Prepared in cooperation with the Vermont Center for Geographic Information


A Logistic Regression Equation for Estimating the Probability of a 

Stream in Vermont Having Intermittent Flow 

Scientific Investigations Report 2006–5217 

U.S. Department of the Interior 

U.S. Geological Survey 
A Logistic Regression Equation for 

Estimating the Probability of a Stream 

in Vermont Having Intermittent Flow 

By Scott A. Olson and Michael C. Brouillette 

Prepared in cooperation with the 

Vermont Center for Geographic Information 

Scientific Investigations Report 2006–5217 

U.S. Department of the Interior 

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

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

P. Patrick Leahy, Acting Director 

U.S. Geological Survey, Reston, Virginia: 2006 

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Suggested citation:


Olson, S.A., and Brouillette, M.C., 2006, A logistic regression equation for estimating the probability of a stream in 


Vermont having intermittent flow: U.S. Geological Survey Scientific Investigations Report 2006–5217, 15 p.

iii 

Contents 

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


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


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


Site Selection..................................................................................................................................................2


Data Collection...............................................................................................................................................2


Basin Characteristics Database Development.........................................................................................4


Logistic Regression Equation.....................................................................................................................10


Limitations of the Logistic Regression Equation............................................................................13


Application of the Logistic Regression Equation...........................................................................14


Summary and Conclusions.........................................................................................................................14


Selected References...................................................................................................................................15


Figures 

1.	 Map showing location of sites observed for perennial and intermittent streamflow 

in Vermont......................................................................................................................................3


2–4. Graphs showing—


2.	 Distribution of A, drainage areas. B, elevations. C, channel slopes. 


D, waterbody areas. E, ratios of basin relief to basin perimeter. F, areas of 


well- or moderately well-drained soils for intermittent and perennial streams 


observed in Vermont ...........................................................................................................9


3.	 Observed frequency of perennial and intermittent streams by drainage area 


in Vermont ...........................................................................................................................10


4.	 Receiver operating characteristic curve for the logistic regression equation 


for estimating the probability of a stream having intermittent flow in Vermont......13


Tables 

1.	 Streamgages monitored during the data collection and their median and 25th and 


75th percentiles of August daily flows for ensuring field observations occurred 


during normal streamflow magnitudes .....................................................................................5


2.	 Basin characteristics developed for testing in the logistic regression analysis...............6


3.	 Diagnostics for explanatory variables used in the logistic regression equation 


for estimating the probability of a stream in Vermont having intermittent flow...............11


4.	 Classification table depicting accuracy of the logistic regression equation 


predicting the perennial or intermittent status of the stream sites held out of the 


logistic regression analysis for equation verification ..........................................................12


5.	 Classification table for the logistic regression equation for estimating the 


probability of a stream in Vermont having intermittent flow, with a probability 


cutpoint ranging from 0 to 1 ......................................................................................................12


6.	 Estimated covariance matrix for the logistic regression equation ....................................14


7.	 Ranges of the basin characteristics used in the logistic regression equation................14

iv 

Conversion Factors and Datum 

Multiply By To obtain 

Length 

inch (in.) 2.54 centimeter (cm) 

foot (ft) 0.3048 meter (m) 

mile (mi) 1.609 kilometer (km) 

Area 

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate 

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

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

°C=(°F-32)/1.8 

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


(NAVD 88).


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


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

Abstract

A logistic regression equation was developed for 

estimating the probability of a stream flowing intermittently 

at unregulated, rural stream sites in Vermont. These 

determinations can be used for a wide variety of regulatory 

and planning efforts at the Federal, State, regional, county 

and town levels, including such applications as assessing fish 

and wildlife habitats, wetlands classifications, recreational 

opportunities, water-supply potential, waste-assimilation 

capacities, and sediment transport. The equation will be used 

to create a derived product for the Vermont Hydrography 

Dataset having the streamflow characteristic of “intermittent” 

or “perennial.” The Vermont Hydrography Dataset is 

Vermont’s implementation of the National Hydrography 

Dataset and was created at a scale of 1:5,000 based on 

statewide digital orthophotos.

The equation was developed by relating field-verified 

perennial or intermittent status of a stream site during normal 

summer low-streamflow conditions in the summer of 2005 to 

selected basin characteristics of naturally flowing streams in 

Vermont. The database used to develop the equation included 

682 stream sites with drainage areas ranging from 0.05 to 

5.0 square miles. When the 682 sites were observed, 126 

were intermittent (had no flow at the time of the observation) 

and 556 were perennial (had flowing water at the time of 

the observation).

The results of the logistic regression analysis indicate that 

the probability of a stream having intermittent flow in Vermont 

is a function of drainage area, elevation of the site, the ratio 

of basin relief to basin perimeter, and the areal percentage of 

well- and moderately well-drained soils in the basin. Using a 

probability cutpoint (a lower probability indicates the site has 

perennial flow and a higher probability indicates the site has 

intermittent flow) of 0.5, the logistic regression equation correctly predicted the perennial or intermittent status of 116 test 

sites 85 percent of the time.

Introduction

The Vermont Hydrography Dataset (VHD) provides a 

consistent, statewide, local-resolution3 hydrography data layer. 

This data layer has significantly improved spatial resolution 

compared to other currently available datasets, as well as data 

characterization based on the National Hydrography Dataset 

(NHD) (U.S. Geological Survey and U.S. Environmental Protection Agency, 2004) framework. However, the classification 

of the intermittent or perennial character of the streamflow, 

an important NHD attribute, was not conflated from the NHD 

data because it was based on cartographic rather than hydrologic methods of determination.

Headwater streams with small drainage areas commonly 

have annually intermittent flows. In the northeastern United 

States, however, the probability of zero-flow occurrences 

generally decreases as drainage area and basin storage increase 

in a downstream direction. This report, prepared by the U.S. 

Geological Survey (USGS) in cooperation with the Vermont 

Center for Geographic Information (VCGI), presents a logistic 

regression equation for estimating the probability that an 

unregulated, rural stream in Vermont flows intermittently 

during normal summer low-streamflow conditions.

The equation can be applied to a wide variety of 

regulatory and planning efforts at the Federal, State, regional, 

county and town levels, including such applications as 

assessing fish and wildlife habitats, wetlands classifications, 

recreational opportunities, water-supply potential, wasteassimilation capacities, and sediment transport. The equation 

will be used to create a derived product for the Vermont 

Hydrography Dataset having the streamflow characteristic of 

“intermittent” or “perennial” and will be disseminated on the 

VCGI Web site (http://www.vcgi.org).

A Logistic Regression Equation for Estimating the 

Probability of a Stream in Vermont Having 

Intermittent Flow

By Scott A. Olson1 and Michael C. Brouillette2

1

 U.S. Geological Survey.

2

 Vermont Center for Geographic Information.

3

 Local resolution VHD created at a nominal scale of 1:5,000, based on 

statewide digital orthophotos created by the Vermont Mapping Program.
Description of Study Area

Vermont comprises 9,615 mi2 in the northeastern United 

States (fig. 1). Land altitudes range from about 100 ft along 

Lake Champlain in the northwestern part of the State to 

4,393 ft in the north-central part of the State. The higher 

elevations dominate the central part of the State from north to 

south. The climate of Vermont is humid, with average annual 

precipitation ranging from about 35 to 40 in. in the Lake 

Champlain and Connecticut River Valleys to about 50 to 

70 in. in the higher elevations. Average annual temperature is 

about 43°F.

Site Selection

The primary goal of the site-selection process for this 

investigation was to obtain a random sampling of all naturally 

flowing rural stream sites draining less than 5 mi2 that covered 

the ranges of basin characteristics that could be observed in 

Vermont. To maximize the number of sites where observations 

could be made statewide within a limited timeframe, another 

goal of the site-selection process was to choose sites that were 

easily accessible. To satisfy the accessibility criteria, potential 

sites were determined by intersecting the Vermont Enhanced 

9-1-1 Board’s roads coverage (State of Vermont Enhanced 

9-1-1 Board, 2005a) with the Vermont Hydrography Dataset 

one-dimensional drain features. This was an attempt to ensure 

that all sites would be accessible by car. The drainage basin 

upstream of each potential site was delineated, and all sites 

having a drainage area smaller than 0.25 mi2 or larger than 

5 mi2 were eliminated. For safety reasons, sites on interstate 

highways and other high traffic volume roads were eliminated. 

This resulted in 8,900 potential sites for field observation.

The target number of stream sites to be observed was 

600. Simple random selection of 600 sites from the 8,900 

potential sites was considered. Because the potential sites 

were found by intersecting streams and roads, and roads are 

commonly built on valley floors, there was a possibility that 

the mean elevation of 600 randomly selected sites would be 

biased low compared to typical Vermont streams. There was 

also a potential for a bias that most sites would be located in 

densely populated areas. To randomly select 600 sites from the 

8,900 potential sites and reduce the biases in representation of 

basin characteristics that may be present in the potential sites, 

software for stratified random site selection (Scott, 1990) was 

utilized. The software, written in Arc Macro Language (AML) 

(Environmental Systems Research Institute, Inc., 1994), provided an approach for random selection of sites that represented combinations of magnitudes of basin characteristics.

Drainage area, site elevation, mean channel slope, mean 

basinwide annual precipitation, and areal location were the 

basin characteristics used in the stratified random selection 

process. In addition to the selected 600 sites, an alternate for 

each site was also selected by the software should the primary 

site prove inaccessible in the field.

The selected 600 sites were examined for basin features 

that could prevent the stream from flowing naturally. If such 

a feature was found, the alternate site replaced the initially 

selected site. This review resulted in two sites being replaced 

because a dam was identified within its watershed, and five 

sites being replaced because of the urbanization or nonrural 

character of the basin. The decision to replace a site because 

of urbanization was subjective. Basins were identified as 

potentially urbanized on the basis of the number and density 

of emergency site locations identified within its watershed 

using the Emergency 9-1-1 Site Location database (State of 

Vermont Enhanced 9-1-1 Board, 2005b). Sites with more than 

40 emergency site locations within its watershed were considered potentially urbanized. Potentially urbanized basins were 

then reviewed using all available mapping; if any urbanization 

or development that could have an impact on the natural flow 

character of the stream was apparent within a site’s basin, the 

site was replaced by its alternate.

Following data collection in July and August 2005 at the 

600 selected sites, about 90 percent of the sites had flow and 

were considered perennial for the purposes of this project. To 

better represent intermittent streams in the database, additional 

sites were selected that had drainage areas between 0.05 and 

0.25 mi2. Because of the time constraints to complete the field 

observations, simple random selection was used to select 100 

sites from a total of 9,101 available sites found intersecting 

GIS databases of roads and streams that had drainage areas 

between 0.05 and 0.25 mi2.

Data Collection

 An important aspect of the investigation was having the 

appropriate hydrologic and climatic conditions under which 

to observe sites for streamflow conditions. The intent of the 

investigation was to provide a methodology for estimating the 

probability that a stream flows intermittently during normal 

summer low streamflows—a condition that typically occurs 

in August or early September. Therefore, the selected sites 

needed to be observed for streamflow during normal summer low-streamflow conditions occurring from mid- to late 

summer. If hydrologic or climatic conditions were excessively 

wet, a site that typically goes dry and would be classified as 

intermittent could have streamflow at the time of observation 

and be classified as perennial. Conversely, if conditions were 

drier than normal, an observation site could be dry and would 

be classified as intermittent when, under normal hydrologic 

conditions, it is actually a site with perennial streamflow.

Sites were observed on selected dates from July 26 to 

August 26, 2005. Hydrologic and climatologic conditions 

during the data-collection period and the months leading up to 

the observation period were at or near normal. According to 

the Northeast Regional Climate Center (2006), precipitation 

 A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
Figure 1. Location of sites observed for perennial and intermittent streamflow in Vermont.

Data Collection 

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0 5 10 15 20 25 MILES

0 5 10 15 20 25 KILOMETERS

72° 73°

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44°

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Bennington

Windsor

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Washington

Chittenden

Franklin

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Essex

Caledonia

EXPLANATION

Perennial streamflow site

Intermittent streamflow site

New

Hampshire

New

York

Massachusetts

CANADA

Lake

Champlain

Connecticut River

Base from Vermont Mapping Program digital elevation map, 1:5,000, 1994-2000

Universal Transverse Mercator projection, zone 18

Vermont State Plane coordinate system

Vermont

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68

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during the winter, spring, and summer in Vermont in 2005 was 

111, 99, and 103 percent of normal, respectively, based on the 

period of record 1971 to 2000. During July 2005, precipitation 

was 0.18 in. above the normal July precipitation of 4.21 in. for 

the period of record. During August 2005, precipitation was 

0.72 in. below the August normal of 4.49 in. for the period of 

record. The weekly Palmer Drought Severity Indices published 

by the National Weather Service (2006) were between -1.9 and 

1.9 statewide for the entire period of data collection, an index 

range considered normal.

Although Vermont precipitation and drought indices 

were within normal ranges, streamflow conditions for June 

and July 2005 were reported by the USGS (2006a) as being 

predominantly above normal. Streamflows receded, however, 

and in August 2005, streamflow conditions were described 

as normal. Ground-water levels in June and July 2005 were 

predominantly in the normal range with some ground-water 

levels above and some below normal. By August 2005, 

water levels at 10 of the 13 ground-water stations in Vermont 

monitored by the USGS were within normal range, with 

the remaining 3 reported as being below normal. Normal 

streamflow or ground-water-levels are defined by the USGS 

(2006b) as being between the 25th and 75th percentile of 

streamflows or ground-water levels for the given month.

Overall, the statewide hydrologic and climatic conditions 

for the period of data collection—July 26 to August 26, 

2005—can be considered at or near normal. Regardless, the 

climate and hydrologic conditions were monitored on a daily 

basis while making streamflow observations. To ensure that 

conditions were normal in the regions where observations 

were being made, additional criteria were followed when 

collecting data. These criteria included less than 0.4 in. of rain 

within 72 hours of a streamflow observation. Upon further 

review of precipitation data and the data-collection locations, 

no rain greater than 0.1 in. occurred within 24 hours of making 

an observation and no rain greater than 0.2 in. occurred 

within 48 hours of making an observation. Another criterion 

required that streamflows at the nearest or most hydrologically 

similar USGS streamgaging station to the observation site fall 

within the 25th and 75th percentile of August daily flows at 

the time of streamflow observation. Because streamflow data 

graphically reporting the percentiles in real time are available 

(U.S. Geological Survey, 2006c), this streamflow criterion was 

closely monitored. The median and the 25th and 75th percentile 

of August daily flows for gages on streams with little to 

no low-streamflow regulation monitored during the data 

collection are listed in table 1.

As stated above in this report, all observation sites 

were located at road crossings to expedite data collection. 

A global positioning system (GPS) was used to pinpoint the 

site. Streamflow conditions were observed at the upstream 

side and downstream side of the road crossing. A site was 

considered perennial if it had any flowing water at the time of 

observation. Sites that had dry channel beds or disconnected 

pools of water were considered intermittent. If a site had 

pooled water throughout the reach, it was considered to be a 

perennial stream site unless a positive determination could be 

made that water was not flowing.

Several sites could not be reached because a roadway 

was either gated or impassable. Other sites were deemed 

inappropriate as an observation site because of the altered 

condition of the stream, such as a stream site within a golf 

course or a site where an artificial pond had been created 

upstream to store water. When a site was visited that was not 

appropriate or could not be reached, it was replaced by its 

alternate site. In some cases, the alternate sites had similar 

problems and could not be used. When this occurred, both the 

site and its alternate were removed from the database. At the 

end of the data collection effort, streamflow observations at 

682 sites (fig. 1) were used to develop the logistic regression 

equation for estimating the probability that a stream has 

intermittent flow. Of the 682 sites, 126 were classified 

as intermittent and 556 were classified as perennial. The 

distribution of the observation sites is shown in figure 1.

Basin Characteristics Database 

Development

Regression analysis involves developing a relation 

between a response variable and one or more explanatory 

variables. In this investigation, the basin characteristics of a 

stream site were used as the explanatory variables. Fifty basin 

characteristics for the 682 stream sites were determined for 

use in the logistic regression analysis. The basin characteristics 

that were computed and the data sources used to compute the 

basin characteristics are listed in table 2.

Basin delineation and the subsequent characterization 

effort required a Digital Elevation Model (DEM) that was 

spatially compliant with the local resolution VHD dataset. 

Barring the existence of such a dataset at any scale, a 

statewide “hydrologically enforced” DEM tiled by subbasin 

and other supporting derivative raster datasets, such as 

flow accumulation and flow direction, were created. The 

“hydrologically enforced” DEM was created with the ArcInfo 

TOPOGRID command and the following inputs: point 

elevation data from the Vermont Mapping Program digital 

orthophoto program; and one- and two-dimensional VHD 

features, such as stream centerlines and lakes and ponds.

The basin characteristics used in the logistic regression 

analysis were generated using ArcInfo® (v.8.0.2) on a UNIX 

platform and AML programming (Environmental Systems 

Research Institute, Inc., 1994). The basic approach to computing each characteristic revolved around the use of the site as 

a watershed outlet point, and its basin extent to control the 

extent of processing for computing basin characteristics.

Selected basin characteristics of the 682 streamflow 

observation sites were grouped by their intermittent or perennial classification and plotted. The plots in figures 2 and 3 

display the distribution of selected basin characteristics by 

 A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
Table 1. Streamgages monitored during the data collection and their median and 25th and 75th percentiles of August daily flows for 

ensuring field observations occurred during normal streamflow magnitudes.

[Streamgages located in Vermont unless otherwise noted; mi2, square miles; ft3/s, cubic feet per second]

Station 

number Streamgage

Drainage 

area, 

mi2

Median of August 

daily flows, 

ft3/s

25th percentile of 

August daily flows, 

ft3/s

75th percentile of 

August daily flows,

ft3/s

01133000 East Branch Passumpsic River near East Haven 53.8 52.8 33.9 71.9

01134500 Moose River at Victory 75.2 56.3 27 87.1

01135150 Pope Brook near North Danville 3.25 2.6 1.7 3.8

01135300 Sleepers River near St. Johnsbury 42.9 30.4 16.9 56.5

01135500 Passumpsic River at Passumpsic 436 281 211 419

01139000 Wells River at Wells River 98.4 44.6 34 78.7

01139800 East Orange Branch at East Orange 8.95 4.3 2.7 6.6

01142500 Ayers Brook at Randolph 30.5 10 6.5 18.3

01144000 White River at West Hartford 690 264 194 477

01150900 Ottauquechee River near West Bridgewater 23.4 17.8 9.3 37.5

01153550 Williams River near Rockingham 112 38.1 28 63.2

01154000 Saxtons River near Saxtons River 72.2 19.1 11 29.2

01169000 North River at Shattuckville, Massachusetts 89.0 35.1 22.6 63.3

01170100 Green River near Colrain, Massachusetts 41.4 17.6 11.6 37.6

01334000 Walloomsac River near North Bennington 111 79.7 61.9 129

04280350 Mettawee River near Pawlet 70.2 33 21.1 71.7

04282000 Otter Creek at Center Rutland 307 187 138 283

04282525 New Haven River at Brooksville 115 91.8 50.8 140

04282650 Little Otter Creek at Ferrisburg 57.1 11 6.3 25.1

04282795 Lewis Creek near North Ferrisburg 77.2 31.2 15.9 39

04282795 LaPlatte River at Shelburne Falls 44.6 7.5 2.9 16.9

04287000 Dog River at Northfield Falls 76.1 25.9 17.5 40.9

04288000 Mad River near Moretown 139 67.1 45.8 112.5

04292000 Lamoille River at Johnson 310 203 154 292

04293000 Missisquoi River near North Troy 131 82.7 54.1 162.2

04293500 Missisquoi River near East Berkshire 479 268 171 440

04294300 Pike River at East Franklin 34.5 11.5 6.2 81.4

04296000 Black River at Coventry 122 70.2 45.5 112

stream classification. Some interesting information can be 

determined from looking at the plots. For instance, figure 2 

shows that the largest drainage area of an intermittent stream 

in this investigation is about 3.4 mi2. It also shows the median 

drainage area, site elevation, and area of well- or moderately 

well-drained soils are different between perennial and intermittent stream sites. In figure 3, the frequency of intermittent 

sites consistently decreases from a drainage area of 0.05 mi2

(the minimum drainage area used in this investigation) to a 

point where there are very few intermittent sites at 1.0 mi2

and greater. Also, the number of intermittent and perennial 

sites with drainage areas between 0.05 and 0.25 mi2 are nearly 

equal—above 0.25 mi2, the number of perennial stream sites 

greatly outnumbers the intermittent stream sites (fig. 3).

Basin Characteristics Database Development   
Table 2. Basin characteristics developed for testing in the logistic regression analysis.

[OFR, Open-File Report; PRISM, Parameter-elevation Regressions on Independent Slopes Model; SSURGO, Soil Survey Geographic Database; USGS, U.S. Geological Survey; UVM, University of Vermont; VCGI, Vermont Center for Geographic Information; VT, Vermont; --, not applicable]

Characteristic description Units Source Minimum Mean Maximum

Compactness ratio1 dimensionless Digital Elevation Model10 1.3 1.7 2.6

Relative relief2 feet/foot Digital Elevation Model10 0.00150 0.0313 0.111Basin azimuth3 degrees from north Digital Elevation Model10 1.0 180.9 360.0

Basin length (basin centerline from divide to basin outlet) feet Digital Elevation Model10 1,235.0 7,122.9 22,226.0Percent of basin above 1,200 feet areal percentage Digital Elevation Model10 0 56 100

Percent of basin above 1,500 feet areal percentage Digital Elevation Model10 0 35 100

Percent of basin above 1,800 feet areal percentage Digital Elevation Model10 0 16 100Mean basin slope feet/foot Digital Elevation Model10 1.5 16.3 44.1

Percent of basin having greater than 10 degree slope areal percentage Digital Elevation Model10 .1 64.7 99.1Percent of basin having greater than 15 degree slope areal percentage Digital Elevation Model10 .0 45.1 96.6

Stateplane x-coordinate of basin centroid meters Digital Elevation Model10 428,525 487,553 576,115

Stateplane y-coordinate of basin centroid meters Digital Elevation Model10 28,375 172,572 278,365Land cover characteristics - Agricultural areal percentage 2002 Land Use/Land Cover Dataset11 .0 15.3 94.1

Land cover characteristics - Barren land areal percentage 2002 Land Use/Land Cover Dataset11 .0 .1 13.8Land cover characteristics - Forested areal percentage 2002 Land Use/Land Cover Dataset11 .0 71.2 99.5

Land use characteristics - Industrial areal percentage 2002 Land Use/Land Cover Dataset11 .0 3.3 75.8

Land use characteristics - Residential areal percentage 2002 Land Use/Land Cover Dataset11 .0 4.2 54.8Mean annual precipitation inches PRISM Precipitation Data12 32 45 73

Mean August precipitation inches PRISM Precipitation Data12 3.6 4.6 7.5

Mean July precipitation inches PRISM Precipitation Data12 3.3 4.3 7.0Mean September precipitation inches PRISM Precipitation Data12 3.29 4.06 7.02

Mean basin elevation feet Digital Elevation Model10 107 1,281 2,937Main channel length feet Vermont Hydrography Dataset13 587 2,993 9,763

Main channel slope percent rise Digital Elevation Model10 .1 4.2 22.0

Elevation of observation point feet Digital Elevation Model10 91 934 2,340Relief4 feet Digital Elevation Model10 39 808 2,938

Basinwide mean annual runoff inches USGS OFR 96-39514 9.80 22.44 39.00Surficial geology: grouping A5 areal percentage VCGI In-House Dataset15 .0 2.73 84.20

Surficial geology: grouping B6 areal percentage VCGI In-House Dataset15 .0 3.46 99.60

Surficial geology: grouping A and B5,6 areal percentage VCGI In-House Dataset15 .0 6.19 99.60

 A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
Table 2. Basin characteristics developed for testing in the logistic regression analysis.—Continued

[OFR, Open-File Report; PRISM, Parameter-elevation Regressions on Independent Slopes Model; SSURGO, Soil Survey Geographic; USGS, United State Geological Survey; UVM, University of Vermont; VCGI, Vermont Center for Geographic Information; VT, Vermont; --, not applicable]

Characteristic description Units Source Minimum Mean Maximum

Number of first order streams count Vermont Hydrography Dataset13 1 4.11 77Stream order at observation point stream order Vermont Hydrography Dataset13 1 1.92 5

Total length of first order streams miles Vermont Hydrography Dataset13 0.0 1.7 14.3

Total length of second order streams miles Vermont Hydrography Dataset13 .0 0.7 8.1Total length of third order streams miles Vermont Hydrography Dataset13 .0 .2 4.0

Soil characteristics - drainage; excessive7 areal percentage SSURGO16 .0 17.3 99.3Soil characteristics - drainage; poor8 areal percentage SSURGO16 .0 14.9 95.5

Soil characteristics - drainage; well9 areal percentage SSURGO16 .0 53.4 99.9

Soil characteristics - infiltration - hydrologic group A areal percentage SSURGO16 .0 4.7 95.7Soil characteristics - Infiltration - hydrologic group B areal percentage SSURGO16 .0 12.9 85.0

Soil characteristics - Infiltration - hydrologic group C areal percentage SSURGO16 .0 43 100

Soil characteristics - Infiltration - hydrologic group D areal percentage SSURGO16 .0 28.2 99.3Soil characteristics - hydraulic conductivity - permeability inches/hour SSURGO16 .0 121.8 999.0

Total length of streams feet Vermont Hydrography Dataset13 64 14,162 152,876Drainage area square miles Digital Elevation Model10 .05 .959 4.99

Geologic-biophysical province province UVM-VT Biodiversity Project17 -- -- --

Waterbody area (lake and ponds) areal percentage Vermont Hydrography Dataset13 .0 .4 16.3Wetland area - lacustrine areal percentage National Wetlands Inventory18 .0 .1 12.0

Wetland area - palustrine areal percentage National Wetlands Inventory18 .0 2.3 37.4Wetland area - lacustrine and palustrine areal percentage National Wetlands Inventory18 .0 2.4 37.4

Basin Characteristics Database Development   
Table 2. Basin characteristics developed for testing in the logistic regression analysis.—Continued

[OFR, Open-File Report; PRISM, Parameter-elevation Regressions on Independent Slopes Model; SSURGO, Soil Survey Geographic; USGS, United State Geological Survey; UVM, University of Vermont; VCGI, Vermont Center for Geographic Information; VT, Vermont; --, not applicable]

1 Ratio of the perimeter of the basin to the perimeter of a circle having the area of the basin.2 Ratio of basin relief to basin perimeter.3 Line from point where main channel, when extended, intersects basin divide to the basin outlet.4 Maximum basin elevation minus the minimum basin elevation.5 Group A consists of beach gravel, delta gravel, delta sand, eolian sand, esker, fluvial, gravel, kame, kame terrace, kame moraine, lake gravel and outwash.6 Group B consists of fluvial sand, lake sand, lake sand veneered with fluvial sand, moraine, pebbly sand, recent alluvium, and terminal moraine.7 Excessive includes soils grouped in SSURGO as excessively and somewhat excessively well drained.8 Poor includes soils grouped in SSURGO as somewhat poorly and poorly drained.9 Well includes soils grouped in SSURGO as well and moderately well drained.10 Vermont Department of Taxes, Vermont Mapping Program (2001).11 University of Vermont Spatial Analysis Lab (2002).12 Daly (2000).13 Vermont Center for Geographic Information, Inc. (2004).14 Randall (1996).15 M.C. Brouilette,Vermont Center for Geographic Information, written commun., 2005.16 U.S. Department of Agriculture, National Resource Conservation Service (2005).17 Capen (1998).18 U.S. Fish and Wildlife Service (2003).

 A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
Figure 2. Distribution of A, drainage areas. B, elevations. C, channel slopes. D, waterbody areas. E, ratios of basin relief 

to basin perimeter. F, areas of well- or moderately well-drained soils for intermittent and perennial streams observed in 

Vermont.

Basin Characteristics Database Development 

EXPLANATION

(126) Number of observations

 1.5 times the interquartile range above 

 the 75th percentile or largest value

 75th percentile

 Mean 

 Median (50th percentile)

 25th percentile

 1.5 times the interquartile range below

 the 25th percentile or smallest value

 Outlier values between 1.5 and 3 times 

 the interquartile range outside the 

 quartiles

 Outlier values greater than 3 times the 

 interquartile range outside the quartiles

PERENNIAL INTERMITTENT

STREAM TYPE

A

0

1

2

3

4

5

DRAINAGE AREA, IN SQUARE MILES

(556) (126)

0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

2,500

PERENNIAL INTERMITTENT

STREAM TYPE

SITE ELEVATION, IN FEET

(556) (126)

B

0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

PERENNIAL INTERMITTENT

STREAM TYPE

CHANNEL SLOPE, IN PERCENT RISE

(556) (126)

C

PERENNIAL INTERMITTENT

STREAM TYPE

F

0

20

40

60

80

100

AREA OF WELL- OR MODERATELY WELL-DRAINED

SOILS, IN PERCENT OF DRAINAGE AREA

(556) (126)

0

2

4

6

8

10

12

14

16

18

PERENNIAL INTERMITTENT

STREAM TYPE

WATERBODY AREA, IN

PERCENT OF DRAINAGE AREA

(556) (126)

D

0

0.02

PERENNIAL INTERMITTENT

STREAM TYPE

RATIO OF BASIN RELIEF TO BASIN PERIMETER

(556) (126)

E

0.04

0.06

0.08

0.10

0.12
Logistic Regression Equation

Regression has been used in many water-resource 

investigations that examine the relation between a waterresource characteristic and one or more characteristics of its 

watershed or environment. The variables used to develop the 

regression equations are commonly continuous variables, and 

a least-squares or linear regression model is developed. In 

this investigation, the response variable being modeled is not 

continuous. The response variable is discrete—it is either a 

“1” for intermittent, or “0” for perennial. Logistic regression 

is the standard method of analysis when working with 

discrete response variables (Hosmer and Lemeshow, 2000). 

The logistic regression equation that is developed estimates 

the probability that the response variable is a “1” or that the 

stream is intermittent. Other investigations have used logistic 

regression to predict the intermittent or perennial classification 

of a stream site; most notable is a study by Bent and Archfield 

(2002) for the State of Massachusetts.

Before the logistic regression analysis began, 20 percent 

of the observations sites were randomly removed from the 

dataset and not used in the analysis for testing the predictive 

accuracy of the final logistic regression equation. This resulted 

in a database of 546 sites used to complete the regression 

analysis. All potential explanatory variables—including the 

basin characteristics (table 2), and the logarithms, squares, and 

square roots of the basin characteristics—for the stream observations sites were tested using SAS statistical software (SAS 

Institute, Inc., 1989). The explanatory variables were evaluated 

using forward selection, backward elimination, stepwise selection, and best subsets selection techniques to determine the 

most significant explanatory variables for intermittent flow.

The following tools and techniques were also used for 

selecting the final variables to use in the logistics regression 

equation. Logit plots and partial residual plots (SAS Institute, 

Inc., 2001) were created for variables. Logit plots reveal 

whether or not there is a linear relation between the predictor 

variable and the response variable and will indicate if the 

predictor variable needs to be treated as a discrete variable. 

Partial residual plots indicate whether or not there is a linear 

relation between the predictor variable and the response 

variable and show what kind of transformation the variable 

may need, such as a logarithmic transformation, to get the 

predictor variable and response variable to have a linear 

relation. Index plots (SAS Institute, Inc., 2001) were created 

to identify influential observations and outliers in the datasets, 

and p-values were used to select the final variables for the 

equation. P-values indicate the significance of predictor 

variables in predicting the response variable. A p-value of 

about 0.01 indicates a positive significance; a p-value of about 

0.001 indicates a strong significance; and a p-value of 0.0001 

or less indicates a very strong significance (SAS Institute, Inc., 

2001) when sample sizes are similar to the sample size found 

in this study.

During the final explanatory variable selection process, 

the soil characteristics data from the Soil Survey Geographic 

(SSURGO) database (U.S. Department of Agriculture, 2005) 

were determined to be significant in predicting the probability 

that a stream has intermittent flow. As of the fall of 2005, however, the SSURGO was not yet available in Caledonia or Essex 

Counties—an area covering about 14 percent of the State. 

Because the SSURGO data could improve the logistic regression equations, stream sites without SSURGO data available 

were removed from the regression analysis. This left 492 

stream sites available to develop the final regression equation.

The Geologic-Biophysical Regions dataset, which divides 

Vermont into eight subregions on the basis of bedrock geology, gross physiography, climate, and broad-scale patterns 

of potential natural vegetation (Capen, 1998), was used to 

categorize sites into regions. Tests of regionalizing the sites 

based on this dataset indicated that a location variable such as 

this does have the potential to improve the predictive accuracy 

of the equation. But this dataset, and others that could be used 

for regionalization of sites, have not been developed at a scale 

and level of detail that was appropriate for this investigation.

The final four basin characteristics that were found to 

be significant in estimating the probability that a stream has 

intermittent flow were (1) drainage area; (2) elevation of the 

site; (3) percentage of the basin with soils classified as well- or 

moderately well-drained soils in the SSURGO database; and 

(4) the relative relief, which is a measure of basin slope. A 

logistic regression equation was created with the final four 

explanatory variables using SAS statistical software as follows:

 

p exp log A

log E log S

= + − + +

+

( ) ( )

( ) ( )

1 1 5 30 1 98

2 38 0 525

10

10 10

/ . .

. .

{ [

( ) ( ) + − 1 165( ) 2

R ]}, (1)

Figure 3. Observed frequency of perennial and intermittent 

streams by drainage area in Vermont. OBSERVED FREQUENCY

DRAINAGE AREA, IN SQUARE MILES

0

20

40

60

80

100

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Perennial stream

Intermittent stream

10 A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
where

p is the probability that a stream has intermittent 

flow;

A is the drainage area, in square miles;

E is the site elevation, in feet;

S is the percentage of the basin with soils 

classified as well- or moderately welldrained soils in the SSURGO database;

and

R is the relative relief, unitless (ratio of 

maximum relief to basin perimeter).

Diagnostics of the parameters used in this regression 

equation are presented in table 3. The p-values—ranging 

from less than 0.0001 to 0.018—indicate that all four of the 

explanatory variables are significant in predicting the response 

variable. The Variance Inflation Factors (VIF)—ranging from 

1.00 to 1.18—indicate how many times greater the variance 

of the variable would be in the absence of collinearity. A VIF 

near 1.0 would indicate no collinearity (Allison, 2000).

The predictive accuracy of equation 1 was tested using 

116 of the 136 sites randomly left out of the database for equation verification purposes. Not all 136 sites could be used for 

testing because 20 sites were in Essex or Caledonia Counties, 

which did not have the SSURGO soils data available. A probability cutpoint of 0.5 was used in this test. Therefore, if the 

probability, p, estimated by the logistic regression equation 

was greater than or equal to 0.5, the stream was predicted to 

have intermittent flow. If the probability, p, was less than 0.5, 

the stream was predicted to have perennial flow. The incorrect 

and correct responses from the regression equations are listed 

in the classification table (table 4). Using the results shown 

in this table, the sensitivity [ratio of the number of streams 

correctly predicted to be intermittent (8) to the total number of 

intermittent streams (23)] was 34.8 percent and the specificity 

[ratio of the number of streams correctly predicted to be 

perennial (91) to the total number of perennial streams (93)] 

was 97.8 percent. Overall, the equation correctly predicted 

the perennial or intermittent characteristic of the test sites 

85.3 percent of the time.

A classification table (table 5) was also computed using 

SAS statistical software with probability cutpoints ranging 

from 0 to 1, using the sites that were used in developing the 

logistic regression equation. As shown in table 5, the sensitivity and the specificity of the logistic regression equation at a 

cutpoint of 0.50 is 28.3 and 95.7 percent, respectively. The 

table also shows that sensitivity and specificity can be optimized between a cutpoint of 0.15 and 0.20. In fact, sensitivity 

equals specificity at a cutpoint of approximately 0.19. At this 

cutpoint, there is a balance between the percentage of sites 

correctly predicted to be perennial or intermittent. There is 

a trade-off using 0.19 as the probability cutpoint; however, 

increasing the percentage of correct intermittent classification 

by lowering the cutpoint to 0.19 from 0.50 decreases the 

percentage of correct perennial stream predictions. The percentage of total correct responses, perennial and intermittent, 

at a cutpoint of 0.50 was more than 10 percent greater than at 

a cutpoint of 0.19 and, thus, 0.50 is the optimal cutpoint.

According to table 5, there is a slight (0.4 percent) 

improvement in the total number of correct predictions at 

a cutpoint of 0.55. However, using the sites held out of the 

logistic regression analysis for equation verification—the 

same sites represented in table 4—the percentage of correct 

predictions decreases from 85.3 to 83.6 percent when the 

cutpoint is increased from 0.50 to 0.55. Therefore, increasing 

the cutpoint to 0.55 is not recommended.

The data in the classification table shown in table 5 were 

used to develop a receiver operating characteristic (ROC) 

curve (fig. 4). This curve graphically depicts the predictive 

accuracy of the logistic regression equation. For a logistic 

model with high predictive accuracy, the ROC curve raises 

quickly and has a larger area under the ROC curve (SAS 

Institute, Inc. 2001). Hosmer and Lemeshow (2000) suggest 

that if the area under the ROC curve is between 0.8 and 0.9, 

the model has excellent discrimination; if the area under 

the curve is between 0.7 and 0.8, the model has acceptable 

discrimination; and if the area under the curve is 0.5, the 

model has no discrimination and is no better than flipping a 

coin. The area under the ROC curve computed for the logistic 

regression equation 1 is 0.79.

Table 3. Diagnostics for explanatory variables used in the logistic regression equation for estimating the probability of a stream in 

Vermont having intermittent flow.

[SAS Institute, Inc., 1989; --, not applicable; log10, base 10 logarithm]

Explanatory variable Parameter 

estimate

95-percent confidence limits for parameter estimates p-valueVariance 

inflation factor

Intercept 5.30 2.89 7.71 <0.0001 --

Log10 (drainage area) -1.98 -2.61 -1.35 <.0001 1.03

Log10 (site elevation) -2.38 -3.22 -1.54 <.0001 1.18

Log10 (areal percent well- or moderately well-drained soils+1) -0.524 -.951 -0.0983 .016 1.00

Relative relief2 165 28.3 302 .018 1.18

2

, Relative relief squared.

Logistic Regression Equation 11
Table 5. Classification table for the logistic regression equation for estimating the probability of a stream in Vermont having 

intermittent flow, with a probability cutpoint ranging from 0 to 1.

[SAS Institute, Inc. (1989); Cutpoint is the probability level that could be used to classify the stream as intermittent or perennial. Sensitivity is the ratio of 

correctly classified intermittent streams to the observed number of intermittent streams. Specificity is the ratio of correctly classified perennial streams to the 

observed number of perennials streams. False positive is the ratio of sites incorrectly predicted to be intermittent to all sites predicted to be intermittent. False 

negative is the ratio of sites incorrectly predicted to be perennial to all sites predicted to be perennial]

Cutpoint

Total correct Total incorrect Percent

Intermittent Perennial Intermittent Perennial Correct Sensitivity Specificity False 

positive

False 

negative

0.00 99 0 393 0 20.1 100 0.0 79.9 0.0

0.05 95 77 316 4 35.0 96.0 19.6 76.9 4.9

0.10 87 171 222 12 52.4 87.9 43.5 71.8 6.6

0.15 79 248 145 20 66.5 79.8 63.1 64.7 7.5

0.20 67 286 107 32 71.7 67.7 72.8 61.5 10.1

0.25 61 321 72 38 77.6 61.6 81.7 54.1 10.6

0.30 55 331 62 44 78.5 55.6 84.2 53.0 11.7

0.35 42 348 45 57 79.3 42.4 88.5 51.7 14.1

0.40 34 358 35 65 79.7 34.3 91.1 50.7 15.4

0.45 32 370 23 67 81.7 32.3 94.1 41.8 15.3

0.50 28 376 17 71 82.1 28.3 95.7 37.8 15.9

0.55 24 382 11 75 82.5 24.2 97.2 31.4 16.4

0.60 17 385 8 82 81.7 17.2 98.0 32.0 17.6

0.65 13 386 7 86 81.1 13.1 98.2 35.0 18.2

0.70 8 389 4 91 80.7 8.1 99.0 33.3 19.0

0.75 6 391 2 93 80.7 6.1 99.5 25.0 19.2

0.80 2 393 0 97 80.3 2.0 100 0.0 19.8

0.85 1 393 0 98 80.1 1.0 100 0.0 20

0.90 0 393 0 99 79.9 0.0 100 0.0 20.1

0.95 0 393 0 99 79.9 0.0 100 0.0 20.1

1.00 0 393 0 99 79.9 0.0 100 0.0 20.1

Table 4. Classification table depicting accuracy of the logistic regression equation 

predicting the perennial or intermittent status of the stream sites held out of the logistic 

regression analysis for equation verification.

Predicted intermittent 

stream

Predicted perennial 

stream Total

Observed intermittent stream 8 15 23

Observed perennial stream 2 91 93

Total 10 106 116

12  A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
 The lower and upper confidence limits of the predicted 

probability of intermittent flow are dependent on the basin 

characteristics input into the equation and can be computed by 

the following equations (SAS Institute, Inc., 1989):

 

P exp log A log E

log

l = + 1 1 − + 5 30 1 98 ( ) ( ) + 2 38( ) ( ) +

0 525

10 10

10

/ . . .

.

{ [

( ) ( ) S + − 1 165( ) R + z SE 2

 / 2 ]}, (2)

and

 

P exp log A log E

log

u = + 1 1 − + 5 30 1 98( ) ( ) + 2 38( ) ( ) +

0 525

10 10

10

/ . . .

.

{ [

( ) ( ) S + − 1 165( ) R − z SE 2

 / 2 ]}, (3)

where

	 Pl is the lower confidence limit of the predicted 

probability;

	 Pu is the upper confidence limit of the predicted 

probability;

	 A is the drainage area, in square miles;

	 E is the site elevation, in feet;

	 S is the percentage of the basin with soils 

classified as well- or moderately welldrained soils in the SSURGO database;

	 R is the relative relief, unitless (ratio of 

maximum relief to basin perimeter);

zα/2 is the percentile point of a standard normal 

distribution at alpha level α (α=0.10 for a 

90-percent prediction interval); 

and

	 SE is the standard error of prediction and can be 

computed as

SE xV x i b i = 

 

′ 1 2/

, (4)

where

xi is a row vector containing a 1, log10(A), 

log10(E), log10(S+1), and R2;

Vb is the estimated covariance matrix of the 

parameter estimates, as shown in table 6; 

and

xi' is the transpose of the xi matrix.

Limitations of the Logistic Regression Equation

The logistic regression equation 1 in this report is 

applicable only to sites on unregulated, naturally flowing 

streams in rural Vermont drainage basins. It cannot be applied 

to streams that have a drainage basin in which there are 

surface-water withdrawals, diversions, or flow augmentation. 

Users of the logistic regression equation also must be aware of 

substantial ground-water withdrawals in a drainage basin and 

evaluate the effect of such withdrawals on streamflow before 

applying the equation. Use of the equation should be limited 

to sites with basin characteristics that are within the range of 

explanatory variables used in the development of the equation. 

The ranges of the basin characteristics used in the analysis are 

shown in table 7. If explanatory variables used in the logistic 

regression equation are outside of the ranges shown in the 

table, the probability prediction is an extrapolation and the 

result could be unreliable. Furthermore, the confidence limits 

of the predicted probability cannot be defined if the probability 

prediction is an extrapolation.

Basin characteristics used to develop the logistic regression equation 1 were determined with a Geographic Information System (GIS) using specific databases as described earlier 

in this report. Determining basin characteristics for use in the 

regression equation with alternative data sources or methods 

could introduce bias and thus produce erroneous results. This 

limitation prevents the use of the logistic regression equation 

at sites in Essex and Caledonia Counties as the SSURGO 

database currently does not include these two counties. In the 

future, if the SSURGO data for these two counties become 

available, the applicability of the equation should be tested, 

because it was developed with sites that had SSURGO data 

outside of those counties.

The observations of streamflow were completed in a 

short time frame (20 non-consecutive days) during the summer 

of 2005. Although overall hydrologic conditions in Vermont 

were considered to be normal summer conditions, accurately 

quantifying normal streamflow at each stream observation site 

was outside of the scope of this study.

Figure 4. Receiver operating characteristic curve for the 

logistic regression equation for estimating the probability of a 

stream having intermittent flow in Vermont.

1 – SPECIFICITY

SENSITIVITY

0

0 0.2 0.4 0.6 0.8 1.0

1.0

0.8

0.6

0.4

0.2

Logistic Regression Equation 13
Application of the Logistic Regression Equation

An example application of the logistic regression 

equation for estimating the probability of a site having 

intermittent flow is provided using a site that has a drainage 

area of 0.25 mi2 and a site elevation of 948 ft. The percentage 

of the basin with well- or moderately well-drained soils is 

9.6 percent and the ratio of the basin relief (1,037 ft) to basin 

perimeter (15,880 ft) is 0.0653 ft/ft. Equation 1 is solved for 

this site as follows:

p exp log log

l

= + 1 1 − + 5 30 1 98( ) ( ) 0 25 2 + 38( ) ( ) 948 +

0 525

10 10 / . . . .

.

{ [

og10

2

( ) ( ) 9 6. + − 1 165( ) 0.0653 ]},

The resulting probability, p, that this stream site has 

intermittent flow is 0.39. This probability is less than the 0.5 

cutpoint probability; therefore, the site would be classified as a 

perennial streamflow site.

To determine the lower and upper confidence limits for 

the probability, the standard error, SE, must be computed using 

equation 4. To solve equation 4, the xi vector for this site,

x log log log i = [1 0( ) 25 ( ) 948 ( ) 9 6 +1 0 0653 ], 10 10 10

2

, . , , . , .

and the covariance matrix, Vb, shown in table 4, is needed. 

Solving the matrix multiplication of equation 4 results in a 

value of 0.0578 so that the standard error can be computed 

by SE=(0.0578)0.5. Thus, the standard error, SE, is 0.240 and 

equations 2 and 3 reduce to 1/{1+exp[0.427 ± zα/20.240]}. If 

the 90-percent confidence interval is desired, then α=1-0.9 and

zα/2, determined from a standard normal distribution, is 1.6449. 

Therefore, the lower and upper 90-percent confidence limits 

for this site are 0.305 and 0.492, respectively.

Summary and Conclusions

A logistic regression equation for estimating the 

probability that an unregulated, rural stream in Vermont 

has intermittent flow was developed by the U.S. Geological 

Survey, in cooperation with the Vermont Center for 

Geographic Information. The database used to develop the 

logistic regression equation consisted of 492 streamflow 

observations completed at 682 sites in July and August of 

2005 during normal summertime hydrologic conditions 

and the basin characteristics of each site. The final logistic 

regression equation incorporates drainage area, elevation 

of the observation site, percentage of the basin containing 

well- and moderately well-drained soils, and relative relief 

(the ratio of the maximum relief of the basin to its perimeter) 

as explanatory variables. The equation correctly predicted 

the perennial or intermittent classification of the stream 

site 85 percent of the time at a 0.50 cutpoint. The cutpoint 

is the probability level used to classify the stream as either 

intermittent or perennial.

Table 6. Estimated covariance matrix for the logistic regression equation.

Intercept Drainage area Site elevation Areal percent well- or 

moderately well-drained soils +1 Relative relief

Intercept 1.513714 0.009184 -0.50145 -0.08015 23.59203

Drainage area 0.009184 .103271 .011219 -.00139 2.460786

Site elevation -.50145 .011219 .185337 .002103 -10.9912

Areal percent well- or moderately 

well-drained soils +1 -.08015 -.00139 .002103 .047288 0.364138

Relative relief 23.59203 2.460786 -10.9912 .364138 4,861.633

Table 7. Ranges of the basin characteristics used in the logistic regression equation.

Basin characteristic Minimum Mean Maximum

Drainage area, in square miles 0.05 0.959 4.99

Site elevation, in feet 91 934 2,340

Areal percent well- or moderately well-drained soils .0 53.4 99.9

Relative relief, unitless .00150 .0313 .111

14  A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow
The logistic regression equation is applicable to sites on 

unregulated, naturally flowing streams in rural Vermont drainage basins. It does not apply to streams that have a drainage 

basin in which there are surface-water withdrawals, diversions, 

or flow augmentation. Users of the logistic regression equation 

also must be aware of ground-water withdrawals in a drainage 

basin and determine if the withdrawals could affect streamflow 

before applying the equation. Because the SSURGO soils 

database did not include Essex and Caledonia Counties at 

the time of this investigation, the applicability of the logistic 

regression equation in those counties will need to be evaluated 

as the data become available.

Selected References

Allison, P.D., 2000, Logistic regression using the SAS system, 

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Selected References 15
Prepared by Publications Service Center 1 

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

Keith W. Robinson, Director 

U.S. Geological Survey 

New Hampshire-Vermont Water Science Center 

361 Commerce Way 

Pembroke, NH 03275 

or visit our Web site at: 

http://nh.water.usgs.gov 
Olson, S.A. and Brouillette, M.C.—A Logistic Regression Equation for Estimating the Probability of a Stream in Vermont Having Intermittent Flow— 

USGS Scientific Investigations Report 2006–5217