U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2020–5003

Prepared in cooperation with U.S. Bureau of Land Management

Extending Seasonal Discharge Records for Streamgage 

Sites on the North Fork Fortymile and Middle Fork Fortymile 

Rivers, Alaska, through Water Year 2019
Cover:

Downstream view of the North Fork Fortymile River's confluence 

with the Middle Fork Fortymile River (right), Alaska. (Photograph by 

Heather Best, U.S. Geological Survey, May 19, 2019.)
Extending Seasonal Discharge Records 

for Streamgage Sites on the North Fork 

Fortymile and Middle Fork Fortymile 

Rivers, Alaska, through Water Year 2019

By Janet H. Curran

Prepared in cooperation with U.S. Bureau of Land Management

Scientific Investigations Report 2020–5003

U.S. Department of the Interior

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

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Suggested citation:

Curran, J.H., 2020, Extending seasonal discharge records for streamgage sites on the North Fork Fortymile and Middle 

Fork Fortymile Rivers, Alaska, through water year 2019: U.S. Geological Survey Scientific Investigations Report 

2020–5003, 11 p., https://doi.org/10.3133/sir20205003.

ISSN 2328-0328 (online)
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................1

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

Methods for Estimating Extended Daily Mean Discharge Records ......................................................4

Selection of Season of Analysis .........................................................................................................4

Selection of Index Streamgage ..........................................................................................................4

Record Extension Technique ..............................................................................................................6

Extended Daily Mean Discharge Records and Error Analysis ...............................................................7

Comparison of Observed and Estimated Records ...........................................................................7

Accuracy and Limitations of Extended Records .............................................................................8

Summary..........................................................................................................................................................9

References Cited..........................................................................................................................................10

Appendix 1. Extended Seasonal Daily Mean Discharge Records for Two Streamgages 

in the Fortymile River Basin, Alaska ............................................................................................11

Figures

1. Map showing location of study streamgages in the Fortymile River Basin, Alaska. ........2

2. Hydrographs of daily mean discharges available for water year 2019 for U.S. 

Geological Survey streamgages 15330000; 15331000; and 15348000 ...................................3

3. Plot of concurrent measured discharge and the maintenance of variance 

extension type 3 regression line at U.S. Geological Survey streamgages 

15330000 and 15348000, offset 1 day earlier, and streamgages 15331000

and 15348000 ..................................................................................................................................6

4. Plot of observed and estimated discharges for the concurrent period of record 

at North Fork Fortymile River above Middle Fork near Franklin, Alaska, and 

Middle Fork Fortymile River near mouth near Chicken, Alaska ............................................9

Tables

1 Drainage area and period of discharge record for U.S. Geological Survey study

streamgages and index streamgage in the Fortymile River Basin, Alaska .........................5

2 Correlation coefficients (Pearson’s r) between logarithms of daily mean

discharge at study and index streamgages in the Fortymile River Basin, Alaska .............5

3 Summary statistics of the concurrent observed and estimated daily mean

discharge records at two study streamgages in the Fortymile River Basin, Alaska .........7

4 Root mean square error and modified Nash-Sutcliffe efficiency coefficients

for MOVE.3 regression models at two study streamgages in the Fortymile River

Basin, Alaska .................................................................................................................................8
iv

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Volume

cubic foot (ft3) 28.32 cubic decimeter (dm3)

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

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

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

°C = (°F – 32) / 1.8.

Datums

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

(NAVD 88).

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

Altitude, as used in this report, refers to distance above the vertical datum.

Abbreviations

MOVE.3 Maintenance of variance extension type 3

NAD 83 North American Datum of 1983

NAVD 88 North American Vertical Datum of 1988

NSE modified Nash-Sutcliffe efficiency coefficient

NWIS National Water Information System

RMSE Root mean square error

USGS U.S. Geological Survey

WY Water year
Extending Seasonal Discharge Records for Streamgage 

Sites on the North Fork Fortymile and Middle Fork 

Fortymile Rivers, Alaska, through Water Year 2019

By Janet H. Curran

Abstract

Daily mean discharge values were estimated for May 

20–September 30 for 1976–82 and 2006–18 for the U.S. 

Geological Survey North Fork Fortymile River and Middle 

Fork Fortymile River streamgage sites in Alaska. A relation 

between study streamgage discharge and discharge for 

an index streamgage on the main-stem Fortymile River 

for a concurrent period in 2019 was developed using the 

maintenance of variance extension type 3 (MOVE.3) record 

extension technique. The relation for North Fork Fortymile 

River discharges incorporated a 1-day-earlier offset to index 

streamgage discharges. No offset was applied to the index 

streamgage discharges for use with the Middle Fork Fortymile 

River discharges. The developed MOVE.3 regressions were 

used to estimate daily mean discharges at the study streamgage 

sites during the study season for the longer period of record of 

the index streamgage. The modified Nash-Sutcliffe efficiency 

coefficients for the estimated records were 0.38 and 0.63 for 

the North Fork Fortymile River and Middle Fork Fortymile 

River streamgages, respectively.

Introduction

Daily mean discharge is a common metric of streamflow 

that forms the basis of analysis for a wide variety of water 

resource management purposes, including engineering 

design, environmental assessment, and development of legal 

agreements of water use. Many agency agreements and legal 

statutes rely on discharge statistics that can quantify historical 

water availability and express wetted channel conditions. 

Discharge values determined from data collected at U.S. 

Geological Survey (USGS) streamgages often provide the 

record from which discharge statistics needed for analysis 

can be computed. Long records of daily mean discharge 

can represent natural variations that occur on annual to 

decadal scales better than short records, but long records are 

not available for many locations where such information 

is needed. To account for longer-term natural variations at 

a shorter-record location, record extension techniques can 

be used to estimate discharge. Record extension relates 

discharges at a streamgage of interest to concurrent discharge 

at a streamgage having a longer period of record, referred to 

as an “index streamgage” (Hirsch, 1979; Hirsch, 1982). That 

relation can then be applied to the longer period of record 

from the index streamgage to estimate a discharge record for 

the study streamgage. Record extension requires a concurrent 

period of record with a closely-correlated index streamgage 

and a longer period of record for the index streamgage from 

which to estimate discharge for the short-record streamgage.

Within the Fortymile River Basin in east-central 

Alaska, the USGS collected discharge data for part of 2019 

at streamgages on two streams, the North Fork Fortymile 

River and the Middle Fork Fortymile River (fig. 1). Longer 

estimates of daily mean discharge for these study streams are 

needed for compilation of streamflow statistics desired for 

management of the streams. In cooperation with the Bureau 

of Land Management, the USGS developed estimated daily 

mean discharge records for streamgages on the North Fork and 

Middle Fork Fortymile Rivers.

Purpose and Scope

This report describes the development of a method for 

estimating daily mean discharge for two streamgages of 

interest in the Fortymile River Basin using the maintenance 

of variation extension type 3 (MOVE.3) record extension 

technique. It documents the selection of a season of analysis 

and an index streamgage, presents estimates of historical daily 

mean discharge for an extended period of record, and presents 

an evaluation of the accuracy of the estimated records. Within 

the limitations discussed, the results of this study are suitable 

for use in preparation of discharge statistics, including the 

number of days that daily mean discharge falls between a 

higher and lower discharge threshold during the season used in 

this report.
2 Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019

tac20-5273_fig 01

Mosquito Fork

Fortymile River

YUKON RIVER

Middle Fork Fortymile River

North Fork

Fortymile River

Dennison Fork

Tanana River

South Fork

Charley River

Seventymile River

West Fork

Walker Fork

5

2

1

2

5

9

TOP OF THE WORLD HIGHWAY

TAYLOR HIGHWAY

Chicken

Eagle

Franklin

Tok

M E R T I E

M O U N TA I N S

UNITED STATES

ALASKA

CANADA

YUKON

15331000

15348000

15330000

UNITED STATES

ALASKA

CANADA

YUKON

Map

area

EXPLANATION

Drainage basin 

USGS streamgage 15348000 

USGS streamgage 15331000

USGS streamgage and No.

USGS streamgage 15330000

15330000

144° 143° 142° 141°

65°

00'

64°

30'

64°

00'

63°

30'

0 10 20 30 40 MILES

0 10 20 30 40 50 KILOMETERS

Base map sources: U.S. Geological Survey, various; Alaska State Geo-Spatial Data Clearinghouse 1:1,000,000 

hydrography; Natural Resources Canada 1:1,000,000 hydrography; and other digital data. Coordinate reference 

system: NAD 1983 2011 Alaska Albers. Horizontal datum is North American Datum of 1983.

Figure 1. Location of study streamgages in the Fortymile River Basin, Alaska. [USGS, U.S. Geological Survey]
Introduction 3

Description of Study Area

The Fortymile River, a tributary to the Yukon River, 

drains more than 6,000 square miles (mi2) in east-central 

Alaska and Canada about 150 miles east of Fairbanks (fig. 1). 

The river contains numerous tributaries, including the North 

Fork Fortymile River, which originates in the northern part 

of the basin, and the Middle Fork Fortymile River, which 

drains the northwestern part of the basin and is a tributary 

of the North Fork. The North Fork Fortymile River joins 

the South Fork Fortymile River to form the main-stem 

Fortymile River upstream of the Taylor Highway (fig. 1). 

Fortymile River Basin topography includes the hilly terrain 

of the Mertie Mountains, which range in altitude from about 

3,000 to 6,000 ft along the western and northern parts of the 

basin, and gently-sloped flats containing extensive wetlands 

in the southern part of the basin. Wetlands also occupy the 

wide valley bottom of the upper reaches of the Middle Fork 

Fortymile River.

The Fortymile River Basin has a continental climate 

characterized by cold, dry winters and warm summers. In the 

basin draining to the USGS Fortymile River streamgage near 

the Taylor Highway (15348000, Fortymile River near Steele 

Creek, Alaska), the mean January temperature for 1971–2000 

(Gibson, 2009a) is -9 degrees Fahrenheit and the mean July 

temperature is 54 degrees Fahrenheit. Precipitation averaged 

15 inches per year in the basin for 1971–2000 (Gibson, 

2009b), which includes snow in the winter. Basin average 

precipitation is highest in the summer months of June–August.

The USGS streamgages on the North Fork Fortymile 

River (15330000, North Fork Fortymile River above Middle 

Fork near Franklin, Alaska) and the Middle Fork Fortymile 

River (15331000, Middle Fork Fortymile River near mouth 

near Chicken, Alaska) are each located a short distance 

upstream from the confluence of the two rivers. Hydrographs 

for the two study streamgages and the main-stem Fortymile 

River during the concurrent period show patterns of abruptly 

rising then falling discharge over several days that generally 

represent discharge response to precipitation (fig. 2). Despite 

the proximity of the study streamgages, slight differences 

appear in the timing of their discharge patterns. Basin 

differences including topography, the spatial distribution of 

wetlands, drainage area, or stream length could at least partly 

explain the apparently faster response to precipitation at the 

North Fork Fortymile River streamgage relative to the Middle 

Fork Fortymile River and Fortymile River streamgage sites.

Water year 2019

Discharge, in cubic feet per second

10

100

1,000

10,000

100,000

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

EXPLANATION

North Fork Fortymile River

Middle Fork Fortymile River

Fortymile River

Figure 2. Hydrographs of daily mean discharges available for water year 2019 for U.S. Geological Survey streamgages 15330000 (North 

Fork Fortymile River above Middle Fork near Franklin, Alaska); 15331000 (Middle Fork Fortymile River near mouth near Chicken, Alaska); 

and 15348000 (Fortymile River near Steele Creek, Alaska).
4 Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019

Methods for Estimating Extended Daily 

Mean Discharge Records

Hydrologic data for analysis consisted of daily 

mean discharge for study streamgages and potential 

index streamgages and were obtained from the USGS 

National Water Information System database (NWIS) at 

https://nwis.waterdata.usgs.gov/ak/nwis/sw (U.S. Geological 

Survey, 2019). For correlation and record extension analysis, 

daily mean discharge data were transformed using a common 

logarithm to improve data distribution. Except where 

specified, analyses used the R language and programming 

environment version 3.6.1 (R Core Team, 2019). Record 

extension was conducted for a limited season using an index 

station that met selection criteria and a record extension 

technique developed for use with hydrologic data, as described 

in the following sections.

Selection of Season of Analysis

The study season of May 20–September 30 was chosen to 

match the concurrent period of gaging for the two streamgage 

records to be extended. The North Fork Fortymile River 

streamgage record includes an additional day of data (May 19, 

2019) that was ignored for the convenience of a single study 

season. Inspection of discharge patterns for the longer period 

of record at the Fortymile River streamgage downstream 

shows that the study season has consistently represented 

a subset of the open-water season, or ice-free period. 

Hydrographs of discharge for the available period of record at 

each study streamgage and for water year1 (WY) 2019 for the 

Fortymile River streamgage, where a water year is defined as 

the period from October 1 to September 30 and designated by 

the calendar year in which it ends, show the relationship of the 

study season to the open-water season for WY2019 (fig. 2).

The Fortymile River streamgage has a total of 21 years 

of record in two periods, WY1976–82 and WY2006–19. For 

the full period of record at the Fortymile River streamgage, the 

initial flush of snowmelt-driven discharges, which are often 

the highest discharges of the year, occurred shortly before 

May 20. The end of the water year and the end of the data 

collection period for the study streamgages (September 30) 

was typically near the end of open-water season but before 

freezing conditions substantially reduced discharge.

1 The 12-month period from October 1 for any given year to September 30 

of the following year. The water year is designated by the calendar year in 

which it ends. Thus, the year ending September 30, 2019, is called the "2019" 

water year.

Selection of Index Streamgage

For each study streamgage, one or more longer-record 

streamgages were sought to serve as index streamgages for 

extending daily mean discharge. Streamgages considered as 

potential index streamgages consisted of USGS streamgages 

in and near the Fortymile River Basin that had a period of 

record overlapping the study streamgage records and a period 

of record outside the study streamgage period of record. 

Additional selection criteria included proximity to the study 

streamgage, the strength and linearity of the correlation of 

daily mean discharges with concurrent daily mean discharges 

at the study streamgage, hydrologic similarity to the study 

streamgage over a range of low to high discharges, and the 

length of record available for extension beyond the concurrent 

record. A combination of multiple index streamgages for 

a single study streamgage was also considered during 

the selection process. Information for the selected index 

streamgage–the main-stem Fortymile River streamgage–and 

the study streamgages is shown in table 1, and the locations of 

the streamgages are shown in figure 1.

Log-scale scatterplots of concurrent daily mean 

discharge for the study and index streamgage (fig. 3) were 

examined for linearity, scatter, and outliers. Log-scale plots 

of daily mean discharge at study and index streamgages for 

the concurrent period (fig. 2) were examined for similarity 

in seasonal discharge patterns, and log-scale plots of daily 

mean discharge for the full index streamgage period of record 

were examined for annual variability in seasonal discharge 

patterns. The Fortymile River streamgage data were offset 1 

day earlier when used as an index streamgage for the North 

Fork Fortymile River streamgage to account for the earlier 

arrival, on average, of discharge patterns at the North Fork 

Fortymile River. To account for the omission of the last day 

of the record in the offsetting process, the Fortymile River 

streamgage discharge for the first day after the study season 

(October 1, 2019) was inserted as the value for the last day of 

the offset record, September 30, 2019. Pearson’s correlation 

coefficients (r) computed for the logarithms of daily mean 

discharge at the study streamgage sites and index streamgage 

site without offsets were 0.766 and 0.926 for the North Fork 

Fortymile River and Middle Fork Fortymile River streamgage, 

respectively (table 2). Application of the 1-day-earlier offset to 

index discharges improved the correlation coefficient for the 

North Fork Fortymile River streamgage to 0.809 (table 2).
Methods for Estimating Extended Daily Mean Discharge Records 5

Table 1. Drainage area and period of discharge record for U.S. Geological Survey study streamgages and index streamgage in the 

Fortymile River Basin, Alaska.

[Abbreviations: AK, Alaska; mi2, square mile; USGS, U.S. Geological Survey]

Period of discharge record

USGS 

streamgage

number

Streamgage name

Drainage 

area, in 

mi2

Month and day Water years

Study streamgages

15330000 North Fork Fortymile River above Middle Fork near Franklin, AK 750 May 19– 

September 30

2019

15331000 Middle Fork Fortymile River near mouth near Chicken, AK 1,070 May 20– 

September 30

2019

Index streamgage

15348000 Fortymile River near Steele Creek, AK 5,850 October 1– 

September 30

1976–82, 

2006–19

Table 2. Correlation coefficients (Pearson's r) between logarithms of daily mean discharge at study and index streamgages in the 

Fortymile River Basin, Alaska.

[mi2, square mile; AK, Alaska; –, not applicable; USGS, U.S. Geological Survey]

Study USGS 

streamgage

number

Study 

streamgage 

name

Study 

streamgage 

drainage area, 

in mi2

Index USGS 

streamgage 

identifier

Index 

streamgage 

name

Index 

streamgage 

drainage area, 

in mi2

Pearson's 

correlation 

coefficient, no 

offset

Pearson's 

correlation 

coefficient, 

1-day-earlier 

offset to index 

streamgage 

data

15330000 North Fork 

Fortymile 

River above 

Middle Fork 

near Franklin, 

AK

750 15348000 Fortymile 

River near 

Steele 

Creek, AK

5,850 0.766 0.809

15331000 Middle Fork 

Fortymile 

River near 

mouth near 

Chicken, AK

1,070 15348000 Fortymile 

River near 

Steele 

Creek, AK

5,850 0.926 –
6 Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019

tac20-5273_fig 03

100 1,000 10,000 100,000

100 1,000 10,000 100,000

100

1,000

10,000

100

1,000

10,000

A

B

Discharge at 15330000 (North Fork Fortymile River above 

Middle Fork near Franklin, Alaska), in cubic feet per second

Discharge at index streamgage 15348000 (Fortymile River near 

Steele Creek, Alaska), offset 1 day earlier, in cubic feet per second

Discharge at index streamgage 15348000 (Fortymile River 

near Steele Creek, Alaska), in cubic feet per second

Discharge at 15331000 (Middle Fork Fortymile River near 

mouth near Chicken, Alaska), in cubic feet per second

Figure 3. Plot of concurrent measured discharge and the 

maintenance of variance extension type 3 (MOVE.3) regression 

line at U.S. Geological Survey (A) streamgages 15330000 (North 

Fork Fortymile River above Middle Fork near Franklin, Alaska) and 

15348000 (Fortymile River near Steele Creek, Alaska), offset 1 day 

earlier, and (B) streamgages 15331000 (Middle Fork Fortymile River 

near mouth near Chicken, Alaska) and 15348000 (Fortymile River 

near Steele Creek, Alaska).

Record Extension Technique

Record extension produces estimates of discharge for 

a study stream location from a longer record of discharge at 

one or more index stream locations. Methods for extending 

discharge records usually employ some form of linear 

regression to establish the relation between concurrent 

observed discharge at the study and index locations or 

streamgages. Although ordinary least squares regression can 

be used, the line of organic correlation method implemented 

by maintenance of variance extension (MOVE) techniques 

provides a better estimate of extended discharge records 

by seeking to maintain the variance of the observed study 

streamgage discharges in the estimated discharges (Hirsch, 

1982; Vogel and Stedinger, 1985; Helsel and Hirsch, 2002). 

The MOVE.3 regression incorporates the mean and standard 

deviation of the concurrent discharges and the mean and 

standard deviation of the nonconcurrent index streamgage 

discharges (Vogel and Stedinger, 1985; Granato, 2009) and 

results in an equation that uses the logarithms of daily mean 

discharge, which then can be rewritten in the form of the 

equation for a straight line:

log10Q = m(log10 Qindex) + b (1)

where

Q is the estimated daily mean discharge at the 

study streamgage, in cubic feet per second 

(ft3/sec),

b is the intercept of the regression line,

Qindex is the observed daily mean discharge at the 

index streamgage, in ft3/s, and

m is the slope of the regression line.

To simplify for use extending daily mean discharge in 

arithmetic units, eq. 1 can be transformed from logarithmic to 

arithmetic units to produce the following:

 Q = 10b Qindexm (2)

All MOVE.3 regressions were developed using the USGS 

Streamflow Record Extension Facilitator (SREF) software 

(Granato, 2009). The resulting equations for estimating daily 

mean discharge at the study streamgages using the Fortymile 

River streamgage are:

Q15330000 = 0.5649 Q15348000offset10.8751 (3)

and

Q15331000 = 0.3657 Q153480000.9644 (4)

where 

subscripts for Q are the USGS streamgage numbers, and

	 offset1 indicates the data are shifted 1 

day earlier.
Extended Daily Mean Discharge Records and Error Analysis 7

For this seasonal record extension, an important 

restriction on equations 3 and 4 is that the equations are only 

intended for use with index streamgage values (Q15348000) that 

occurred during the study season, May 20–September 30. 

Outside these date ranges, different processes might govern 

discharge and the relation between study and index streamgage 

discharges might vary. Particularly, very low discharges from 

winter conditions and very high discharges from snowmelt 

conditions before the study season are not represented by the 

observed discharges used to develop this equation.

Extended Daily Mean Discharge 

Records and Error Analysis

Daily mean discharge at the two study streamgages 

during the study season was estimated for the full period of 

record of the index streamgage, 1976–82 and 2006–19, using 

the MOVE.3 regressions in equations 3 and 4, respectively 

(appendix 1). The extended estimates (estimated data through 

2018) can be merged with the observed data for the concurrent 

period in 2019, available from NWIS, to form a composite 

dataset. The estimated discharges for the concurrent period 

were used to compare to the observed discharges for the concurrent period as a measure of accuracy.

Comparison of Observed and Estimated Records

The fit of the estimated discharges to the concurrent 

observed discharges varied across the range of discharges, as 

can be seen from the variability of the scatter in fig. 3 plots at 

various discharge ranges. On average, the estimated discharges for the concurrent period of record are similar to the 

observed discharges; the means of the observed and estimated 

discharges are within 7 percent or less of each other (table 3). 

Median estimated discharges are larger than median observed 

discharges for the Middle Fork Fortymile River streamgage 

record. Observed and estimated discharges were plotted as a 

hydrograph of daily means (fig. 4) to further examine their fit. 

The estimated discharges underestimated many of the highest discharges for the North Fork Fortymile River streamgage 

record. Figure 4 shows that the MOVE.3 regressions generally 

overestimated discharges early in the season and underestimated discharges later in the season. This variation in the fit 

of the estimated discharges could be related to basin-specific 

factors such as a difference in runoff-generating processes 

across the season between basins or uneven spatial distribution 

of rainfall, but investigation of these differences was beyond 

the scope of this study.

Table 3. Summary statistics of the concurrent observed and estimated daily mean discharge records at two study streamgages in the 

Fortymile River Basin, Alaska.

[AK, Alaska; ft3/s, cubic feet per second; USGS, U.S. Geological Survey]

Daily mean discharge

Mean Median Standard deviation

Study USGS 

streamgage

number

Study 

streamgage 

name

Observed, in 

ft3/s

Estimated, in 

ft3/s

Observed, in 

ft3/s

Estimated, in 

ft3/s

Observed, in 

ft3/s

Estimated, in 

ft3/s

15330000 North Fork 

Fortymile 

River above 

Middle Fork 

near Franklin, 

AK

722 673 599 607 507 400

15331000 Middle Fork 

Fortymile 

River near 

mouth near 

Chicken, AK

964 929 685 813 747 631
8 Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019

Accuracy and Limitations of Extended Records

Several measures are available to evaluate the fit of a 

MOVE.3 regression model and the accuracy of the predicted 

records. The root mean square error (RMSE) between the 

observed discharge used to develop the model and the 

concurrent predicted discharge is a common measure of 

accuracy. The RMSE is the mean of the absolute distance 

between the observed and estimated discharges and is lower 

for models that have a better fit. The RMSE values for the 

North Fork and Middle Fork Fortymile River streamgage 

models are shown in table 4. The modified Nash-Sutcliffe 

efficiency coefficient (NSE) provides a measure of the 

predictive ability of a model (Legates and McCabe, 1999). 

Computed from the observed and estimated discharges for 

the study streamgage, the modified NSE ranges from 1 for 

a perfect fit of modeled to observed data to minus infinity 

for a model having no predictive ability. A modified NSE of 

0 indicates that the mean of the observed data is as good a 

predictor as the model. The modified NSE is computed as

 (5)

where

n is the number of measurements,

Yi is the ith observed daily mean discharge,

Yp is the estimated daily mean discharge, and _

Y is the average of the observed daily mean 

discharges.

The modified NSE for the North Fork and Middle Fork 

Fortymile River streamgage MOVE.3 models are shown in 

table 4.

In addition to measures of accuracy, the user should 

consider the limitations of the data used to develop equations 

when using estimates to construct discharge statistics. Mean 

discharge during the concurrent period was lower than 

the long-term mean for the same season at the Fortymile 

River streamgage. The range of daily mean discharge for 

the concurrent period was also less than the range of daily 

mean discharge for the same season in the rest of the record. 

The highest daily mean discharge for the Fortymile River 

streamgage for the concurrent period was 16,900 ft3/s, 

whereas daily mean discharges for the study season for the full 

period of record reached 62,700 ft3/s. Estimated daily mean 

discharges corresponding to days when index streamgage 

discharges exceeded 16,900 ft3/s required extrapolation 

of the upper end of the relation between study and index 

streamgage discharges. Confidence in the upper end of the 

relation is typically lower because fewer large discharges 

occur naturally than mid-range discharges and because the 

timing and spatial extent of periods of large discharge is 

variable. The extrapolation of the MOVE.3 regression for 

discharges larger than an index streamgage value of 16,900 

ft3/s, corresponding to 2,830 ft3/s at the North Fork Fortymile 

River streamgage and 4,370 ft3/s at the Middle Fork Fortymile 

River streamgage, creates additional uncertainty for these 

large discharges, which represent 5 percent of the extended 

record. Careful interpretation of discharge statistics using 

the extrapolated discharges at the upper end of the relation 

is advised. Extrapolation was also required for discharges at 

the lower end of the relation but affected fewer records (the 

smallest 2 percent of the extended period of record). The lower 

end of the relation is typically subject to less uncertainty. 

However, discharge statistics using estimated daily mean 

discharges extrapolated from index daily mean discharges less 

than the smallest index streamgage daily mean discharge for 

the concurrent period (809 ft3/s), or discharges less than 198 

ft3/s at the North Fork Fortymile River streamgage and 233 

ft3/s at the Middle Fork Fortymile River streamgage, should be 

interpreted with caution.

modified NSE

Y Y

Y Y

i

n i p

i

n i

  







1

1

1





Table 4. Root mean square error and modified Nash-Sutcliffe efficiency coefficients for MOVE.3 regression models at two study 

streamgages in the Fortymile River Basin, Alaska.

Study USGS 

streamgage 

number

Study streamgage name

Index USGS 

streamgage 

identifier

Index streamgage 

name

Offset applied 

to index 

streamgage 

data

Root 

mean 

square 

error

Modified 

NashSutcliffe 

efficiency 

coefficient

15330000 North Fork Fortymile River 

above Middle Fork near 

Franklin, AK

15348000 Fortymile River near 

Steele Creek, AK

1 day earlier 330 0.38

15331000 Middle Fork Fortymile River 

near mouth near Chicken, 

AK

15348000 Fortymile River near 

Steele Creek, AK

0 286 0.63
Summary 9

tac20-5273_fig 04

May June July Aug. Sept.

Discharge, in cubic feet per second

100

1,000

10,000

2019

Discharge, in cubic feet per second

100

1,000

10,000

A. 15330000 (North Fork Fortymile River above Middle Fork near Franklin, AK)

B. 15331000 (Middle Fork Fortymile River near mouth near Chicken, AK)

EXPLANATION

Observed record

Estimated record

Figure 4. Plot of observed and estimated discharges for the concurrent period of 

record at (A) North Fork Fortymile River above Middle Fork near Franklin, Alaska, and (B) 

Middle Fork Fortymile River near mouth near Chicken, Alaska.

Summary

Daily mean discharge records collected for one season 

in 2019 for two study streamgage sites in the Fortymile River 

Basin were extended to provide an additional 20 years of 

estimated seasonal daily mean discharge record. The extended 

records were estimated using the MOVE.3 record extension 

technique and a longer period of record at a single index 

streamgage (15348000, Fortymile River near Steele Creek, 

Alaska) located downstream of the study streamgages. Index 

streamgage records were offset 1 day earlier for one study 

streamgage to account for differences in timing of discharge 

patterns. The Pearson correlation coefficient for concurrent 

discharges at the two study streamgages (15330000, North 

Fork Fortymile River above Middle Fork near Franklin, 

Alaska; and 15331000, Middle Fork Fortymile River near 

mouth near Chicken, Alaska) and the index streamgage (after 

application of an offset for use with the North Fork Fortymile 

River streamgage) was 0.809 and 0.926, respectively. The 

modified Nash-Sutcliffe coefficient of efficiency for the 

MOVE.3 regression models for estimating discharge was 0.38 

and 0.63, respectively.
10 Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019

References Cited

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1971–2000: National Park Service, Alaska Regional Office, 

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Gibson, W., 2009b, Mean precipitation for Alaska 1971–2000: 

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WR021i005p00715.
 Appendix 1 11

Appendix 1. Extended Seasonal Daily Mean Discharge Records for Two 

Streamgages in the Fortymile River Basin, Alaska

Table A1 is a comma-separated values (.csv) file that 

presents estimated daily mean discharge records for two 

study streamgages in the Fortymile River Basin for May 

20–September 30 for 1976–1982 and 2006–19. The study 

streamgages are U.S. Geological Survey (USGS) 15330000 

(North Fork Fortymile River above Middle Fork near 

Franklin, Alaska) and 15331000 (Middle Fork Fortymile 

River near mouth near Chicken, Alaska). The estimated values 

presented here were computed from maintenance of variation 

extension type 3 (MOVE.3) record extension regressions 

described in the body of this report and data from USGS 

streamgage 15348000 (Fortymile River near Steele Creek, 

Alaska). Differences in rounding can produce slight variations 

between values in table A1 and values produced by equations 

3 and 4 in the body of the text. The extended records can 

be combined with observed data for a composite record for 

analysis of discharge statistics.

Table A1. Extended seasonal daily mean discharge records for two streamgages in the Fortymile River Basin, Alaska.

[Table A1 is a comma separated value (CSV) file file available for download at https://doi.org/10.3133/sir20205003]

Publishing support provided by the U.S. Geological Survey

Science Publishing Network, Tacoma Publishing Service Center

For more information concerning the research in this report, contact the

Director, Alaska Science Center

U.S. Geological Survey

4210 University Drive

Anchorage, Alaska 99508

https://www.usgs.gov/centers/asc/
Curran— Extending Records for Streamgage Sites in the Fortymile River Basin, Alaska, through Water Year 2019—Scientific Investigations Report 2020-5003

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20205003