U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5111

Prepared in cooperation with the Iowa Department of Natural Resources

Comparison Between Two Statistically Based Methods, and 

Two Physically Based Models Developed to Compute Daily 

Mean Streamflow at Ungaged Locations in the Cedar River 

Basin, Iowa
Cover Photograph: Cedar River at Waterloo, Iowa (photograph taken by Don Becker, U.S. Geological Survey).
Comparison Between Two Statistically 

Based Methods, and Two Physically Based 

Models Developed to Compute Daily Mean 

Streamflow at Ungaged Locations in the 

Cedar River Basin, Iowa

By S. Mike Linhart, Jon F. Nania, Daniel E. Christiansen, Kasey J. Hutchinson, 

Curtis L. Sanders, Jr., and Stacey A. Archfield

Prepared in cooperation with the Iowa Department of Natural Resources

Scientific Investigations Report 2013–5111

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

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

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Suggested citation:

Linhart, S.M., Nania, J.F., Christiansen, D.E., Hutchinson, K.J., Sanders, C.L., Jr., and Archfield, S.A., 2013, Comparison between two statistically based methods, and two physically based models developed to compute daily mean 

streamflow at ungaged locations in the Cedar River Basin, Iowa: U.S. Geological Survey Scientific Investigations 

Report 2013–5111, 7 p., http://pubs usgs.gov/sir/2013/5111.
iii

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)

Contents

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

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

Study Area.......................................................................................................................................................1

Comparison of Methods and Models .........................................................................................................4

Method and Model Results..........................................................................................................................4

Conclusion and Discussion of Methods and Models ..............................................................................5

References Cited............................................................................................................................................7

Figures

1. Map showing U.S. Geological Survey streamgages in the Cedar River Basin..................2

2. Map showing Cedar River Basin landform regions ................................................................3

3. Graphs showing observed and estimated hydrographs of daily mean streamflow for 

U.S. Geological Survey streamgage 05464000, Cedar River at Waterloo, Iowa, for the 

period October 1, 2001, to September 30, 2009 ........................................................................6

Tables

1. U.S. Geological Survey streamgages used in the Cedar River Basin included in the 

comparison of the Flow Duration Curve Transfer method, the Flow Anywhere method, 

the Precipitation Runoff Modeling-System model, and the Soil and Water Assessment 

Tool model ......................................................................................................................................4

2. Comparison results between the two statistically based methods and the two physically based models of the observed and estimated daily mean streamflows, October 1, 

2001, to September 30, 2009 ........................................................................................................5
iv

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 technical assistance with 

regression analysis; Ken Eng, for assistance with initial project development; Julie Kiang, for 

technical assistance with regression analysis. 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.
Abstract

A variety of individuals from water resource managers 

to recreational users need streamflow information for planning and decisionmaking at locations where there are no 

streamgages. To address this problem, two statistically based 

methods, the Flow Duration Curve Transfer method and the 

Flow Anywhere method, were developed for statewide application and the two physically based models, the Precipitation 

Runoff Modeling-System and the Soil and Water Assessment 

Tool, were only developed for application for the Cedar River 

Basin. Observed and estimated streamflows for the two 

methods and models were compared for goodness of fit at 

13 streamgages modeled in the Cedar River Basin by using 

the Nash-Sutcliffe and the percent-bias efficiency values. 

Based on median and mean Nash-Sutcliffe values for the 

13 streamgages the Precipitation Runoff Modeling-System and 

Soil and Water Assessment Tool models appear to have performed similarly and better than Flow Duration Curve Transfer and Flow Anywhere methods. Based on median and mean 

percent bias values, the Soil and Water Assessment Tool model 

appears to have generally overestimated daily mean streamflows, whereas the Precipitation Runoff Modeling-System 

model and statistical methods appear to have underestimated 

daily mean streamflows. The Flow Duration Curve Transfer 

method produced the lowest median and mean percent bias 

values and appears to perform better than the other models.

Introduction

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

streamflow information is available. A variety of individuals 

from water resource managers to recreational users rely on 

streamflow information in their planning and decisionmaking. 

Often there is a need for daily mean streamflow information 

at locations where there are no streamgages. To address this 

problem, the USGS in cooperation with the Iowa Department 

of Natural Resources evaluated two statistically based methods and two physically based watershed models for estimating 

daily mean streamflow at ungaged locations within the Cedar 

River Basin, Iowa. The two statistically based methods are the 

Flow Duration Curve Transfer method and the Flow Anywhere method, and the two physically based models are the 

Precipitation Runoff Modeling-System (PRMS) and the Soil 

and Water Assessment Tool (SWAT). This report compares 

the results of these methods and models developed to estimate daily mean streamflow at ungaged locations within the 

Cedar River Basin, Iowa. The two statistically based methods 

are presented in one report (Linhart and others, 2012), and 

the two physically based models are presented in two reports 

(Christiansen, 2012; Hutchinson and Christiansen, 2013). 

Although the two statistically based methods were developed 

for estimating daily mean streamflow at ungaged locations for 

the entire state of Iowa, the two physically based models were 

specifically developed for only the Cedar River Basin.

Study Area

The Cedar River Basin extends from its headwaters in 

southern Minnesota to its confluence with the Iowa River 

in southeastern Iowa .The Cedar River is the largest tributary 

to the Iowa River with a drainage area of approximately 

7,815 square miles (fig. 1) (Iowa Department of Natural 

Resources, 2006; Squillace and others, 1996). Four of the 10 

distinct landform regions in Iowa are present in the Cedar 

River Basin (Prior and others, 2009) (fig. 2). Corn and 

soybean row-crop agriculture is the dominate land use in 

the basin. The basin has extensive, artificial drainage which 

includes open ditches and subsurface drainage tile; both of 

which are designed to remove excess water from the land 

and soil subsurface (Iowa Department of Natural Resources, 

2006). Confined and unconfined livestock operations that 

Comparison Between Two Statistically Based Methods, 

and Two Physically Based Models Developed to Compute 

Daily Mean Streamflow at Ungaged Locations in the Cedar 

River Basin, Iowa

By S. Mike Linhart, Jon F. Nania, Daniel E. Christiansen, Kasey J. Hutchinson, Curtis L. Sanders, Jr., and 

Stacey A. Archfield
2 Comparison between Two Statistically Based Methods, and Two Physically-Based Models

# #

#

##

#

#

#

#

#

#

#

#

#

Hudson

Dysart

Conesville

Ionia

Finchford

Shell Rock

New

Hartford

1

9

8

7

6 5

4

3

2

14

13

12

11

10

Waterloo

Cedar 

Rapids

Mason

City

Austin

Charles

City

Nashua

Waverly

Janesville

93° 92° 91°

44°

43°

42°

IOWA

WISCONSIN

ILLINOIS

Iowa River

Iowa River

Iowa River

Cedar River

Base from U.S. Geological Survey digital data, 2006, 1:24,000

Universal Transverse Mercator projection, Zone 15 

North American Datum of 1983 (NAD 83)

Iowa River

Little Cedar River

West Fork Cedar River

Shell Rock River

Cedar River

Beaver Creek

Black Hawk Creek

Wolf Creek

0 25 50 MILES

0 25 50 KILOMETERS

1

#

EXPLANATION

Streamgage and map number 

 (table 1)

Winnebago River

Cedar River

basin

IOWA

MINNESOTA

NEBRASKA

MISSOURI

ILLINOIS

WISCONSIN

SOUTH DAKOTA

MINNESOTA

Boundary of 

study area

Figure 1. U.S. Geological Survey streamgages in the Cedar River Basin.
Study Area 3

Figure 2. Cedar River Basin landform regions.

Hudson

Dysart

Conesville

Ionia

New

Hartford

Cedar 

Rapids

Mason

City

Austin

Charles

City

Nashua

Waverly

93° 92° 91°

44°

43°

42°

MINNESOTA

IOWA WISCONSIN

ILLINOIS

Iowa River

Iowa River

Iowa River

Cedar River

Base from U.S. Geological Survey digital data, 2006, 1:24,000

Universal Transverse Mercator projection, Zone 15 

North American Datum of 1983 (NAD 83)

Iowa River

Little Cedar River

West Fork Cedar River

Shell Rock River

Cedar River

Beaver Creek

Black Hawk Creek

Wolf Creek

0 25 50 MILES

0 25 50 KILOMETERS

EXPLANATION

Landform regions

Des Moines Lobe

Iowa-Cedar Lowland

Iowan Surface 

Southern Iowa Drift Plain

Winnebago River

Boundary of 

study area

Janesville

Shell Rock

Waterloo

Finchford

Landform regions from Prior and others, 2009
4 Comparison between Two Statistically Based Methods, and Two Physically-Based Models

include beef and dairy cattle, hogs, sheep, and poultry are 

located throughout the basin (Iowa Department of Natural 

Resources, 2006). Designated uses for the Cedar River include 

primary contact recreation and drinking water supply (Iowa 

Department of Natural Resources, 2006). There are 14 USGS 

streamgages in the Cedar River Basin (fig. 1, table 1), 13 of 

which were used in this comparison. 

Comparison of Methods and Models

Observed and estimated streamflows for the two methods and two models were compared for goodness of fit at 

each of the streamgages (table 2) by using the Nash-Sutcliffe 

(NS) (Nash and Sutcliffe, 1970) and the percent bias (PBIAS) 

efficiency values (Gupta and others, 1999). The NS value is a 

measure of how well the method and model estimates match 

the observed values. NS values range from -∞ to 1. Values of 

0.0 or less indicate unacceptable model performance; a value 

of 1 indicates a perfect fit between observed and estimated values (Moriasi and others, 2007). The PBIAS value is a measure 

of the average tendency of the method or model estimates to 

be larger or smaller than the observed values, with an optimal value of 0.0. Positive values indicate method or model 

underestimation bias and negative values indicate method or 

model overestimation bias. Method and model estimates can 

be considered satisfactory if NS is greater than 0.50 and the 

absolute value of PBIAS is less than 25 percent (Moriasi and 

others, 2007). For the Flow Duration Curve Transfer method, 

NS values ranged from 0.09 to 0.79 with median and mean 

values of 0.55 and 0.54, respectively; PBIAS values ranged 

from -13.2 to 20.0 with median and mean values of 4.6 and 

3.3, respectively. For the Flow Anywhere method, NS values 

ranged from 0.15 to 0.77 with median and mean values of 0.37 

and 0.43, respectively; PBIAS values ranged from 5.4 to 46.2 

with median and mean values of 14.8 and 18.7, respectively. 

For the PRMS model, NS values ranged from 0.04 to 0.87 

with median and mean values of 0.66 and 0.61, respectively; 

PBIAS values ranged from -27.5 to 19.8 with median and 

mean values of 6.6 and 4.6, respectively. For the SWAT model, 

NS values ranged from 0.44 to 0.78 with median and mean 

values of 0.63 and 0.62, respectively; PBIAS values ranged 

from -26.1 to 11.2 with median and mean values of -9.1 and 

-8.1, respectively. 

Method and Model Results

Observed and estimated hydrographs of the daily mean 

streamflow for the two methods and two models for the 

streamgage 05464000, Cedar River at Waterloo, Iowa (see 

location at fig. 1, map number 11) for the period October 1, 

2001, to September 30, 2009 are shown in figure 3. A visual 

comparison of the Flow Duration Curve Transfer hydrographs 

(fig. 3A) show the observed as compared to the estimated daily 

mean streamflows appear to be a combination of underesTable 1. U.S. Geological Survey streamgages used in the Cedar River Basin included in the comparison of the Flow Duration Curve 

Transfer method, the Flow Anywhere method, the Precipitation Runoff Modeling-System model, and the Soil and Water Assessment 

Tool model.

[USGS, U.S. Geological Survey; latitude and longitude in degrees, minutes, and seconds; mi2, square miles]

Map 

number 

(fig. 1)

USGS 

streamgage 

number

USGS streamgage name Latitude (north) Longitude (west)

Drainage area 

measured at 

streamgage (mi2)

1 05457000 Cedar River near Austin, Minnesota 43°38’14” 92°58’28” 399

2 05457700 Cedar River at Charles City, Iowa 43°03’44” 92°40’25” 1,054

3 05458000 Little Cedar River near Ionia, Iowa 43°01’60” 92°30’12” 306

4 105458300 Cedar River at Waverly, Iowa 42°44’14” 92°28’12” 1,547

5 05458500 Cedar River at Janesville, Iowa 42°38’54” 92°27’54” 1,661

6 05458900 West Fork Cedar River at Finchford, Iowa 42°37’46” 92°32’36” 846

7 05459500 Winnebago River at Mason City, Iowa 43°09’54” 93°11’33” 526

8 05462000 Shell Rock River at Shell Rock, Iowa 42°42’43” 92°34’58” 1,746

9 05463000 Beaver Creek at New Hartford, Iowa 42°34’22” 92°37’04” 347

10 05463500 Black Hawk Creek at Hudson, Iowa 42°24’28” 92°27’47” 303

11 05464000 Cedar River at Waterloo, Iowa 42°29’44” 92°20’03” 5,146

12 05464220 Wolf Creek near Dysart, Iowa 42°15’06” 92°17’55” 299

13 05464500 Cedar River at Cedar Rapids, Iowa 41°58’19” 91°40’01” 6,510

14 05465000 Cedar River near Conesville, Iowa 41°24’33” 91°17’25” 7,787

1

Used only as a validation site for the Precipitation-Runoff Modeling System model. The site was not used for any of the other models.
Conclusion and Discussion of Methods and Models 5

timated and overestimated streamflows computed from the 

method, but overall, the estimated daily mean streamflows 

from the method are underestimated. A visual comparison 

of observed and estimated daily mean streamflows using the 

Flow Anywhere method (fig. 3B) indicates that, for the most, 

part daily mean streamflows are underestimated. For the 

PRMS model (fig. 3C), daily mean streamflows are underestimated, especially at low flows. For the SWAT model (fig. 3D), 

daily mean streamflows appear to be underestimated at very 

low streamflows and overestimated at higher streamflows; in 

general, the PBIAS results indicate daily mean streamflows 

are overestimated. On the basis of the NS values for the Cedar 

River at Waterloo, Iowa, streamgage 05464000, the PRMS 

model appears to provide the best estimates with the highest 

NS value of 0.87, whereas the Flow Duration Curve Transfer 

method appears to provide the poorest estimate with the lowest NS value of 0.43. On the basis of the PBIAS values for 

the same streamgage, the PRMS model appears to provide the 

best estimates with the lowest absolute PBIAS value of 7.4 

and the SWAT model appears to provide the poorest estimates 

with the highest absolute PBIAS value of -26.1. On the basis 

of both the NS and PBIAS values, the PRMS model appears to 

provide the best prediction of streamflow for the Cedar River 

at Waterloo, Iowa, streamgage 05464000.

Conclusion and Discussion of Methods 

and Models

Based on median and mean Nash-Sutcliffe values for 

the 13 streamgages modeled in the Cedar River Basin; the 

Precipitation Runoff Modeling-System and the Soil and Water 

Assessment Tool models appear to have performed similarly 

and better than the Flow Duration Curve Transfer and Flow 

Anywhere methods. Based on median and mean percent bias 

values, the Soil and Water Assessment Tool model appears 

to have generally overestimated daily mean streamflows, 

whereas the statistical methods and Precipitation Runoff 

Modeling-System model appear to have underestimated daily 

mean streamflows. The Flow Duration Curve Transfer method 

produced the lowest median and mean percent bias values and 

appears to perform better than the Flow Anywhere method and 

the Precipitation Runoff Modeling-System and the Soil and 

Table 2. Comparison results between the two statistically based methods and the two physically based models of the observed and 

estimated daily mean streamflows, October 1, 2001, to September 30, 2009.

[PRMS, Precipitation Ruoff Modeling System; SWAT, Soil and Water Assessment Tool; NS, Nash-Sutcliffe Efficiency Value; PBIAS, percent bias.]

USGS 

streamgage 

number

USGS streamgage name

1

Flow Duration 

Curve Transfer

Flow Anywhere 

method PRMS SWAT

NS PBIAS NS PBIAS NS PBIAS NS PBIAS

05457000 Cedar River near Austin, Minnesota 0.27 20.0 0.15 14.2 0.29 -11.4 0.44 -10.1

05457700 Cedar River at Charles City, Iowa 0.71 4.9 0.37 9.4 0.04 -27.5 0.49 -10.9

05458000 Little Cedar River near Ionia, Iowa 0.73 -5.2 0.30 15.3 0.50 -0.5 0.6 -17.3

05458500 Cedar River at Janesville, Iowa 0.47 4.6 0.55 8.7 0.63 -8.1 0.67 -7.8

05458900 West Fork Cedar River at Finchford, Iowa 0.79 12.3 2NA 2NA 0.71 13.9 0.6 -12.8

05459500 Winnebago River at Mason City, Iowa 0.64 6.7 0.37 46.2 0.68 13.1 0.69 -2.4

05462000 Shell Rock River at Shell Rock, Iowa 0.72 -3.1 0.66 5.4 0.66 4.5 0.56 -23.1

05463000 Beaver Creek at New Hartford, Iowa 0.73 15.4 0.41 30.5 0.63 16.8 0.68 -0.6

05463500 Black Hawk Creek at Hudson, Iowa 0.53 14.4 0.35 27.8 0.63 19.8 0.66 11.2

05464000 Cedar River at Waterloo, Iowa 0.43 -13.2 0.77 7.5 0.87 7.4 0.48 -26.1

05464220 Wolf Creek near Dysart, Iowa 0.55 -5.4 0.34 22.4 0.66 19.2 0.63 7.7

05464500 Cedar River at Cedar Rapids, Iowa 0.35 -2.7 3NA 3NA 0.86 6.6 0.78 -9.1

05465000 Cedar River near Conesville, Iowa 0.09 -5.8 3NA 3NA 0.82 6.1 0.74 -4.6

Maximum 0.79 20.0 0.77 46.2 0.87 19.8 0.78 11.2

Minimum 0.09 -13.2 0.15 5.4 0.04 -27.5 0.44 -26.1

Median 0.55 4.6 0.37 14.8 0.66 6.6 0.63 -9.1

Mean 0.54 3.3 0.43 18.7 0.61 4.6 0.62 -8.1

1

Model estimates of streamflow are missing for some days because observed streamflow values were outside the applicable computational range of the Flow 

Duration Curve Tranfer method.

2

Reference streamgage for the Flow Anywhere method.

3

Drainage areas are too large for the Flow Anywhere method.
6 Comparison between Two Statistically Based Methods, and Two Physically-Based Models 100 1,000 10,000 100,000 Estimated streamflow Observed streamflow Reference streamgage 05463000 Beaver Creek at New Hartford, Iowa Flow Duration Curve Transfer methodEXPLANATION 100 1,000 10,000 100,000 1,000,000 1,000,000 B 05464000 C e d a r R iv e r a t W a te rlo o , Io w a Reference streamgage 05458900 West Fork Cedar River at Finchford, Iowa

10/1/2001 10/1/2002 10/1/2003 10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

Date (month/day/year)

100

1,000

10,000

100,000

1,000,000

Streamflow, in cubic feet per second

10/1/2001 10/1/2002 10/1/2003 10/1/2004 10/1/2005 10/1/2006 10/1/2007 10/1/2008 9/30/2009

100

1,000

10,000

100,000

1,000,000

A. 05464000 Cedar River at Waterloo, Iowa B. 05464000 Cedar River at Waterloo, IowaC. 05464000 Cedar River at Waterloo, Iowa D. 05464000 Cedar River at Waterloo, Iowa

Estimated streamflowObserved streamflow

Flow Anywhere method

EXPLANATION

Estimated streamflowObserved streamflow

Soil and Water Assessment  Tool model

EXPLANATION

Estimated streamflowObserved streamflow

Precipitation Runoff Modeling- System model

EXPLANATION

Figure 3. Observed and estimated hydrographs of daily mean streamflow for U.S. Geological Survey streamgage 05464000, Cedar River at Waterloo, Iowa, using; 

A, the 

Flow Duration Curve Transfer method; 

B, the Flow Anywhere method; 

C, the Precipitation Runoff Modeling-System model; and 

D, the Soil and Water Assessment Tool 

model for the period October 1, 2001, to September 30, 2009.
References Cited 7

Water Assessment Tool models. It is likely that no one method 

or model out-performs other methods or models for all magnitudes of streamflow (high, low, or mid-range streamflows). 

A more detailed study is needed to determine which methods 

or models will perform best at specific magnitudes of streamflows. For estimating very large streamflows with exceedance 

probabilities of less than 1 percent, the Flow Duration Curve 

Transfer method is not applicable because these streamflows 

are outside the computational range of the current model. The 

Flow Anywhere method is limited to estimating streamflow 

for basins less than 5,500 square miles (Linhart and others, 

2012). The Precipitation Runoff Modeling-System and the 

Soil and Water Assessment Tool models are limited to estimating streamflow for only the Cedar River Basin.

References Cited

Christiansen, D.E., 2012, Simulation of daily streamflows 

at gaged and ungaged locations within the Cedar River 

Basin, Iowa, using a Precipitation-Runoff Modeling System 

model: U.S. Geological Survey Scientific Investigations 

Report 2012–5213, 20 p.

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. 

Hutchinson, K.J., and Christiansen, D.E., 2013, Use of the 

soil and water assessment tool (SWAT) for simulating 

hydrology and water quality in the Cedar River Basin, 

Iowa, 2000–2010: U.S. Geological Survey Scientific 

Investigations Report 2013–5002, 36 p.

Iowa Department of Natural Resources, 2006, Total maximum 

daily load for nitrate, Cedar River, Linn County, Iowa, 

2006: Iowa Department of Natural Resources, Des Moines, 

Iowa, 62 p. (Also available at http://www.epa.gov/waters/

tmdldocs/32009_IACedarRiverTMDL.pdf).

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.

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, p. 885–900

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., Kohrt, C.J., and Quade, D.J., 2009, The landform 

regions of Iowa: Iowa City, Iowa, Iowa Geological Survey, 

Iowa Department of Natural Resources, vector digital data, 

accessed December 15, 2011, at http://www.igsb.uiowa.edu/

webapps/nrgislibx/.

Squillace, P.J., Caldwell, J.P., Schulmeyer, P.M., and Harvey, 

C.A., 1996, Movement of agricultural chemicals between 

surface water and ground water, lower Cedar River Basin, 

Iowa: U.S. Geological Survey Water–Supply Paper 2448, 

59 p.

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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—Comparison Between Two Statistically Based Methods, and Two Physically Based Models—Scientific Investigations Report 2013–5111