance 

probability range used for this study cannot be estimated. On 

those days when streamflows could not be estimated by using 

the Flow Duration Curve Transfer method, those daily mean 

streamflows for the same days for the observed and estimated 

Flow Anywhere streamflows also were removed to compute 

and compare the cumulative daily mean streamflows.

Uncertainty of Estimated Streamflows

The total uncertainty associated with estimated time 

series of unregulated, daily mean flow at an ungaged location 

determined by using the Flow Anywhere method is impossible 

to quantify. The regional regression equations have quantified standard errors (table 4). Differences between actual and 

estimated daily mean streamflows are attributed to the possible unequal effect of localized storm events at the reference 

streamgage and ungaged location. It is impossible to quantify 

the uncertainty associated with differences in rainfall patterns 

because the intensity and location of all storm events are not 

known. Although local regions were sized so that basin characteristics were similar in each region, some differences can 

be attributed to the unique physiographic characteristics of the 

basins, such as storage along channels, channel shape, stream 

slope, and infiltration properties.
Table 5. Results of validation study for the Flow Anywhere and Flow Duration Curve Transfer methods. [USGS, U.S. Geological Survey; FA, Flow Anywhere; FDCT, Flow Duration Curve Transfer; Min, minimum; ft3/s, cubic foot per second; Max, maximum; SD, standard deviatiNA, not applicable; RMSE, root mean square error; PRMSE, percent root mean square error; RSR, RMSE observations standard deviation ratio; PBIAS, percent bias; NS, Nash

Statistic USGS streamgage 05387440 USGS streamgage 05411850 USGS stream

Observed FA FA Observed FDCT FDCT Observed FA FA Observed FDCT FDCT Observed FA FA 

Min (ft3/s) 53.0 52.7 53.0 45.0 68.0 103 68.0 76.0 152 155 Max (ft3/s) 13,800 10,000 3,780 2,260 35,600 19,600 5,390 4,010 32,100 29,600 Median (ft3/s) 203 159 201 196 277 310 274 298 425 469 Mean (ft3/s) 363 271 326 296 579 529 505 500 832 799 SD (ft3/s) 594 429 347 316 1,220 840 639 586 1,450 1,270 MAE (ft3/s) NA 99.5 NA 75.1 NA 196 NA 160 NA 230 RMSE (ft3/s) NA 237 NA 169 NA 593 NA 334 NA 641 PRMSE NA 26.2 NA 25.6 NA 65.9 NA 55.3 NA 63.4 PRMSE (log) NA 5.3 NA 4.4 NA 8.0 NA 6.9 NA 5.5 RSR NA 0.40 NA 0.49 NA 0.48 NA 0.52 NA 0.44 PBIAS NA 25.4 NA 9.3 NA 8.6 NA 0.94 NA 4.0 NS NA 0.84 NA 0.76 NA 0.77 NA 0.73 NA 0.81 NS (log) NA 0.86 NA 0.89 NA 0.78 NA 0.81 NA 0.83 

Statistic USGS streamgage 05416900 USGS streamgage 05421740 USGS stream

Observed FA FA Observed FDCT FDCT Observed FA FA Observed FDCT FDCT Observed FA FA 

Min (ft3/s) 29.0 49.3 29.0 28.2 144 97.9 144 173 27.0 46.1 Max (ft3/s) 14,200 6,000 14,200 1,810 31,000 21,300 19,900 9,740 10,100 2,800 Median (ft3/s) 137 167 135 109 786 832 769 784 203 244 Mean (ft3/s) 320 270 271 210 1,590 1,340 1,380 1,420 379 364 SD (ft3/s) 768 335 533 293 2,520 1,420 1,730 1,630 610 350 MAE (ft3/s) NA 177 NA 114 NA 674 NA 469 NA 182 RMSE (ft3/s) NA 617 NA 419 NA 1,690 NA 906 NA 465 PRMSE NA 113 NA 57.5 NA 64.7 NA 52.9 NA 115 PRMSE (log) NA 11.7 NA 12.5 NA 7.5 NA 6.5 NA 13.0 RSR NA 0.80 NA 0.79 NA 0.67 NA 0.52 NA 0.76 PBIAS NA 15.7 NA 22.7 NA 16.1 NA -2.8 NA 4.0 NS NA 0.35 NA 0.38 NA 0.55 NA 0.73 NA 0.42 NS (log) NA 0.56 NA 0.48 NA 0.73 NA 0.79 NA 0.58 
Flow Anywhere Method Analytical Procedures 29

Limitations of Methods

The regional regression equations developed in this study 

apply only to stream locations in Iowa where flows are not 

significantly affected by regulation, diversion, or urbanization. The applicability and accuracy of the regional equations 

depend on whether the measured drainage area for an ungaged 

stream location is within the range of drainage areas used to 

develop the equations. The acceptable range of drainage areas 

used to develop the regional regression equations (table 4) is 

tabulated as maximum and minimum values in table 6. The 

applicability of the regional equations when the drainage area 

at the ungaged location is smaller than the minimum drainage 

area or larger than the maximum drainage area used to develop 

the regression equation for that particular region is unknown. 

In addition, drainage areas at ungaged locations should be 

measured by using the same techniques used in this study. 

Estimates of daily mean streamflow at ungaged locations 

computed from the regression equations that are less than 

0.1 ft3/s should be reported as less than 0.1 ft3/s. For aggregated region 3, estimates of daily mean streamflow at ungaged 

locations computed from the ordinary-least-squares regression 

equation that are less than 0.1 ft3/s also should be reported as 

less than 0.1 ft3/s to maintain a consistent reporting limit for 

Iowa.

The reliability or use of the method for other streamflow 

durations (monthly or annual mean streamflow) or classifications (annual peak streamflow) is uncertain or inappropriate 

(Asquith and others, 2006).

Computations made on a stream segment on which a 

streamgage is located should be made with caution. The resulting estimated streamflow at the ungaged location should be 

verified to be hydrologically reasonable with respect to the 

streamflows at the streamgage. A general “rule of thumb” in 

other regression analyses is to use the traditional drainagearea ratio (equation 1) to estimate streamflow when the ratio 

of the drainage area of the ungaged location to that of the 

streamgage is between 0.5 and 1.5 (Hortness, 2006). Although 

the drainage-area ratio attempts to ensure continuity in streamflow as the distance between gages decreases, Archfield and 

Vogel (2010) noted that this rule of thumb generally appears 

to result in poorer agreement between observed and estimated 

streamflows. Users need to consider the limitations of both 

approaches when applying these methods in practice.

The estimation of daily mean streamflows at ungaged 

locations with the Flow Anywhere method is appropriate 

for any date after September 30, 1977, provided that valid 

daily mean streamflow data are available for the associated 

reference streamgage for the days of interest. Estimation of 

daily mean streamflows on or prior to this date would not be 

appropriate as a result of trends in streamflow, as described in 

Figure 9. Observed and estimated daily mean streamflow 

relative to the 1:1 line for U.S. Geological Survey streamgages 

(A) 05387440, Upper Iowa River at Bluffton, Iowa; and (B) 

05416900, Maquoketa River at Manchester, Iowa, showing the 

(A) closest and (B) poorest agreement between unregulated 

observed and estimated mean daily streamflow, October 1, 2004, 

to September 30, 2009, determined by using the Flow Anywhere 

method.

10

100

1,000

10,000

100,000

10 100 1,000 10,000 100,000

Observed streamflow, in cubic feet per second

1:1 line

1:1 line

Estimated streamflow, in cubic feet per second

A 05387440, Upper Iowa River at Bluffton, Iowa

B 05416900, Makuoketa River at Manchester, Iowa

10

100

1,000

10,000

100,000

Estimated streamflow, in cubic feet per second

10 100 1,000 10,000 100,000

Observed streamflow, in cubic feet per second
30 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Figure 10. Observed and estimated hydrographs for U.S. Geological Survey streamgages (A) 05387440, Upper Iowa River at 

Bluffton, Iowa; and (B) 05416900, Maquoketa River at Manchester, Iowa, showing the (A) closest and (B) poorest agreement between 

unregulated observed and estimated, daily mean streamflows, October 1, 2004, to September 30, 2009, determined by using the Flow 

Anywhere method.

Estimated streamflow

Observed streamflow

EXPLANATION

Reference streamgage: 05413500,

Grant River at Burton, Wisconsin

10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

10

100

1,000

10,000

100,000

Sreamflow, in cubic feet per second

A 05387440, Upper Iowa River at Bluffton, Iowa

10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

10

100

1,000

10,000

100,000

Streamflow, in cubic feet per second

B 05416900, Maquoketa River at Manchester, Iowa

Date

Date

Estimated streamflow

Observed streamflow

EXPLANATION

Reference streamgage 05388250,

Upper Iowa River near Dorchester, Iowa
Flow Anywhere Method Analytical Procedures 31

Figure 11. Observed and estimated cumulative daily mean streamflows for U.S. Geological Survey streamgages (A) 05387440, Upper 

Iowa River at Bluffton, Iowa; and (B) 05416900, Maquoketa River at Manchester, Iowa, October 1, 2004, to September 30, 2009.

EXPLANATION

10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

0

200,000

400,000

600,000

100,000

300,000

500,000 Observed streamflow

Estimated streamflow using the Flow

Duration Curve Transfer method

Estimated streamflow using the

Flow Anywhere method

A 05387440, Upper Iowa River at Bluffton, Iowa

10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

B 05416900, Maquoketa River at Manchester, Iowa

0

100,000

200,000

300,000

400,000

500,000

Cumulative streamflow, in cubic feet per second Cumulative streamflow, in cubic feet per second

EXPLANATION

Observed streamflow

Estimated streamflow using the Flow

Duration Curve Transfer method

Estimated streamflow using the

Flow Anywhere method

Date

Date
32 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Table 6. Statistical summary of drainage areas used 

to develop regional regression equations in Iowa.

[GIS, Geographical information system. Locations of aggregated regions are shown in fig. 5]

Statistic GIS drainage area 

(mi2

)

Aggregated region 1

Maximum 4,310

Minimum 34.3

Mean 648

Median 370

Aggregated region 2

Maximum 3,425

Minimum 56.1

Mean 861

Median 526

Aggregated region 3

Maximum 5,464

Minimum 2.60

Mean 1,065

Median 574

the Trend Analysis section above. Computations of estimated 

daily mean streamflow at ungaged locations after September 30, 2009, are to be made with the assumption that no 

trends occur in the streamflow records and that no significant 

changes have been made to basins that would alter the relation 

between streamflows used in the development of the method. 

By using documented regression techniques, the error values 

of equation 2 can be computed for results produced from the 

regression equations. The final equations then can be used to 

estimate a daily mean streamflow at ungaged locations in Iowa 

with an associated percent error.

Flow Duration Curve Transfer 

Analytical Procedures

Data used for the Flow Duration Curve Transfer method 

were retrieved for 113 continuous-record streamgages located 

in Iowa and within a 50-mi buffer of Iowa in the neighboring 

States of Illinois, Minnesota, Missouri, Nebraska, and Wisconsin (table 1). Streamgages with at least 10 complete years 

of daily mean streamflow data through September 30, 2009, 

at locations where streamflow is unaffected by regulation or 

diversion were selected for evaluation in the study, which 

included 84 streamgages in Iowa and 29 streamgages in adjacent states. Streamgages in neighboring states were included 

to improve representation of basin characteristics near the 

Iowa border and to improve regressions near the state border. 

Streamgages in South Dakota within the 50-mi buffer of Iowa 

were not used because of upstream regulation or diversion. 

Daily mean streamflow values for dates earlier than October 1, 

1977, were not retrieved as a result of trends found in the 

record, as described in the Trend Analysis section above. Daily 

mean streamflow data for the 113 streamgages were retrieved 

from the USGS NWIS database. The drainage areas of the 

113 streamgages were measured by using a GIS. The drainage areas were measured by following procedures in Eash and 

Barnes (2012). The drainage-area values from the GIS are 

compared with the values published in NWIS in table 1. The 

GIS drainage-area value was used to develop the regression 

equations in this study in order to remain consistent with the 

measurement techniques used in a Web-based tool similar to 

the USGS Streamstats interface (Ries and others, 2009).

Regression Methods

To develop the quantile-based regression equations, the 

dependent variable, the streamflow quantiles, and the independent variables, which are the physical and climate basin characteristics, were quantified for each of the 113 streamgages. 

The physical and climatic basin characteristics are shown in 

table 7 for three streamgages: 05412500, Turkey River at Garber, Iowa (fig. 1, map no. 13, and table 1); 05452200, Walnut 

Creek near Hartwick, Iowa (fig. 1, map no. 32, and table 1); 

and 06483500, Rock River near Rock Valley, Iowa (fig. 1, map 

no. 93, and table 1). To compute the streamflow quantiles, the 

observed daily streamflows were ranked and an exceedance 

probability was computed. Streamflow quantiles were estimated at the following exceedance probabilities: 0.01, 0.05, 

0.10, 0.15, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.85, 0.90, 

0.95, and 0.99. Streamflow quantiles at each of the 15 exceedance probabilities were estimated from the observed streamflow records by using the nonparametric quantile estimators 

presented in Vogel and Fennessey (1994, eq. 2a and 2b). A 

total of 57 physical and climate basin characteristics were 

tested for use as explanatory (independent) variables (table 7). 

A detailed description of the basin characteristics, as well as 

details about their source, methodology, and resolution, can be 

found in Eash and Barnes (2012).

Regression equations were developed for the 0.01-, 0.05-, 

0.10-, 0.15-, 0.20-, 0.30-, 0.40-, 0.50-, 0.60-, 0.70-, 0.80-, 

0.85-, 0.90-, and 0.95-exceedance probability streamflow 

values by using WLS regression. The regression equation for 

the 0.99-percent exceedance probability streamflow value 

was developed by using a left-censored regression equation 

(table 8). When WLS regression was used, regression weights 

were applied to the dependent variable and were computed 

as a function of the number of years of observed streamflow 

on which the estimated streamflow statistic was based. For 

the left-censored regression equation for the 0.99-percent 

exceedance probability streamflow values, there were 9 values less than or equal to the censor threshold of 0.1 ft3

/s and 

5 zero flows. Two sets of regression equations initially were 
Flow Duration Curve Transfer Analytical Procedures 33

Table 7. Basin, climate, and land-use characteristics at three U.S. Geological streamgages, tested for use in the estimation of 

streamflow at ungaged sites.

[USGS, U.S. Geological Survey. Elevation characteristics are determined from the U.S. Geological Survey (USGS) 30-meter National Elevation Dataset]

Basin, climate, or land-use characteristic

USGS streamgage number and name

05412500, Turkey River at 

Garber, Iowa

0545220, Walnut Creek 

near Hartwick, Iowa

06483500, Rock River near 

Rock Valley, Iowa

Drainage area (in square miles) 1,553 70.5 1,584

Average basin slope (in percent) 6.6 5.7 2.4

Main channel slope (between points 10 and 85 percent 

of length, in feet per mile)

4.5 8.1 3.8

Slope of entire length main channel (in feet per mile) 5.0 10.2 5.6

Percent basin area within Des Moines Lobe landform 

region (in percent area)

0.0 0.0 13.7

Base-flow index (mean ratio of base flow to annual 

streamflow)

0.6 0.5 0.5

Hydrograph separation and analysis (median percentage 

of baseflow to annual streamflow, in percent)

57.7 53.2 55.6

Annual base-flow recession time constant (rate of baseflow recession between storm events, in days)32.1 24.4 25.5

2-year runoff coefficient 0.2 0.2 0.1

5-year runoff coefficient 0.3 0.3 0.2

10-year runoff coefficient 0.3 0.3 0.2

25-year runoff coefficient 0.4 0.4 0.3

50-year runoff coefficient 0.5 0.4 0.4

100-year runoff coefficient 0.6 0.4 0.5

24-hour, 2-year precipitation (in inches) 3.0 3.0 2.7

24-hour, 5-year precipitation (in inches) 3.8 3.8 3.3

24-hour, 10-year precipitation (in inches) 4.3 4.5 3.9

24-hour, 25-year precipitation (in inches) 5.4 5.0 4.8

24-hour, 50-year precipitation (in inches) 6.0 6.0 5.6

24-hour, 100-year precipitation (in inches) 6.2 6.5 6.6

Row crop production 2001 (in percent basin area) 58.1 69.9 82.8

Streamflow-variability index (a measure of the steepness 

of the slope of a duration curve)

0.4 0.6 0.6

Mean annual precipitation 1971–2000 (in inches) 34.8 35.6 27.7

Mean January precipitation 1971–2000 (in inches) 1.0 1.1 0.6

Mean February precipitation 1971–2000 (in inches) 1.0 1.1 0.6

Mean March precipitation 1971–2000 (in inches) 2.1 2.2 1.9

Mean April precipitation 1971–2000 (in inches) 3.6 3.5 2.8

Mean May precipitation 1971–2000 (in inches) 4.0 4.3 3.4

Mean June precipitation 1971–2000 (in inches) 4.6 4.7 4.3

Mean July precipitation 1971–2000 (in inches) 4.3 4.2 3.5

Mean August precipitation 1971–2000 (in inches) 4.9 4.5 3.6

Mean September precipitation 1971–2000 (in inches) 3.3 3.6 2.6

Mean October precipitation 1971–2000 (in inches) 2.4 2.7 2.0
34 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Table 7. Basin, climate, and land-use characteristics at three U.S. Geological streamgages, tested for use in the estimation of 

streamflow at ungaged sites.—Continued

[USGS, U.S. Geological Survey. Elevation characteristics are determined from the U.S. Geological Survey (USGS) 30-meter National Elevation Dataset]

Basin, climate, or land-use characteristic

USGS streamgage number and name

05412500, Turkey River at 

Garber, Iowa

0545220, Walnut Creek 

near Hartwick, Iowa

06483500, Rock River near 

Rock Valley, Iowa

Mean November precipitation 1971–2000 (in inches) 2.3 2.4 1.6

Mean December precipitation 1971–2000 (in inces) 1.3 1.3 0.7

Percent of area with slopes greater than 30 percent 1.4 0.0 0.0

Percent of area with slopes greater than 30 percent facing north0.5 0.0 0.0

Percent of area underlain by hydrologic soil type A (in 

percent area)

2.0 0.3 1.2

Percent of area underlain by hydrologic soil type B (in 

percent area)

87.8 82.4 96.7

Percent of area underlain by hydrologic soil type C (in 

percent area)

4.8 16.7 1.2

Percent of area underlain by hydrologic soil type D (in 

percent area)

2.7 0.2 0.1

Clay content of soil as a percent (by percent volume) 23.4 30.0 27.3

Sand content of soil as a percent (by percent volume) 28.7 11.9 22.6

Average saturated hydraulic conductivity of soil (in 

micrometers per second)

20.8 8.1 15.3

Relative relief (basin relief/basin perimeter) 2.4 3.7 2.4

Shape factor (measure of basin shape) 4.3 5.0 3.0

Elongation ratio (measure of basin shape) 0.5 0.5 0.7

Rotundity of basin (measure of basin shape) 3.3 3.9 2.3

Compactness ratio (measure of basin shape) 2.3 2.1 2.2

Main channel sinuosity ratio 1.8 1.1 1.9

Stream density (in miles per square mile) 2.1 2.2 2.1

Slenderness ratio 14.5 6.2 10.5

Constant of channel maintenance (in square miles per 

mile)

0.5 0.5 0.5

Ruggedness number (in feet per mile) 1,614 506 1,557

Ratio of main channel slope to average basin slope 0.7 1.4 1.6

Drainage frequency (number of first-order streams per 

square mile)

1.3 1.8 1.1

Relative stream density 0.3 0.4 0.3

developed; one set of equations resulted from the use of the 

ordinary-least-squares (OLS) method and the other set of 

equations resulted from the use of the WLS method or the 

left-censored method, as was mentioned previously. The 

OLS method was used for preliminary model selection and to 

decrease the candidate pool of potential explanatory variables. 

With the exception of the equation (left-censored) for the 

0.99-percent exceedance probability, all final equations for the 

exceedance probabilities were developed by using the WLS 

method (table 8). Percent exceedance streamflow values used 

as the dependent variables in the regression equations were 

estimated by using at least 10 years of daily observations. The 

dependent variables and the independent variables, drainage 

area, were transformed to base-10 logarithms to obtain linear 

regression equations. The form of the equation developed by 

using the original units (anti-logarithm) is

1 2

1 2 1 0 10 bo b b bn ei Y XX X i n = ... , (4) 
Flow Duration Curve Transfer Analytical Procedures 35

where

Yi is the dependent variable (the exceedanceprobability streamflows),

Xn is the independent variables (basin 

characteristics),

bn is the regression-estimated coefficient for the 

explanatory variable Xn,

bo is the regression-estimated constant term, and

ei is the residual error (difference between 

the observed and predicted values of the 

independent variable) for site i.

Initial OLS regression analyses were performed using 

Spotfire S+® statistical software (TIBCO Software Inc., 

2008). Prior to OLS, initial selections of significant independent variables were performed by using the Efroymson 

stepwise selection method (Efroymson, 1960), which is an 

automatic procedure for regression-model selection when 

the number of potential independent variables is large. The 

Efroymson analyses produced a subset of potential significant basin characteristics for each exceedance-probability 

streamflow statistic. Each subset of basin characteristics then 

was iteratively tested by using OLS regression analyses to 

identify the best sets of equations, as determined by the model 

diagnostic statistics listed below, and in which no more than 

three significant independent variables (basin characteristics) 

were used. A limit of three independent variables per equation 

was used to minimize overfitting of the regression models. 

Results of the OLS models were evaluated to determine their 

adequacy by using graphical relations and residual plots, 

variance inflation factor (VIF), high-leverage points, the average standard error of estimate (SEE), and the adjusted coefficient of determination (adj-R2

) (Helsel and Hirsch, 2002). 

The selection of the independent variables, and the signs and 

magnitudes of their respective regression coefficients, were 

evaluated to ensure that they are hydrologically valid in the 

Table 8. Regression equations for estimating flow-duration statistics for unregulated streams in Iowa.

[SEE, average standard error of estimate; SEP, average standard error of prediction; D01–D99, daily mean streamflow at 0.01-, 0.05-, 0.10-, 0.15-, 

0.20-, 0.30-, 0.40-, 0.50-, 0.60-, 0.70-, 0.80-, 0.85-, 0.90-, 0.95-, and 0.99-exceedance probability; DRNAREA, drainage area; PRECIP, mean annual 

precipitation 1971–2000; SOILCSSURGO, percent area underlain by hydrologic soil type C; NA, not applicable; RSD, relative stream density; HYSEP, 

hydrograph separation and analysis is the median percentage of baseflow to annual streamflow; STREAM_VAR, streamflow-variability index, a measure 

of the steepness of the slope of a duration curve; SOILBSSURGO, percent area underlain by hydrologic soil type B; SOILDSSURGO, percent area 

underlain by hydrologic soil type D]

Weighted-least-squares regression equations

Flow Duration Curve Transfer statistic

Number of streamgages 

used to develop equation

SEP 

(percent)

SEE 

(percent)

D01=10-0.717DRNAREA0.974100.045(PRECIP)100.003(SOILCSSURGO) 113 23.5 NA

D05=10-2.039DRNAREA1.110100.051(PRECIP)101.142(RSD) 113 23.6 NA

D10=10-1.977DRNAREA1.133100.038(PRECIP)101.362(RSD) 113 24.2 NA

D15=10-2.603DRNAREA1.113100.009(HYSEP)100.055(PRECIP) 113 24.6 NA

D20=10-2.726DRNAREA1.102100.011(HYESP)100.053(PRECIP) 113 22.1 NA

D30=10-2.931DRNAREA1.085100.014(HYESP)100.051(PRECIP) 113 17.1 NA

D40=10-3.187DRNAREA1.075100.017(HYESP)100.050(PRECIP) 113 14.9 NA

D50=10-3.449DRNAREA1.065100.020(HYESP)100.050(PRECIP) 113 16.4 NA

D60=10-3.770DRNAREA1.066100.024(HYESP)100.049(PRECIP) 113 22.1 NA

D70=10-4.083DRNAREA1.079100.027(HYESP)100.047(PRECIP) 113 32.4 NA

D80=10-0.883DRNAREA1.17910-2.050(STREAM_VAR)100.006(SOILBSSURGO) 113 40.1 NA

D85=10-0.888DRNAREA1.20710-2.365(STREAM_VAR)100.006(SOILBSSURGO) 113 42.5 NA

D90=10-0.970DRNAREA1.24110-2.716(STREAM_VAR)100.007(SOILBSSURGO) 113 51.0 NA

D95=10-1.225DRNAREA1.31710-3.170(STREAM_VAR)100.008(SOILBSSURGO) 113 74.9 NA

Left-censored regression equation

D99=10-0.18302282DRNAREA1.3742078410-4.60344452(STREAM_VAR)10-0.01341188(SOILDSSURGO) 108 NA 97.7
36 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

context of the different exceedance-probability statistics. All 

independent variables selected through use of OLS regression 

in this study were statistically significant at the 95-percent 

confidence level. Independent variables were selected to 

minimize SEE and to maximize adj-R2

. Adj-R2 is a measure of 

the proportion of the variation in the dependent variable that is 

explained by the independent variables, and is adjusted for the 

number of streamgages and independent variables used in the 

analysis. Correlation between the independent variables and 

VIF (Marquardt, 1970; Helsel and Hirsch, 2002) was used to 

evaluate multicollinearity in the regression models. By using a 

regression diagnostics tool implemented in the USGS library 

version 4.0 (Lorenz and others, 2011) for Spotfire S+® statistical software (TIBCO Software Inc., 2008), multicollinearity 

problems were identified by checking each independent variable for VIF greater than 2.

WLS multiple linear regression was used to develop 14 

of the final regression equations for Iowa streamflow because 

all exceedance-probability streamflows were greater than zero 

and because the lengths of record varied. WLS regression 

adjusts for the variation in the reliability of the dependentvariable estimates by using a weight for each streamgage to 

account for differences in length of streamflow records. WLS 

regression analyses were performed by using the WREG 

program (version 1.01) (Eng and others, 2009). A user-defined 

weighting matrix was used to weight streamgages in Iowa and 

the 50-mi buffer extending into Illinois, Minnesota, Missouri, 

and Nebraska for application of WREG for the development of exceedance-probability streamflow equations. The 

weighting matrix was developed on the basis of record length 

and was computed as the number of years of record at the 

streamgage divided by the average number of years of record 

of all streamgages in the regression dataset. Thus, streamgages 

with shorter periods of record received less weight in the 

regression analyses and those with longer periods of record 

received greater weight. WLS models were selected for use 

over the OLS models for the development of the statewide 

regression equations because the WLS models give greater 

weight to the dependent-variable estimates with longer record 

lengths; therefore, the WLS equations are assumed to be more 

accurate. Final WLS regression models (table 8) were selected 

primarily on the basis of minimizing values of the average 

standard error of prediction (SEP). 

Left-censored regression was used to develop one equation for Iowa because the number of streamgages in Iowa with 

estimates of zero flow for exceedance-probability streamflows 

was less than 5 percent. A censoring threshold of 0.1 ft3/s 

was used to censor small dependent-variable discharges and 

zero flows estimated for the 0.99-percent exceedance probability statistic (table 8). Censored and uncensored dependentvariable data can be included together in a censored regression 

analysis (Eash and Barnes, 2012). To develop the left-censored 

regression equation for this study, an AMLE procedure implemented in the USGS library version 4.0 (Lorenz and others, 

2011) for Spotfire S+® statistical software (TIBCO Software 

Inc., 2008) was used. The final left-censored regression model 

was selected primarily on the basis of minimizing values of 

the SEE. 

Determination of Reference Streamgages

In order to determine how well the Flow Duration Curve 

Transfer method might estimate streamflow at ungaged sites, 

gaged sites were iteratively treated as ungaged, or nonreference, sites. Comparisons then could be made by examining the 

observed and estimated streamflows for the gaged sites. In this 

section, sites that are referred to as ungaged (nonreference) 

sites are actually gaged sites that were treated as ungaged sites 

for comparison purposes. In the Flow Duration Curve Transfer method, a single reference streamgage was selected from 

the 113 reference streamgages in this study (fig. 1; table 1). 

In this study, 10 years of record (October 1, 1999, through 

September 30, 2009) were used for the reference streamgages 

because 10 years was the minimum period of record used to 

generate the flow-duration curves and regression equations. 

Values of streamflow at the reference streamgage were not 

used in the Flow Duration Curve Transfer method; only the 

date and exceedance probabilities at the reference streamgage 

were used.

In the Flow Duration Curve Transfer method, it is implied 

that the date on which a specific streamflow is exceeded 

at the nonreference site is the same as that at the reference 

streamgage (that is, if the streamflow on October 1, 1999, is 

exceeded 95 percent of the time at the reference streamgage, 

the streamflow exceeded 95 percent of the time at the nonreference site also occurred on October 1, 1999). The same is 

true for the other exceedance probabilities; in the Flow Duration Curve Transfer method, it is assumed that the high-flow, 

midrange-flow, and low-flow events occur on the same day at 

both the reference streamgage and the nonreference site. As 

a result, the most appropriate reference streamgage would be 

the one for which the largest number of streamflows correlate 

with those at the nonreference site. The Flow Duration Curve 

Transfer method quantifies the correlation between the timing 

of the streamflows at 112 reference streamgages and those at 

the nonreference site by using Pearson’s r correlation coefficient (equation 3) (Helsel and Hirsch, 2002). The likelihood of 

equivalent exceedance probabilities occurring on the same day 

is greater for two sites that have a value of Pearson’s r correlation coefficient near 1, which indicates that the high-flow, 

midrange-flow, and low-flow events occur on the same day at 

both the reference streamgage and the nonreference site, than 

for two sites that have a lower Pearson’s r correlation coefficient value. 

The Pearson’s r correlation coefficient can be calculated for two gaged sites but cannot be measured directly 

for streamflows at a gaged and an ungaged site. As a result, 
Flow Duration Curve Transfer Analytical Procedures 37

the Flow Duration Curve Transfer method is used to estimate the correlation between the logarithm (base 10) of the 

streamflows at the nonreference site and each possible reference streamgage and then selects the reference streamgage 

for which logarithms (base 10) of the daily streamflow are 

estimated to have the highest correlation with the logarithms 

(base 10) of the daily streamflows at the nonreference site. 

The correlation between the streamflows at a nonreference site and those at a potential reference gage is estimated 

by examining the spatial patterns of streamflow correlation 

across all gages in the study area. Time-series correlations 

at gaged sites were spatially interpolated to ungaged areas 

by using kriging (Isaaks and Srivastava, 1989), a geostatistical method. For a particular reference streamgage, the 

Pearson’s r correlation coefficient value was computed from 

the logarithms of observed, concurrent daily streamflows at 

the given reference streamgage and each of the other reference streamgages used in the Flow Duration Curve Transfer 

method. A spherical variogram model (Isaaks and Srivastava, 

1989) then was developed for each reference streamgage to 

quantify the relation between the distances between each pair 

of reference streamgages and the differences in the Pearson’s 

r correlation coefficient values between each pair of reference 

streamgages. Each variogram model quantifies the Pearson’s r

correlation coefficient value for the relation between streamflow at any ungaged site and that at a reference streamgage. 

The reference streamgage with the highest Pearson’s r correlation coefficient value between streamflow at the reference 

site and that at the ungaged site is then selected for use with 

the Flow Duration Curve Transfer method. The Flow Duration 

Curve Transfer method requires only the Universal Transverse 

Mercator (UTM) coordinates of the ungaged site in order to 

select the reference streamgage. The variogram models can 

be used to create prediction maps of the Pearson’s r correlation coefficient value for each reference streamgage; these 

maps show the correlation between streamflow at a reference 

streamgage and that at any ungaged site in Iowa. For this 

report, prediction maps were generated for three streamgages 

(fig. 12). For the 05412500, Turkey River at Garber, Iowa, 

streamgage (fig. 12A), the areas with the higher estimated correlations form a triangle but the correlations tend to be slightly 

greater along the major axis from northwest to southeast 

than elsewhere. For the 05452200, Walnut Creek near Hartwick, Iowa, streamgage (fig. 12B), the areas with the higher 

estimated correlations form an ellipsoid with the major axis 

trending northwest-southeast. For the 06483500, Rock River 

near Rock Valley, Iowa, streamgage (fig. 12C), the areas with 

the higher estimated correlations form an ellipsoid with the 

major axis trending southwest-northeast. If the Flow Duration 

Curve Transfer method ultimately is implemented as the most 

accurate model for estimating streamflow at ungaged sites, 

variograms would be generated for all the streamgages in the 

study area.

Comparison of Observed and Estimated 

Streamflows

In the Flow Duration Curve Transfer method, a time 

series of unregulated, daily mean streamflow at an ungaged 

site is constructed in the following order: (1) solve the 

regression equations, (2) interpolate between the regressionestimated streamflow quantiles to obtain a daily flow-duration 

curve for the ungaged site, (3) select the reference streamgage 

from the kriged maps of Pearson’s r correlations, and (4) apply 

the Flow Duration Curve Transfer method to compute the 

estimated streamflow at the ungaged site for the desired 

time period. To evaluate the Flow Duration Curve Transfer 

method for use in estimating daily, unregulated streamflows 

at an ungaged site, a validation procedure was used at six 

streamgages that were not used either to develop the regression equations or to conduct the kriging procedure because 

they did not have at least 10 years of record. These same six 

sites were used in developing the regression for the Flow Anywhere method and in the Flow Anywhere validation procedure 

by removing one of the six streamgages at a time. Five years 

of record were used for the validation procedure for these six 

streamgages. In effect, the validation procedure evaluates the 

estimates of streamflow at a streamgage that was not used in 

the development of the Flow Duration Curve Transfer method. 

The six streamgages used were 05387440, Upper Iowa River 

at Bluffton, Iowa (fig. 1, table 1, map no. 4); 054118850, 

Turkey River near Eldorado, Iowa (fig. 1, table 1, map no. 10); 

05412020, Turkey River above French Hollow Creek at 

Elkader, Iowa (fig. 1, table 1, map no. 11); 05416900, Maquoketa River at Manchester, Iowa (fig. 1, table 1, map no. 16); 

05421740, Wapsipinicon River near Anamosa, Iowa (fig. 1, 

table 1, map no. 21); and 06483290, Rock River below Tom 

Creek at Rock Rapids, Iowa (fig. 1, table 1, map no. 92).

As for the Flow Anywhere method, observed and estimated streamflows were compared for goodness of fit at each 

of the streamgages (table 5) by using the mean-absolute-error 

(MAE), root-mean-square-error (RMSE), percent-root-meansquare-error (PRMSE), RMSE-observations standard-deviation ratio (RSR), percent-bias (PBIAS), and Nash-Sutcliffe 

(NS) efficiency values (Nash and Sutcliffe, 1970). The 

PRMSE and NS values also were computed for each of the six 

streamgages by using the base-10 logarithmic values of the 

observed and estimated daily streamflows (table 5). For the 

Flow Duration Curve Transfer method, differences between 

the RMSE and the MAE (differences not shown in table 5) 

ranged from 437 ft3/s at 05421740, Wapsipinicon River near 

Anamosa, Iowa, to 93.9 ft3/s at 05387440, Upper Iowa River 

at Bluffton, Iowa, signifying a greater occurrence of outliers 

with respect to the relation between observed and estimated 

streamflows at 05421740, Wapsipinicon River near Anamosa, Iowa, than at the other five streamgages. RMSE values 

ranged from 906 ft3/s at 05421740, Wapsipinicon River near 
9

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98° 96° 94° 92° 90° 

44°42°40°

IOWA

MISSOURI

MINNESOTA

NEBRASKA

SOUTH

DAKOTA

KANSAS

Base from U.S. Geological Survey digital data, 2005, 1:24,000Universal Transverse Mercator projection, Zone 15

0 50 100 MILES0 50 100 KILOMETERS 

EXPLA

Estimated Pearson’s r correlati

coefficient 

0.2–0.30.3–0.40.4–0.50.5–0.6

0.6–0.70.7–0.80.8–0.90.9–1.0

A

Figure 12. Estimated Pearson’s r correlations of the logarithm of daily streamflows at the U.S. Geological Survey streamgages (A) 05412500, Turkey River at Garber, Iowa; (B) 05452200, Walnut Creek near Hartwick, Iowa; and (C) 06483500, Rock River near Rock Valley, Iowa (streamgages are listed and identified by map number in table 1).
9

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98° 96° 94° 92° 90° 

44°42°40°

IOWA

MISSOURI

MINNESOTA

NEBRASKA

SOUTH

DAKOTA

KANSAS

Base from U.S. Geological Survey digital data, 2005, 1:24,000Universal Transverse Mercator projection, Zone 15

0 50 100 MILES0 50 100 KILOMETERS 

EXPLA

Estimated Pearson’s r correlation 

coefficient 

0.4–0.50.5–0.6

0.6–0.7

0.7–0.80.8–0.90.9–1.0

B

Figure 12. Estimated Pearson’s r correlations of the logarithm of daily streamflows at the U.S. Geological Survey streamgages (A) 05412500, Turkey River at Garber, Iowa; (B) 05452200, Walnut Creek near Hartwick, Iowa; and (C) 06483500, Rock River near Rock Valley, Iowa (streamgages are listed and identified by map number in table 1).—Continued
9

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98° 96° 94° 92° 90° 

44°42°40°

IOWA

MISSOURI

MINNESOTA

NEBRASKA

SOUTH

DAKOTA

KANSAS

Base from U.S. Geological Survey digital data, 2005, 1:24,000Universal Transverse Mercator projection, Zone 15

0 50 100 MILES0 50 100 KILOMETERS 

EXPLA

Estimated Pearson’s r correlati

coefficient 

0.2–0.30.3–0.40.4–0.50.5–0.6

0.6–0.70.7–0.80.8–0.90.9–1.0

C

Figure 12. Estimated Pearson’s r correlations of the logarithm of daily streamflows at the U.S. Geological Survey streamgages (A) 05412500, Turkey River at Garber, Iowa; (B) 05452200, Walnut Creek near Hartwick, Iowa; and (C) 06483500, Rock River near Rock Valley, Iowa (streamgages are listed and identified by map number in table 1).—Continued
Flow Duration Curve Transfer Analytical Procedures 41

Anamosa, Iowa, to 169 ft3/s at 05387440, Upper Iowa River 

at Bluffton, Iowa. PRMSE values ranged from 67 percent at 

06483290, Rock River below Tom Creek at Rock Rapids, 

Iowa, to 25.6 percent at 05387440, Upper Iowa River at Bluffton, Iowa. The logarithm (base 10) streamflow PRMSE ranged 

from 12.5 percent at 05416900, Maquoketa River at Manchester, Iowa, to 4.4 percent at 05387440, Upper Iowa River 

at Bluffton, Iowa. RSR values ranged from 0.79 at 05416900, 

Maquoketa River at Manchester, Iowa, to 0.40 at 05412020, 

Turkey River above French Hollow Creek at Elkader, Iowa. 

PBIAS values ranged from 22.7 percent at 05416900, Maquoketa River at Manchester, Iowa, to 0.94 percent at 05411850, 

Turkey River near Eldorado, Iowa, and 05412020, Turkey 

River above French Hollow Creek at Elkader, Iowa. For the 

Flow Duration Curve Transfer method, NS values ranged 

from 0.84 at 05412020, Turkey River above French Hollow 

Creek at Elkader, Iowa, to 0.38 at 05416900, Maquoketa River 

at Manchester, Iowa, by using the untransformed observed 

and estimated daily streamflows, and from 0.89 at 05387440, 

Upper Iowa River at Bluffton, Iowa, to 0.48 at 05416900, 

Maquoketa River at Manchester, Iowa, by using the base-10 

logarithmic values of the observed and estimated daily streamflows. On the basis of all the ranges of statistics reported 

above, including the difference between the RMSE and 

MAE, the observed and estimated daily mean streamflows for 

streamgages with the closest and poorest agreement over the 

5-year period, 05387440, Upper Iowa River at Bluffton, Iowa 

(fig. 1, table 1, map no. 4), and 05416900, Maquoketa River 

at Manchester, Iowa (fig. 1, table 1, map no. 16), respectively, 

are shown in figure 13. For the closest agreement between the 

observed and estimated daily mean streamflows (fig. 13A), 

the relation at the higher flows appears to show a “hook-like” 

feature, which may indicate that the assumption of a log-linear 

relation between streamflow quantiles at the highest flows (and 

possibly the lowest flows) may not be appropriate (Archfield 

and others, 2009). The lowest flows in figure 13B appear to be 

underestimated. 

Observed and estimated hydrographs (in logarithmic 

space) for streamgages with the closest (05387440, Upper 

Iowa River at Bluffton, Iowa), and poorest (05416900, 

Maquoketa River at Manchester, Iowa) agreements over the 

period October 1, 2004, through September 30, 2009, are 

shown in figures 14A and 14B, respectively. A visual comparison of the hydrographs in figure 14A shows relatively 

good agreement between observed and estimated streamflows, 

whereas those in figure 14B appear to indicate that streamflows are substantially underestimated for much of the time 

period. Estimated cumulative streamflow (fig. 11) for the 

period October 1, 2004, to September 30, 2009, is underestimated for 05387440, Upper Iowa River at Bluffton, Iowa, and 

05416900, Maquoketa River at Manchester, Iowa, by -9.3 and 

-22.7 percent, respectively, and verifies the degree to which 

streamflows are underestimated for the closest (figs. 13A and 

14A) and poorest (figs. 13B and 14B) agreements for the six 

validation sites.

For both the closest and poorest agreements between 

observed and estimated daily mean streamflows, a set of 

data points that plot horizontally can be seen at about 500 

and 360 ft3/s in figures 13A and 13B, respectively. These 

results for 05387440, Upper Iowa River at Bluffton, Iowa, 

and 05416900, Maquoketa River at Manchester, Iowa (flowduration curves not shown), correspond to those portions 

of the transferred (estimated flows) flow-duration curve, 

as is evident in the flow-duration curve for the streamgage 

05412500, Turkey River at Garber, Iowa (fig. 15A), where 

Figure 13. Observed and estimated daily mean streamflows 

for U.S. Geological Survey streamgages (A) 05387440, Upper 

Iowa River at Bluffton, Iowa; and (B) 05416900, Maquoketa River 

at Manchester, Iowa, showing the (A) closest and (B) poorest 

agreement between unregulated observed and estimated 

daily mean streamflow, October 1, 2004, to September 30, 2009, 

determined by using the Flow Duration Curve Transfer method.

10 100 1,000 10,000

100

1,000

10,000

A 05387440, Upper Iowa River at Bluffton, Iowa

Estimated streamflow, in cubic feet per second Estimated streamflow, in cubic feet per second

Observed streamflow, in cubic feet per second

10 100 1,000 10,000

10

100

1,000

10,000

B 05416900, Maquoketa River at Manchester, Iowa

Observed streamflow, in cubic feet per second

1:1 line

10

1:1 line
42 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

along the curve at the higher flows, one estimated streamflow value becomes greater than the previous streamflow as 

the exceedance probabilities increase (lower flows). Also in 

figure 15A, along the lower flows, one estimated streamflow 

value becomes less than the previous value as the exceedance 

probabilities decrease (greater flows). This is a limitation of 

the Flow Duration Curve Transfer method (Archfield and 

others, 2009) and is discussed in the Limitations of Methods 

section for this method. This “jagging” occurs at the exceedance probabilities (10 to 15 percent and 80 to 70 percent) at 

which the basin characteristics used in the regression equations change appreciably (table 8). Of the streamgages used 

for the Flow Duration Curve Transfer method, this “jagging” 

occurs at 12 streamgages in Iowa, 5 streamgages in Nebraska, 

5 streamgages in Wisconsin, and 1 streamgage in Missouri; 

these streamgages are primarily in either the western or northeastern portion of the study area. Of these 23 streamgages, this 

“jagging” occurs only for 11 streamgages, all in the northeastern part of the study area, and only at the high flows. It occurs 

only at the low flows for nine streamgages, all in the western 

portion of the study area, and at both high and low flows for 

three streamgages, all in the northeastern portion of the study 

area. 

Uncertainty of Estimated Streamflows

The overall uncertainty inherent in estimating a time 

series of unregulated, daily mean flow at an ungaged site by 

using the Flow Duration Curve Transfer method is difficult 

to quantify. The key components are (1) estimation of the 

flow-duration curve at the ungaged site, (2) choosing a reference streamgage on the basis of maps of cross-correlations 

among flow records from existing gaged sites, and (3) transfer of daily streamflows from the reference streamgage to 

the ungaged site by using the Flow Duration Curve Transfer 

method and its inherent assumptions. Each component of the 

Flow Duration Curve Transfer method adds unique uncertainty 

to the estimated streamflows at the ungaged site, in addition to 

the measurement error associated with the observed streamflows used to develop the regression equations and the selection and use of the reference gage. As previously mentioned in 

the discussion of the Flow Anywhere Method, localized storm 

events could introduce additional uncertainty into the observed 

streamflows, and as a result introduce error into the estimated 

streamflows. 

If the Flow Duration Curve Transfer method were based 

on a single modeling approach or a physically based model, 

standard methods of uncertainty analysis could be used; 

however, because the estimated streamflows used in the Flow 

Duration Curve Transfer method are derived through a variety 

of complex modeling steps, the standard methods of uncertainty analysis do not provide meaningful prediction intervals 

(Archfield and others, 2009). In this report, to address the 

issue of uncertainty for the Flow Duration Curve Transfer 

method, the conditions under which one might be expected to 

obtain the type of goodness-of-fit values reported are documented in table 5. Because the goodness-of-fit values are 

based on cross-validation tests, they may indicate a range of 

uncertainty that could be expected in future uses of the Flow 

Duration Curve Transfer method for estimating streamflows 

at ungaged sites, although it would have been preferable to 

use more than six sites for the validation tests. Only six sites 

were used, however, as a result of the limited availability of 

streamgages that were not used in the Flow Duration Curve 

Transfer method.

Limitations of Methods

One of the limitations of the Flow Duration Curve Transfer method for estimating time series of unregulated, daily 

mean streamflow is that the use of the regression equations is 

limited to the range of basin characteristics (table 9) used to 

develop those equations. The appropriateness of the statewide 

equations is unknown when basin characteristics outside the 

range of measured basin characteristics are used to develop the 

regression equations. As previously mentioned, for the three 

components of the Flow Duration Curve Transfer method, 

(1) regression equations, (2) reference-streamgage selection 

criteria, and (3) the assumption of equivalent exceedance 

probabilities on the same day, all contribute to the uncertainty 

associated with estimates of unregulated, daily mean streamflows. There is no current theoretical framework from which 

prediction or confidence intervals for the Flow Duration Curve 

Transfer method-estimated daily streamflows can be derived 

(Archfield and others, 2009).

The regression equations developed for the Flow Duration Curve Transfer method were intended for use as a statewide model similar to that described by Archfield and others 

(2009), and no attempt was made to develop smaller regional 

equations because of potential complications involving the 

kriging for selection of the reference streamgages around 

smaller regional boundary areas. It is possible that the SEE for 

some areas in Iowa could improve, whereas the SEE for other 

parts of the state, especially around the boundary areas, could 

increase.

As indicated in the Limitations of Methods section for 

the Flow Anywhere method, because of the uncertainties 

associated with measuring and estimating streamflows less 

than 0.1 ft3/s, the censoring threshold used to develop the 

left-censored regression equation for the 99-percent exceedance probability was set to 0.1 ft3

/s. As a result and to provide 

consistency, daily mean streamflow estimates computed from 

the regression equations at ungaged locations for any exceedance probabilities where estimates are less than 0.1 ft3

/s are 

reported as less than 0.1 ft3/s. 

Also, as previously mentioned in the Limitations of 

Methods section for the Flow Anywhere method, estimates 

of daily mean streamflows by using the Flow Duration Curve 

Transfer method at unregulated, ungaged locations in Iowa are 

limited to days after September 30, 1977 (32 years of record). 
Flow Duration Curve Transfer Analytical Procedures 43

Figure 14. Observed and estimated hydrographs for U.S. Geological Survey streamgages (A) 05387440, Upper Iowa River at 

Bluffton, Iowa; and (B) 05416900, Maquoketa River at Manchester, Iowa, showing the (A) closest and (B) poorest agreement between 

unregulated observed and estimated, daily mean streamflow, October 1, 2004, to September 30, 2009, determined by using the Flow 

Duration Curve Transfer method.

10/1/2004 10/1/2005 10/1/2006

Date

10/1/2007 10/1/2008 9/30/2009

10

100

1,000

10,000

100,000

A 05387440, Upper Iowa River at Bluffton, Iowa

Streamflow, in cubic feet per second

10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

10

100

1,000

10,000

100,000

B 05416900, Maquoketa River at Manchester, Iowa

Streamflow, in cubic feet per second

Estimated streamflow

Observed streamflow

EXPLANATION

Reference streamgage 05388250,

Upper Iowa River near Dorchester, Iowa

Estimated streamflow

Observed streamflow

EXPLANATION

Reference streamgage 05412500,

Turkey River at Garber, Iowa

Date
44 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Figure 15. Observed and 

estimated flow duration 

exceedance probabilities 

for selected streamgages in 

Iowa.

100

1,000

10,000

A 05412500, Turkey River at Garber, Iowa

0

1

10

100

1,000

B 05452200, Walnut Creek near Hartwick, Iowa

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Exceedence probability

1

10

100

1,000

10,000

C 06483500, Rock River near Rock Valley, Iowa

Streamflow, in cubic feet per second Streamflow, in cubic feet per second Streamflow, in cubic feet per second

Estimated streamflow

Observed streamflow

EXPLANATION
Summary 45

Two streamgages have only 10 years of record (the minimum 

for the Flow Duration Curve Transfer method); therefore, if 

those streamgages were selected as reference gages, estimated 

daily mean streamflows could be computed only for days after 

September 30, 1999 (table 1). Most streamgages used for the 

Flow Duration Curve Transfer method have 32 years of record 

(October 1, 1977, to September 30, 2009). 

Another limitation of the Flow Duration Curve Transfer 

method is the “jagging” that occurs along the Flow Duration 

Curve Transfers for some streamgages where along the curve 

at the higher flows, an estimated streamflow value becomes 

greater than the previous streamflow value as the exceedance 

probabilities increase (smaller flows), and where along the 

curve at lower flows, an estimated streamflow value becomes 

smaller than the previous value as the exceedance probabilities 

decrease (greater flows). As a result, the inherent structure of 

the Flow Duration Curve Transfer data at some of the potential 

reference streamgages is a physical impossibility. This issue 

has been addressed in a previous study by recursively regressing against other estimated streamflow quantiles (Archfield 

and others, 2009). As previously mentioned, this condition 

occurs at 23 streamgages in the study area for the Flow Duration Curve Transfer method, but no effort was made to address 

this issue in this study.

Table 9. Range of basin characteristics used for final regression 

equations for estimating flow-duration statistics for unregulated 

streams in Iowa.

[DA, drainge area; PRECIP, mean annual precipitation 1971–2000; 

SOILCSSURGO, percent area underlain by hydrologic soil type C; RSD, relative stream density; HYSEP, hydrograph separation and analysis is the median 

percentage of baseflow to annual streamflow; STREAM_VAR, streamflowvariability index, a measure of the steepness of the slope of a duration curve; 

SOILBSSURGO, percent area underlain by hydrologic soil type B; 

SOILDSSURGO, percent area underlain by hydrologic soil type D]

Summary

This study is part of a larger project conducted by the 

U.S. Geological Survey (USGS) in cooperation with the Iowa 

Department of Natural Resources (IDNR) to develop a variety 

of methods for estimating daily mean streamflow at ungaged 

locations in Iowa. In this study, two methods for estimating 

streamflow at ungaged locations were investigated: a variation 

of the drainage-area-ratio method (Flow Anywhere method) 

and a quantile-based regression model (Flow Duration Curve 

Transfer method). The regression equations for both methods 

were developed for use only in Iowa from recorded daily mean 

streamflows and basin characteristics for streamgages within 

the study area, which includes the entire State of Iowa and 

adjacent areas within a 50-mile buffer of Iowa in the neighboring states of Illinois, Minnesota, Missouri, Nebraska, and 

Wisconsin. No streamgages in the South Dakota buffer area 

were used as a result of upstream regulation or diversion. 

The Flow Anywhere method is a variation of the drainage-area-ratio method in which same-day streamflow information is transferred from a reference streamgage to an ungaged 

location by using the daily mean streamflow at the reference 

streamgage and the drainage-area ratio of the two locations. 

The drainage-area-ratio method was modified to regionalize 

the equations for Iowa and select the most appropriate reference streamgage. In the development of the Flow Anywhere 

method, streamgages with at least 5 complete years of daily 

mean streamflow record through September 30, 2009, and 

minimally affected by regulation or diversion were selected 

for evaluation. This process resulted in 92 streamgages in 

Iowa and 31 streamgages in adjacent states. Historic streamflow records prior to October 1, 1977, were not included in 

this analysis because trends were found in the data.

In the Flow Anywhere method, the correlation of historical streamflows between streamgages in the study area is first 

examined to determine local region boundaries. The local 

regions are defined so that the basins within the regions are 

physiographically similar. Some streamgages in the neighboring states were found to have low correlation to any 

streamgages within Iowa. These streamgages were removed 

from the study with the likelihood that they lie in a local 

region completely outside Iowa, and therefore are not relevant 

to this study. The remaining 107 streamgages were used in 

the development of the Flow Anywhere method. Reference 

streamgages were selected for each local region by examining 

results of an ordinary-least-squares regression. Streamgages 

in local regions that exhibit similar hydrologic properties were 

grouped together into three aggregated regions. Regression 

computations were completed to develop regional regression 

equations to compute streamflow for ungaged locations. Leftcensored regression analyses were performed in aggregated 

regions 1 and 2 where there were observed zero streamflows. 

An ordinary-least-squares regression analysis was used in 

aggregated region 3, where zero flows were not observed. 

Two additional streamgages were removed from the regression analyses because streamgages with drainage areas larger 

Basin 

characteristic Minimum Maximum Median Mean

DA 15.5 7,782 491 999

PRECIP 27.7 38.0 34.6 34.1

SOILCSSURGO 0.09 83.5 5.4 15.3

RSD 0.22 0.49 0.34 0.34

HYSEP 20.3 78.0 54.5 50.3

STREAM_VAR 0.21 0.76 0.59 0.57

SOILBSSURGO 5.7 99.4 89.3 78.9

SOILDSSURGO 0 57.0 0.63 3.6
46 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

than 5,500 square miles greatly influenced the results for the 

local region to which they belong, bringing the total number 

of streamgages used in the Flow Anywhere method to 105. 

The accuracy of the final regression equations for aggregated 

regions 1, 2, and 3 was quantified. The final equations are presented in this report along with the associated standard errors 

of the model.

The performance of the Flow Anywhere method in each 

aggregated region was examined by comparing the observed 

and estimated streamflows throughout the aggregated region. 

No obvious range of streamflows that were consistently 

over- or underestimated were found, with the exception of 

the extreme low streamflows, which generally appear to be 

slightly overestimated. Removing or adding local regions 

within the study area from or to different aggregated regions 

did not improve the estimates for the lower streamflows; therefore, the final equations presented in the report are believed to 

produce the best possible results that can be achieved with the 

dataset.

To evaluate the use of the Flow Anywhere method for 

estimating streamflow at ungaged locations, a validation 

procedure was completed for six streamgages in the study 

area. For each of the six streamgages, the regional regression 

equations were redeveloped without that particular streamgage 

in the dataset, thus simulating the scenario of computing 

daily mean streamflow at an ungaged location. To quantify 

the goodness of fit between observed and estimated flows at 

each of the six streamgages, the mean absolute error (MAE), 

root-mean-square error (RMSE), percent root-mean-square 

error (PRMSE), RMSE-observations standard-deviation 

ratio (RSR), percent bias (PBIAS), and Nash-Sutcliffe 

(NS) efficiency value were computed. Differences between 

the RMSE and the MAE ranged from 1,016 ft3/s at USGS 

streamgage 05421740, Wapsipinicon River near Anamosa, 

Iowa (all streamgages named below are in Iowa), to 138 ft3/s 

at 05387440, Upper Iowa River at Bluffton, signifying a 

greater occurrence of outliers between observed and estimated 

streamflows at 05421740, Wapsipinicon River near Anamosa. 

RMSE values ranged from 1,690 ft3/s at 05421740, Wapsipinicon River near Anamosa, to 237 ft3

/s at 05387440, Upper Iowa 

River at Bluffton. PRMSE values ranged from 115 percent at 

06483290, Rock River below Tom Creek at Rock Rapids, to 

26.2 percent at 05387440, Upper Iowa River at Bluffton. The 

logarithm (base 10) of the streamflow PRMSE ranged from 

13.0 percent at 06483290, Rock River below Tom Creek at 

Rock Rapids, to 5.3 percent at 05387440, Upper Iowa River at 

Bluffton. RSR values ranged from 0.80 at 05416900, Maquoketa River at Manchester, to 0.40 at 05387440, Upper Iowa 

River at Bluffton. PBIAS values ranged from 25.4 percent 

at 05387440, Upper Iowa River at Bluffton, to 4.0 percent at 

both 05412020, Turkey River above French Hollow Creek 

at Elkader, and 06483290, Rock River below Tom Creek at 

Rock Rapids. Untransformed streamflow NS values ranged 

from 0.84 at 05387440, Upper Iowa River at Bluffton, to 0.35 

at 05416900, Maquoketa River at Manchester. The logarithm 

(base 10) of the streamflow NS values ranged from 0.86 to 

0.56 for the same two sites, respectively. These statistics 

indicate that the closest match was for 05387440, Upper 

Iowa River at Bluffton, and the poorest was for 05416900, 

Maquoketa River at Manchester. Also, a visual comparison of 

observed and estimated hydrographs for the same streamgages 

shows relatively close agreement between observed and 

estimated streamflows for 05387440, Upper Iowa River 

at Bluffton, Iowa, whereas the estimated streamflows for 

05416900, Maquoketa River at Manchester, Iowa, appear to 

be substantially either under- or overestimated for much of the 

time period. 

Because of the uncertainty inherent in measuring and 

estimating flows less than 0.1 ft3/s, the censoring threshold 

used to develop the left-censored regression equations for 

aggregated regions 1 and 2 was set to 0.1 ft3/s. Therefore, daily 

mean streamflow estimates computed from the regression 

equations for ungaged locations that are less than 0.1 ft3/s are 

to be reported as less than 0.1 ft3/s for all ungaged locations to 

maintain a consistent reporting limit. Estimates of streamflows 

made on the same stream segment as a streamgage are to be 

made with caution because the resulting estimated streamflow 

at the ungaged location needs to be verified as hydrologically 

reasonable with respect to the streamflows at the streamgage. 

Also, a general “rule of thumb” used in other regression 

analyses is to use the traditional drainage-area ratio to estimate streamflow when the ratio of the drainage area of the 

ungaged location to that of the streamgage is between 0.5 and 

1.5. The data used in the development of the Flow Anywhere 

method consisted of daily mean streamflows from October 1, 

1977, to September 30, 2009. Computations of estimated 

daily mean streamflows at ungaged locations can be made for 

any date after September 30, 1977, provided that daily mean 

streamflow values for the associated reference streamgage are 

available for the days of interest. The Flow Anywhere method 

should not be applied to dates prior to October 1, 1977, as a 

result of trends found in annual mean streamflows. Computations of estimated daily mean streamflow at ungaged locations 

for dates after September 30, 2009, should be made with the 

assumptions that trends do not exist in the streamflow records 

and that no changes to basins have been made that would alter 

the relation between streamflows used in the development of 

the method.

Daily mean streamflow data used in the Flow Duration 

Curve Transfer method were retrieved for 113 continuousrecord streamgages located in and within a 50-mile buffer 

of Iowa in the neighboring states. No streamgages in South 

Dakota were used as a result of regulation or diversion. 

Streamgages with at least 10 complete years of daily mean 

streamflow record through September 30, 2009, and minimally affected by regulation or diversion, which included 

84 streamgages in Iowa and 29 streamgages in adjacent states, 

were selected for evaluation. Daily mean streamflow values 

prior to October 1, 1977, were not retrieved because trends 

were found in the record. Prior to the final selection of the 

streamgages used in this method, 102 streamgages in Iowa 

with periods of record greater than 10 years were tested by 
Summary 47

using Kendall’s tau hypothesis test; positive trends were found 

in the annual mean streamflow quantiles at the 90-percent 

exceedance probability statistic for 61 of those streamgages. 

Trends in these data could introduce a bias into the Flow Duration Curve Transfer analyses, violating the assumption that 

flow-duration statistics are independent and stationary over 

time. Tests for trends in streamflow also were completed for 

the 50-percent and 10-percent exceedance probabilities; however, the number of streamgages showing trends in streamflow decreased with decreasing percent exceedances (higher 

streamflows). For the annual mean streamflow 90-percent 

exceedance probability statistic, 1978 was found to be the 

latest date beyond which the streamflow data do not exhibit a 

trend as determined by using the trend analysis test.

To develop the quantile-based regression equations, the 

dependent variable, the streamflow quantiles, and the independent variables, which are the physical and climate basin characteristics, were quantified for each of the 113 streamgages. 

To compute the streamflow quantiles, the observed daily 

streamflows were ranked and an exceedance probability 

was computed. Streamflow quantiles were estimated at the 

following exceedance probabilities: 0.01, 0.05, 0.10, 0.15, 

0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.85, 0.90, 0.95, and 

0.99. Regression equations then were developed for the above 

quantiles. A total of 57 physical and climate basin characteristics were tested for use as explanatory (independent) variables. 

Two sets of regression equations initially were developed; one 

set of equations was generated using ordinary-least-squares 

regression and one set of equations resulted from the use 

of the weighted-least-squares method or the left-censored 

method. With the exception of the equation (left-censored) for 

the 0.99-percent exceedance probability, all final equations 

were developed by using the weighted-least-squares method. 

For the left-censored regression equation for the 0.99-percent 

exceedance probability streamflow values, nine values were 

less than or equal to the censor threshold of 0.1 ft3/s. Five 

values were zero flows. The dependent variables and the independent variable, drainage area, were transformed to base-10 

logarithms to obtain linear-regression equations.

In the Flow Duration Curve Transfer method, a single 

reference streamgage was selected from the 113 reference 

streamgages in Iowa, Illinois, Minnesota, Missouri, Nebraska, 

and Wisconsin. Each streamgage in turn was treated as an 

ungaged (nonreference) site. The Flow Duration Curve Transfer method requires that daily streamflow records are available 

for both the reference streamgage and the nonreference site 

for the time period of interest. For this study, a 10-year period 

of record (October 1, 1999, through September 30, 2009) was 

used for the reference streamgages, because 10 years was the 

minimum period of record used to generate the flow-duration 

curves and regression equations. It is implied that the date 

of a specific streamflow being exceeded at the nonreference 

site is the same as that at the reference streamgage (that is, 

if the streamflow on October 1, 1999, is exceeded 95 percent of the time at the reference streamgage, the streamflow 

exceeded 95 percent of the time at the nonreference site also 

occurred on October 1, 1999). The same is true for the other 

exceedance probabilities. As a result, the most appropriate 

reference streamgage would be the one for which the most 

streamflows are correlated to those at the nonreference site. 

The Flow Duration Curve Transfer method quantifies the correlation between the timing of the streamflows at 112 reference streamgages and those at the nonreference site by using 

Pearson’s r correlation coefficient. 

Time-series correlations between the nonreference site 

and each reference streamgage were achieved through kriging. 

A spherical variogram model then was then developed for 

each reference streamgage to quantify the relation between 

the distances between each pair of reference streamgages and 

the differences in the Pearson’s r correlation coefficient values 

between each pair of reference streamgages. Each variogram 

model quantifies the Pearson’s r correlation coefficient value 

for any ungaged site in relation to a reference streamgage. The 

reference streamgage with the highest Pearson’s r correlation 

coefficient value in relation to the ungaged site is then selected 

for use with the Flow Duration Curve Transfer method. The 

variogram models can be used to create prediction maps of 

the Pearson’s r correlation coefficient value for each reference 

streamgage, which show the correlation between streamflow at 

a reference streamgage and at any ungaged site in Iowa.

To evaluate the Flow Duration Curve Transfer method for 

use in estimating daily, unregulated streamflows at an ungaged 

site, a validation procedure was used at six streamgages 

that were not used to develop the regression equations 

and were not used in the kriging procedure. Five years of 

record were used for the validation procedure for these six 

streamgages. Observed and estimated streamflows for each 

of the streamgages were compared for goodness of fit by 

using the mean absolute error (MAE), root-mean-square error 

(RMSE), percent root-mean-square error (PRMSE), RMSEobservations standard-deviation ratio (RSR), percent bias 

(PBIAS), and Nash-Sutcliffe (NS) efficiency values. For the 

Flow Duration Curve Transfer method, differences between 

the RMSE and the MAE ranged from 437 ft3/s at 05421740, 

Wapsipinicon River near Anamosa, Iowa (all streamgages 

named below are in Iowa), to 93.9 ft3/s at 05387440, Upper 

Iowa River at Bluffton, signifying a greater occurrence of 

outliers between observed and estimated streamflows at 

05421740, Wapsipinicon River near Anamosa. RMSE values ranged from 906 ft3

/s at 05421740, Wapsipinicon River 

near Anamosa, to 169 ft3/s at 05387440, Upper Iowa River at 

Bluffton. PRMSE values ranged from 67 percent at 06483290, 

Rock River below Tom Creek at Rock Rapids, to 25.6 percent 

at 05387440, Upper Iowa River at Bluffton. The logarithm 

(base 10) of the streamflow PRMSE ranged from 12.5 percent 

at 05416900, Maquoketa River at Manchester, to 4.4 percent 

at 05387440, Upper Iowa River at Bluffton. RSR values 

ranged from 0.79 at 05416900, Maquoketa River at Manchester, to 0.40 at 05412020, Turkey River above French Hollow 

Creek at Elkader. PBIAS values ranged from 22.7 percent at 

05416900, Maquoketa River at Manchester, to 0.94 percent at 

05411850, Turkey River near Eldorado, and 05412020, Turkey 
48 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

River above French Hollow Creek at Elkader. For the Flow 

Duration Curve Transfer method, NS values ranged from 0.84 

at 05412020, Turkey River above French Hollow Creek at 

Elkader, to 0.38 at 05416900, Maquoketa River at Manchester, 

as determined by using the untransformed observed and estimated daily streamflows, and from 0.89 at 05387440, Upper 

Iowa River at Bluffton, to 0.48 at 05416900, Maquoketa River 

at Manchester, as determined by using the base-10 logarithms 

of the observed and estimated daily streamflows. Of the six 

validation sites, the closest and poorest agreements between 

the observed and estimated daily mean streamflows for 

streamgages over the 5-year period were found for 05387440, 

Upper Iowa River at Bluffton, and 05416900, Maquoketa 

River at Manchester, respectively. A visual comparison of 

observed and estimated hydrographs for the same streamgages 

shows relatively close agreement between observed and 

estimated streamflows for 05387440, Upper Iowa River at 

Bluffton, whereas the estimated streamflows for 05416900, 

Maquoketa River at Manchester, appear to be substantially 

underestimated for much of the time period. Estimated cumulative streamflow for the period October 1, 2004, to September 30, 2009, are underestimated for 05387440, Upper Iowa 

River at Bluffton, and 05416900, Maquoketa River at Manchester, by -9.3 and -22.7 percent, respectively.

The overall uncertainty of estimating a time series of 

unregulated, daily mean streamflow at an ungaged site with 

the Flow Duration Curve Transfer method is difficult to quantify. To address this issue, the goodness-of-fit values (NS and 

percent RMSE) are documented. For the three components 

of the Flow Duration Curve Transfer method, (1) regression 

equations, (2) reference-streamgage selection criteria, and 

(3) the assumption of equivalent exceedance probabilities on 

the same day, all contribute to the uncertainty associated with 

estimates of unregulated, daily mean streamflows determined 

by using the Flow Duration Curve Transfer method. No theoretical framework currently exists from which prediction or 

confidence intervals for the daily streamflows estimated with 

the Flow Duration Curve Transfer method can be derived.

References Cited

Archfield, S.A., Vogel, R.M., Steeves, P.A., Brandt, S.L., 

Weiskel, P.K., and Garabedian, S.P., 2009, The Massachusetts Sustainable-Yield Estimator—A decision-support tool 

to assess water availability at ungaged stream locations in 

Massachusetts: U.S. Geological Survey Scientific Investigations Report 2009–5227, 41 p. plus CD-ROM. (Also available at http://pubs.usgs.gov/sir/2009/5227/.)

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, doi10.1029/2009WR008481, 

15 p.

Asquith, W.H., Roussel, M.C., and Vrabel, Joseph, 

2006, Statewide analysis of the drainage-area ratio 

method for 34 streamflow percentile ranges in Texas: 

U.S. Geological Survey Scientific Investigations 

Report 2006–5286, 34 p., 1 app. (Also available at 

http://pubs.usgs.gov/sir/2006/5286/.)

Cohn, T.A., 1988, Adjusted maximum likelihood estimation 

of moments of lognormal populations from type I censored 

samples: U.S. Geological Survey Open-File Report 88–350, 

34 p.

Eash, D.A., 2001, Techniques for estimating flood-frequency 

discharges for streams in Iowa: U.S. Geological Survey 

Water-Resources Investigations Report 00–0423, 88 p. 

(Also available online at http://ia.water.usgs.gov/pubs/

reports/WRIR_00-4233.pdf.)

Eash, D.A., and Barnes, K.K., 2012, Methods for estimating 

selected low-flow frequency statistics and harmonic mean 

flows for streams in Iowa: U.S. Geological Survey Scientific Investigations Report 2012–5171, 94 p. (Also available 

at http://pubs.usgs.gov/sir/2012/5171/.)

Efroymson, M.A., 1960, Multiple regression analysis, in

Ralston, A., and Wilf, H.S., eds., Mathematical methods for 

digital computers: New York, John Wiley and Sons, Inc., 

p. 191–203.

Emerson, D.G., Vecchia, A.V., and Dahl, A.L, 2006, Evaluation of drainage-area ratio method used to estimate streamflow for the Red River of the North basin, North Dakota and 

Minnesota: U.S. Geological Survey Scientific Investigations 

Report 2005–5017, 13 p. (Also available at http://pubs.usgs.

gov/sir/2005/5017/.)

Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide 

to the weighted-multiple-linear-regression program (WREG 

version 1.0): U.S. Geological Survey Techniques and Methods, book 4, chap. A8, 21 p. (Also available at http://pubs.

usgs.gov/tm/tm4a8/.)

Esralew, R.A., and Smith, S.J., 2010, Methods for estimating 

flow-duration and annual mean-flow statistics for ungaged 

streams in Oklahoma: U.S. Geological Survey Scientific 

Investigations Report 2009–5267, 131 p. (Also available at 

http://pubs.usgs.gov/sir/2009/5267/.)

Fennessey, N.M., 1994, A hydro-climatological model of daily 

streamflow for the northeast United States: Unpublished 

Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Tufts University, Medford, Mass., variously paged.

Gupta, H.V., Sorooshian, S., and Yapo, P.O., 1999, Status of 

automatic calibration for hydrologic models: Comparison 

with multilevel expert calibration: Journal of Hydrologic 

Engineering, v. 4, no. 2, p. 135–143. 
References Cited 49

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 3, chap. A3, 522 p.

Hortness, J.E., 2006, Estimating low-flow frequency statistics 

for unregulated streams in Idaho: U.S. Geological Survey 

Scientific Investigations Report 2006–5035, 31 p. (Also 

available at http://pubs.usgs.gov/sir/2006/5035/.)

Hughes, D.A., and Smakhtin, V.U., 1996, Daily flow time 

series patching or extension—A spatial interpolation 

approach based on Flow Duration Curve Transfers: Journal 

of Hydrological Sciences, v. 41, no. 6, p. 851–871. 

Isaaks, E.H., and Srivastava, R.M., 1989, An introduction to 

applied geostatistics: New York and Oxford, U.K., Oxford 

University Press, 561 p.

Legates, D.R., and McCabe, G.J., Jr., 1999, Evaluating the use 

of "goodness-of-fit" measures in hydrologic and hydroclimatic model validation: Water Resources Research, v. 35, 

no. 1, p. 233–241.

Lorenz, D.L., Ahearn, E.A., Carter, J.M., Cohn, T.A., and others, 2011, USGS library for S-PLUS for Windows—Release 

4.0: U.S. Geological Survey Open-File Report 2011–1130, 

accessed October 4, 2012, at http://pubs.er.usgs.gov/

publication/ofr20111130.

Lumb, A.M., Kittle, J.L., and Flynn, K.M., 1990, Users 

manual for ANNIE, a computer program for interactive 

hydrologic analyses and data management: U.S. Geological 

Survey Water-Resources Investigations Report 89–4080, 

236 p. (Also available at http://water.usgs.gov/software/

lists/surface)water.)

Mahamoud, Y.M., 2008, Prediction of daily Flow Duration 

Curve Transfers and streamflow for ungauged catchments 

using regional Flow Duration Curve Transfers: Journal of 

Hydrological Sciences, v. 53, no. 4, p. 706–724.

Marquardt, D.W., 1970, Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation: 

Technimetrics, v. 12, no. 3, p. 591–612. (Also available at 

http://www.jstor.org/stable/1267205.)

Moriasi, D.N., Arnold, J.G., Van Liew, M.W., Binger, R.L., 

Harmel, R.D., and Veith, T.L, 2007, Model evaluation 

guidelines for systematic quantification of accuracy in 

watershed simulations: American Society of Agricultural 

and Biological Engineers, v. 50, no. 3, p. 885–900

Nalley, G.M., Gorman, J.G., Goodrich, R.D., Miller, V.E., 

Turco, M.J., and Linhart, S.M., 2002, Water resources data 

Iowa, water year 2001, volume 1: Surface water–Mississippi River Basin: U.S. Geological Survey Water-Data 

Report IA–01–1, 397 p. (Also available at http://ia.water.

usgs.gov/pubs/annualreports/2001/WDR_IA-01-1.pdf.)

Nash, J.E., and Sutcliffe, J.V., 1970, River flow forecasting 

through conceptual models, part I–A discussion of principles: Journal of Hydrology, v. 10, no. 3, p. 282–290.

Prior, J.C., 1991, Landforms of Iowa: Iowa City, Iowa, University of Iowa Press, 154 p.

Prior, J.C., Kohrt, C.J., and Quade, D.J., 2009, The landform regions of Iowa: Vector digital data, Iowa Geological Survey, Iowa Department of Natural Resources, Iowa 

City, Iowa, accessed February 16, 2011, at http://www.igsb.

uiowa.edu/webapps/nrgislibx/.

Ries, K.G., III, Steeves, P.A., Guthrie, J.D., Rea, A.H., and 

Stewart, D.W., 2009, Stream-network navigation in the U.S. 

Geological Survey streamStats Web application, Conference Paper: Proceedings of the International Conference 

on Advanced Geographic Information Systems and Web 

Services, GEOWS 2009, p. 80–84.

Riggs, H.C., 1968, Some statistical tools in hydrology: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A1, 39 p.

R Development Core Team, 2010, R—A language and environment for statistical computing: Vienna, Austria, R Foundation for Statistical Computing, accessed February 16, 

2012, at http://www.R-project.org.

Risley, J.C., Stonewall, A.J., and Haluska, T.L., 2008, Estimating flow-duration and low-flow frequency statistics for 

unregulated streams in Oregon: U.S. Geological Survey 

Scientific Investigations Report 2008–5126, 23 p. (Also 

available at http://pubs.usgs.gov/sir/2008/5126/.)

Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load 

estimator (LOADEST)—A FORTRAN program for 

estimating constituents loads in streams and rivers: U.S. 

Geological Survey Techniques and Methods, book 4, chap. 

A5, 69 p., accessed February 14, 2012, at http://pubs.usgs.

gov/tm/2005/tm4A5/pdf/508final.pdf.

Sanders, C.L., 2002, Daily values flow comparison and 

estimates using program HYDCOMP, version 1.0: U.S. 

Geological Survey Open-File Report 02–286, 52 p.

Schilling, K.E., 2005, Relation of baseflow to row crop 

intensity in Iowa: Agriculture, Ecosystems and Environment, v. 105, no. 1–2, p. 433–438, accessed February 13, 2012, at http://www.sciencedirect.com/

science?_ob=ArticleURL&_udi=B6T3Y-4CPD8FG-3&_

user=696292&_coverDate=01%2F31%2F2005&_

rdoc=1&_fmt=high&_orig=gateway&_

origin=gateway&_sort=d&_docanchor=&view=c&_

searchStrId=1709861362&_rerunOrigin=google&_

acct=C000038819&_version=1&_urlVersion=0&_userid=

696292&md5=83e59e04aff6fff8afbfdb57a097318c&search

type=a.
50 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods

Schilling, K.E., and Libra, R.D., 2003, Increased baseflow 

in Iowa over the second half of the 20th century: Journal of American Water Resources Association, v. 39, 

no. 4, p. 851–860, accessed February 13, 2012, at http://

onlinelibrary.wiley.com/doi/10.1111/j.1752-1688.2003.

tb04410.x/pdf.

Smakhtin, V.U., 1999, Generation of natural daily flow time 

series in regulated rivers using a non-linear spatial interpolation technique: Regulated Rivers—Research and Management, v. 15, p. 311–323.

Smakhtin, V.U., and Masse, B., 2000, Continuous daily hydrograph simulation using duration curves of a precipitation 

index: Hydrological Processes, v. 14, p. 1,083–1,100.

TIBCO Software Inc., 2008, TIBCO Spotfire S+® 8.1 for 

Windows® user’s guide: Palo Alto, Calif., 582 p., accessed 

February 17, 2012, at http://stn.spotfire.com/stn/UserDoc.

aspx?UserDoc=spotfire_client_help%2fintro%2fintro_

introduction.htm&Article=%2fstn%2fDefault.aspx.

U.S. Geological Survey, 2011, National Water Information 

System (NWIS Web) data, accessed October 4, 2012, at 

http://waterdata.usgs.gov/nwis/sw.

Vogel, R.M., and Fennessey, N.M., 1994, Flow Duration 

Curve Transfers I—A new interpretation and confidence 

intervals: American Society of Civil Engineers, Journal of 

Water Resources Planning and Management, v. 120, no. 4, 

p. 715–723.

Waldron, M.C., and Archfield, S.A., 2006, Factors affecting 

firm yield for selected streamflow-dominated drinkingwater-supply reservoirs in Massachusetts: U.S. Geological 

Survey Scientific Investigations Report 2006–5044, 39 p. 

(Also available at http://pubs.usgs.gov/sir/2006/5044/.)

Publishing support provided by the: 

Rolla, West Trenton, and Denver Publishing Service Centers 

For more information concerning this publication, contact:

Director, USGS Iowa Water Science Center

P.O. Box 1230

Iowa City, IA 52244

(319) 337–4191

Or visit the Iowa Water Science Center Web site at:

http://ia.water.usgs.gov

Linhart and others—Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods—SIR 2012–5232