Prepared in cooperation with the Minnesota Pollution Control Agency

Methods to Estimate Historical Daily Streamflow 

for Ungaged Stream Locations in Minnesota

Scientific Investigations Report 2015–5181

U.S. Department of the Interior

U.S. Geological Survey
Cover photograph: Redwood River near Redwood Falls, Minnesota. 

Photograph by the U.S. Geological Survey.
Methods to Estimate Historical Daily 

Streamflow for Ungaged Stream Locations 

in Minnesota

David L. Lorenz and Jeffrey R. Ziegeweid

Prepared in cooperation with the Minnesota Pollution Control Agency

Scientific Investigations Report 2015–5181

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, Director

U.S. Geological Survey, Reston, Virginia: 2016

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Suggested citation:

Lorenz, D.L., and Ziegeweid, J.R., 2016, Methods to estimate historical daily streamflow for ungaged stream locations 

in Minnesota: U.S. Geological Survey Scientific Investigations Report 2015–5181, 18 p., http://dx.doi.org/10.3133/

sir20155181.

ISSN 2328-0328 (online)
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................2

Description of the Study Area ............................................................................................................2

Methods to Estimate Historical Daily Streamflow ..................................................................................2

Estimation of the Ungaged Flow-Duration Curve ............................................................................4

Selection of Index Streamgages in Minnesota and Neighboring States....................................4

Estimation of Unaltered Daily Mean Streamflow ............................................................................4

Evaluation of Index Streamgages ...............................................................................................................4

Evaluation of Estimated Daily Streamflow.................................................................................................4

StreamStats ....................................................................................................................................................6

Limitations of the Methods...........................................................................................................................8

Summary..........................................................................................................................................................8

Acknowledgments.........................................................................................................................................8

References Cited............................................................................................................................................8

Figures

1. Map showing Minnesota and parts of neighboring States showing selected index 

streamgages..................................................................................................................................3

2. Graphs showing example of the QPPQ method used to estimate daily mean 

streamflow at ungaged locations for part of the annual hydrograph showing the 

gaged hydrograph; the gaged flow-duration curve; the estimated flow-duration curve; 

and the estimated ungaged hydrograph...................................................................................5

3. Graphs showing observed and estimated streamflows for two target streamgages. 

streamgage....................................................................................................................................7

Tables

1. Index streamgages in Minnesota and neighboring States .................................................12

2. Selected pairs of streamgages for assessment of performance of the QPPQ 

method for estimating ungaged streamflow in Minnesota....................................................6
iv

Conversion Factors

Inch/Pound to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

Datum

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

Supplemental Information

Water year is the 12-month period of October 1 through September 30 and is designated by the 

calendar year in which it ends.

Abbreviations

BaSE Baseline Streamflow Estimator

FDC flow-duration curve

GIS geographic information system

LFF low-flow frequency

MA SYE Massachusetts Sustainable-Yield Estimator

MOVE maintenance of variance extension

MPCA Minnesota Pollution Control Agency

NSE Nash-Sutcliffe efficiency

NYSET New York Streamflow Estimation Tool

USGS U.S. Geological Survey
Abstract

Effective and responsible management of water resources 

relies on a thorough understanding of the quantity and quality 

of available water; however, streamgages cannot be installed 

at every location where streamflow information is needed. 

Therefore, methods for estimating streamflow at ungaged 

stream locations need to be developed. This report presents a 

statewide study to develop methods to estimate the structure 

of historical daily streamflow at ungaged stream locations in 

Minnesota. Historical daily mean streamflow at ungaged locations in Minnesota can be estimated by transferring streamflow 

data at streamgages to the ungaged location using the QPPQ 

method. The QPPQ method uses flow-duration curves at an 

index streamgage, relying on the assumption that exceedance 

probabilities are equivalent between the index streamgage and 

the ungaged location, and estimates the flow at the ungaged 

location using the estimated flow-duration curve. Flowduration curves at ungaged locations can be estimated using 

recently developed regression equations that have been incorporated into StreamStats (http://streamstats.usgs.gov/), which 

is a U.S. Geological Survey Web-based interactive mapping 

tool that can be used to obtain streamflow statistics, drainagebasin characteristics, and other information for user-selected 

locations on streams.

Introduction

Effective and responsible management of water resources 

relies on a thorough understanding of the quantity and quality 

of available water. Streamgages provide valuable water-quantity information that facilitates responsible management of 

water resources, including reservoir management, recreational 

activities, maintenance of aquatic habitat, and contaminant 

monitoring; however, streamgages cannot be installed at every 

location where streamflow information is needed. Therefore, 

methods for estimating daily mean streamflow at ungaged 

locations need to be developed. Approaches for estimating 

daily streamflow have been developed into estimation tools by 

the U.S. Geological Survey (USGS) in Massachusetts (Massachusetts Sustainable-Yield Estimator [MA SYE]; Archfield 

and others, 2010), Pennsylvania (Baseline Streamflow Estimator [BaSE]; Stuckey and others, 2012), and New York (New 

York Streamflow Estimation Tool [NYSET]; Gazoorian, 

2015). The MA SYE, BaSE, and NYSET tools apply the 

QPPQ method introduced by Fennessey (1994) and used by 

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

Masse (2000), Mahamoud (2008), Shu and Ouarda (2012), 

and Linhart and others (2013). The QPPQ method uses flowduration curves (FDCs) at an index streamgage, relying on 

the assumption that exceedance probabilities are equivalent 

between the index streamgage and the ungaged location, and 

estimates the flow at the ungaged location using the estimated 

FDC. The MA SYE and BaSE tools have been effective at 

estimating the natural, unaltered daily streamflow hydrograph at ungaged locations in their respective study areas and 

provide user-friendly ways of computing streamflow statistics 

commonly used for water-resource management and habitat 

protection. Recently, regression equations were developed to 

estimate flow-duration exceedance probabilities and low-flow 

frequency (LFF) statistics for ungaged locations on streams 

in Minnesota (Ziegeweid and others, 2015). These regression 

equations can be used to develop methods for estimating daily 

mean streamflow.

The QPPQ method can be used to assist water-resource 

managers and researchers to describe and quantify hydrologic variability and describe the hydrologic response of a 

river basin, and within a wide range of uncertainty, estimate 

the streamflow at ungaged sites. The measures of variability 

and streamflow can be used for irrigation planning, wasteload allocation, water-quality management, categorizing fish 

assemblages and other characteristics of aquatic organisms, 

and other tasks that require knowledge of the variability of 

streamflow in small basins.

In 2012, the USGS initiated a statewide study in cooperation with the Minnesota Pollution Control Agency (MPCA) 

to develop methods for estimating historical daily streamflow 

at ungaged stream locations in Minnesota. For this study, 

methods were developed that use FDCs based on regression 

equations (Ziegeweid and others, 2015) to estimate historical 

daily streamflow data for ungaged locations on small streams 

(that is, those with drainage areas less than 3,000 square miles 

[mi2]) in Minnesota. 

Methods to Estimate Historical Daily Streamflow for 

Ungaged Stream Locations in Minnesota

By David L. Lorenz and Jeffrey R. Ziegeweid
2 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota

This study for ungaged stream locations in Minnesota 

builds upon the work presented in Ziegeweid and others 

(2015) who developed regression equations for estimating 

13 FDC statistics. Those FDC statistics are needed for estimating historical daily streamflow using the QPPQ method at 

ungaged stream locations in Minnesota.

Purpose and Scope

This report describes how regression equations developed 

by Ziegeweid and others (2015) can be used to estimate historical daily streamflow in small streams at ungaged locations 

in Minnesota. The steps described include (1) constructing 

FDCs at ungaged locations, (2) selecting index streamgages, 

and (3) transferring hydrographs from the index streamgage 

to the ungaged location. Methods presented in this report 

apply only to streams in Minnesota with drainage areas less 

than 3,000 mi2 and flows that are not substantially affected by 

regulation, diversion, or urbanization, which are limitations set 

by the analysis done by Ziegeweid and others (2015).

The purpose of estimating historical daily streamflow 

is to describe the hydrograph structure—variability of flow 

and approximate timing of flows—rather than the actual daily 

streamflow at the ungaged location. As such, the estimated 

streamflow is more suitable for management of recreational 

activities and maintenance of aquatic habitat than for studies of contaminant transport and load estimation, where more 

accurate streamflow is required. The estimated FDCs could be 

modified by other mass-balance methods to estimate streamflow that more nearly match the expected daily streamflow 

for use in water budgets and possibly contaminant transport. 

Those methods are beyond the scope of this report.

Description of the Study Area

The study area (fig. 1) includes the State of Minnesota 

and a 50-mile (mi) buffer around Minnesota in the neighboring States of Iowa, North Dakota, South Dakota, and Wisconsin. Canadian portions of the basins were not included because 

basin characteristics were not available in StreamStats (U.S. 

Geological Survey, 2015). The study area is divided into five 

hydrologic regions (fig. 1) developed using a combination of 

statistical analyses from previous studies (Jacques and Lorenz, 

1988; Lorenz and others, 1997; Lorenz and others, 2010) 

and the concept of hydrologic landscape units (Winter, 2001; 

Wolock and others, 2004). Ziegeweid and others (2015) state 

“Region BC represents the combined regions B and C from 

Lorenz and others (2010) because not enough streamgages 

with low-flow data were available in region C to develop 

regional regression equations. Residual analyses confirmed 

that regions B and C could be combined without affecting 

the ability of the regional regression equations to accurately 

estimate FDC and LFF statistics.”

Differences among the five hydrologic regions are 

described using the hydrologic landscape unit information 

presented in Lorenz and others (2010). Region A is the most 

heterogeneous region, with generally low slopes that become 

increasingly moderate near the drainage boundary. Most of 

region BC is dominated by sandy soils and low to moderate 

slopes, but the northeastern portion of region BC along the 

north shore of Lake Superior and the northeastern Canadian 

border generally is high in slope. Low slopes near the center 

of region D change to moderate slopes and less sandy soils 

around the drainage boundaries. Region E is similar to the 

drainage boundaries of region D, with moderate slopes and 

low sand content in the soils; however, there are distinct differences in the drainage patterns between regions D and E. 

Finally, high slope areas in region F change to moderately 

sloped areas along the western drainage boundary.

The study area (fig. 1) includes selected index 

streamgages in the State of Minnesota, but some selected 

index streamgages are in the surrounding States of Iowa, 

North Dakota, South Dakota, and Wisconsin. For the 

neighboring States, only those streamgages that were 

used in Ziegeweid and others (2015) are used as index 

streamgages. For Minnesota, inactive streamgages that

have at least 10 years of record and all active (as of 2015) 

streamgages that are unaffected by regulation, diversion, or 

urbanization are used as index streamgages. Table 1 ( at the 

back of this report) provides additional information for the 

index streamgages shown on figure 1.

Methods to Estimate Historical Daily 

Streamflow 

Daily mean streamflow can be estimated for ungaged 

locations in Minnesota by transferring streamflow data at 

index streamgages to the ungaged location using the QPPQ 

method (Fennessey, 1994). The QPPQ method uses FDCs 

at ungaged locations and index streamgages and relies on 

the assumption that exceedance probabilities are equivalent 

between an ungaged location and an index streamgage. Details 

of applying the method are presented in the following sections.

If the ungaged location was previously gaged for a 

period long enough to establish an FDC (10 years), then the 

FDC for the location can be based on measured streamflow 

rather than estimated streamflow. If the gaging period was 

not long enough to establish an FDC, then the estimated FDC 

can be used and possibly adjusted by the mean flow to closer 

approximate streamflow at the ungaged location. In addition, 

other record-extension methods can be used for previously 

gaged locations. One common record-extension method is the 

maintenance of variance extension (MOVE), which adjusts for 

changes in flow conditions between the concurrent and nonconcurrent records (Hirsch, 1982; Vogel and Stedinger, 1985).
Methods to Estimate Historical Daily Streamflow 3

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with map number corresponding 

to detailed information (table 1−1)—

Streamgages located outside 

Minnesota were assigned to 

hydrologic regions shown in 

table 1−1

Hydrologic region

EXPLANATION

A

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Base from U.S. Geological Survey and Minnesota 

Department of Natural Resources, various scales

Universal Transverse Mercator projection, zone 15

Horizontal coordinate information is referenced 

to the North American Datum of 1983 

157

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WISCONSIN

IOWA

NORTH

DAKOTA

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DAKOTA

Lake of the Woods

Upper

Red Lake

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LAKE

SUPERIOR

Mille

 Lacs

UNITED

STATES

Figure 1. Minnesota and parts of neighboring States showing selected index streamgages.
4 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota

Estimation of the Ungaged Flow-Duration Curve

An FDC is a cumulative frequency curve that shows 

the fraction of time that specified streamflow is equaled or 

exceeded (Searcy, 1959). Typically, FDCs are constructed 

using the complete records for the index streamgage, but 

FDCs can be constructed from any reference time period. An 

FDC is built by sorting streamflow observed during a given 

period of time by magnitude and calculating the probability 

that a specified streamflow value will be equaled or exceeded. 

For this report, the fraction of time that the streamflow is 

equaled or exceeded is termed exceedance probability.

At an ungaged location, the FDC is constructed from 

point estimates of streamflow for 13 exceedance probabilities 

(0.0001, 0.001, 0.02, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99, 

0.999, and 0.9999) that cover the range of streamflow. Regression equations, developed using physical and climatic basin 

characteristics and streamflow data from a subset of index 

streamgages, are applied to estimate each of the 13 exceedance 

probabilities (Ziegeweid and others, 2015). To construct a continuous daily FDC, streamflow at all other exceedance probabilities is determined by log-q-normal interpolation, which 

interpolates values based on the log of streamflow and the 

quantile of the normal distribution based on the probability, 

completing the FDC between the 13 exceedance-probability 

estimates for the ungaged location.

Selection of Index Streamgages in Minnesota 

and Neighboring States

Selection of an index streamgage is an important step 

in obtaining the best estimates of daily streamflow in an 

unaltered stream at an ungaged location. Index streamgages 

can be identified using several methods. Archfield and others 

(2010) used kriging to maximize the correlation in streamflow between streamgages and potential ungaged locations 

to identify index streamgages, an approach that works well 

when examining fixed periods of time. In contrast, Farmer and 

others (2014) selected index streamgages using the nearestneighbor method. Once index streamgages were selected, 

both studies (Archfield and others, 2010; Farmer and others, 2014) used the QPPQ method, which is described in the 

“Estimation of Unaltered Daily Mean Streamflow” section, 

to estimate daily streamflow at ungaged stream locations. For 

this Minnesota study, the nearest-neighbor method was used to 

determine the Spearman rank correlation coefficients (Spearman’s rho; Helsel and Hirsch, 2002) between streamgages 

separated by various distances, and Spearman’s rho was used 

to evaluate whether compared streamgages were suitable 

index streamgages.

The index streamgage must be unaltered by regulation and similar to the ungaged locations of interest. For the 

purposes of this report, an index streamgage is defined as the 

outlet of a basin that has upstream land cover, geology, and 

hydrologic characteristics similar to the ungaged basin and is 

based on a similar term in Stuckey and others (2012). A set of 

index streamgages from the streamgage network in Minnesota 

and surrounding States was identified to estimate correlations 

with ungaged locations (table 1). Other streamgages maintained by the USGS, the Minnesota Department of Natural 

Resources, or other agencies could be used once they have 

established records of at least 10 years length. It is important 

that the index streamgage basin characteristics should be 

relatively similar to the ungaged basin characteristics, particularly the location of lakes or wetlands that affect the timing of 

streamflow. Possible effects, including peak-flow attenuation 

and slower response to rainfall, from large lakes and wetlands 

just upstream from the ungaged or potential index streamgage 

should be considered when selecting the index streamgage.

Estimation of Unaltered Daily Mean Streamflow

Daily mean streamflow in unaltered small streams at 

ungaged locations in Minnesota can be estimated using the 

QPPQ method (Fennessey, 1994). The three-step process 

of the QPPQ method is shown in figure 2: (1) for each day, 

the observed daily mean streamflow at the index station (the 

“gaged hydrograph”) is determined; (2) the probability of 

exceeding that observed streamflow is determined from the 

“gaged flow-duration curve” and transferred to the “estimated 

flow-duration curve”; and (3) the estimated flow for the 

ungaged location for that day is determined and the “estimated 

ungaged hydrograph” is constructed.

Evaluation of Index Streamgages

For streamgages in this study, the nearest-neighbor 

method produced consistently better Spearman’s rho, computed from the estimated and observed streamflows, when 

drainage-area ratios for the compared streamgages were 

between 0.25 and 4 than when drainage-area ratios were outside of this range; however, within this range of drainage-area 

ratios, the Spearman’s rho decreased as the distance between 

streamgages increased. For streamgages about 10 mi apart, 

Spearman’s rho for daily streamflow between streamgages was 

0.87. When the distances between streamgages were increased 

to about 50 mi, Spearman’s rho decreased to 0.78. In the study 

area, the only potential ungaged locations without a suitable 

index streamgage within 50 mi are some tributaries to Lake 

Superior.

Evaluation of Estimated Daily 

Streamflow

Observed and estimated streamflows were compared for 

nine pairs of streamgages (table 2) to assess the performance 

of the QPPQ method for streams within the study area. The 
Evaluation of Estimated Daily Streamflow 5

nine pairs of streamgages were randomly selected from the 

streamgages used in Ziegeweid and others (2015) based on 

a distance of less than 50 mi, drainage-area ratios ranging 

from 0.25 to 4, and concurrent record. The selected pairs of 

streamgages represent a range in distance from 5 to 43 miles 

and drainage-area ratios from 0.3 to 2.72 (table 2). Only data 

from the most recent complete water year available from the 

USGS National Water Information System (U.S. Geological Survey, 2013) common to the pair of streamgages were 

used in the comparison; a water year is the 12-month period 

of October 1 through September 30 and is designated by 

the calendar year in which it ends. For each pair, the index 

streamgage had the smaller streamgage station number and the 

target streamgage had the larger streamgage station number. 

The QPPQ method was applied for the pair after the FDC was 

estimated at the target streamgage using the regional regression equations. The Spearman’s rho values for the selected 

water year ranged from 0.62 to 0.92, and the mean Spearman’s 

Observed streamflow 

Probability

Estimated streamflow

Day

10

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200

500

1,000

Observed daily mean streamflow, in cubic feet per second

A. Gaged hydrograph 

10

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1,000

B. Gaged flow-duration curve

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1,000

0 0.2 0.4 0.6 0.8 1.0

Probability of exceedence

D. Estimated flow-duration curve

10

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1,000

Estimated daily mean streamflow, in cubic feet per second

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

July 2015

C. Estimated ungaged hydrograph

Figure 2. Example of the QPPQ method (Fennessey, 1994) used to estimate daily mean streamflow at ungaged locations for part of 

the annual hydrograph showing A, the gaged hydrograph; B, the gaged flow-duration curve; C, the estimated flow-duration curve; 

and D, the estimated ungaged hydrograph.
6 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota

rho of 0.79 closely approximates the mean Spearman’s rho 

for streamgages in the study area within 50 mi of each other 

(0.78).

Observed and estimated streamflows for two target 

streamgages listed in table 2 are compared in figure 3. The 

observed and estimated streamflows for streamgage Elk River 

near Big Lake, Minn. (05275000; fig. 3A) had the largest 

Spearman’s rho between index and target streamgages (0.92). 

Although the estimated streamflow generally is overestimated 

for low flows and underestimated for peak flows, the estimated 

streamflow closely approximates the timing of changes in the 

measured hydrograph. The observed and estimated streamflows for streamgage South Fork Crow River near Mayer, 

Minn. (05279000; fig. 3B) had the smallest Spearman’s rho 

between index and target streamgages (0.62). The relation 

between the estimated and observed low flows (less than 500 

cubic feet per second [ft3/s] at streamgage 05279000 and less 

than 300 ft3/s at streamgage 05275000) was less consistent at 

streamgage 05279000 (fig. 3B) than at streamgage 05275000 

(fig. 3A), and the timing and magnitude of the measured 

spring peak associated with ice-out was misrepresented by the 

estimated streamflow at streamgage 05279000. In addition, the 

estimated streamflow peaks in June and July for streamgage 

05279000 were greatly overestimated. 

The hydrographs shown in figure 3 illustrate how the 

magnitudes of observed and estimated streamflows can vary 

greatly using the methods presented in this report. In figure 

3A, the observed peak streamflow (in early June) was about 

1.8 times larger than the estimated peak streamflow, whereas 

in figure 3B, the estimated peak streamflow in May was 

about 2.3 times larger than the observed peak streamflow. In 

addition, for target streamgage Roseau River at Ross, Minn. 

(05107500), the estimated mean streamflow of 1,400 ft3/s was 

about 3.5 times larger than the observed mean streamflow of 

406 ft3/s. Such a large difference between the estimated and 

observed streamflows is unusual for streamgages in region A 

(fig. 1), where the standard error of the median flow regression 

is 79 percent (Ziegeweid and others, 2015). 

Several methods can be used to evaluate the accuracy of 

estimated streamflow. The Nash-Sutcliffe efficiency (NSE; 

Nash and Sutcliffe, 1970) is useful in evaluating estimated 

streamflow when the goal of the estimation is to closely 

approximate the actual measured streamflow (Ziegeweid and 

Magdalene, 2015). Values of the NSE can range from negative 

infinity to 1.0, and values close to 1.0 indicate that estimated 

streamflows closely approximate measured streamflows. The 

largest NSE value determined for the 9 target streamgages 

(table 2) was 0.74. Three of the target streamgages had NSE 

values less than 0, indicating the method was worse than the 

mean of the data at predicting a given streamflow. However, 

the goal of using the QPPQ method is to reproduce the structure of the hydrograph, not to predict actual streamflow; thus, 

the results of the NSE analysis are less important for evaluating the QPPQ method that the results of the Spearman’s rho 

analysis. 

StreamStats

StreamStats is a USGS Web-based geographic information system (GIS) tool (http://streamstats.usgs.gov/; Ries and 

others, 2008) that allows users to obtain streamflow statistics, 

drainage-basin characteristics, and other information for 

user-selected locations on streams. Users can select stream 

locations of interest from an interactive map and can obtain 

information for these locations. If a user selects the location 

of a USGS streamgage, the user will get previously published 

information for the streamgage from a database. If a stream 

location is selected where no data are available (an ungaged 

location), a GIS program will estimate information for the 

location. The GIS program determines the boundary of the 

drainage basin upstream from the stream location, calculates 

the basin characteristics of the drainage basin, and solves 

the appropriate regression equations, based on the physical 

characteristics of the basin, to estimate streamflow statistics 

for that location. The results are presented in a table and a 

Table 2. Selected pairs of streamgages for assessment of performance of the QPPQ method (Fennessey, 1994) for estimating ungaged 

streamflow in Minnesota.

Index station 

number

Target station 

number

Drainage area ratio 

(index/target)

Distance 

(miles) Water year Spearman’s rho Nash-Sutcliffe efficiency

04014500 05124480 0.55 43 1993 0.77 -0.72

04018900 04019300 2.72 19 1978 0.86 0.44

05087500 05093000 0.92 29 1956 0.81 -0.20

05093000 05107500 0.27 28 1956 0.84 -1.45

05270500 05275000 1.87 32 2012 0.92 0.74

05275000 05279000 0.48 31 1979 0.62 0.60

05372000 05374500 0.30 18 1951 0.77 0.27

05376000 05376500 1.29 5 1971 0.91 0.62

05420680 05457700 0.32 26 2012 0.78 0.42
StreamStats 7

0

200

400

600

800

1,000

1,200

1,400

1,600

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

2011 2012

Water year 2012

A

0

1,000

2,000

3,000

4,000

5,000

6,000

Streamflow, in cubic feet per second

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

1978 1979

Water year 1979

B

 Observed streamflow Estimated streamflow

EXPLANATION

Figure 3. Observed and estimated streamflows for two target streamgages. A, streamgage 05275000. B, streamgage 05279000.
8 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota

map showing the basin-boundary outline. These estimates are 

applicable for stream locations not substantially affected by 

regulation, diversions, or urbanization. The regression equations developed by Ziegeweid and others (2015) to estimate 

FDC and LFF statistics in the study area have been incorporated into StreamStats. StreamStats can estimate FDCs at 

ungaged locations on unaltered streams; the estimated FDCs 

are then used in the QPPQ method to estimate streamflow.

Limitations of the Methods

The methods presented in this study have several 

limitations. The regional regression equations developed by 

Ziegeweid and others (2015) apply only to stream locations 

in Minnesota where streamflow is not substantially affected 

by regulation, diversions, or urbanization. Furthermore, the 

applicability and accuracy of the regional equations depend 

on whether the basin characteristics calculated for an ungaged 

stream location are within the range of the characteristic 

values used to develop the regression equations. In addition, selection of an index streamgage is based primarily on 

proximity of the streamgage to the ungaged location. Although 

the closest streamgage should provide good estimates of 

streamflow statistics, other factors need to be considered in 

order to select the index streamgage that provides the most 

accurate estimates of streamflow statistics. For example, if the 

streamflow upstream from the nearest streamgage is affected 

substantially by an upstream lake or wetland, and the ungaged 

location is not affected substantially by a lake or wetland, then 

the user might consider selecting a different index streamgage 

that is unaffected by lakes or wetlands upstream from the 

streamgage.

Summary

Effective and responsible management of water resources 

relies on a thorough understanding of the quantity and quality 

of available water; however, streamgages cannot be installed 

at every location where streamflow information is needed. 

Therefore, methods for estimating streamflow at ungaged locations need to be developed. This report presents the results of 

a statewide study to develop methods to estimate the structure 

of historical daily streamflow at ungaged stream locations in 

Minnesota. Historical daily mean streamflow at ungaged locations in Minnesota can be estimated by transferring streamflow 

data at streamgages to the ungaged location using the QPPQ 

method. The QPPQ method uses flow-duration curves at index 

streamgages and ungaged locations and relies on the assumption that exceedance probabilities are equivalent between an 

index streamgage and an ungaged location. Flow-duration 

curves at ungaged locations can be estimated using recently 

developed regression equations that have been incorporated 

into StreamStats (http://streamstats.usgs.gov/), which is a 

USGS Web-based interactive mapping tool that can be used to 

obtain streamflow statistics, drainage-basin characteristics, and 

other information for user-selected locations on streams. 

Nine pairs of streamgages and Spearman’s rho were used 

to evaluate the ability of the QPPQ method to predict measured (observed) hydrographs. Spearman’s rho for the nine 

target streamgages ranged from 0.62 to 0.92, with a mean 

(0.79) that closely approximates the mean Spearman’s rho for 

streamgages in the study area within 50 miles of each other 

(0.78).

Acknowledgments

Scott Bennett, a contract employee at the U.S. Geological Survey (USGS) Minnesota Water Science Center, created 

the study area map and compiled the basin characteristics. 

Erik Smith of the USGS Minnesota Water Science Center 

and David Bender of the USGS South Dakota Water Science 

Center improved the report by their careful reviews.

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Table 1
12 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota Table 1. Index streamgages in Minnesota and neighboring States. [Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota] Map number (fig. 1) Station number Station name Region Drainage area (square miles) Water years with streamflow record

1 04010500 Pigeon River at Middle Falls near Grand Portage, Minn. BC 607 1921‒22, 1924‒20122 04012500 Poplar River at Lutsen, Minn. BC 113 1913‒17, 1930‒32, 1934‒47, 1953‒61, 2008‒113 04014500 Baptism River near Beaver Bay, Minn. BC 138 1930‒47, 1949‒93, 2009‒104 04017000 Embarrass River at Embarrass, Minn. BC 94.5 1943‒645 04018900 East Two River near Iron Junction, Minn. BC 41.7 1967‒796 04019300 West Swan River near Silica, Minn. BC 15.3 1963‒787 04019500 East Swan River near Toivola, Minn. BC 136 1954‒62, 1965‒718 04024098 Deer Creek near Holyoke, Minn. BC 7.56 1977‒20019 04024430 Nemadji River near South Superior, Wis. BC 421 1974‒2012

10 04025500 Bois Brule River at Brule, Wis. BC 151 1943‒81, 1984‒2012

11 040263205 Whittlesey Creek near Ashland, Wis. BC 11.4 1999‒2012

12 040263491 North Fish Creek near Moquah, Wis. BC 84.9 1990‒91, 1995‒97, 2001‒1013 04027000 Bad River near Odanah, Wis. BC 596 1915‒22, 1948‒201214 05047500 Mustinka River above Twelvemile Creek near Charlesville, Minn.

D 200 1943‒55

15 05048000 Mustinka River below Twelvemile Creek near Charlesville , Minn.

D 722 1943‒55

16 05049000 Mustinka River above Wheaton, Minn.

D 787 1916‒17, 1919‒24, 1931‒58

17 05051600 Wild Rice River near Rutland, N. Dak.

D 414 1960‒2012

18 05051650 La Belle Creek near Veblen, S. Dak.

D 9.49 1988‒99

19 05059600 Maple River near Hope, N. Dak.

A 20.6 1965‒2012

20 05059700 Maple River near Enderlin, N. Dak.

A 824 1956‒2012

21 05060000 Maple River near Mapleton, N. Dak.

A 1,440 1959‒75, 2001‒12

22 05060500 Rush River at Amenia, N. Dak.

A 91.6 1947‒2012

23 05061000 Buffalo River near Hawley, Minn.

A 336 1945‒80, 1983‒2012

24 05061500 South Branch Buffalo River at Sabin, Minn.

A 461 1945‒80, 1984‒2012

25 05062000 Buffalo River near Dilworth, Minn.

A 986 1931‒2012

26 05062500 Wild Rice River at Twin Valley, Minn.

A 934 1910‒17, 1931‒83, 1990‒2001, 2003‒12

27 05066500 Goose River at Hillsboro, N. Dak.

A 1,190 1931‒32, 1934‒2012

28 05069000 Sand Hill River at Climax, Minn.

A 459 1943‒2012

29 05077700 Ruffy Brook near Gonvick, Minn.

A 46.7 1960‒78, 1986

30 05078000 Clearwater River at Plummer, Minn.

A 553 1939‒79, 1982‒2012
Table 1 13

Map 

number 

(fig. 1)

Station number Station name Region Drainage area (square miles) Water years with streamflow record

31 05078230 Lost River at Oklee, Minn. A 249 1960‒201232 05078500 Clearwater River at Red Lake Falls, Minn. A 1,360 1910‒17, 1935‒201233 05083000 Turtle River at Manvel, N. Dak. A 518 1946‒7034 05087500 Middle River at Argyle, Minn. A 251 1945, 1951‒201235 05088000 South Branch Park River near Park River, N. Dak. A 185 1940‒5036 05089100 Middle Branch Park River near Union, N. Dak. A 13 1966‒8637 05089500 Cart Creek at Mountain, N. Dak. A 13.2 1955‒8438 05092200 Pembina County Drain 20 near Glasston, N. Dak. A 81.3 1972‒8639 05093000 South Branch Two Rivers at Pelan, Minn. A 272 1929‒38, 1954‒5640 05095000 Two Rivers at Hallock, Minn. A 670 1911‒14, 1929‒30, 1941‒43, 2008‒1141 05095500 Two Rivers below Hallock, Minn. A 691 1945‒5542 05096000 North Branch Two Rivers near Lancaster, Minn. A 31.6 1929‒38, 1941‒5543 05101500 Tongue River at Cavalier, N. Dak. A 158 1939‒5144 05104000 South Fork Roseau River near Malung, Minn. A 214 1911‒14, 1929‒38, 1940‒4645 05104500 Roseau River below South Fork near Malung, Minn. A 428 1947‒201246 05106000 Sprague Creek near Sprague, Manitoba, Canada A 164 1929‒81, 2000‒1247 05107000 Pine Creek near Pine Creek, Minn. A 31.1 1929‒5348 05107500 Roseau River at Ross, Minn. A 1,010 1929‒91, 1995‒201249 05112000 Roseau River below State Ditch 51 near Caribou, Minn. A 1,410 1917, 1920‒19, 1970‒201250 05124480 Kawishiwi River near Ely, Minn. BC 251 1966‒201251 05124500 Isabella River near Isabella, Minn. BC 340 1953‒61, 1976‒7752 05124990 Filson Creek In Sesw Sec. 24 near Winton, Minn. BC 9.52 1975‒8553 05125000 South Kawishiwi River near Ely, Minn. BC 442 1952‒61, 1976‒78, 2003‒1254 05125500 Stony River near Isabella, Minn. BC 175 1953‒6455 05126500 Bear Island River near Ely, Minn. BC 65.8 1953‒62, 1975‒7756 05127205 Burntside River near Ely, Minn. BC 68.8 1967‒7857 05127210 Armstrong Creek near Ely, Minn. BC 5.83 1967‒7858 05127215 Longstorff Creek near Ely, Minn. BC 8.09 1967‒7859 05127220 Burgo Creek near Ely, Minn. BC 2.98 1967‒7860 05127230 Shagawa River at Ely, Minn. BC 99.6 1967‒78

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
14 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota Map number (fig. 1) Station number Station name Region Drainage area (square miles) Water years with streamflow record 61 05128500 Pike River near Embarrass, Minn. BC 114 1954‒64, 1977‒78 62 05129115 Vermilion River near Crane Lake, Minn. BC 909 1980‒2012 63 05130500 Sturgeon River near Chisholm, Minn. BC 186 1943‒2009 64 05131500 Little Fork River at Littlefork, Minn. BC 1,700 1910‒16, 1929‒2012 65 05132000 Big Fork River at Big Falls, Minn. BC 1,500 1910, 1929‒79, 1983‒93, 1998‒2012 66 05134200 Rapid River near Baudette, Minn.

A 581 1957‒85, 2008‒11

67 05139500 Warroad River near Warroad, Minn.

A 168 1946‒80

68 05140000 Bulldog Run near Warroad, Minn.

A 11.2 1946‒51, 1966‒77

69 05140500 East Branch Warroad River near Warroad, Minn.

A 51.2 1946‒54, 1966‒77

70 05212700 Prairie River near Taconite, Minn. BC 364 1967‒83, 2001‒1271 05217000 Swan River near Warba, Minn. BC 245 1954‒6972 05244000 Crow Wing River at Nimrod, Minn. BC 917 1910‒14, 1931‒81, 1992‒201273 05245100 Long Prairie River at Long Prairie, Minn. BC 448 1972‒201274 05270500 Sauk River near St. Cloud, Minn. BC 1,040 1910‒13, 1929‒81, 1991‒201275 05275000 Elk River near Big Lake, Minn. BC 555 1911‒17, 1931‒87, 1991‒201276 05276000 North Fork Crow River near Regal, Minn.

D 210 1944‒54

77 05278500 South Fork Crow River at Cosmos, Minn.

D 234 1945‒64

78 05279000 South Fork Crow River near Mayer, Minn.

D 1,150 1934‒79

79 05280000 Crow River at Rockford, Minn.

D 2,640 1909‒17, 1929‒2012

80 05286000 Rum River near St. Francis, Minn. BC 1,390 1929‒201281 05287890 Elm Creek near Champlin, Minn. BC 86.9 1979‒201282 05289985 Big Coulee Creek near Peever, S. Dak.

D 12.1 1988‒2003

83 05290000 Little Minnesota River near Peever, S. Dak.

D 449 1940‒81, 1990‒2002, 2009‒12

84 05291000 Whetstone River near Big Stone City, S. Dak.

D 406 1910‒12, 1931‒2012

85 05292704 North Fork Yellow Bank River near Odessa, Minn.

D 209 1992‒2003

86 05293000 Yellow Bank River near Odessa, Minn.

D 459 1940‒99, 2001‒12

87 05294000 Pomme De Terre River at Appleton, Minn.

D 865 1931‒99, 2004‒12

88 05299700 Cobb Creek near Gary, S. Dak.

D 70.4 1993‒2002

89 05300000 Lac Qui Parle River near Lac Qui Parle, Minn.

D 959 1910‒14, 1931‒32, 1934‒99, 2001‒12

90 05304500 Chippewa River near Milan, Minn.

D 1,870 1938‒2012

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
Table 1 15

Map 

number 

(fig. 1)

Station number Station name Region Drainage area (square miles) Water years with streamflow record

91 05311400 South Branch Yellow Medicine River at Minneota, Minn. D 115 1960‒81, 1983‒8792 05313500 Yellow Medicine River near Granite Falls, Minn. D 667 1931‒38, 1940‒201293 05315000 Redwood River near Marshall, Minn. D 259 1940‒201294 05316500 Redwood River near Redwood Falls, Minn. D 624 1910‒14, 1931‒201295 05317000 Cottonwood River near New Ulm, Minn. D 1,310 1910‒13, 1931‒37, 1939‒201296 05317200 Little Cottonwood River near Courtland, Minn. D 169 1974‒200997 05318000 East Branch Blue Earth River near Bricelyn, Minn. D 120 1951‒7098 05319500 Watonwan River near Garden City, Minn. D 847 1940‒45, 1977‒201299 05320270 Little Cobb River near Beauford, Minn. D 128 1996‒99, 2002‒12

100 05320500 Le Sueur River near Rapidan, Minn. D 1,110 1940‒45, 1950‒2012101 05327000 High Island Creek near Henderson, Minn. D 240 1974‒2012102 05331833 Namekagon River at Leonards, Wis. BC 126 1996‒2001, 2005‒12103 05333500 St. Croix River near Danbury, Wis. BC 1,540 1914‒81, 1985‒2012104 05336000 St. Croix River near Grantsburg, Wis. BC 2,960 1923‒70, 2008‒10105 05336200 Glaisby Brook near Kettle River, Minn. BC 26.4 1960‒70106 05336700 Kettle River below Sandstone, Minn. BC 871 1968‒2012107 05338500 Snake River near Pine City, Minn. BC 969 1914‒17, 1952‒81, 1992‒2012108 05340000 Sunrise River near Stacy, Minn. BC 168 1949‒64109 05353800 Straight River near Faribault, Minn. D 436 1966‒2012

110 05365000 Duncan Creek at Chippewa Falls, Wis. BC 118 1943‒55

111 05366500 Eau Claire River near Fall Creek, Wis. BC 759 1943‒55

112 053674464 Yellow River at Barron, Wis. BC 140 1992‒2005113 05367500 Red Cedar River near Colfax, Wis. BC 1,090 1914‒61, 1990114 05368000 Hay River at Wheeler, Wis. BC 432 1951‒2012115 05369945 Eau Galle River at Low-wtr Bridge at Spring Valley, Wis. F 48 1982‒83, 1986‒95116 05370500 Eau Galle River at Elmwood, Wis. F 91.6 1943‒53117 05372000 Buffalo River near Tell, Wis. F 403 1933‒51118 05374000 Zumbro River at Zumbro Falls, Minn. F 1,150 1910‒17, 1929‒80119 05374500 Zumbro River at Theilman, Minn. F 1,340 1938‒56

120 05374900 Zumbro River at Kellogg, Minn. F 1,420 1976‒90, 2010‒12

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
16 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota Map number (fig. 1) Station number Station name Region Drainage area (square miles) Water years with streamflow record 121 05376000 North Fork Whitewater River near Elba, Minn. F 100 1940‒41, 1968‒93 122 05376500 South Fork Whitewater River near Altura, Minn. F 78 1940‒71 123 05376800 Whitewater River near Beaver, Minn. F 271 1975‒85, 1991, 1994‒99, 2008‒12 124 05377500 Whitewater River at Beaver, Minn. F 288 1940‒56 125 05378183 Joos Valley Creek near Fountain City, Wis. F 6.02 1991‒95, 2003‒07 126 05378185 Eagle Creek at Ct Highway G near Fountain City, Wis. F 14.4 1991‒95, 2003‒07 127 05378300 Straight Valley Creek near Rollingstone, Minn. F 5.12 1971‒85 128 05379400 Trempealeau River at Arcadia, Wis. F 554 1961‒77, 2002‒04 129 05379500 Trempealeau River at Dodge, Wis. F 626 1914‒19, 1934‒2012 130 05382325 La Crosse River at Sparta, Wis. F 168 1993‒2005, 2009‒12 131 05382500 Little La Crosse River near Leon, Wis. F 77.4 1934‒61, 1979‒81 132 05383950 Root River near Pilot Mound, Minn. F 566 2003‒12 133 05384000 Root River near Lanesboro, Minn. F 616 1910‒14, 1916‒17, 1941‒85, 1987‒90 134 05384500 Rush Creek near Rushford, Minn. F 132 1943‒79 135 05385000 Root River near Houston, Minn. F 1,250 1910‒17, 1929‒83, 1991‒2000, 2004‒08 136 05386000 Root River below South Fork near Houston, Minn. F 1,540 1938‒61 137 05387440 Upper Iowa River at Bluffton, Iowa F 367 2003‒12 138 05387500 Upper Iowa River at Decorah, Iowa F 511 1952‒83, 2003‒12 139 05388000 Upper Iowa River near Decorah, Iowa F 569 1914, 1919‒27, 1934‒51 140 05388250 Upper Iowa River near Dorchester, Iowa F 768 1939, 1976‒2012 141 05388500 Paint Creek at Waterville, Iowa F 41.7 1953‒73 142 05389000 Yellow River near Ion, Iowa F 219 1935‒51, 2005‒12

143 05389400 Bloody Run Creek near Marquette, Iowa F 34.3 1992‒2012144 05404116 West Branch Baraboo River at Hillsboro, Wis. F 39 1989‒2012145 05407470 Kickapoo River at State Highway 33 at Ontario, Wis. F 117 2002‒12146 05408000 Kickapoo River at La Farge, Wis. F 266 1939‒2012147 05408500 Knapp Creek near Bloomingdale, Wis. F 8.48 1955‒69148 05409830 North Fork Nederlo Creek near Gays Mills, Wis. F 2.28 1968‒79149 05409890 Nederlo Creek near Gays Mills, Wis. F 10.1 1968‒80150 05410000 Kickapoo River at Gays Mills, Wis. F 616 1914‒34, 1964‒77

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
Table 1 17

Map 

number 

(fig. 1)

Station number Station name Region Drainage area (square miles) Water years with streamflow record

151 05410490 Kickapoo River at Steuben, Wis. F 687 1983‒2012152 05410500 Kickapoo River-old Site-at Steuben, Wis. F 689 1933‒82153 05411400 Sny Magill Creek near Clayton, Iowa F 27.6 1992‒2001154 05411600 Turkey River at Spillville, Iowa F 177 1957‒73, 1978‒91, 2010‒12155 05411850 Turkey River near Eldorado, Iowa F 641 2001‒12156 05412000 Turkey River at Elkader, Iowa F 894 1933‒42157 05412020 Turkey River above French Hollow Cr at Elkader, Iowa F 906 2002‒12158 05412060 Silver Creek near Luana, Iowa F 4.11 1986‒98159 05412100 Roberts Creek above Saint Olaf, Iowa F1 70.6 1986‒2001160 05420560 Wapsipinicon River near Elma, Iowa D 96.5 1959‒92161 05420680 Wapsipinicon River near Tripoli, Iowa D 346 1996‒98, 2001‒04, 2007‒12162 05448500 West Branch Iowa River near Klemme, Iowa D 115 1948‒58163 05449000 East Branch Iowa River near Klemme, Iowa D 134 1948‒76, 1978‒95164 05457700 Cedar River at Charles City, Iowa D 1,070 1965‒95, 1997, 2001‒12165 05458000 Little Cedar River near Ionia, Iowa D 297 1955‒2012166 05459000 Shell Rock River near Northwood, Iowa D 302 1946‒86167 05459500 Winnebago River at Mason City, Iowa D 488 1933‒2012168 05460500 Shell Rock River at Marble Rock, Iowa D 1,300 1943‒53169 05476000 Des Moines River at Jackson, Minn. D 1,240 1931‒2012170 05476500 Des Moines River at Estherville, Iowa D 1,400 1952‒94171 05478000 East Fork Des Moines River near Burt, Iowa D 421 1952‒74172 06479215 Big Sioux River near Florence, S. Dak. E 68.2 1985‒12173 06479438 Big Sioux River near Watertown, S. Dak. E 525 1973‒2012174 06479515 Willow Creek near Watertown, S. Dak. E 109 1972‒86175 06479529 Stray Horse Creek near Castlewood, S. Dak. E 74.1 1969‒85176 06479640 Hidewood Creek near Estelline, S. Dak. E 163 1969‒85177 06479770 Big Sioux River near Bruce, S. Dak. E 2,400 2001‒12178 06479910 Sixmile Creek near Brookings, S. Dak. E 60.1 1971‒80179 06479980 Medary Creek near Brookings, S. Dak. E 197 1981‒90180 06480400 Spring Creek near Flandreau, S. Dak. E 61.3 1983‒93

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
18 Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota Map number (fig. 1) Station number Station name Region Drainage area (square miles) Water years with streamflow record 181 06480650 Flandreau Creek above Flandreau, S. Dak.

E 101 1982‒91

182 06481480 Skunk Creek near Chester, S. Dak.

E 262 1985‒87, 2002‒12

183 06481500 Skunk Creek at Sioux Falls, S. Dak.

E 620 1948‒2001, 2004‒12

184 06482610 Split Rock Creek at Corson, S. Dak.

E 482 1966‒89, 2002‒12

185 06483270 Rock River at Rock Rapids, Iowa

E 788 1960‒74

186 06483290 Rock River below Tom Creek at Rock Rapids, Iowa

E 844 2001‒12

187 06483500 Rock River near Rock Valley, Iowa

E 1,580 1949‒2012

188 06484000 Dry Creek at Hawarden, Iowa

E 49 1949‒69

189 06485696 Brule Creek near Elk Point, S. Dak.

E 205 1983‒94

190 06600100 Floyd River at Alton, Iowa

E 266 1956‒2012

191 06600300 West Branch Floyd River near Struble, Iowa

E 178 1956‒94

192 06603000 Little Sioux River near Lakefield, Minn.

D 15.6 1949‒62

193 06603500 Jackson County Ditch #11 near Lakefield, Minn.

D 7.65 1949‒60

194 06605000 Ocheyedan River near Spencer, Iowa

D 438 1978‒2012

195 06605600 Little Sioux River at Gillett Grove, Iowa

D 1,350 1959‒73

196 06605850 Little Sioux River at Linn Grove, Iowa

D 1,560 1973‒2012

1Not used in analysis.

Table 1. Index streamgages in Minnesota and neighboring States.—Continued[Water year is the 12-month period of October 1 through September 30 and is designated by the calendar year in which it ends. Minn., Minnesota; Wis., Wisconsin; N. Dak., North Dakota; S. Dak., South Dakota]
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For more information concerning this publication, contact:

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Mounds View, Minnesota 55112

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Or visit the Minnesota Water Science Center Web site at: 

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Lorenz and Ziegeweid—Methods to Estimate Historical Daily Streamflow for Ungaged Stream Locations in Minnesota—Scientific Investigations Report 2015–5181

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20155181