Estimation of Monthly Water Yields and Flows 

for 1951–2012 for the United States Portion of 

the Great Lakes Basin with AFINCH

Scientific Investigations Report 2014–5192

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

U.S. Department of the Interior

U.S. Geological Survey
Cover image. The United States portion of the Great Lakes Basin.
Estimation of Monthly Water Yields and Flows 

for 1951–2012 for the United States Portion of 

the Great Lakes Basin with AFINCH

By Carol L. Luukkonen, David J. Holtschlag, Howard W. Reeves, C.J. Hoard, and Lori M. Fuller 

Scientific Investigations Report 2014–5192

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: 2015

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Suggested citation:

Luukkonen, C.L., Holtschlag, D.J., Reeves, H.W., Hoard, C.J., and Fuller, L.M., 2015, Estimation of monthly water yields 

and flows for 1951–2012 for the United States portion of the Great Lakes Basin with AFINCH: U.S. Geological Survey 

Scientific Investigations Report 2014–5192, 83 p, http://dx.doi.org/10.3133/sir20145192. 

ISSN 2328-0328 (online)
iii

Contents

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

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

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

Description of the Great Lakes Basin.........................................................................................................2

Data Integration within AFINCH and NHDPlus.........................................................................................2

AFINCH Modeling Approach ..............................................................................................................2

Predictor Step ..............................................................................................................................2

Corrector Step..............................................................................................................................8

Model Limitations.........................................................................................................................9

NHDPlus Geospatial Data Frame .......................................................................................................9

Response Data ......................................................................................................................................9

Monthly Streamflow Data ..........................................................................................................9

Monthly Water-Use Data..........................................................................................................10

Explanatory Data.................................................................................................................................11

PRISM Monthly Climatic Data .................................................................................................11

National Land Cover Data ........................................................................................................11

NHDPlus National Catchment Characteristics Data ..........................................................11

User-Supplied Catchment Characteristics Data ..................................................................11

SSURGO Soil Data ............................................................................................................11

GAP Vegetation and Land-Use Pattern Data ...............................................................11

Growing Degree Day Data ..............................................................................................12

Output Data..........................................................................................................................................12

Methods of Flow and Water-Yield Estimation for Study Areas............................................................14

Study Area 1.........................................................................................................................................15

Study Area 2.........................................................................................................................................23

Study Area 3.........................................................................................................................................33

Study Area 4.........................................................................................................................................41

Study Area 5.........................................................................................................................................47

Study Area 6.........................................................................................................................................55

Study Area 7.........................................................................................................................................63

Summary........................................................................................................................................................75

References Cited..........................................................................................................................................75

U.S. Geological Survey Water-Data Reports for Michigan and the 

St. Lawrence River Basin.....................................................................................................77

Regional compilations (listed chronologically).....................................................................77

Michigan data only (listed chronologically)..........................................................................77

Appendix 1 ............................................................................................................................................................78
iv

Figures

1. Map showing the hydrologic subregions and cataloguing units in the 

U.S. Great Lakes Basin ................................................................................................................3

2. Map showing the distribution of estimated water yields for August 

averaged over 1951–2012 ..........................................................................................................12

3. Time-series plot of monthly flows at flowline 11959440, streamgaging 

station 04058000, Middle Branch Escanaba River near Ishpeming, Michigan ................13

4. Map showing the location of study area 1 (hydrologic subregions 0401 and 0402) 

in the U.S. Great Lakes Basin ...................................................................................................15

5. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 1 (hydrologic subregions 0401 and 0402) 

in the U.S. Great Lakes Basin ...................................................................................................21

6. Map showing the location of study area 2 (hydrologic subregion 0403 

and cataloguing units 04040002, 04040003, 04060106, 04060107, 04070001, 

and 04070002) in the U.S. Great Lakes Basin .........................................................................23

7. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 2 (hydrologic subregion 0403 and cataloguing 

units 04040002, 04040003, 04060106, 04060107, 04070001, and 04070002) 

in the U.S. Great Lakes Basin .........................................................................................................32

8. Map showing the location of study area 3 (hydrologic subregion 0405 

and cataloguing unit 04040001) in the U.S. Great Lakes Basin ...........................................33

9. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 3 (hydrologic subregion 0405 and cataloguing 

unit 04040001) in the U.S. Great Lakes Basin .........................................................................40

10. Map showing the location of study area 4 (cataloguing units 04060101, 

04060102, 04060103, 04060104, 04060105, 04070003, 04070004, 04070005, 

04070006, and 04070007) in the U.S. Great Lakes Basin .......................................................41

11. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 4 (cataloguing units 04060101, 04060102, 

04060103, 04060104, 04060105, 04070003, 04070004, 04070005, 04070006, 

and 04070007) in the U.S. Great Lakes Basin .........................................................................46

12. Map showing the location of study area 5 (hydrologic subregions 0408 

and 0409) in the U.S. Great Lakes Basin .................................................................................47

13. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 5 (hydrologic subregions 0408 and 0409) 

in the U.S. Great Lakes Basin ...................................................................................................54

14. Map showing the location of study area 6 (hydrologic subregions 0410 

and 0411) in the U.S. Great Lakes Basin .................................................................................55

15. Graph showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 6 (hydrologic subregions 0410 and 0411) 

in the U.S. Great Lakes Basin ...................................................................................................62
v

Figures (continued)

16. Map showing the location of study area 7 (hydrologic subregions 0412, 

0413, 0414, and 0415) in the U.S. Great Lakes Basin .............................................................63

17. Map showing the t-value-indexed colors corresponding to each 

explanatory variable in the monthly regression equation for estimating 

water yield for study area 7 (hydrologic subregions 0412, 0413, 0414, 

and 0415) in the U.S. Great Lakes Basin .................................................................................74

Tables

1. Summary of study area information ........................................................................................14

2. Streamgaging stations considered for analysis of study area 1 (hydrologic 

subregions 0401 and 0402) in the U.S. Great Lakes Basin, by water year.........................16

3. Selected explanatory variables for each study area............................................................20

4. Regression statistics and explanatory variables used in the AFINCH 

analysis of flows in study area 1 (hydrologic subregions 0401 and 0402), 

in the U.S. Great Lakes Basin, by month.................................................................................21

5. Streamgaging stations considered for analysis of study area 2 

(hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 

04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, 

by water year...............................................................................................................................24

6. Regression statistics and explanatory variables used in the AFINCH 

analysis for study area 2 (hydrologic subregion 0403 and cataloguing 

units 04040002, 04040003, 04060106, 04060107, 04070001, and 04070002) 

in the U.S. Great Lakes Basin, by month.................................................................................32

7. Streamgaging stations considered for analysis of study area 3 

(hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year....................................................................................34

8. Regression statistics and explanatory variables used in the AFINCH 

analysis for study area 3 (hydrologic subregion 0405 and cataloguing 

unit 04040001) in the U.S. Great Lakes Basin, by month.......................................................40

9. Streamgaging stations considered for analysis of study area 4 

(cataloguing units 04060101, 04060102, 04060103, 04060104, 04060105, 

04070003, 04070004, 04070005, 04070006, and 04070007) in the 

U.S. Great Lakes Basin, by water year....................................................................................42

10. Regression statistics and explanatory variables used in the AFINCH 

analysis for study area 4 (cataloguing units 04060101, 04060102, 04060103, 

04060104, 04060105, 04070003, 04070004, 04070005, 04070006, and 04070007) 

in the U.S. Great Lakes Basin, by month.................................................................................46

11. Streamgaging stations considered for analysis of study area 5 

(hydrologic subregions 0408 and 0409) in the U.S. Great Lakes Basin, 

by water year...............................................................................................................................48

12. Regression statistics and explanatory variables used in the AFINCH 

analysis for study area 5 (hydrologic subregions 0408 and 0409) 

in the U.S. Great Lakes Basin, by month.................................................................................54
vi

Tables (continued)

13. Streamgaging stations considered for analysis of study area 6 

(hydrologic subregions 0410 and 0411) in the U.S. Great Lakes Basin, 

by water year...............................................................................................................................56

14. Regression statistics and explanatory variables used in the AFINCH 

analysis for study area 6 (hydrologic subregions 0410 and 0411) in the 

U.S. Great Lakes Basin, by month............................................................................................62

15. Streamgaging stations considered for analysis of study area 7 

(hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year....................................................................................64

16. Regression statistics used in the AFINCH analysis for study area 7 

(hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by month............................................................................................74

Appendix Tables

1–1. Revisions to NHDPlus flowline value-added attribute (VAA) information ........................78

1–2. Description of classes in the 2006 National Land Cover Database. ..................................82

1–3. Description of soil groups in the Soil Survey Geography (SSURGO) database. ..............83

1–4. Description of variables from Aquatic Gap Analysis Program (GAP) 

used in the analysis....................................................................................................................83
vii

Conversion Factors and Datums

Multiply By To obtain

Length

mile (mi) 1.609 kilometer (km)

kilometer (km) 0.6214 mile (mi)

Area

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2) 

Volume

cubic mile (mi3

) 4.168 cubic kilometer (km3) 

Flow rate

cubic foot per second (ft3

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

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

°F=(1.8×°C)+32

Vertical coordinate information is referenced to the North Geodetic Vertical Datum of 1929 

(NGVD 29).

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.

A water year is the 12-month period October 1 through September 30. The water year is 

designated by the calendar year in which it ends and which includes 9 of the 12 months. Thus, 

the year ending September 30, 2002, is called the “2002 water year.”

Abbreviations

AFINCH Analysis of Flows In Networks of CHannels

GAP USGS National Gap Analysis Program

HUC hydrologic unit code

NED National Elevation Dataset

NHD National Hydrography Dataset

NLCD National Land Cover Data

NPDES National Pollutant Discharge Elimination System

OLS ordinary least square

POA period of analysis

PRISM Parameter-elevation Regressions on Independent Slopes Model

R2 coefficient of determination

RMSE root mean square error

SSURGO Soil Survey Geography

USGS U.S. Geological Survey

VAA value-added attributes

Estimation of Monthly Water Yields and Flows 

for 1951–2012 for the United States Portion of the 

Great Lakes Basin with AFINCH

By Carol L. Luukkonen, David J. Holtschlag, Howard W. Reeves, C.J. Hoard, and Lori M. Fuller 

provide a framework that can be used to help enhance existing data networks. In addition, this information can be used to 

assess the status of stream ecosystems, to identify and prioritize locations to focus stream restoration efforts, to plan and 

manage game and non-game species, to protect and enhance 

aquatic systems for recreational use, to provide tools for assessing disturbance of aquatic ecosystems, to plan adaptive management strategies, and to aid in implementation of the Great 

Lakes-St. Lawrence River Basin Water Resources Compact 

(Council of Great Lakes Governors, 2005). 

The Analysis of Flows In Networks of CHannels 

(AFINCH) application (Holtschlag, 2009) was applied to estimate monthly time series of yields and flows for water years 

1951–2012 within the U.S. Great Lakes Basin (Hydrologic 

Region 04) (Seaber and others, 1987). The resulting long-term 

flow time series can be used to describe monthly flow-duration 

characteristics and to investigate trends at 107,691 stream segments in the U.S. Great Lakes Basin. AFINCH is an interactive program used to facilitate the estimation of time series 

of monthly water yields from catchments and flows in stream 

reaches defined within the 1:100,000-scale NHDPlus geospatial data framework (McKay and others, 2012). NHDPlus is an 

integrated suite of application-ready geospatial-data products 

that includes features from the National Hydrography Dataset 

(NHD; U.S. Geological Survey, 2009a), the National Elevation Dataset (NED; U.S. Geological Survey, 2009b), and the 

National Watershed Boundary Dataset (U.S. Department of 

Agriculture-Natural Resources Conservation Service, 2009; 

U.S. Geological Survey, 2008), which describes the geometry 

and attributes of the hydrologic units. Monthly streamflow 

data at included streamgages, adjusted for upstream water 

use, along with monthly climatic data and land-cover or basin 

characteristics provide a basis for developing regression equations to estimate natural monthly water yields at individual 

Abstract

Monthly water yields from 105,829 catchments and corresponding flows in 107,691 stream segments were estimated 

for water years 1951–2012 in the Great Lakes Basin in the 

United States. Both sets of estimates were computed by using 

the Analysis of Flows In Networks of CHannels (AFINCH) 

application within the NHDPlus geospatial data framework. 

AFINCH provides an environment to develop constrained 

regression models to integrate monthly streamflow and wateruse data with monthly climatic data and fixed basin characteristics data available within NHDPlus or supplied by the user. 

For this study, the U.S. Great Lakes Basin was partitioned into 

seven study areas by grouping selected hydrologic subregions 

and adjoining cataloguing units. This report documents the 

regression models and data used to estimate monthly water 

yields and flows in each study area. Estimates of monthly water 

yields and flows are presented in a Web-based mapper application. Monthly flow time series for individual stream segments 

can be retrieved from the Web application, The Great Lakes 

Restoration Initiative (GLRI) Mapper for Monthly Streamflow 

and Yield of Catchments using Analysis of Flows in Networks 

of CHannels (AFINCH), http://cida.usgs.gov/glri/afinch/, and 

used to approximate monthly flow-duration characteristics and 

to identify possible trends.

Introduction

A regionally consistent estimate of streamflow provides 

unified information across the U.S. Great Lakes Basin for restoration, assessment, management, and conservation of stream 

ecosystems. These estimated flows provide information for 

natural resource professionals and the general public to assess 

stream ecosystems across State jurisdictional boundaries and 
2

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

catchments. Streamflows are estimated from the catchment 

yields and flow is conserved through the NHDPlus network. 

Chloropleth maps of monthly water yield and flow can be 

generated and analyzed. Estimated monthly flows can be 

displayed within AFINCH, examined for nonstationarity, and 

tested for monotonic trends. Monthly flows also can be used 

to estimate flow-duration characteristics at stream segments 

within AFINCH. 

Purpose and Scope

The purpose of this report is to document regression models and estimates of monthly water yields and flows developed 

for seven study areas spanning the U.S. Great Lakes Basin for 

the period 1951–2012. These models were developed within 

the AFINCH modeling environment by using the NHDPlus 

geospatial data framework to estimate monthly water yields 

and flows for 105,829 catchments and 107,691 flowlines in the 

region. The estimated flows are constrained to be consistent 

with measured flows at 823 U.S. Geological Survey (USGS) 

streamgages. These constraints also adjust regression estimates upstream from streamgages to generally improve flow 

estimates from regression estimates. Monthly water-use data 

were applied, where available, to mitigate effects of water use 

on the regionalization process. 

Description of the Great Lakes Basin

The Great Lakes Basin in the northeastern United States 

and southeastern Canada contains the five Laurentian Great 

Lakes of Superior, Michigan, Huron, Erie, and Ontario. These 

Great Lakes make up the largest surface freshwater system on 

Earth (U.S. Environmental Protection Agency, 2014), and contain approximately 5,500 cubic miles (mi3

) of water (Waples 

and others, 2008). The approximate land drainage area of the 

basin is 201,460 square miles (mi2), water area is 94,250 mi2, 

and the total area of the basin is 296,000 mi2 (Government of 

Canada and U.S. Environmental Protection Agency, 1995). 

Parts of the States of Michigan, New York, Ohio, Wisconsin, 

Indiana, Minnesota, Illinois, and Pennsylvania, and the provinces of Ontario and Quebec drain into the Great Lakes.

Hydrologic Region 04 subdivides the U.S. Great Lakes 

Basin into 15 hydrologic subregions based on surfacewater divides (watersheds) (U.S. Geological Survey, 2008) 

(fig. 1). The hierarchical hydrologic unit code (HUC) system 

describes increasingly refined levels of subdivision by 

appending a 2-digit code onto the end of the code identifying 

the previous level. In particular, the coding system divides 

surface-water drainage basins in the U.S. and the Caribbean 

into 21 hydrologic regions (2 digits), 221 subregions (4 digits), 

378 accounting units (6 digits), and 2,264 cataloguing units 

(8 digits). The subregions and cataloguing units in the 

U.S. Great Lakes Basin were formed into seven study areas 

for analysis with AFINCH. These study areas facilitated the 

analysis by (1) combining hydrologically similar areas, 

(2) utilizing a larger pool of streamgaging stations than would 

have been possible by analyzing subregions individually, and 

(3) improving consistency of estimates between study areas.

Data Integration within AFINCH and 

NHDPlus

The AFINCH modeling approach and method of estimating flows along with descriptions of potential explanatory 

variables are described in the following sections. 

AFINCH Modeling Approach

AFINCH implements a two-step predictor-corrector 

process. The predictor step is based on a user-specified 

multiple-linear-regression equation, which estimates monthly 

yields using selected monthly climatic and basin characteristics data and flows at streamgages. The corrector step adjusts 

the regression estimates to match measured flows at included 

streamgages. 

Predictor Step

The predictor step in an AFINCH analysis is based on the 

statistical relation between a response variable that is a function of monthly flows and one or more explanatory variables 

that may be formed from time-varying monthly climatic data 

or fixed basin characteristics data. In particular, a user-specified multiple-linear-regression model is used to predict the 

response variable for each NHDPlus catchment in the study 

area. As discussed later in more detail, catchment yield (the 

response variable in this study) is defined as the streamflow 

contribution from the catchment divided by the catchment 

area. The estimated square root of yield is transformed and 

multiplied by catchment area to produce a runoff or catchment flow. The catchment flows are accumulated downstream 

by using the stream network topology described in NHDPlus. 

The following paragraphs develop the notational conventions 

underlying the AFINCH model. 
Data Integration within AFINCH and NHDPlus

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0401

0402

0403

0404

0405

0406

0406

0407

0407

0408

0409

0410 0411

0412

0413

0414

0415

Figure 1. Hydrologic subregions and cataloguing units in the U.S. Great Lakes Basin. 

A time series of monthly flows for the period of analysis at each NHDPlus flowline in the 

study area is the primary output from an AFINCH analysis. Monthly measured flows mea

QGage( ,i j).

for water year index i and streamgage index j, are critical to developing these estimates. Streamflow data are typically reported as mean daily flows at the streamgage; monthly flows used in 

this study are the mean of the daily flows for each month. This set of monthly measured flows at 

included streamgages in water year i can be formed into a column vector with length ni , written mea

Qni ×1.

In some stream reaches, withdrawals, diversions, or augmentations associated with water 

use can augment or diminish flows measured at downstream streamgages. If monthly water-use 

data are available to document these uses, measured flows at streamgages can be adjusted to more 

accurately represent natural flow conditions, that is, without water use. For example, if a consumptive water use of 1 cubic foot per second (ft3

/s) is withdrawn from a reach upstream of one or 

more streamgages, the natural flow at the affected streamgages would be expected to have 

1 ft3/s more than the measured flow. Understanding natural flow conditions helps regionalize flow 

information with AFINCH. Measured flows that have been adjusted with available water use are 

designated as mea

QGage i j

 , . ( )

,
4

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Streamflow generally occurs in dendritic drainage patterns in which headwater streams 

converge to form tributaries that combine flow from upstream branches. This process 

progresses downstream as tributaries continue to merge until only a main stem remains. 

A streamgaging network follows this pattern, so some streamflow is commonly measured by 

multiple streamgages. To avoid this redundancy in streamflow information, AFINCH computes 

an incremental flow, ∆

mea

QGage( ,i j) , and a corresponding incremental drainage area, ∆

ba AGage i jsin

( ) ,

for each streamgage based on the stream network configuration. Consider, for example, a 

simple two-gage network in which the water measured at the upstream gage is combined with 

additional flow as it moves downstream and is re-measured at the downstream gage. In this 

network, the incremental flow and area for the upstream streamgage is the same as the measured flow and total area; at the downstream streamgage, however, the incremental flow is the 

measured flow minus the flow measured at the upstream gage. Similarly, the incremental area is 

the contributing drainage area at the downstream gage minus the contributing drainage area at 

the upstream gage. 

Over a significant range of flows and drainage areas, (incremental) streamflow is proportional to the (incremental) drainage area. For example, all other factors being equal in a local 

flow system, the mean streamflow at a stream site with twice the drainage area of another 

stream site is likely to have twice the mean flow. The dominant effect of drainage areas on 

flows can mask more subtle effects statistically associated with the impact that land use and 

land cover, monthly precipitation and temperature, and other factors might have on streamflow. To increase the sensitivity of the analysis to these more subtle basin and climate effects, 

AFINCH analysis is based on water yield, which is obtained by dividing incremental flows by 

corresponding incremental areas as ∆ ∆ ∆

mea

Gage i j

mea

Gage i j

ba

Gage i j Y Q , , A sin, / ( ) ( ) ( ) = or in vector notation 

∆ ∆ Y Q n n ∆ A ba

i i ni × ×

− = × 1 11

1  sin . This approach removes drainage area as a possible explanatory variable, which also mitigates some concerns about developing parameter estimates from analysis 

of (incremental) streamgage basins, made up of hundreds of individual NHDPlus catchments, 

for prediction at individual catchments. 

A multiple regression model provides a basis for prediction and for assessing the uncertainty of the prediction. This uncertainty is based on simplifying assumptions concerning 

the characteristics and distribution of model residuals ε formed by the differences between 

measured and predicted values of the response. In particular, model residuals are assumed to be 

independently and identically distributed with a normal (Gaussian) distribution having a mean 

of 0 and a variance of σε

2 (Draper and Smith, 1998). So that this assumption is more likely satisfied, a square-root transformation was applied to the incremental yield to reduce its skewness. 

Skewness is a measure of the departure of a distribution from a symmetric distribution like the 

normal distribution. The transformed yield data are denoted by ∆ ∆

mea

Gage i j

mea

Gage i j Y Y ,

.

( ) ( ) , = 0 5 and 

the residuals are formed as ε n

mea

n

est

n i i i × × 1 1 = − Y Y ×

0 5

1

0 5

∆ ∆

. . .

In the multiple regression model underlying AFINCH, the response variable of monthly 

water yields—expressed generically for any individual water year i with ni streamgages in the 

study area as ∇ mea

Yni

0 5. —is linearly related to a design matrix containing a column of 1’s, corresponding to an intercept term, augmented on the right with a set of explanatory variables. 

Explanatory variables are user specified, but generally include monthly climatic and basin characteristics. All columns have the same number of elements (lengths of ni

) and the rows must be 

independent as 

,
Data Integration within AFINCH and NHDPlus

(1) ∆

∆

mea

n n n k k n

mea

n

Y X

Y

i i i

i





× × × +

×

= 

  1 ⋅ + 0 5

1 1

1

0 5

1

.

.

1 β ε ,

where

is an n -column vector of the square-roots of measured incr i emental 

yields, adjusted for water use;

1n n k i i

 × × X  1 

 is a design matrix of explanatory variables in which the first 

n -vector of ones for the intercept i term,

 which is augmented on the right by an n k i ×

βk +1 k ×1 column vector of parameters relating the explanatory

ε ni ni-column vector of regression residuals, which are assumed 

 to be independent and identically distributed random variables

following a normal (Gaussian) distribution with mean and v 0 ariance .

2 σε

water

column is a

matrix of

explanatory variables indexed over water years by i;

is a 

variables to the response variable; and

is an

 

In cases where the k explanatory variables can be partitioned into a set of kv time-varying characteristics such as monthly precipitation, and a set of k f time-invariant (fixed) characteristics 

such as soil types, the design matrix for a selected month in the i

th year can be written as

X X X (2) n k k

i

n

i

n k i v f i ni kv × + ( ) + = i f × 

  1 ×  1

 

Ordinary least-square (OLS) estimates of the parameter vector βi for monthly water yields in 

the i

th water year can be computed (Draper and Smith, 1998) as 

(3)

 

ˆ

ˆ

ˆ

β

β

β

0

1 1

i

k

i

k

i

n k k

i

v n k k

f

i v f i v f

X X

























= ( )

′

⋅ × + ( ) + × + ( ) +

i

n k k

i mea X Yn i v f i

















⋅( )

′

⋅

−

× + ( ) + ×

1

1 1

0 5

∆  .

Annual estimates of parameters may be useful in cases where the relation between the explanatory and response variables is suspected of being time varying. For example, a trend in parameter estimates might occur if an explanatory variable, such as land use, is treated as fixed when 

it is actually time varying. More commonly, the design matrix for the user-specified period of 

analysis (POA) for N years can be developed by vertically stacking design matrixes for individual water years and corresponding water yield vectors ∆

mea

Yni

 ×1

0 5. as

(4)

 

X X

X

X

X

n k k

n k k

n k k

n k k

i

i

v f

v f

v f

N v f

= ∑ = + +

× + ( ) +

× + ( ) +

× + ( ) +

,1

1

1

1

2

1

1

2



N

n

i

n k

n n k

n

X X

X X

X

ni kv i f

n kv i f

N

































=

×

×

×

×

1

1

1

1

2 2

2



nN kv i f

N Xn k × ×




























6

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

The corresponding OLS estimate of the regression parameter vector for the period of analysis is 

(5)

ˆ

ˆ

ˆ

β

β

β

0 1

1

poa

k

poa

k

poa

mea

v n

f

i

i

X X X Y

























= ′ ⋅ 

  ⋅ ′ ⋅ −

∆ ×



∑

0 5.

In AFINCH, 12 equations are individually estimated for monthly yields (either annually or 

for the POA) providing the flexibility to include different explanatory variables, β, in different 

monthly equations. A stepwise-selection process is used to automate the selection process in 

which the user specifies an α − level (the probability of a type I error, which in this example, 

is incorrectly rejecting the null hypothesis that individual parameters are equal to zero) to 

control the apparent statistical significance of included explanatory variables. Stepwise selection is an iterative process in which p-values (the apparent probability that the magnitude of a 

parameter estimate, relative to its uncertainty, would occur by chance under the null hypothesis) 

are repeatedly computed and compared to the specified α − level. Explanatory variables with 

p-values smaller than the α − level are maintained in the equation. The user can override the 

stepwise-selection process by specifying which explanatory variables to include in the monthly 

regression equations regardless of their apparent statistical significance. Finally, the user can 

specify whether OLS or robust parameter estimates are to be used in the estimation of catchment water yields. Robust parameter estimates use a bisquare weight function with a tuning 

constant of 4.685 by default (The MathWorks, Inc., 2012). Robust estimates may be preferred 

to OLS estimates to reduce the sensitivity of parameter estimates to one or more irresolvable outliers in the water yield series; however, for the estimates presented in this report, OLS 

parameter estimates were used. 

Once the monthly regression equations are developed from streamflow information at 

gaged basins, the results are applied to estimate water yields for all gaged and ungaged NHDPlus 

catchments. For the case where estimation equations are developed by using POA parameter 

estimates, monthly estimates of water yield for individual water years are computed as 

(6) where

β

ˆ

k

poa

+1 is the vector of parameter estimates.

est

M M k k

poa y x  ×1 = ⋅ × + ( ) +

0 5

1 1

. ˆ

β ,

est

My ×1

0 5. is the estimated vector of natural water yields 

 (adjusted for water use), in the square-root

metric, for all M NHDPlus catchments-water

xM k × + ( ) 1

years in the period of analysis;

are catchment characteristics that correspond

to basin characteristics for all the water-years

in equation [4]; and
Data Integration within AFINCH and NHDPlus

Estimated runoff (flows) from individual catchments are computed from estimated yields 

and catchment areas as

(7)

.

 is the vector of natural flows (runoff) for all 

catchments-water years in the period of 

is the estimated natural catchment yield, and

est

M

est

M

catch

M q y a × × 1 1 = ( ) ×

0 5 2

1

. ,

analysis,

where

is a vector of NHDPlus catchment areas.

est

Mq ×1

est

My ( ) ×1

0 5 2 .

catch

a M ×1

For notational simplicity, let est

M

est

m

i q q   wy i poa × × 1 1 → ∀ ( )∈ . Then accumulate monthly 

flows from catchments (runoff) forming the incremental areas upstream of included 

streamgages in water year i as

(8)

.

 is the vector of accumulated AFINCH estimates of incremental 

flows at the ni

 active streamgages in water year i,

is the set of all study area catchments in the incremental area of 

where

is the natural monthly runoff from the set of catchments 

∆

∆

est

n

i est

catch

i

catch catch

Q q i

Gage i j StudyArea nBa

  ×

= ∩

=

( )

1

,

sin

,

Ani×

∑ 1

est

n

i

i ∆Q ×1 

catch

individual streamgages monitored in water year i, and

forming the incremental streamgage areas in the ith water year. 

q est

catch

i



and compare with measured flows. 
8

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Corrector Step

A corrector step is used to adjust AFINCH estimated monthly water yields upstream 

from an included gage so that resulting AFINCH constrained monthly flows match measured 

flows at every streamgage for each water year in the period of analysis as ∆ ∆

con

Gage

i mea

Gage

i Q Q j j

  ≡ .

The adjustment is applied to the catchment corresponding to the NHDPlus flowline where the 

streamgage is located and to estimated yields on all catchments upstream of the streamgage. 

The flow-based correction ratio is computed as

 (9)    qRatioGage Q Q i mea

Gage

est

Gage j j j = × ×

−

∆ ∆ 1 1

1

(10)

 is the constrained estimate of water yields in NHDPlus

catchments forming the incremental drainage area 

upstream of the jth streamgage in the ith water year,

where

is a constant for the jth streamgage and ith water year. 

usGagej is the set of catchments contributing to flowlines 

In ungaged areas and areas downstream from active 

con

usGage

i est

usGage

i

Gage

i y y qRatio j j j

  = ⋅  ,

gages, estimated water yields are unconstrained.

con

usGage y j

i

qRatioGage

i

j



upstream from Gagej, and

Constrained monthly water yields for each catchment and water year are used with 

corresponding catchment areas to compute constrained runoff con

catch

i con

catch

i

catch q y   =  a .

The constrained runoffs are accumulated downstream by using the NHDPlus flowline 

topology to compute constrained accumulated AFINCH flows con

flowline

i Q . Lastly, wateruse information is added to affected flowlines and combined with con

flowline

i Q so that 

con

Gage

i mea

Gage

i Q Q j i j j ≡ ∀ ∈Steamgage Network in water year .
Data Integration within AFINCH and NHDPlus

Model Limitations

The regression model structure underlying AFINCH 

has some inconsistencies with the data structure that may 

affect the reliability of reported statistics (p-values) used for 

assessing model suitability. In particular, model residuals 

are assumed to be independent in regression models, but the 

data structure provides repeated (annual) measures from a 

network of streamgages. Thus, residual series from individual 

streamgages may not be independent in time, and residual 

series from different streamgages may not be identically 

distributed. These limitations are likely to be exacerbated 

when there are few streamgages with relatively long periods 

of record. Lack of temporal independence and non-identically 

distributed residuals series could inflate the apparent significance (reducing p-values) of individual explanatory variables, 

thus leading to greater type I errors than what would be consistent with the specified α − level. To mitigate this potential 

problem, the number of explanatory variables potentially 

included in the regression model might be constrained, say to 

a number less than the square root of the number of included 

streamgages, or the α − level might be otherwise reduced. 

NHDPlus Geospatial Data Frame

NHDPlus describes the geometry and the attributes of the 

hydrologic units and links flowlines to catchments and to other 

flowlines. Notably, NHDPlus includes the flowline topology, 

which is the routing information providing the upstream and 

downstream connections for each flowline. AFINCH estimates of water yields are based on incremental flows and 

areas within streamgage networks. These incremental flows 

are summed down the network from the headwaters to the 

downstream-most segment in the watershed under analysis. 

There are 105,829 catchments making up Hydrologic Region 

04 (U.S. Great Lakes Basin), which have an average area of 

1.16 mi2. Each catchment, which is uniquely identified by 

a Gridcode, is associated with a flowline (stream segment), 

which is uniquely identified by a ComID, that drains the 

catchment. 

The 107,691 flowlines characterizing the drainage network in the U.S. Great Lakes Basin include streams and rivers, 

canals and ditches, pipelines, artificial paths, coastlines, and 

connectors. Flowlines in the U.S. Great Lakes Basin average 

about 1 mile (mi) in length; some flowlines have no associated catchments. The topology of flowlines defined within 

NHDPlus provides a mechanism to accumulate flows from 

catchments and route flows through a drainage network. Initial 

inspection of some of the network design matrixes and the 

drainage area plots produced by AFINCH indicated the need 

for revisions to the flowline routing. In addition, early estimated flows also indicated the need for changes to the specified diversions for some flowlines. These revisions to flowline 

routing and diversion information are outlined in appendix 1, 

table 1–1. 

Response Data

AFINCH uses multiple regression analysis to regionalize and spatially distribute water yields across catchments 

spanning (stream) gaged and ungaged basins in the study area. 

Monthly streamflow and water-use data are used together to 

describe the response variable. 

Removing effects of artificial augmentations and diversions from directly impacted streamflow records helps 

describe natural streamflow conditions and associated yields, 

which can be regionalized. From these natural streamflow 

conditions, regression analysis describes how monthly 

climatic and basin characteristics affect the distribution of 

natural water yields across catchments. Catchment yields 

with corresponding drainage areas are used to compute runoff 

(flow), which can be accumulated downstream by using the 

NHDPlus streamflow topology. In gaged basins, the regression yield estimates are adjusted (constrained) so that resulting 

flows, with water-use data re-applied, match measured 

monthly flows. In ungaged basins, the natural water yields are 

used (without constraints) to estimate flows, with available 

water-use data re-applied to provide the final estimates of flow. 

Monthly Streamflow Data

The NHDPlus GageLoc is a shapefile that locates USGS 

streamgages along flowlines. A USGS streamgage is uniquely 

identified by its station number; other information included in 

the analysis is the drainage area at the gage. In the U.S. Great 

Lakes Basin (Hydrologic Region 04), 1,339 streamgages are 

identified; however, stations that (1) represented lake sites, 

(2) had no specified drainage area, and (or) (3) did not have 

complete data for at least 1 water year within the period 

1951–2012 were excluded from the analysis. Therefore, data 

from 823 streamgages were compiled for the AFINCH analysis. Time series of monthly streamflow values were computed 

from data obtained through the USGS cooperative streamgaging program (Wahl and others, 1995). 
10

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Occasionally, within NHDPlus, one or more streamgages 

may be located at different points along a single flowline. The 

streamgage that best represents flow conditions, for example 

the gage with the longer period of record, was selected for the 

analysis. In each subregion, flow at sites that were regulated or 

influenced by water withdrawals and diversions, as indicated 

by station descriptions or analysis of the water yield graphs, 

was not included in the analysis if water-use or routing data 

were not readily available to adjust the flow to more natural conditions. NHDPlus routing tables were used to route 

flow upstream to headwaters or downstream to discharge 

points. For each streamgaging station, all upstream flowlines 

(and associated catchments) were identified by using the 

NHDPlusV2 Flow Table Navigator Toolbar in ArcMap 

(Horizon Systems Corporation, 2014).

Monthly Water-Use Data

In AFINCH, water use (including withdrawals, augmentations, and diversions) can be associated with flowlines and 

accounted for along with catchment flows. Monthly flows can 

be adjusted for specified water uses by using a companion 

(currently (2014) unpublished) program to AFINCH, which 

aids with water-use accounting and tracks withdrawals or 

returns from their point of origin to the downstream-most 

segment in the analysis. The Water Use Data Tool is available 

upon request from the USGS Michigan Water Science Center. 

Water withdrawals are indicated by negative water-use values, 

and flow augmentations are indicated by positive water-use 

values. Monthly water-use data for each water year within 

the period of analysis were specified for those flowlines with 

readily available data; however, determination of monthly 

water use for the period of analysis at each possible location 

was beyond the scope of this study. In addition, much of these 

data are unavailable, incomplete, or are not in a format that is 

readily amenable for inclusion in this analysis. Collection of 

additional data would likely improve the estimates and permit 

inclusion of additional streamgage data in the analysis.

Water withdrawals, diversions, and augmentations were 

determined from available records for selected flowlines 

in hydrologic subregions 0402, 0403, and 0409 using data 

from the National Pollutant Discharge Elimination System 

(NPDES) permit program, USGS Annual Data Reports, and 

(or) other USGS studies. The NPDES permit program requires 

industrial, municipal, and other facilities to report point-source 

discharges to surface-water bodies. Data were retrieved using 

the Permit Compliance System (U.S. Environmental Protection Agency, 2001). Monthly discharges that could be linked 

to an adjacent flowline were included in the AFINCH analysis 

each year the discharge occurred for subregions 0403 and 

0409. Other withdrawal and diversion data were available 

from USGS Annual Data Reports (U.S. Geological Survey 

Water-Data Reports for Michigan and the St. Lawrence River 

Basin, 1958–2012). For example, reservoir stage data are 

collected that can be related to a flow or change in storage in 

the reservoir or to a withdrawal and later release to a different flowline. Data from these sources were included in the 

AFINCH analysis for subregions 0402 and 0403. In addition, 

local data used in the Kalamazoo area study (Luukkonen and 

others, 2004), describing water diversions to Portage Creek for 

selected years during 1966–2002, were used to estimate wateruse data for hydrologic subregion 0405 for this time period. 

In hydrologic subregion 0402, at streamgaging station 

04034000 Bond Falls Reservoir near Paulding, Michigan, 

water is diverted to South Branch Ontonagon River through 

Bond Falls Canal (streamgaging station 04033500), and water 

is used for power production at Victoria Dam near Rockland. 

Gage height data provided by Upper Peninsula Power Company are converted to acre-feet by USGS (Neal Craig, 

U.S. Geological Survey, oral commun., 2011). Water diverted 

from Schweitzer Reservoir to this subregion as described 

below also was included in the analysis. Data for 1950–2010 

were used in the AFINCH analysis for subregion 0402.

In hydrologic subregion 0403, at streamgaging station 

04057811 Greenwood Reservoir near Greenwood, Mich., 

water can flow over a concrete spillway into the Middle 

Branch Escanaba River below streamgaging station 04057814 

Greenwood Release near Greenwood, Mich., with some 

downstream diversions by local industries above streamgaging 

station 04058000. An outlet structure also permits flow from 

the reservoir into the afterbay (conservation pool) where water 

can be diverted to Green Creek gaged at Greenwood Diversion 

(streamgaging station 04057813) or released to the Middle 

Branch Escanaba River below streamgaging station 04057814. 

Beginning in October 1979, some water also was released 

after use to the East Branch Escanaba River via Goose Lake 

Outlet. Since January 1973, Greenwood Reservoir diverts 

some impounded water to Schweitzer reservoir (streamgaging 

station 04058190 Schweitzer Reservoir near Palmer, Mich.) 

for use in iron ore processing. Some flow from this reservoir 

is diverted to the city of Ishpeming, Mich., for municipal 

supply and discharged to the Carp River Basin (in hydrologic 

subregion 0402). After processing, water is returned to Green 

Creek or, beginning in 1980, to Goose Lake Outlet. Data for 

1963–2009 were used in the AFINCH analysis for hydrologic 

subregion 0403.
Data Integration within AFINCH and NHDPlus

Explanatory Data

Multiple regression analyses relate explanatory variables 

consisting of time varying (monthly) climatic characteristics, 

and time invariant (fixed) catchment characteristics to monthly 

varying water yields. In this study, Parameter-elevation 

Regressions on Independent Slopes Model (PRISM) monthly 

precipitation and temperature data were used, and catchment 

characteristics in the National Land Cover Data (NLCD) set 

were supplemented or replaced with user-specified catchment 

characteristics. The source and characteristics of explanatory 

variables used in this analysis are described in the following 

sections.

PRISM Monthly Climatic Data

For this report, average monthly air temperature and total 

precipitation data were computed for each year during the 

period 1950–2012 for all catchments in the U.S. portion of 

the Great Lakes Hydrologic Region (04) (fig. 1). The climatic 

data are based on 2.5 arc-minute (approximately 4 kilometers) 

grids of PRISM data by Daly and Taylor (1998a, b). Monthly 

minimum and maximum air temperature and precipitation 

datasets for 1895–2012 from the PRISM Climate Group 

(2013) were overlain with polygons representing catchment 

boundaries to estimate spatially averaged precipitation and 

temperature values. The average of the minimum and maximum temperature values was used to estimate the average 

monthly temperature. 

National Land Cover Data

Land-cover information for the conterminous United 

States for 2006 is available through the NLCD from the MultiResolution Land Characteristics Consortium (Fry and others, 

2011). The 16-class land-cover classification scheme includes 

more broadly defined land-cover classes including water, 

developed, barren, forest, shrub land, herbaceous, planted or 

cultivated, and wetlands (appendix 1, table 1–2). Percentages 

of these categories were determined for each catchment in 

Hydrologic Region 04. 

NHDPlus National Catchment Characteristics 

Data 

NHDPlus includes a stream network based on the 

medium resolution (1:100,000 scale) NHD, with connectivity 

within the stream network and to associated catchments. 

Stream order is a method of assigning a numeric order to links 

within a stream network and in NHDPlus is a modified version 

of stream order as defined by Strahler (1957). The Strahler 

stream order algorithm does not account for flow splits in the 

network. The NHDPlus algorithm for stream order does take 

flow splits into consideration. These value-added attributes 

(VAA) are computed from upstream to downstream (McKay 

and others, 2012).

The NHDPlus suite of data includes information from the 

NED (Gesch and others, 2009). For each NHDPlus catchment, 

average catchment elevations were determined using the zonal 

statistics ArcMap toolbox command (ESRI, 2012). In a similar 

way, average and minimum catchment slope were determined 

for each catchment using the ArcMap toolbox commands for 

slope and zonal statistics (ESRI, 2012). 

User-Supplied Catchment Characteristics Data

The user may provide one or more sets of shapefiles containing catchment attributes that can be used as explanatory 

variables in the subsequent regression analysis. User-specified 

variables for this analysis included soil information from the 

Soil Survey Geography (SSURGO) database (U.S. Department of Agriculture-Natural Resources Conservation Service, 

2011), surficial and bedrock geology from the USGS National 

Gap Analysis Program (GAP), and growing degree day data 

(computed using PRISM air temperature data).

SSURGO Soil Data

The SSURGO database contains information about 

soil components and properties as collected by the National 

Cooperative Soil Survey and is available for most areas in the 

United States. The hydrologic group is based on estimates of 

runoff potential and are assigned according to the rate of water 

infiltration when the soils are not protected by vegetation, are 

thoroughly wet, and receive precipitation from long-duration 

storms (appendix 1, table 1–3). If a soil is assigned to a dual 

hydrologic group (A/D, B/D, or C/D), the first letter is for 

drained areas and the second is for undrained areas. Only the 

soils that in their natural condition are in group D are assigned 

to dual classes.

GAP Vegetation and Land-Use Pattern Data

The USGS National GAP Land Cover Data Set includes 

detailed vegetation and land-use patterns for the continental 

United States to aid in State or regional assessments of natural 

resources and to provide for a regionally consistent database 

with uniformity across State boundaries (U.S. Geological 

Survey, 2011). GAP is a nationwide effort under the direction 
12

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

of the USGS and provides information on the distribution of 

native vegetation types, modified and introduced vegetation, 

developed areas, and agricultural areas of the United States. 

Surficial and bedrock geology variables used in the AFINCH 

analysis are shown in appendix 1, table 1–4. 

Growing Degree Day Data

Growing degree days provide a measure of heat accumulation because plant and animal development is related to the 

accumulation of heat or temperature units above a threshold 

or base temperature below which little growth occurs. The 

average annual growing degree days for the continental United 

States were calculated for 1971–2000 from downloaded 

PRISM air temperature datasets (Mike Slattery, U.S. Geological Survey, written commun., 2013). The base temperature 

(10 degrees Celsius (°C)) was subtracted from the average 

of the maximum and minimum monthly air temperatures. 

Only values equal to or greater than 0 °C were used and the 

resulting grid was then multiplied by the number of days in 

the month; the total from the previous month was added in a 

cumulative method to arrive at an approximation of the 

average annual growing degree days.

Output Data

The AFINCH program writes comma-delimited ASCII 

files with constrained and unconstrained monthly yields and 

flows for all the stream segments in the part of the NHDPlus 

area being analyzed and for each month and water year of the 

time period of the analysis. These flows and yields are indexed 

by the ComID of the stream segment or the Gridcode of the 

catchment. Headers in these files help document the analyses 

by describing explanatory variables, estimated parameters, 

and other user specifications. A representative chloropleth map 

showing the distribution of water yields for August averaged 

over 1951–2012 is shown in figure 2. An example time-series 

plot of monthly flows for a streamgaging station in hydrologic 

subregion 0403 showing the square root of measured flow 

with the square root of estimated incremental flow is shown 

in figure 3. Estimated flows and yields have been incorporated 

into a mapper application by the USGS Center for Integrated 

Data Analytics, http://cida.usgs.gov/glri/afinch/, for ease of 

use, display, and retrieval. These long-term flow series can 

be used to investigate trends or to characterize monthly flow 

durations.

Figure 2. Distribution of estimated water yields for August averaged over 1951–2012.

0.00–0.05

0.06–0.10

0.11–0.25

0.26–0.50

0.51–0.75

0.76–1.25

1.26–3088.7

AUGMN

EXPLANATION
Figure 3. Time-series plot of monthly flows at flowline 11959440, streamgaging station 04058000, Middle Branch Escanaba River near Ishpeming, Mic
14

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Methods of Flow and Water-Yield 

Estimation for Study Areas

Flows and water yields for water years 1951–2012 were 

estimated for 107,691 flowlines and 105,829 catchments in 

Hydrologic Region 04 representing the portion of the Great 

Lakes Basin in the U.S. (fig. 1). The 15 hydrologic subregions 

were combined to form 7 study areas consisting of multiple subregions and (or) cataloguing units for analysis with 

AFINCH (table 1). Details on the analysis and estimation of 

flows and water yields are presented for each study area. Each 

section includes (1) location map, (2) table of the streamgaging stations in the study area indicating each year each 

streamgage was active during the analysis period and whether 

or not the streamgage data were included in the analysis, 

(3) the regression coefficients and fit statistics for each variable, and (4) graph showing the t-values for each explanatory 

variable by month.

The regression coefficients indicate the size and direction 

(positive or negative) of the effect that each variable has on the 

yield estimate. However, some of the differences in coefficient 

magnitudes are owing to the fact that the potential explanatory variables are in different units, for example, variables 

with larger values would likely have smaller coefficients. To 

aid in the interpretation of the effect of each variable, graphs 

of t-values for all variables in the multiple-linear-regression 

equation are shown for each study area. The magnitudes of the 

t-values are test statistics that are used to interpret the likelihood that individual parameters in the regression equation 

are equal to zero. The sign of the t-values indicate whether 

the corresponding parameter is positive or negative. The cells 

in the image are white if the magnitude of the corresponding 

test statistic did not indicate significance at the level prescribed by the user. Cells are graded with increasing tones 

of red for increasingly significant parameters with negative 

signs. Similarly, cells are graded with increasing tones of blue 

for increasingly significant parameters with positive signs. 

The color scale at the bottom indicates the magnitude of the 

t-statistics. This visual representation permits interpretation of 

the information used to estimate water yields by each variable 

and for each month. For example, parameters (represented in 

each horizontal band) with most months tinted in shades of 

blue and (or) red likely provide more information in estimating the water-yield response than would a variable where most 

months are white indicating that the test statistics were not 

significant. Likewise, months (represented in each vertical 

band) with most cells tinted blue and (or) red would be estimated using multiple parameters, whereas months where most 

cells are white would not be estimated using much parameter 

information. The regression-fit statistics include the rootmean-square error (RMSE), F statistic, and the coefficient of 

determination (R2

)for the fit to the square-root of water yield. 

As noted previously, drainage area is so strongly correlated 

to streamflow that this relation is built into the analysis by 

writing the regression equation in terms of yield (streamflow 

divided by drainage area). Examination of the tables reveals 

that the reported R2 values for the fit to the square root of yield 

can be fairly low (0.2–0.7); however, the corresponding R2 for 

the fit of estimated to measured streamflows can be quite high 

(0.8–0.9) because of the strong correlation between area and 

streamflow. 

Selection of explanatory variables was guided by knowledge of each study area, identification of variables likely 

to affect water yields, and inspection of the images showing monthly parameter t-values. Furthermore, an additional 

consideration was to improve the estimation of yields and 

flows during April (higher flow month) and August (lower 

flow month) in order for the estimates to be more useful for 

Table 1. Summary of study area information.

Study 

area

Hydrologic subregions (4-digits) and (or) 

cataloguing units (8-digits)

Drainage area 

(square miles)

Number of 

streamgages

Number of 

flowlines

Number of 

catchments

1 0401 and 0402 16,632 76 15,442 15,221

2 0403, 04040002, 04040003, 04060106, 04060107, 

04070001, and 04070002

23,133 177 16,529 16,153

3 0405 and 04040001 13,620 105 11,523 11,300

4 04060101, 04060102, 04060103, 04060104, 

04060105, 04070003, 04070004, 04070005, 

04070006, and 04070007 

14,844 61 7,946 7,808

5 0408 and 0409 12,881 116 13,303 13,151

6 0410 and 0411 14,942 120 16,935 16,713

7 0412, 0413, 0414, and 0415 21,655 168 26,013 25,483
ecological stream-classification work. The variables selected 

for each study area represent those with the most significance 

of the combinations that were considered during the regression 

analysis; however, consideration of all possible variables and 

combinations was beyond the scope of this report. It is possible that there are areas where local conditions differ greatly 

from the variable characteristics that were selected for the 

study area and that in these areas flow and yield estimates are 

not as representative of actual conditions than they could be 

with a different variable set. It also is possible that a regionally 

important variable was not included in the analysis. Equally 

likely is the potential that major water uses (withdrawals, augmentations, or diversions) were not accounted for during the 

analysis. However, regionally these estimates present a reasonable, consistent, and defensible set of flow and yield estimates 

for the U.S. Great Lakes Basin.

Study Area 1

Study area 1 is formed by hydrologic subregions 0401 

and 0402 in the western part of the U.S. Great Lakes Basin 

and encompasses parts of Minnesota, Wisconsin, and the 

Upper Peninsula of Michigan (fig. 4). The number of stations 

included in the analysis ranged from 17 (1986, 1998, 1999, 

2001, 2007, 2008, and 2009) to 30 (1954 and 1955) (table 2). 

Nine explanatory variables were selected during the regression analysis with the number of variables specified for 

each monthly equation ranging from 6 (June) to 8 (October, 

November, December, January, April, May, and August). 

Selected explanatory variables are summarized in table 3. 

Variables and regression statistics based on the stepwise 

regression for each month are indicated in table 4 and 

figure 5. 

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0401

0402

Methods of Flow and Water-Yield Estimation for Study Areas

Figure 4. Location of study area 1 (hydrologic subregions 0401 and 0402) in the U.S. Great Lakes Basin.
16

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 2 Streamgaging stations considered for analysis of study area 1 (hydrologic subregions 0401 and 0402) in the U.S. Great Lakes Basin, by 

water year.—Continued

[●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04010500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● 

04010510 

04010530 

04012500 ● ● ● ● ● ● ● ● ● 

04014500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04015330 ● ● ○ ● ● ● ● ● 

04015410 

04015455 ● ● ● 

04015475 ● ● ● ● 

04015500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04016000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04016500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04017000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04018000 ● ● ● ● ● ● ● ● ● 

04018750 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04018900 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04019000 ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04019300 ● ● ● ● ● ● ○ ● ● ● ● ● ● ○ ● 

04019500 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04020000 ● ● ● ● ● ● ● ● ● 

04021520 

04021530 

04024000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04024090 ○ ○ 

04024093 ○ ○ 

04024098 ● ● ● ● ● ● 

04024314 ● ● 

04024315 ○ ○ 

04024318 ○ ○ 

04024430 ● ● ● ● ● ● ● ● 

04025500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04026190 ● 

040263205 

04026347 ● ● ● 

04026348 ○ ○ 

04026349 ● ● 

040263491 
Table 2. Streamgaging stations considered for analysis of study area 1 (hydrologic subregions 0401 and 0402) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

1983198419851986

Station 

number

19871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04010500

04010510

04010530

04012500

04014500

04015330

04015410

04015455

04015475

04015500

04016000

04016500

04017000

04018000

04018750

04018900

04019000

04019300

04019500

04020000

04021520

04021530

04024000

04024090

04024093

04024098

04024314

04024315

04024318

04024430

04025500

04026190

040263205

04026347

04026348

04026349

040263491

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●
Table 2 Streamgaging stations considered for analysis of study area 1 (hydrologic subregions 0401 and 0402) in the U.S. Great Lakes Basin, by 

water year.—Continued

[●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04026450 ● ○ ● ● ● 

04026500 ○ ○ ● ● ● 

04026870 ○ ○ ○ ○ ○ 

04027000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● 

04027500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04028000 ● ● ● ● 

04029990 

04030000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04031000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04031500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04032000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04032500 ● ● ● ● ● 

04033000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04033500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04034500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04035000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04035500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04036000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04037500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04039500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04040000 ● ● ● ● ● ● ● ● ● ● ○ ● ○ ○ ● ● ○ ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ● 

04040500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04041500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04042500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04043000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● 

04043050 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04043140 

04043150 

04043238 

04043244 

04043275 

04043800 

04044400 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04044563 ● ● 

04044573 ● ● 

04044583 ○ ○ ○ ○ ○ ○ ○ 

04044595 ● ● 

04044724 

04045500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 2. Streamgaging stations considered for analysis of study area 1 (hydrologic subregions 0401 and 0402) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

198319841985

Station 

1986

number

19871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04026450

04026500

04026870

04027000

04027500

04028000

04029990

04030000

04031000

04031500

04032000

04032500

04033000

04033500

04034500

04035000

04035500

04036000

04037500

04039500

04040000

04040500

04041500

04042500

04043000

04043050

04043140

04043150

04043238

04043244

04043275

04043800

04044400

04044563

04044573

04044583

04044595

04044724

04045500

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20

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 3. Selected explanatory variables for each study area.

[PRISM, Parameter-elevation Regressions on Independent Slopes Model; NLCD, National Land Cover Data; SSURGO, Soil Survey Geography; GAP, USGS 

National Gap Analysis Program; GDD, growing degree days]

Explanatory variables Study 

area 1

Study 

area 2

Study 

area 3

Study 

area 4

Study 

area 5

Study 

area 6

Study 

area 7

PRISM

Current precip, in hundredths of millimeters X X X X X X X

Preced precip, in hundredths of millimeters X X X X X X X

Current temp, in degrees Celsius * 100 X X X X X X X

NLCD

Open water, in percent X X

Developed, in percent X

Deciduous and evergreen forest, in percent X

Forest, in percent X X X X X

Grass herbaceous, in percent X

Pasture hay, in percent X X

Row crops, in percent X X X

Pasture hay and row crops, in percent X X X

Wetland woody, in percent X

Wetland herbaceous, in percent X X

NHDPlus catchment characteristics

Stream order, dimensionless X X X X X

Mean elevation, in centimeters X X X

Mean slope, in centimeters/meter X X X X

SSURGO

Hydric group A and AD, in percent X

Hydric group B and BD, in percent X

Hydric group C and CD, in percent X

Hydric groups C, CD, and D, in percent X X

GAP

Coarse outwash, in percent X X

Fine end and ground moraines, in percent X

Medium end and ground moraines, in percent X

Coarse end and ground moraines, in percent X X

Coarse outwash and ice contact, in percent X X

Coarse stratified sediment, in percent X

Till, in percent X

GDD

Average GDD, in days X X X
Methods of Flow and Water-Yield Estimation for Study Areas

Table 4. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of Channels) analysis of 

flows in study area 1 (hydrologic subregions 0401 and 0402), in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; RMSE, root mean square error; R2, coefficient of determination. See appendix tables for variable descriptions]

Month

Regression coefficients Regression fit statistics

Intercept Current 

precipitation

Preceding 

precipitation

Current 

temperature

Forest

Coarse 

end and 

ground 

moraines

Mean 

elevation

Hydric 

groups C, 

CD, and D

Stream 

order RMSE F-statistic R2

October 0.797 0.116 0.080 – – – – -0.326 -0.203 0.236 391.3 0.537

November 1.133 0.120 0.068 -0.011 – 0.073 -6.0E-06 -0.379 -0.180 0.221 144.4 0.428

December 1.314 0.060 0.062 0.015 0.113 0.145 -7.0E-06 -0.496 -0.158 0.184 144.4 0.462

January 1.279 0.027 0.054 0.008 0.225 0.193 -9.0E-06 -0.547 -0.132 0.192 124.3 0.425

February 1.261 – 0.049 0.015 0.307 0.196 -9.0E-06 -0.498 -0.111 0.193 125.7 0.395

March 0.926 0.091 0.047 0.068 0.681 0.074 -7.0E-06 – – 0.254 248.5 0.525

April 0.395 0.101 0.089 -0.036 0.887 −0.285 – 0.709 0.278 0.465 62.1 0.24

May 1.064 0.146 0.066 -0.048 – −0.262 – -0.121 0.169 0.343 137.1 0.37

June 0.818 0.133 0.071 -0.016 – −0.134 -4.0E-06 -0.241 – 0.246 184 0.45

July 1.296 0.123 0.061 -0.037 0.150 – -1.0E-05 -0.385 – 0.225 263.7 0.540

August 0.044 0.086 0.060 0.028 0.290 – -9.0E-06 -0.470 – 0.217 213 0.486

September 0.781 0.100 0.064 – 0.156 – -6.0E-06 -0.458 -0.158 0.222 229.5 0.505
CurrentPrecip

PrecidPrecip

CurrentTemper

Forest

C3_endm_cD3_grndm_c

meanElev

HydgrpCHydgrpCDHydgrpD

StreamOrde

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

22Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Figure 5. Image showing the t-value-indexed colors corresponding to each explanatory variable in 

the monthly regression equation for estimating water yield for study area 1 (hydrologic subregions 

0401 and 0402) in the U.S. Great Lakes Basin.
Study Area 2

Study area 2 is formed by hydrologic subregion 0403 and 

cataloguing units 04040002, 04040003, 04060106, 04060107, 

04070001, and 04070002 on the western and northern side of 

Lake Michigan and encompasses parts of Wisconsin, northern Illinois, and the Upper Peninsula of Michigan (fig. 6). 

The number of stations included in the analysis ranged from 

21 (1951 and 1953) to 47 (2005) (table 5). Ten explanatory 

variables were selected during the regression analysis with 

the number of variables specified for each monthly equation 

ranging from 6 (March and June) to 10 (February) (table 3). 

Variables and regression statistics based on the stepwise 

regression for each month are indicated in table 6 and figure 7. 

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0403

0404

0406 0407

Methods of Flow and Water-Yield Estimation for Study Areas

Figure 6. Location of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 04060106, 

04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin.
24

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 

04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year 

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04046000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04049500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04052500 

04052600 

04054500 ● ● ● ● 

04055000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04056000 ● ● ● ● ● ● 

04056500 ○ ● ○ ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04057000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04057004 

04057510 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04057800 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04057813 ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04057814 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04057820 ● ● ● ● ● ● ● ● ● ● 

04057900 ● ● ● ● ● ● ● 

04058000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04058100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04058130 ● ● ● ● ● ● 

04058200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04058300 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04058400 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04058500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04059000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04059400 ● ● ● ● ● ● 

04059500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04060500 ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ● ● 

04060993 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04061000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04061500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04062000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04062011 

04062100 ● ● ● ● ● ● ● 

04062200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04062230 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04062270 ○ ○ ○ ○ ○ 

04062300 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04062400 ● ● ● ○ ● ○ ● ● ● ● ● ● ● ● ● ● 

04062500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04063000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04063500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04063640 ● 

04063700 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04064500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04065106 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 

04040003, 04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984

number

1985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04046000

04049500

04052500

04052600

04054500

04055000

04056000

04056500

04057000

04057004

04057510

04057800

04057813

04057814

04057820

04057900

04058000

04058100

04058130

04058200

04058300

04058400

04058500

04059000

04059400

04059500

04060500

04060993

04061000

04061500

04062000

04062011

04062100

04062200

04062230

04062270

04062300

04062400

04062500

04063000

04063500

04063640

04063700

04064500

04065106

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26

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 

04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year 

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04065300 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04065393 ● ● ● ● ● ● ● ● ● 

04065397 ○ ○ ○ ○ ○ 

04065500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04065600 ● ● ● ● ● ● ● ● ● ● 

04065722 

04066000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04066003 

04066030 

04066500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04066800 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04067000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04067500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04067651 

04067958 

04069416 

04069500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04069530 

04071000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04071765 

04071775 

04071795 

04071858 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04072150 

04072410 

04072750 ● ● ● ● ● 

04072845 

04073050 ● ● ● ● ● ● ● 

04073365 

04073405 ● ● 

04073462 

04073468 

04073473 

04073500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04073970 

04074538 ● ● ● ● ● 

04074548 ● ● 

04074950 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04075200 ● ● ● ● ● ● 

04075365 

04075500 ● ● ● ● ● ● ● ● ● ● ● ● 

04077000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04077400 

04077630 

04078500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 

04040003, 04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984

number

1985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04065300

04065393

04065397

04065500

04065600

04065722

04066000

04066003

04066030

04066500

04066800

04067000

04067500

04067651

04067958

04069416

04069500

04069530

04071000

04071765

04071775

04071795

04071858

04072150

04072410

04072750

04072845

04073050

04073365

04073405

04073462

04073468

04073473

04073500

04073970

04074538

04074548

04074950

04075200

04075365

04075500

04077000

04077400

04077630

04078500

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28

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 

04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year 

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04079000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04079602 ● ● ● ● ● ● 

04079700 ● ● 

04080000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04080798 

04080950 ● ● ● ● ● ● 

04081000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04081800 ○ 

04082400 

04083000 ● ● ● ● 

04083420 

04083423 

04083425 

04083500 ● ● ● ● 

04083545 

04084445 

04084475 

04084500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04085046 

04085054 

04085059 

04085068 

04085109 

04085118 

04085119 

04085200 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04085281 ● ● ● ● ● ● ● ● ● ● 

04085330 

04085395 

04085427 ● ● ● ● ● ● ● ● ● ● 

04085492 

04085746 

04085845 ● ● ● ● 

04086000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04086150 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04086175 

04086200 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04086340 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04086360 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04086488 

04086500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04086600 

04087000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04087010 

04087018 ● ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 

04040003, 04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984

number

1985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04079000

04079602

04079700

04080000

04080798

04080950

04081000

04081800

04082400

04083000

04083420

04083423

04083425

04083500

04083545

04084445

04084475

04084500

04085046

04085054

04085059

04085068

04085109

04085118

04085119

04085200

04085281

04085330

04085395

04085427

04085492

04085746

04085845

04086000

04086150

04086175

04086200

04086340

04086360

04086488

04086500

04086600

04087000

04087010

04087018

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30

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 

04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year 

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04087019 ○ ○ 

04087030 ● ● ● ● ● 

04087040 ● ● ● ● 

04087047 

04087048 

04087050 ● ● ● ● 

04087060 ● ● ● ● 

04087070 ● ○ 

04087088 ● ● ● ● ● ● 

04087119 ● ● ● ● 

04087120 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ● ● ● ● ● 

04087125 ○ ○ ○ ○ 

04087138 

04087140 ○ 

04087142 

04087159 

04087160 ○ ○ ○ ○ ○ ○ 

04087170 

04087204 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04087214 

04087220 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04087233 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04087240 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04087257 ● ● ● ● ● ● ● ● ● ● ● 

04127918 ● ● ● ● ● ● ● ● ● ● 

040445315 

040590345 

040734644 

040851325 

040851378 

040851385 

040857005 

040860041 

040863075 

040869415 

040869416 

040871473 

040871475 

040871476 

040871488 

040874126 

0407809265 

0408570045 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 5. Streamgaging stations considered for analysis of study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 

04040003, 04060106, 04060107, 04070001, and 04070002) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984

number

1985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04087019

04087030

04087040

04087047

04087048

04087050

04087060

04087070

04087088

04087119

04087120

04087125

04087138

04087140

04087142

04087159

04087160

04087170

04087204

04087214

04087220

04087233

04087240

04087257

04127918

040445315

040590345

040734644

040851325

040851378

040851385

040857005

040860041

040863075

040869415

040869416

040871473

040871475

040871476

040871488

040874126

0407809265

0408570045

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Table 6. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of Channels) analysis for 

study area 2 (hydrologic subregion 0403 and cataloguing units 04040002, 04040003, 04060106, 04060107, 04070001, and 04070002) in the 

U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; RMSE, root mean squared error; R2, coefficient of determination. See appendix tables for variable 

descriptions]

Month

Regression coefficients Regression fit statistics

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature

Pasture 

hay and 

row crops

Forest Wetland 

woody

Wetland 

herbaceous

Hydric 

group C 

and CD

Coarse 

stratified

sediment

Till RMSE F-statistic R2

October 0.534 0.100 0.072 −0.010 −0.299 – −0.267 – −0.150 0.109 -0.066 0.197 402 0

November 0.336 0.139 0.076 −0.006 −0.167 0.131 – – −0.100 0.125 – 0.194 408.2 0.

December 0.479 0.124 0.073 0.023 −0.132 0.359 −0.331 0.418 – 0.200 – 0.199 235.5 0.4

January 0.411 0.091 0.086 0.020 −0.077 0.510 −0.585 0.525 – 0.309 0.111 0.194 150.4 0.3

February 0.433 0.121 0.055 0.022 −0.099 0.419 −0.639 0.592 0.199 0.316 0.152 0.211 113.3 0.3

March 0.653 0.119 0.097 0.029 0.225 – – 0.839 0.293 – – 0.285 282.8 0.450

April 1.366 0.139 0.076 −0.029 – – 1.333 1.630 0.273 −0.775 −0.725 0.320 263.9 0.

May 1.238 0.134 0.068 −0.033 −0.221 – 0.537 – – −0.430 −0.390 0.271 345.3 0

June 0.419 0.140 0.075 – −0.356 – −0.166 – – −0.072 −0.140 0.233 492.6 0

July 1.057 0.103 0.066 −0.028 −0.518 −0.232 −0.800 – −0.176 0.231 – 0.197 404.7 

August 0.343 0.081 0.043 0.008 −0.538 – −0.836 – −0.223 0.258 0.066 0.195 263.6 0.

September 0.411 0.106 0.050 – −0.410 – −0.600 −0.341 −0.189 0.159 – 0.203 446 0

CurrentPrecip

PrecidPrecip

CurrentTemper

Forest

C3_endm_cD3_grndm_c

meanElev

HydgrpCHydgrpCDHydgrpD

StreamOrde

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

32Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Figure 7. Image showing the t-value-indexed colors corresponding to each explanatory variable in 

the monthly regression equation for estimating water yield for study area 2 (hydrologic subregion 0403 

and cataloguing units 04040002, 04040003, 04060106, 04060107, 04070001, and 04070002) in the U.S. Great 

Lakes Basin.
Study Area 3

Study area 3 is formed by hydrologic subregion 0405 

and cataloguing unit 04040001 in the south-central part of 

the U.S. Great Lakes Basin along the southeastern side of 

Lake Michigan and encompasses parts of Michigan, Indiana, 

and a small part of Illinois (fig. 8). The number of stations 

included in the analysis ranged from 27 (1951) to 54 (1976) 

(table 7). Thirteen explanatory variables were selected during 

the regression analysis with the number of variables specified 

for each monthly equation ranging from 5 (April) to 12 

(September) (table 3). Variables and regression statistics based 

on the stepwise regression for each month are indicated in 

table 8 and figure 9. 

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0404

0405

Methods of Flow and Water-Yield Estimation for Study Areas

Figure 8. Location of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the U.S. Great Lakes Basin.
34

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1951 1952 1953 1954

number

1955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04092677

04092750

04093000

04093200

04093500

04094000

04094500

04095050

04095090

04095092

04095100

04095300

04095380

04096015

04096100

04096272

04096312

04096325

04096340

04096400

04096405

04096500

04096515

04096600

04096900

04097060

04097170

04097195

04097200

04097500

04097540

04097970

04098500

04099000

04099510

04099610

04099750

04099808

04099850

04100000

04100222

04100252

04100295

04100377

04100465

04100500

04101000

04101370

04101500

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Methods of Flow and Water-Yield Estimation for Study Areas

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984 1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04092677

04092750

04093000

04093200

04093500

04094000

04094500

04095050

04095090

04095092

04095100

04095300

04095380

04096015

04096100

04096272

04096312

04096325

04096340

04096400

04096405

04096500

04096515

04096600

04096900

04097060

04097170

04097195

04097200

04097500

04097540

04097970

04098500

04099000

04099510

04099610

04099750

04099808

04099850

04100000

04100222

04100252

04100295

04100377

04100465

04100500

04101000

04101370

04101500

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36

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1951 1952 1953 1954

number

1955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04101800

04102000

04102320

04102420

04102500

04102700

04102776

04102850

04103010

04103500

04104000

04104500

04104945

04105000

04105500

04105700

04105800

04106000

04106180

04106190

04106300

04106320

04106400

04106500

04106906

04107850

04108500

04108600

04108670

04108800

04108801

04109000

04109500

04110000

04111000

04111379

04111500

04112000

04112500

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Methods of Flow and Water-Yield Estimation for Study Areas

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984 1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04101800

04102000

04102320

04102420

04102500

04102700

04102776

04102850

04103010

04103500

04104000

04104500

04104945

04105000

04105500

04105700

04105800

04106000

04106180

04106190

04106300

04106320

04106400

04106500

04106906

04107850

04108500

04108600

04108670

04108800

04108801

04109000

04109500

04110000

04111000

04111379

04111500

04112000

04112500

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38

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1951 1952 1953 1954

number

1955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04112850

04112904

04113000

04113097

04114000

04114498

04114500

04115000

04115265

04116000

04116500

04117000

04117500

04118000

04118500

04119000

04119300

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Methods of Flow and Water-Yield Estimation for Study Areas

Table 7. Streamgaging stations considered for analysis of study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station Water year 1983 1984 1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04112850

04112904

04113000

04113097

04114000

04114498

04114500

04115000

04115265

04116000

04116500

04117000

04117500

04118000

04118500

04119000

04119300

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Table 8. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of CHannels) analysis for study area 

0405 and cataloguing unit 04040001) in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; GDD, growing degree days; RMSE, root mean square error; R2, coefficient of determination. See append

tions]

Month

Regression coefficients 

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature Pasture hay Row crops Forest Open water Wetland herbaceous Stream order Mean elevation Mean slope Coarse outwash Average GDD 

October 0.529 0.091 0.055 – −0.289 – 0.277 −2.622 – −2.2E-05 0.110 0.077 0.501 – 

November 0.648 0.103 0.065 −0.011 −0.334 – 0.490 −1.802 −2.646 −2.0E-05 0.065 – 0.359 4.8E-05 

December 0.710 0.110 0.074 0.016 −0.337 – 0.545 −1.131 −3.075 −1.4E-05 – – 0.236 4.5E-05 January 0.805 0.120 0.104 0.032 −0.286 – 0.305 – −4.094 −1.2E-05 – – 0.183 4.9E-05 February 0.972 0.155 0.049 0.021 −0.586 – – −1.331 −3.384 −1.3E-05 0.042 – 0.145 5.0E-05 March 1.161 0.118 0.094 – −0.331 – – −2.131 – −7.0E-06 – – −0.057 – 

April 1.039 0.080 0.070 −0.013 −0.568 – – −1.655 – – – – – – 

May 0.818 0.094 0.074 −0.015 −0.439 – – −2.226 – −9.0E-06 0.043 0.090 0.202 – 

June 0.412 0.103 0.072 – −0.593 – – −2.306 −2.858 −1.2E-05 0.070 0.082 0.355 – July 0.372 0.069 0.066 – −0.661 −0.115 – −2.336 −4.678 −1.5E-05 0.099 0.127 0.472 – August 0.449 0.057 0.058 – −0.595 −0.187 – −2.584 −4.794 −1.9E-05 0.120 0.139 0.509 – September 0.711 0.076 0.047 −0.016 −0.571 −0.172 – −2.538 −5.036 −2.2E-05 0.114 0.129 0.523 2.9E-05 

Figure 9. Image showing the t-value-indexed colors corresponding to each explanatory variable in the monthly regression equation for estimating water yield for study area 3 (hydrologic subregion 0405 and cataloguing unit 04040001) in the U.S. Great Lakes Basin.

CurrentPrecip

PrecidPrecip

CurrentTemper

Forest

WetlandWoody

HydgrpCHydgrpCD

stratsed_c

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

WetlandHerbaceous

till

PastureHayRowCrops
Methods of Flow and Water-Yield Estimation for Study Areas

Study Area 4

Study area 4 is formed by cataloguing units 04060101, 

04060102, 04060103, 04060104, 04060105, 04070003, 

04070004, 04070005, 04070006, and 04070007 near the 

central part of the U.S. Great Lakes Basin in the northern part 

of the Lower Peninsula of Michigan (fig. 10). The number 

of stations included in the analysis ranged from 15 (1994) to 

30 (1970) (table 9). Seven explanatory variables were selected 

during the regression analysis with the number of variables 

specified for each monthly equation ranging from 5 (May) to 

7 (December, January, February, and July) (table 3). Variables 

and regression statistics based on the stepwise regression for 

each month are indicated in table 10 and figure 11. 

Figure 10. Location of study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 04060105, 04070003, 04070004, 

04070005, 04070006, and 04070007) in the U.S. Great Lakes Basin.

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0406

0407
42

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 9. Streamgaging stations considered for analysis of study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 04060105, 

04070003, 04070004, 04070005, 04070006, and 04070007) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

195119521953

Station 

number

19541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04120293

04121000

04121300

04121500

04121650

04121900

04121944

04121970

04122000

04122100

04122150

04122200

04122500

04123000

04123500

04124000

04124200

04124500

04125000

04125200

04125210

04125350

04125450

04125460

04125500

04125510

04125550

04126000

04126200

04126740

04126802

04126970

04127000

04127565

04127800

04127997

04128000

04128500

04128990

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Methods of Flow and Water-Yield Estimation for Study Areas

Table 9. Streamgaging stations considered for analysis of study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 

04060105, 04070003, 04070004, 04070005, 04070006, and 04070007) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04120293

04121000

04121300

04121500

04121650

04121900

04121944

04121970

04122000

04122100

04122150

04122200

04122500

04123000

04123500

04124000

04124200

04124500

04125000

04125200

04125210

04125350

04125450

04125460

04125500

04125510

04125550

04126000

04126200

04126740

04126802

04126970

04127000

04127565

04127800

04127997

04128000

04128500

04128990

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44

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 9. Streamgaging stations considered for analysis of study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 04060105, 

04070003, 04070004, 04070005, 04070006, and 04070007) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

195119521953

Station 

number

19541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04129000

04129500

04130000

04130500

04131000

04131500

04132000

04132500

04133000

04133500

04133501

04134000

04134500

04135000

04135500

04135600

04135700

04136000

04136500

04136900

04137005

04137500

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Methods of Flow and Water-Yield Estimation for Study Areas

Table 9. Streamgaging stations considered for analysis of study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 

04060105, 04070003, 04070004, 04070005, 04070006, and 04070007) in the U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04129000

04129500

04130000

04130500

04131000

04131500

04132000

04132500

04133000

04133500

04133501

04134000

04134500

04135000

04135500

04135600

04135700

04136000

04136500

04136900

04137005

04137500

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Table 10. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of CHannels) 

analysis for study area 4 (cataloguing units 04060101, 04060102, 04060103, 04060104, 04060105, 04070003, 04070004, 04070005, 

04070006, and 04070007) in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; RMSE, root mean square error; R2, coefficient of determination. See appendix tables for 

variable descriptions]

Month

Regression coefficients Regression fit statistics

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature

Deciduous 

and evergreen 

forest

Row 

crops

Hydric 

group A 

and AD

Stream 

order RMSE F-statistic R2

October −0.329 0.050 0.036 – 1.048 0.847 0.294 0.133 0.145 303.6 0.57

November −0.086 0.053 0.043 – 0.839 0.763 0.200 0.122 0.147 208.1 0.48

December 0.109 0.060 0.041 0.020 0.755 0.689 0.202 0.113 0.151 155.3 0.446

January 0.093 0.040 0.054 0.021 0.766 0.979 0.243 0.139 0.152 166.6 0.464

February 0.111 0.047 0.028 0.019 0.695 1.017 0.251 0.145 0.160 126.7 0.397

March 0.497 0.072 0.057 0.028 0.366 0.830 – 0.138 0.177 144 0.390

April 1.096 0.048 0.046 −0.016 0.377 – −0.373 0.075 0.206 41.9 0.1

May 0.332 0.062 0.033 – 0.565 0.285 – 0.122 0.154 154.8 0.364

June −0.202 0.048 0.032 – 0.754 0.635 0.321 0.166 0.145 230.5 0.50

July −0.379 0.039 0.035 −0.008 0.945 0.724 0.468 0.207 0.141 268.4 0.5

August −0.612 0.028 0.023 – 1.091 0.891 0.530 0.194 0.141 318.5 0.58

September −0.642 0.043 0.030 – 1.127 0.958 0.457 0.186 0.144 359.4 0.61

CurrentPrecip

PrecidPrecip

CurrentTemper

StreamOrde

HydgrpAHydgrpAD

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

till

RowCrops

ForestDecidForestEGreen

46Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Figure 11. Image showing the t-value-indexed colors corresponding to each explanatory variable in 

the monthly regression equation for estimating water yield for study area 4 (cataloguing units 04060101, 

04060102, 04060103, 04060104, 04060105, 04070003, 04070004, 04070005, 04070006, and 04070007) in the 

U.S. Great Lakes Basin.
Study Area 5

Study area 5 is formed by hydrologic subregions 0408 

and 0409 near the central part of the U.S. Great Lakes Basin 

along the southwestern side of Lake Huron in the Lower 

Peninsula of Michigan (fig. 12). The number of stations 

included in the analysis ranged from 21 (2008) to 52 (1966) 

(table 11). Eleven explanatory variables were selected during 

the regression analysis with the number of variables specified 

for each monthly equation ranging from 6 (March) to 

10 (August) (table 3). Variables and regression statistics based 

on the stepwise regression for each month are indicated in 

table 12 and figure 13. 

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0408

0409

Methods of Flow and Water-Yield Estimation for Study Areas

Figure 12. Location of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes Basin.
48

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04138000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04138500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04139000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04139500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04140000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ 

04140500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04141000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04141500 ● ● ● ● ● ● ● ● ● ● ● ● 

04142000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04143500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04143900 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04144000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04144500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ○ ● ○ ● ● 

04145000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04145500 ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04146000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04146063 ● ● 

04146500 ○ ○ 

04147500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● 

04147990 ● ● ● ● ● ● ● ● ● ● ● ● 

04148000 ● ● 

04148140 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04148160 ● ● ● ● ● ● ● ● ● ● ● ● 

04148200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04148300 ● ● ● ● ● ● ● ● ● ● ● ● 

04148440 ● ● ● ● ● ● ● ● ● ● ● ● 

04148500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04148720 ● ● ● ● ● ● ● ● ● ● ● ● 

04149000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04150000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04150500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04150800 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04151000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04151500 ● ● ● ● ○ ○ ● ● ○ ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ○ ○ ● ● ● ● ● 

04152238 

04152500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04153500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04154000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04154500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04155000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04155500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04156000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04157000 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04138000

04138500

04139000

04139500

04140000

04140500

04141000

04141500

04142000

04143500

04143900

04144000

04144500

04145000

04145500

04146000

04146063

04146500

04147500

04147990

04148000

04148140

04148160

04148200

04148300

04148440

04148500

04148720

04149000

04150000

04150500

04150800

04151000

04151500

04152238

04152500

04153500

04154000

04154500

04155000

04155500

04156000

04157000

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50

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04157500 ○ ○ ○ ○ 

04158000 ○ ○ ○ ○ 

04158500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04159000 ○ ○ 

04159010 

04159488 ○ ○ ○ ○ 

04159492 

04159500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● 

04159900 ● ● ● ● ● ● ● ● ● ● ● ● 

04160000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04160398 

04160570 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04160600 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04160625 

04160800 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04160900 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04161000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04161100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04161500 

04161540 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04161580 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04161800 ● ○ ○ ● ○ ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● 

04161820 ● ○ ● ● 

04162010 ○ ○ ○ 

04162400 ○ ○ ○ 

04162900 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ○ ○ 

04163000 ● ● ● ● 

04163030 

04163400 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04163500 ● ● ● ● ● ● ● ● ● ● ● ○ 

04164000 ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ● ● ● ● ● ● ● ● 

04164010 ● ● ● ● ● ● 

04164050 ● ● ● ● ● 

04164100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04164150 ○ ○ ● ● ● 

04164200 ● ● ● ● ● 

04164250 ○ ○ ○ ○ ○ 

04164300 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ○ ○ 

04164350 ○ ○ ○ ○ ○ 

04164360 ○ ○ ○ ○ ○ 

04164400 ● ● ● ● ● 

04164450 ● ● ● ● ● 

04164500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04157500

04158000

04158500

04159000

04159010

04159488

04159492

04159500

04159900

04160000

04160398

04160570

04160600

04160625

04160800

04160900

04161000

04161100

04161500

04161540

04161580

04161800

04161820

04162010

04162400

04162900

04163000

04163030

04163400

04163500

04164000

04164010

04164050

04164100

04164150

04164200

04164250

04164300

04164350

04164360

04164400

04164450

04164500

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52

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04164600 ● ● ● ● ● 

04164800 ● ● ● ● ○ ○ ● ● ● ● ● ● ● ● ● ● ● ● ● 

04164980 

04165200 ● ● ● ● ● 

04165500 ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ○ ● ○ ● ● ● ● ● ● ● ● ● ● ● 

04165557 

04165559 

04166000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04166040 

04166100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04166200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04166300 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04166470 

04166500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04166750 

04167000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04167150 

04167625 

04168000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ○ ● ● ○ ● ● ● ● ● ● ● ● 

04168400 

04168530 

04168580 

04169500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04170000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● 

04170500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04171500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04172000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● 

04172500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04173000 ● ● ● ● ● ● ○ ● ● ● ● ● ● ○ ○ ● ○ ● ○ ● ○ ● ● ● 

04173500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● 

04174500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04174518 

04174800 ○ ○ ○ ○ ○ ○ ○ ○ 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 11. Streamgaging stations considered for analysis of study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

number

1985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04164600

04164800

04164980

04165200

04165500

04165557

04165559

04166000

04166040

04166100

04166200

04166300

04166470

04166500

04166750

04167000

04167150

04167625

04168000

04168400

04168530

04168580

04169500

04170000

04170500

04171500

04172000

04172500

04173000

04173500

04174500

04174518

04174800

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Table 12. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of CHannels) analysis for study area 5 

subregions 0408 and 0409) in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; GDD, growing degree days; RMSE, root mean square error; R2, coefficient of determination. See appendix tables for variab

Month

Regression coefficients Regression 

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature Pasture hay Row crops Grass herbaceous Stream order Mean slope Hydric group B and BD Coarse outwash Average GDD RMSE F-sta

October −0.3694 0.1091 0.0838 – −0.8654 – 2.4942 0.1163 0.1746 −0.1944 −0.1569 8.3E-05 0.181 48

November 0.0815 0.1212 0.0795 −0.0137 −0.5761 −0.1675 – 0.1342 0.1100 −0.1647 – – 0.203 29

December 0.0984 0.1531 0.0849 0.0183 −0.5279 – 1.0235 0.1541 0.0898 −0.2045 – – 0.231 25January 0.1645 0.1383 0.1078 0.0443 −0.5149 0.1856 1.5386 0.2060 0.1442 −0.2622 – – 0.232 28February 0.4007 0.2092 0.0878 0.0459 – – 1.3320 0.1089 0.0582 −0.1176 −0.1112 – 0.261 27

March 1.0156 0.1500 0.1153 – −0.2659 0.3633 – – – – −0.1671 −9.5E-05 0.284 17

April 0.9775 0.1122 0.0418 −0.0237 −0.4124 – 1.6675 0.0963 0.0418 – −0.2228 −6.8E-05 0.262 8May 0.2966 0.1606 0.0782 −0.0242 −0.7910 – 2.5436 0.1041 0.0765 – −0.1402 4.0E-05 0.184 51

June −0.1800 0.1280 0.0757 – −0.9983 – 2.5563 0.1166 0.0973 −0.1399 −0.1198 4.1E-05 0.201 32July −0.3059 0.0998 0.0745 – −1.0679 – 2.3501 0.1598 0.1173 −0.2079 −0.1211 4.8E-05 0.186 28August −0.4740 0.0731 0.0575 0.0114 −1.0729 −0.0674 2.2346 0.1539 0.1379 −0.2591 −0.1841 6.2E-05 0.194 18September 0.1771 0.1088 0.0530 −0.0180 −0.7754 −0.2785 – 0.1527 0.1148 −0.1551 −0.1159 – 0.200 32

CurrentPrecip

PrecidPrecip

CurrentTemper

StreamOrde

meanSlpe

HydgrpBHydgrpBD

A3outwsh_c

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

GrassHerbaceous

RowCrops

PastureHay

Awg_GDD

Figure 13. Image showing the t-value-indexed colors corresponding to each explanatory variable in the monthly regression equation for estimating water yield for study area 5 (hydrologic subregions 0408 and 0409) in the U.S. Great Lakes Basin.
Study Area 6

Study area 6 is formed by hydrologic subregions 0410 

and 0411 in the southeastern part of the U.S. Great Lakes 

Basin and encompasses parts of Michigan, Ohio, Indiana, and 

a small part of Pennsylvania (fig. 14). The number of stations included in the analysis ranged from 26 (1953, 1963, 

1982, and 1983) to 48 (2002) (table 13). Eleven explanatory 

variables were selected during the regression analysis with the 

number of variables specified for each monthly equation ranging from 7 (July) to 11 (April and September) (table 3). Variables and regression statistics based on the stepwise regression 

for each month are indicated in table 14 and figure 15. 

Figure 14. Location of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes Basin.

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0410 0411

Methods of Flow and Water-Yield Estimation for Study Areas
56

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes Basin, 

by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04175340 ● ● ● ● ● ● ● ● ● ● ● 

04175600 ● ● ● ● ● ● ● ● ● ● ● 

04175700 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04175957 

04176000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04176400 ● ● ● ● ● ● ● ● ● ● ● ● 

04176500 ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ○ ○ ○ ● ○ ○ ● ● ● ● ● ● ● 

04176605 

04177000 ● ● ● ● ● ● 

04177720 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04178000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04179000 ● ○ ● ○ ○ ○ ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ○ 

04179500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04179520 

04180000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04180500 

04180988 

04181500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04182000 ● ● ● ● ● ○ ● ● ● ○ ● ● ○ ● ● ○ ● ● ○ ● ● ● ● ● ● ○ ○ ● ● ● ● ● 

04182590 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04182810 

04182950 

04183000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04183500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04184500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04185000 ● ● ○ ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ○ ○ ○ ● ○ ● ○ ● 

04185440 

04186500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04187100 

04187500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04188337 

04188400 

04188433 

04188496 

04188500 ● ● ● ● ● ● 

04189000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04189500 ● 

04189950 

04191000 ○ ○ ○ 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04175340

04175600

04175700

04175957

04176000

04176400

04176500

04176605

04177000

04177720

04178000

04179000

04179500

04179520

04180000

04180500

04180988

04181500

04182000

04182590

04182810

04182950

04183000

04183500

04184500

04185000

04185440

04186500

04187100

04187500

04188337

04188400

04188433

04188496

04188500

04189000

04189500

04189950

04191000

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58

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes Basin, 

by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04191500 ● ○ ○ ○ ● ● ● ● ● ○ ○ ○ ○ ○ ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ○ ● 

04192000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04192500 ● ○ ○ ○ ○ ○ ○ ● ○ ● ● ○ ○ ○ ○ ● ○ ○ ○ ○ ● ● ● ● ○ ● ○ ● 

04193500 ○ ● ● ● ● ○ ● ● ○ ● ○ ● ○ ○ ○ ● ● ● ○ ○ ● ● ● ● ● ● ● ○ ● ○ ● ○ 

04194085 

04195500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04195600 ○ ○ 

04195820 

04195825 

04195830 

04196000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04196200 ● ● ● ● ● 

04196500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● 

04196800 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04197000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04197020 ● ● ● 

04197100 ● ● ● ● ● ● 

04197170 

04197300 ● ● ● ● ● 

04197450 ● ● ● ● ● 

04198000 ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ○ ● ● ○ ○ ● ● ○ ○ 

04199000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04199155 

04199287 

04199500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● 

04200430 ○ ○ 

04200500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04201300 ○ 

04201404 

04201495 

04201500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04202000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04203900 

04204000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04204500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04205000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04205700 ● ● ● ● ● ● 

04206000 ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04206014 

04206021 

04206029 

04206038 

04206043 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04191500

04192000

04192500

04193500

04194085

04195500

04195600

04195820

04195825

04195830

04196000

04196200

04196500

04196800

04197000

04197020

04197100

04197170

04197300

04197450

04198000

04199000

04199155

04199287

04199500

04200430

04200500

04201300

04201404

04201495

04201500

04202000

04203900

04204000

04204500

04205000

04205700

04206000

04206014

04206021

04206029

04206038

04206043

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60

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes Basin, 

by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station 

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04206208 

04206210 

04206211 

04206212 

04206215 

04206220 

04206250 ● ● ● ● ● ● 

04206420 

04206448 

04207016 

04207200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04207500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04208000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ○ ○ ○ ○ ● ● ● 

04208460 

04208501 

04208502 ● ● ● ● ● ● ● ● ● ● 

04208504 

04208690 ● ● ● 

04209000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04210000 ● ● ● ● ● ● ● ● 

04211000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04211500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04211820 

04212000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04212100 ● ● ● ● ● ● ● ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 13. Streamgaging stations considered for analysis of study area 6 (hydrologic subregions 0410 and 0411) in the U.S. Great Lakes 

Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04206208

04206210

04206211

04206212

04206215

04206220

04206250

04206420

04206448

04207016

04207200

04207500

04208000

04208460

04208501

04208502

04208504

04208690

04209000

04210000

04211000

04211500

04211820

04212000

04212100

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Table 14. Regression statistics and explanatory variables used in the AFINCH (Analysis of Flows In Networks of CHannels) analysis for study area 6 

subregions 0410 and 0411) in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; RMSE, root mean square error; R2, coefficient of determination. See appendix tables for variable descriptions

Month

Regression coefficients Reg

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature

Pasture 

hay and 

row crops 

Forest

Fine end 

and ground 

moraines

Medium end 

and ground 

moraines

Coarse 

outwash and 

ice conract

Stream 

order

Mean 

elevation Mean slope RMSE 

October 0.151 0.148 0.100 – −0.334 −0.383 – 0.140 0.201 0.115 −1.4E-05 0.098 0.2216 

November 0.421 0.226 0.090 −0.015 −0.355 −0.063 0.076 0.259 – – −1.5E-05 0.074 0.267 December 0.097 0.284 0.145 0.008 – 0.343 0.182 0.415 0.235 0.079 −2.5E-05 0.099 0.311 January 0.495 0.288 0.081 0.037 – 0.406 0.128 0.448 – 0.084 −1.9E-05 0.075 0.310 February 0.617 0.265 0.056 0.023 – 0.545 0.189 0.396 – – −1.2E-05 0.052 0.337 March 0.930 0.254 0.047 −0.035 – 0.677 0.177 0.527 – 0.095 −2.3E-05 0.047 0.335 April 0.981 0.214 0.050 −0.011 −0.151 0.453 0.164 0.521 0.209 0.087 −3.0E-05 0.071 0.249 May 0.985 0.200 0.072 −0.018 −0.218 – – 0.263 0.105 – −2.4E-05 0.104 0.244 June 0.087 0.183 0.094 0.010 −0.240 −0.237 – 0.193 0.185 0.131 −2.5E-05 0.110 0.233 

July 0.029 0.160 0.079 – −0.406 −0.668 – – – 0.077 −7.0E-06 0.106 0.246 

August 0.246 0.123 0.071 – −0.503 −0.497 0.107 0.252 0.340 0.121 −1.6E-05 0.088 0.216 September 0.338 0.141 0.077 −0.011 −0.521 −0.601 0.113 0.156 0.339 0.099 −1.2E-05 0.080 0.218 

CurrentPrecip

PrecidPrecip

CurrentTemper

StreamOrde

meanElev

A3outwsh_cB3icent_c

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

PastureHayRowCrops

Forest

meanSlpe

C1_endm_fD1_grndm_f

C2_endm_mD2_grndm_m

Figure 15. Image showing the t-value-indexed colors correspto each explanatory variable in the monthly regression equatioestimating water yield for study area 6 (hydrologic subregions 0411) in the U.S. Great Lakes Basi
Study Area 7

Study area 7 is formed by hydrologic subregions 0412, 

0413, 0414, and 0415 in the eastern part of the U.S. Great 

Lakes Basin and encompasses parts of Pennsylvania, 

New York, and a small part of Ohio (fig. 16). The number of 

stations included in the analysis ranged from 31 (1951 and 

1953) to 65 (1967) (table 15). Twelve explanatory variables 

were selected during the regression analysis with the number 

of variables specified for each monthly equation ranging from 

6 (February) to 11 (March) (table 3). Variables and regression 

statistics based on the stepwise regression for each month are 

indicated in table 16 and figure 17. 

75° 

80° 

85° 

90° 

95° 

42° 30’

47° 30’

OHIO

MINNESOTA

ILLINOIS

WISCONSIN

NEW YORK

INDIANA

MICHIGAN

PENNSYLVANIA

MICHIGAN

EXPLANATION

Hydrologic Subregion 

Hydrologic Region

Great Lakes Basin boundary

0 125 250 Miles Base from The Great Lakes 

Information Network, 2014;

hydrologic units from 

U.S. Geological Survey, 2005 0 125 250 Kilometers

Target study areas

Lake Superior

Lake Michigan

Lake Huron

Lake Erie

Lake Ontario

0412

0413

0414

0415

Methods of Flow and Water-Yield Estimation for Study Areas

Figure 16. Location of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the U.S. Great Lakes Basin.
64

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04213000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04213040 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04213075 

04213410 ● ● ● ● 

04213440 ○ ○ ○ 

04213450 ● ● ● ● ● ● 

04213492 ● ● 

04213500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04214200 ● ● ● ● ● 

04214400 ● ● ● ● ● 

04214500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04215000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04215500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04216000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04216200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04216418 ● ● ● ● ● 

04216500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04217000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● 

04217500 ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ○ ○ ● ● ● ● ● ● ○ ● ● ● 

04217750 

04218000 ● ● ● ● ● ● ○ ● ● ● ● ● ● 

04218450 ● ● ● ● ● 

04218500 ● ● ● ● ● ● ● ● ● ● ● ● ○ ● ● ● ● 

04218518 ● ● ● ● ● ● ● ● ● ● 

04219940 ○ ○ 

04220250 

04220470 ● ● ● ● 

04220500 ● ● ● ● ● 

04221000 ● ● ● ● ● ● ● ● ● ● ● ● ● 

04221500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04221600 ● ● ● ● 

04221720 ● ● ● ● 

04221820 ● ● 

04221991 ● ● ● ● ● ● ● ● ● ● ● ● 

04222000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04222900 ● ● ● ● 

04223000 ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04224650 ● ● ● ● 

04224775 ● ● ● ● ● ● ● ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04213000

04213040

04213075

04213410

04213440

04213450

04213492

04213500

04214200

04214400

04214500

04215000

04215500

04216000

04216200

04216418

04216500

04217000

04217500

04217750

04218000

04218450

04218500

04218518

04219940

04220250

04220470

04220500

04221000

04221500

04221600

04221720

04221820

04221991

04222000

04222900

04223000

04224650

04224775

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66

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04225000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04225500 ● ● ● ● ○ ● ● ● ● 

04226000 ● ● 

04227000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04227500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04227995 

04228900 ○ ○ ○ ○ 

04229500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04230380 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04230500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04231000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04231600 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04232000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04232034 

04232040 ● ● 

04232046 ● ● 

04232047 ● ● ● ● ● ● ● ● ● 

04232050 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04232100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04232482 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04232630 ● ● ● ● 

04232650 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04232730 

04233000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04233286 

04233300 

04233678 ○ 

04233700 ● ● 

04234000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04234018 ● ● ● ● 

04234055 ● ● ● ● 

04234061 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04234200 ● ● ● 

04234232 

04234270 ● ● ● ● 

04235000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04235150 ● ● ● ● ● ● ● ● ● ● ● ● 

04235250 ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04235271 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04225000

04225500

04226000

04227000

04227500

04227995

04228900

04229500

04230380

04230500

04231000

04231600

04232000

04232034

04232040

04232046

04232047

04232050

04232100

04232482

04232630

04232650

04232730

04233000

04233286

04233300

04233678

04233700

04234000

04234018

04234055

04234061

04234200

04234232

04234270

04235000

04235150

04235250

04235271

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68

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04235276 

04235300 ○ ● ● ● ● ● ● ● 

04235440 

04235500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04235600 

04235820 

04237500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04237944 

04237946 

04237962 

04239000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04240010 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04240100 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04240105 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04240120 ● ● ● ● ● ● ● ● ● 

04240145 

04240150 

04240180 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04240200 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04240300 ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04241200 ● ● 

04242500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04243500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04244000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04245000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04245200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04245236 ○ ○ ○ ○ ○ 

04245250 ○ 

04245840 ● ● 

04246500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04246601 

04247000 

04249000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04249910 ○ 

04250200 

04250750 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04252000 ○ 

04252500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04253000 ● 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04235276

04235300

04235440

04235500

04235600

04235820

04237500

04237944

04237946

04237962

04239000

04240010

04240100

04240105

04240120

04240145

04240150

04240180

04240200

04240300

04241200

04242500

04243500

04244000

04245000

04245200

04245236

04245250

04245840

04246500

04246601

04247000

04249000

04249910

04250200

04250750

04252000

04252500

04253000

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70

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

04253275 ○ ○ ○ ○ 

04253500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04254000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04254500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04256000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04256460 

04256485 ○ ○ ○ ○ 

04257000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04258000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04258500 ● ● ● ● ● ● 

04258700 ● ● ● ● ● ● ● ● ● ● ● ● 

04260500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04261000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04262000 ● ● ● ● ● ○ ● ● ● ○ ● ● ● ● ● ● ● ● 

04262500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04263000 ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04264331 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04264700 ● ● ● ● ● 

04265000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04265100 ● ● ● ● ● ● ● ● ● ● 

04265432 

04265605 

04266500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04267500 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04268000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 

04268390 ● ● ● 

04268600 ● ● ● ● ● ● ● ● ● ● 

04268700 ● ● ● ● ● ● ● ● ● ● 

04268800 ● ● ● ● ● ● ● ● ● ● 

04269000 ● ● ● ● ● ● ● ● ● ○ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04269043 ● ● ● ● ● 

04269500 ● ● ● ● ● ● ● ● ● ● 

04270000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04270200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04270500 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

04270510 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 

0422026250 

0423204140 

0423204141 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

19831984

Station 

1985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

04253275

04253500

04254000

04254500

04256000

04256460

04256485

04257000

04258000

04258500

04258700

04260500

04261000

04262000

04262500

04263000

04264331

04264700

04265000

04265100

04265432

04265605

04266500

04267500

04268000

04268390

04268600

04268700

04268800

04269000

04269043

04269500

04270000

04270200

04270500

04270510

0422026250

0423204140

0423204141

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72

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Station

number

Water year

19511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982

0423204920 

0423205010 ○ 

0423205023 ○ 

0423205025 

0423368620 

0424014980 

0424016205 

0424016825 

0424016975 

0426545290 ● ● 

0426545295 ○ ○ ○ ○ 
Methods of Flow and Water-Yield Estimation for Study Areas

Table 15. Streamgaging stations considered for analysis of study area 7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the 

U.S. Great Lakes Basin, by water year.—Continued

[ ●, station active and included in the analysis; ○, station active but not included in the analysis]

Water year

Station 

198319841985

number

198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

0423204920 ● ● ● ● ● ● ● ● ● ● ● ●

0423205010 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

0423205023 ○

0423205025 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

0423368620 ○

0424014980 ○ ○ ○ ○ ○ ○

0424016205 ●

0424016825 ●

0424016975 ●

0426545290

0426545295
Table 16. Regression statistics used in the AFINCH (Analysis of Flows In Networks of CHannels) analysis for study area 7 (hydrologic subregions 041

0415) in the U.S. Great Lakes Basin, by month.

[ –, indicates variable not included in monthly regression equation; GDD, growing degree days; RMSE, root mean square error; R2, coefficient of determination. See appendix ta

descriptions]

Month

Regression coefficients R

Intercept

Current 

precipitation

Preceding 

precipitation

Current 

temperature Open water Forest Developed Mean slope Hydric group C, CD, and D Coarse outwash and ice conract Coarse end and ground moraines Average GDD Pasture hay and row crops RM

October 0.480 0.144 0.118 −0.024 0.833 −0.141 – −0.646 −0.008 −0.094 0.216 – – 0.2

November 0.462 0.179 0.107 −0.011 – – −0.221 −0.726 −0.030 – – – 5.1E-05 0.2

December 0.390 0.184 0.090 0.023 1.668 0.507 – – −0.026 0.087 – −0.176 – 0.2

January 1.061 0.170 0.085 0.045 – – −0.480 −0.403 −0.017 0.071 – – – 0.2

February 1.176 0.143 0.062 0.066 – 0.222 −0.176 – −0.020 – – – – 0.2March 2.051 0.155 0.046 0.039 −3.962 −0.520 −1.088 −0.817 – 0.253 −0.203 −0.263 −1.1E-04 0.3

April 2.641 0.165 0.088 −0.032 −2.673 −1.039 −1.726 −1.738 – 0.117 – – −1.5E-04 0.3May 1.208 0.165 0.067 −0.024 1.809 −0.383 −0.543 −0.778 – – 0.178 0.140 – 0.2

June 0.669 0.141 0.078 −0.017 1.423 −0.203 – −0.464 – −0.108 0.251 0.085 – 0.1

July 0.772 0.119 0.077 −0.018 1.089 −0.459 – −0.562 – −0.115 0.359 0.082 – 0.1August 0.822 0.106 0.084 −0.021 – −0.507 – −0.662 – −0.078 0.415 – – 0.2September 0.061 0.152 0.094 – 1.058 −0.305 – −0.671 – −0.133 0.304 – 4.0E-05 0.2

CurrentPrecip

PrecidPrecip

CurrentTemper

WaterOpen

Developed

A3outwsh_cB3icent_c

Monthly t-values for Significant (p<=0.01) Parameters for the period of analysis

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

−10 −5 0 5 10

PastureHayRowCrops

Forest

meanSlpe

HydgrpCHydgrpCDHydgrpD

C3_endm_cD3_grndm_c

Avg_GDD

Figure 17. Image showing the t-value-indexed colors corresponding to each explanatory variable in the monthly regression equation for estimating water yield for study are7 (hydrologic subregions 0412, 0413, 0414, and 0415) in the U.S. Great Lakes Basi
References Cited

Summary

A regionally consistent estimate of streamflow provides 

unified information across the United States portion of the 

Great Lakes Basin for restoration, assessment, management, 

and conservation of stream ecosystems. Monthly water yields 

from catchments and corresponding flows for stream segments 

(flowlines) were estimated for water years 1951–2012 for the 

U.S. Great Lakes Basin by using the computer application 

Analysis of Flows In Networks of CHannels (AFINCH). The 

AFINCH approach to estimate ungaged flows is a two-step 

process. The predictor step is based on a user-specified multiple-linear-regression equation to estimate monthly yields using 

selected monthly climatic and basin characteristics data and 

flows at streamgages. The corrector step adjusts the regression 

estimates to match measured flows at the streamgages. 

The 15 hydrologic subregions comprising the U.S. Great 

Lakes Basin were combined to form 7 study areas consisting 

of multiple subregions and (or) cataloguing units for analysis 

with AFINCH. Input data, explanatory variables, and regression details used in the estimation of water yields and flows 

are described for each study area. Data from 823 streamgages 

were compiled for the AFINCH analysis and were used to 

estimate monthly flows and water yields for 107,691 stream 

segments (flowlines) and 105,829 catchments in Hydrologic 

Region 04 for 1951–2012. These long-term flow series can be 

used to describe monthly flow-duration characteristics and to 

investigate trends for the stream segments in the U.S. Great 

Lakes Basin.

AFINCH utilizes the NHDPlus geospatial framework 

to provide a basis for integrating monthly flow measured at 

U.S. Geological Survey (USGS) streamgages, available wateruse data, monthly climatic data, land-cover characteristics, 

and catchment attributes described in user-defined shapefiles 

to develop sets of multiple-linear-regression equations for 

estimating monthly water yields. The explanatory variables 

describing monthly precipitation for the current month, 

monthly precipitation for the preceding month, and average 

monthly temperatures were included in the multiple-linearregression equations for all seven study areas. National landcover characteristics defining forest, pasture, and cultivated 

areas were significant explanatory variables in most of the 

study areas. NHDPlus variables defining stream order, as well 

as catchment elevation and (or) slope, and Soil Survey Geography (SSURGO) soil data also were significant explanatory 

variables in most of the study areas. Surficial areas of coarse 

outwash tended to be included in the regression equations 

for study areas in the southern and eastern parts of the 

U.S. Great Lakes Basin. Growing degree day data and areas 

with end and ground moraines also were important in several 

study areas. In general, coefficient of determination (R2

) values and F-statistics for the study areas were lowest in the late 

spring and early summer months (February–April) and higher 

in the late summer and early winter months (July–October). 

Considering a potential additional variable, such as an index 

relating to snow pack, would likely be significant and might 

improve the estimates during months of lower flow conditions. 

Regionally, however, these estimates present a reasonable, 

consistent, and defensible set of flow and yield estimates for 

the U.S. Great Lakes Basin.

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2011, at http://websoilsurvey.nrcs.usda.gov/. 

U.S. Environmental Protection Agency, 2001, EPA/OW Permit 

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are hydrologic units?, accessed November 24, 2008, at 

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(GAP)—Land cover data and modeling, accessed May 

2011, at http://gapanalysis.usgs.gov/gaplandcover/data.

Wahl, K.L., Thomas, W.O., Jr., and Hirsch, R.M., 1995, 

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2014, at http://pubs.usgs.gov/circ/circ1123/index.html.

Waples, J.T.; Eadie, Brian; Klump, J.V.; Squires, Margaret; 

Cotner, James; and McKinley, Galen, 2008, Chapter 7—

The Laurentian Great Lakes, in Hales, Burke; Cai, Wei-Jun; 

Mitchell, B.G., Sabine, C.L., and Schofield, Oscar, eds., 

North American Continental Margins—A Synthesis and 

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Michigan and the St. Lawrence River Basin

Regional compilations (listed chronologically)

Wells, J.V.B., 1958, Compilation of records of surface waters 

of the United States through September 1950—Part 4, 

St. Lawrence River Basin: U.S. Geological Survey 

Water-Supply Paper 1307, 397 p.

Hendricks, E.L., 1964, Compilation of records of surface 

waters of the United States, October 1950 to September 

1960—Part 4, St. Lawrence River Basin: U.S. Geological 

Survey Water-Supply Paper 1727, 379 p.

U.S. Geological Survey, 1971, Surface water supply of the 

United States, 1961–65—Part 4, St. Lawrence River 

Basin—Volume 1, Basins of streams tributary to Lakes 

Superior, Michigan, and Huron: U.S. Geological Survey 

Water-Supply Paper 1911, 651 p.

U.S. Geological Survey, 1974, Surface water supply of the 

United States, 1966–70—Part 4, St. Lawrence River 

Basin—Volume 1, Basins of streams tributary to Lakes 

Superior, Michigan and Huron: U.S. Geological Survey 

Water-Supply Paper 2111, 754 p.

Michigan data only (listed chronologically)

U.S. Geological Survey, 1961–4, Surface water records of 

Michigan [annual data reports, water years 1961–4].

U.S. Geological Survey, 1965–75, Water resources data 

for Michigan, Part 1, Surface water records [annual data 

reports, water years 1965–74].

U.S. Geological Survey, 1976–82, Water resources data, 

Michigan, water years 1975–81: U.S. Geological Survey 

Water-Data Reports MI-75-1 through MI-81-1.

Miller, J.B., Oberg, J.L., and Sieger, Theodore, Jr., 1983–85, 

Water resources data, Michigan, water years 1982–84: 

U.S. Geological Survey Water-Data Reports MI-82-1 

through MI-84-1.

Miller, J.B., Oberg, J.L., and Failing, J.C., 1986, Water 

resources data, Michigan, water year 1985: U.S. Geological 

Survey Water-Data Report MI-85-1, 297 p.

Miller, J.B., Failing, J.C., and Larson, W.W., 1987, Water 

resources data, Michigan, water year 1986: U.S. Geological 

Survey Water-Data Report MI-86-1, 353 p.

Blumer, S.P., Failing, J.C., Larson, W.W., Whited, C.R., and 

LeuVoy, R.L., 1988–90, Water resources data, Michigan, 

water years 1987–89: U.S. Geological Survey Water-Data 

Reports MI-87-1 through MI-89-1.

Blumer, S.P., Larson, W.W., Minnerick, R.J., Whited, C.R., 

and LeuVoy, R.L., 1991–92, Water resources data, Michigan, water years 1990–91: U.S. Geological Survey WaterData Reports MI-90-1 through MI-91-1.

Blumer, S.P., Behrendt, T.E., Larson, W.W., Minnerick, R.J., 

LeuVoy, R.L., and Whited, C.R., 1993–94, Water resources 

data, Michigan, water years 1992–93: U.S. Geological Survey Water-Data Reports MI-92-1 through MI-93-1.

Blumer, S.P., Behrendt, T.E., Ellis, J.M., Minnerick, R.J., LeuVoy, R.L., and Whited, C.R., 1995–2004, Water resources 

data, Michigan, water years 1994–2003: U.S. Geological 

Survey Water-Data Reports MI-94-1 through MI-03-1.

Blumer, S.P., Behrendt, Whited, C.R., T.E., Ellis, J.M., Minnerick, R.J., and LeuVoy, R.L., 2005, Water resources data, 

Michigan, water year 2004: U.S. Geological Survey WaterData Report MI-04-1, 496 p.

Blumer, S.P., Whited, C.R., Ellis, J.M., Minnerick, R.J., and 

LeuVoy, R.L., 2006, Water resources data, Michigan, water 

year 2005: U.S. Geological Survey Water-Data Report 

MI-05-1, 572 p.

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United States, water years 2006–12 [annual data compilations for stations 04034000 Bond Falls Reservoir near 

Paulding, Mich.; 04033500 Bond Falls Canal near Paulding, 

Mich.; 04057811 Greenwood Reservoir near Greenwood, 

Mich.; 04057814 Greenwood Release near Greenwood, 

Mich.; 04057813 Greenwood Diversion near Greenwood, 

Mich.; 04058000 Middle Branch Escanaba River near 

Ishpeming, Mich.; 04058190 Schweitzer Reservoir near 

Palmer, Mich.; and 04058400 Goose Lake Outlet near 

Sands Station, Mich.; accessed July 5, 2011, at http://wdr.

water.usgs.gov/.
Table 1–1. Revisions to NHDPlus flowline value-added attribute (VAA) information.—Continued [--, not changed] Subregion ComID Original values Modified values FromNode ToNode Hydroseq Divergence Startflag FromNode ToNode Hydroseq 

0401 1798775 -- -- 90072931 1 -- -- -- 90072920 

1798903 90003017 90003052 90072920 2 0 9003052 9003017 90072931 

1771252 -- -- -- 1 -- -- -- -- 

1772034 -- -- -- 2 0 -- -- -- 

0402 11951467 90021466 90021629 90046042 1 -- 90021629 90021466 90046053 

11952189 90021629 90021470 90040541 -- -- 90021470 90021629 90046185 11951469 90021470 90021630 90036575 -- -- 90021630 90021470 90046186 11952191 90021630 90021472 90033483 -- -- 90021472 90021630 90046187 11951473 90021472 90021631 90031008 -- -- 90021631 90021472 90046188 11952193 90021631 90021628 90028979 -- 0 90021628 90021631 90046189 11951459 -- -- -- 1 -- -- -- -- 

11930450 -- -- -- 1 0 -- -- -- 

11930458 -- -- -- 2 -- -- -- -- 

11929798 -- -- -- 1 -- -- -- -- 11929802 -- -- -- 2 -- -- -- -- 11930458 -- -- -- 2 -- -- -- -- 11930450 90019836 90023688 -- 1 -- 90023688 90019836 -- 

12027444 -- -- -- -- 0 -- -- -- 

0403 14444692 -- -- -- 1 -- -- -- -- 

6820848 -- -- -- 1 0 -- -- -- 

6849469 -- -- -- 2 -- -- -- -- 

11959514 -- -- -- -- 0 -- -- -- 

14444674 -- -- -- -- -- -- -- -- 

9027663 -- -- -- 2 0 -- -- -- 

6809298 -- -- -- 1 -- -- -- -- 

14444312 -- -- -- -- 0 -- -- -- 

12006809 -- -- -- 2 -- -- -- -- 

12006813 -- -- -- 1 -- -- -- -- 

6865517 -- -- -- 1 0 -- -- -- 

6866125 -- -- -- 2 -- -- -- -- 

6821620 -- -- -- 2 -- -- -- -- 

6821578 -- -- -- 1 -- -- -- -- 
Table 1–1. Revisions to NHDPlus flowline value-added attribute (VAA) information.—Continued[--, not changed]

Subregion ComID Original values Modified values FromNode ToNode Hydroseq Divergence Startflag FromNode ToNode Hydroseq 

0403 

(continued)

12174040 -- -- -- 2 0 -- -- -- 

12174028 -- -- -- 1 -- -- -- -- 

9036437 -- -- -- 2 0 -- -- -- 

9036449 -- -- -- 1 -- -- -- -- 

11959396 -- -- 90098082 -- 1 -- -- 90017082 11959398 -- -- -- -- 0 -- -- -- 11959926 -- 90021774 -- -- -- -- 90082911 -- 

0404 3397118 -- -- -- 2 -- -- -- -- 

3396784 -- -- -- 1 0 -- -- -- 

0405 12261958 -- -- -- 1 -- -- -- -- 

12260476 -- -- -- 2 0 -- -- -- 

13032275 90030086 90040059 90051985 2 -- 90040059 90030086 90044497 

13032045 90040059 90040060 90044497 -- 0 90040060 90040059 90051985 

12233796 -- -- -- 1 -- -- -- -- 

12260238 -- -- -- 1 -- -- -- -- 

12263234 -- -- -- 2 0 -- -- -- 

12258396 -- -- -- 1 0 -- -- -- 

12258498 -- -- -- 2 -- -- -- -- 

12263190 -- -- -- 2 0 -- -- -- 

12260112 -- -- -- 1 -- -- -- -- 

0406 12222264 90029225 90029214 90067021 2 0 90029214 90029225 90067041 

12221900 -- -- -- 1 -- -- -- -- 

12222160 -- -- -- 2 -- -- -- -- 

12221662 -- -- -- 1 -- -- -- -- 

0407 12502899 -- -- -- 1 -- -- -- -- 

12502901 -- -- -- 0 -- -- -- -- 

12962413 -- -- -- 2 0 -- -- -- 

12962487 -- -- -- 1 -- -- -- -- 
Table 1–1. Revisions to NHDPlus flowline value-added attribute (VAA) information.—Continued [--, not changed] Subregion ComID Original values Modified values FromNode ToNode Hydroseq Divergence Startflag FromNode ToNode Hydroseq 

0408 12944858 -- -- -- 2 -- -- -- -- 

12944468 90036462 90036538 1 0 90036538 90036462 

12944860 -- -- -- 1 0 -- -- -- 

13046031 -- -- -- 2 0 -- -- -- 

13016527 -- -- 90044601 -- -- -- -- 90018387 

13016547 -- -- 90052133 1 -- -- -- 90018934 

13016565 90038914 90039104 90052132 2 -- 90039104 90038914 90019518 

13019475 90039104 90039109 90044580 -- -- 90039109 90039104 90020159 

13019493 90039109 90039117 90035767 -- -- 90039117 90039109 90020830 13019523 90039117 90039292 90032845 -- -- 90039292 90039117 90021565 

13020129 90039292 90039294 90030478 -- -- 90039294 90039292 90022385 

13020133 90039294 90039129 -- -- -- 90039129 90039294 -- 

13019559 90039129 90039298 90022385 -- -- 90039298 90039129 90030478 

13020141 90039298 90039135 90021565 -- -- 90039135 90039298 90032845 

13019577 90039135 90039138 90020830 -- -- 90039138 90039135 90035500 

13019583 90039138 90039142 90020159 -- -- 90039142 90039138 90035550 

13019591 90039142 90039300 90019518 -- -- 90039300 90039142 90044601 

13020145 90039300 90039299 90018934 -- 0 90039299 90039300 90052132 

13020143 -- -- 90018387 -- 0 -- -- 90052133 

13019637 -- -- 90052102 -- -- -- -- 90064410 

13020157 -- -- 90044561 -- -- -- -- 90064405 

13019631 -- -- 90039494 -- -- -- -- 90064400 

13020155 -- -- 90035756 -- -- -- -- 90064395 

13019605 -- -- 90032841 -- -- -- -- 90064390 

13020147 -- -- 90030477 -- -- -- -- 90064385 

13007650 -- -- -- 1 0 -- -- -- 

13007796 -- -- -- 1 0 -- -- -- 

13007622 -- -- -- 1 0 -- -- -- 

13020539 -- -- -- 1 0 -- -- -- 

13031999 -- -- -- 2 -- -- -- -- 

13017263 -- -- -- 1 -- -- -- -- 

13028773 -- -- -- 2 0 -- -- -- 
Table 1–1. Revisions to NHDPlus flowline value-added attribute (VAA) information.—Continued[--, not changed]

Subregion ComID Original values Modified values FromNode ToNode Hydroseq Divergence Startflag FromNode ToNode Hydroseq 

0408

(continued)

13029155 -- -- -- 2 0 -- -- -- 

13028795 -- -- -- 1 -- -- -- -- 

13006714 -- -- -- 1 -- -- -- -- 

13009450 -- -- -- 2 0 -- -- -- 

13008924 -- -- -- 1 -- -- -- -- 

0409 13192736 -- -- -- 2 -- -- -- -- 

13192794 -- -- -- 2 -- -- -- -- 

13192762 -- -- -- 2 -- -- -- -- 

13192474 -- -- -- 2 0 -- -- -- 

13194146 -- -- -- 2 0 -- -- -- 

13194090 -- -- -- 1 -- -- -- -- 

13193728 -- -- -- 1 0 -- -- -- 

13193748 -- -- -- 2 -- -- -- -- 

0410 15612436 90060257 90060500 1 0 90060500 90060257 

15613610 -- -- -- -- 0 -- -- -- 

15644452 -- -- -- 2 -- -- -- -- 

15627609 -- -- -- 1 0 -- -- -- 

15627613 -- -- -- 2 0 -- -- -- 

15636243 -- -- -- 2 0 -- -- -- 

15627291 -- -- -- 1 -- -- -- -- 

15610538 -- -- -- 2 0 -- -- -- 

15605172 -- -- -- 1 -- -- -- -- 
82

Estimation of Monthly Water Yields and Flows for 1951–2012 for the United States Portion of the Great Lakes Basin with AFIN

Table 1–2. Description of classes in the 2006 National Land Cover Database.

Class Code Description

Open water 11 areas of open water, generally with less than 25 percent cover of vegetation or soil

Perennial ice/snow 12 areas characterized by a perennial cover of ice and (or) snow, generally greater than 25 percent of 

total cover

Developed-open space 21 areas with a mixture of some constructed materials, but mostly vegetation in the form of lawn 

grasses. Impervious surfaces account for less than 20 percent of total cover. These areas most 

commonly include large-lot single-family housing units, parks, golf courses, and vegetation 

planted in developed settings for recreation, erosion control, or aesthetic purposes.

Developed-low intensity 22 areas with a mixture of constructed materials and vegetation. Impervious surfaces account for 20 

to 49 percent of total cover. These areas most commonly include single-family housing units.

Developed-medium intensity 23 areas with a mixture of constructed materials and vegetation. Impervious surfaces account for 50 to 

79 percent of the total cover. These areas most commonly include single-family housing units.

Developed-high intensity 24 highly developed areas where people reside or work in high numbers. Examples include apartment 

complexes, row houses, and commercial/industrial. Impervious surfaces account for 80 to 

100 percent of the total cover.

Barren land 31 areas of bedrock, desert pavement, scarps, talus, slides, volcanic material, glacial debris, sand 

dunes, strip mines, gravel pits, and other accumulations of earthen material. Generally, vegetation accounts for less than 15 percent of total cover.

Deciduous forest 41 areas dominated by trees generally greater than 5 meters tall, and greater than 20 percent of total 

vegetation cover. More than 75 percent of the tree species shed foliage simultaneously in 

response to seasonal change.

Evergreen forest 42 areas dominated by trees generally greater than 5 meters tall, and greater than 20 percent of total 

vegetation cover. More than 75 percent of the tree species maintain their leaves all year. 

Canopy is never without green foliage.

Mixed forest 43 areas dominated by trees generally greater than 5 meters tall, and greater than 20 percent of total 

vegetation cover. Neither deciduous nor evergreen species are greater than 75 percent of total 

tree cover.

Shrub/scrub 52 areas dominated by shrubs less than 5 meters tall with shrub canopy typically greater than 

20 percent of total vegetation. This class includes true shrubs, young trees in an early successional stage, or trees stunted from environmental conditions.

Grassland/herbaceous 71 areas dominated by gramanoid or herbaceous vegetation, generally greater than 80 percent of 

total vegetation. These areas are not subject to intensive management such as tilling, but can be 

utilized for grazing.

Pasture/hay 81 areas of grasses, legumes, or grass-legume mixtures planted for livestock grazing or the production 

of seed or hay crops, typically on a perennial cycle. Pasture/hay vegetation accounts for greater 

than 20 percent of total vegetation.

Cultivated cropland 82 areas used for the production of annual crops, such as corn, soybeans, vegetables, tobacco, and cotton, and also perennial woody crops such as orchards and vineyards. Crop vegetation accounts 

for greater than 20 percent of total vegetation. This class also includes all land being actively 

tilled.

Woody wetlands 90 areas where forest or shrubland vegetation accounts for greater than 20 percent of vegetative cover 

and the soil or substrate is periodically saturated with or covered with water

Herbaceous wetlands 95 areas where perennial herbaceous vegetation accounts for greater than 80 percent of vegetative 

cover and the soil or substrate is periodically saturated with or covered with water
Appendix 1

Table 1–3. Description of soil groups in the Soil Survey Geography (SSURGO) database.

Group Description

A Soils having a high infiltration rate (low runoff potential) when thoroughly wet. These consist mainly of deep, well drained to 

excessively drained sands or gravelly sands. These soils have a high rate of water transmission.

B Soils having a moderate infiltration rate when thoroughly wet. These consist chiefly of moderately deep or deep, moderately 

well drained or well drained soils that have moderately fine texture to moderately coarse texture. These soils have a moderate rate of water transmission.

C Soils having a slow infiltration rate when thoroughly wet. These consist chiefly of soils having a layer that impedes the downward movement of water or soils of moderately fine texture or fine texture. These soils have a slow rate of water transmission.

D Soils having a very slow infiltration rate (high runoff potential) when thoroughly wet. These consist chiefly of clays that have 

a high shrink-swell potential, soils that have a high water table, soils that have a claypan or clay layer at or near the surface, 

and soils that are shallow over nearly impervious material. These soils have a very slow rate of water transmission.

Table 1–4. Description of variables from Aquatic Gap 

Analysis Program (GAP) used in the analysis.

Code Group Landform (texture)

Surficial geology

1 A3 outwash (coarse)

2 B3 ice-contact (coarse)

3 C1 end-moraine (fine)

4 C2 end-moraine (medium)

5 C3 end-moraine (coarse)

6 D1 ground-moraine (fine)

7 D2 ground-moraine (medium)

8 D3 ground-moraine (coarse)

Bedrock geology

Coarse-grained stratified sediment

Till

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Luukkonen and others—Estimation of Monthly Water Yields and Flows for 1951–2012 for the U.S. Great Lakes Basin—Scientific Investigations Report 2014–5192

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20145192