Prepared in cooperation with the Vermont Department of Environmental Conservation

Concentration, Flux, and the Analysis of Trends of Total and 

Dissolved Phosphorus, Total Nitrogen, and Chloride in 

18 Tributaries to Lake Champlain, Vermont and New York, 

1990–2011

Scientific Investigations Report 2013–5021

U.S. Department of the Interior

U.S. Geological Survey
Cover. Aerial photograph of Otter Creek outlet into Lake Champlain, western Vermont. Photograph by the U.S. Department of Agriculture, 

Farm Service Agency.
Concentration, Flux, and the Analysis of 

Trends of Total and Dissolved Phosphorus, 

Total Nitrogen, and Chloride in 18 Tributaries 

to Lake Champlain, Vermont and New York, 

1990–2011

By Laura Medalie

Prepared in cooperation with the 

Vermont Department of Environmental Conservation

Scientific Investigations Report 2013–5021

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

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

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Suggested citation:

Medalie, Laura, 2013, Concentration, flux, and the analysis of trends of total and dissolved phosphorus, total nitrogen, 

and chloride in 18 tributaries to Lake Champlain, Vermont and New York, 1990–2011: U.S. Geological Survey Scientific Investigations Report 2013–5021, 29 p., http://pubs.usgs.gov/sir/2013/5021/.
iii

Contents

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

Introduction.....................................................................................................................................................2

Study Methods ...............................................................................................................................................3

Assembling and Modifying Data ........................................................................................................3

Estimating Annual Average Concentration, Annual Flux, and Trends .........................................5

Determining the Relation Between Trends and Basin Characteristics.......................................7

Calculating Flux Bias............................................................................................................................7

Annual Average Concentration, Annual Flux, and Trends ......................................................................7

Total Phosphorus ................................................................................................................................14

Dissolved Phosphorus........................................................................................................................14

Total Nitrogen ......................................................................................................................................15

Chloride.................................................................................................................................................15

Discussion of Trends ...................................................................................................................................15

Is Progress Being Made in Reducing Phosphorus? .....................................................................16

Influence of Season and Discharge on Changes in Total Phosphorus......................................16

Ratios of Dissolved to Total Phosphorus Concentration and Flux ..............................................18

Trends in Total Nitrogen.....................................................................................................................18

Trends in Chloride ...............................................................................................................................18

Relating Trends in Total Phosphorus to Basin Characteristics............................................................20

Physical and Demographic Factors.................................................................................................20

Point Sources of Phosphorus ...........................................................................................................20

Land Use and Agricultural Statistics...............................................................................................20

Best-Management Practices ...........................................................................................................24

Summary and Conclusions.........................................................................................................................24

References Cited..........................................................................................................................................25

Appendixes 1–8............................................................................................................................................29
iv

Figures

1. Map showing Lake Champlain Basin, physiographic provinces, water-quality

monitoring stations, tributary boundaries, and parts of tributaries that include only

the 12-digit hydrologic unit closest to the monitoring station...............................................4

2. Graphs showing annual percent changes in flow-normalized concentrations of total

phosphorus, dissolved phosphorus, total nitrogen, and chloride between 1990 and

2000 and between 2000 and 2010 .............................................................................................12

3. Graphs showing annual percent changes in flow-normalized fluxes of total

phosphorus, dissolved phosphorus, total nitrogen, and chloride between 1990 and

2000 and between 2000 and 2010 .............................................................................................13

4. Contour plots of the seasonal differences in estimated total phosphorus concentrations between 1994 and 2010 in the A, Saranac River, B, Mettawee River, C, Otter

Creek, and D, Missisquoi River.................................................................................................17

5. Graphs showing patterns of the ratio of A, concentration and B, flux of flownormalized dissolved phosphorus to flow-normalized total phosphorus for

tributaries to Lake Champlain, from 1990 through 2011........................................................19

6. Bar graph showing aggregate reported point-source fluxes of total phosphorus for

the 18 monitored Lake Champlain tributaries in 1991, 2000, and 2011 ...............................23

7. Graph showing the relation between changes in flux of total phosphorus from

point sources and in dissolved phosphorus from Lake Champlain tributaries from

1991 to 2011..................................................................................................................................23

Tables

1. Sources of data for basin characteristics that were tested for correlation with

concentration and flux of total phosphorus for tributaries to Lake Champlain..................5

2. Flux bias statistic comparing WRTDS regression model estimates with observed

water-quality observations for total phosphorus, dissolved phosphorus, total

nitrogen, and chloride for tributaries to Lake Champlain ......................................................7

3. Net change in flow-normalized concentrations of total phosphorus, dissolved

phosphorus, total nitrogen, and chloride in the monitored Lake Champlain tributaries

for three time periods...................................................................................................................8

4. Net change in flow-normalized fluxes of total phosphorus, dissolved phosphorus,

total nitrogen, and chloride in the monitored Lake Champlain tributaries for three

time periods .................................................................................................................................10

5. Basin characteristics that were tested for correlation with total phosphorus

concentration and flux, and correlation test results for tributaries to

Lake Champlain...........................................................................................................................21
v

Conversion Factors, Datum, and Abbreviations

Inch/Pound to SI

Multiply By To obtain

Length

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2)

Volume

cubic foot (ft3

) 0.02832 cubic meter (m3)

Flow rate

cubic foot per second (ft3

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

cubic foot per second per square mile 

[(ft3

/s)/mi2]

0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

cubic foot per day (ft3

/d) 0.02832 cubic meter per day (m3/d)

Mass

ton, short (2,000 lb) 0.9072 megagram (Mg)

short ton per day per square mile 

[(ton/d)/mi2

]

0.3503 megagram per day per square 

kilometer [(Mg/d)/km2]

short ton per year (ton/yr) 0.9072 metric ton per year

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).

Concentrations of chemical constituents in water are given in milligrams per liter (mg/L).

Abbreviations

BMP best-management practice

CSUB county/subbasin area

HUC hydrologic unit code

LTMP long-term water quality and biological monitoring project

t metric tons

NYSDEC New York State Department of Environmental Conservation

USDA U.S. Department of Agriculture

USGS U.S. Geological Survey

VTDEC Vermont Department of Environmental Conservation

WRTDS weighted regression on time, discharge, and season
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Concentration, Flux, and the Analysis of Trends of Total 

and Dissolved Phosphorus, Total Nitrogen, and Chloride in 

18 Tributaries to Lake Champlain, Vermont and New York, 

1990–2011

By Laura Medalie

Abstract

Annual concentration, flux, and yield for total phosphorus, dissolved phosphorus, total nitrogen, and chloride for 

18 tributaries to Lake Champlain were estimated for 1990 

through 2011 using a weighted regression method based on 

time, tributary streamflows (discharges), and seasonal factors. The weighted regression method generated two series 

of daily estimates of flux and concentration during the period 

of record: one based on observed discharges and a second 

based on a flow-normalization procedure that removes random 

variation due to year-to-year climate-driven effects. The flownormalized estimate for a given date is similar to an average 

estimate of concentration or flux that would be made if all of 

the observed discharges for that date were equally likely to 

have occurred. The flux bias statistic showed that 68 of the 

72 flux regression models were minimally biased. Temporal 

trends in the concentrations and fluxes were determined by 

calculating percent changes in flow-normalized annual fluxes 

for the full period of analysis (1990 through 2010) and for the 

decades 1990–2000 and 2000–2010.

Basinwide, flow-normalized total phosphorus flux 

decreased by 42 metric tons per year (t/yr) between 1990 and 

2010. This net result reflects a basinwide decrease in flux 

of 21 metric tons (t) between 1990 and 2000, followed by a 

decrease of 20 t between 2000 and 2010; both results were 

largely influenced by flux patterns in the large tributaries on 

the eastern side of the basin. A comparison of results for total 

phosphorus for the two separate decades of analysis found that 

more tributaries had decreasing concentrations and flux rates 

in the second decade than the first.

An overall reduction in dissolved phosphorus flux of 

0.7 t/yr was seen in the Lake Champlain Basin during the full 

period of analysis. That very small net change in flux reflects 

substantial reductions between 1990 and 2000 from eastern 

tributaries, especially in Otter Creek and the LaPlatte and 

Winooski Rivers that largely were offset by increases in the 

Missisquoi and Saranac Rivers in the second decade (between 

2000 and 2010). The number of tributaries that had increases 

in dissolved phosphorus concentrations stayed constant at 13 

or 14 during the period of analysis. 

Total nitrogen concentration and flux for most of the 

monitored tributaries in the Lake Champlain Basin have 

decreased since 1990. Between 1990 and 2010, flow-normalized total nitrogen flux decreased by 386 t/yr, which reflects 

an increase of 440 t/yr between 1990 and 2000 and a decrease 

of 826 t/yr between 2000 and 2010. All individual tributaries 

except the Winooski River had decreases in total nitrogen concentration and flux between 2000 and 2010. The decrease in 

total nitrogen flux over the period of record could be related to 

the decrease in nitrogen from atmospheric deposition observed 

in Vermont or to concurrent benefits realized from the implementation of agricultural best-management practices in the 

Lake Champlain Basin that were designed primarily to reduce 

phosphorus runoff.

For chloride, large increases in flow-normalized concentrations and flux between 1990 and 2000 for 17 of the 18 tributaries diminished to small increases or decreases between 

2000 and 2010. Between 1990 and 2010, flow-normalized flux 

increased by 32,225 t/yr, 78 percent of which (25,163 t) was 

realized during the first decade, from 1990 through 2000. The 

five tributaries that had decreasing concentration and flux of 

chloride between 2000 and 2010 were all on the eastern side 

of Lake Champlain, possibly related to reductions since 1999 

in winter road salt application in Vermont. 

Positive correlations of phosphorus flux and changes 

in phosphorus concentration and flux in tributaries with 

phosphorus inputs to basins from point sources, suggest that 

point sources have an effect on stream phosphorus chemistry. 

Several measures of changes in agricultural statistics, such 

as agricultural land use, acres of land in farms, acres of 

cropland, and acres of corn for grain or seed, are positively 

correlated with changes in phosphorus concentration or flux 

in the tributaries. Negative correlations of the amount of 

money spent on agricultural best-management practices with 

changes in phosphorus concentration or flux in the tributaries, 

suggest that best-management practices may be an effective 
2 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

tool, along with point-source reductions, in making progress 

towards management goals for phosphorus reductions in 

Lake Champlain.

Introduction

High concentrations of phosphorus from tributary 

inputs and the ensuing eutrophication in Lake Champlain 

are identified in the 2010 Lake Champlain management plan 

(Lake Champlain Steering Committee, 2010) as a serious 

environmental problem. The plan specifies that reducing 

phosphorus inputs to Lake Champlain is one of eight highest 

priority goals needed to meet the vision for the lake, and one 

that has been specified in every version of that plan since 

it was first published in 1996. Nine out of 13 segments of 

Lake Champlain were included on the 2000 Vermont list 

of impaired waters submitted to the U.S. Environmental 

Protection Agency under section 303(d) of the Clean Water 

Act due to phosphorus pollution (Vermont Department of 

Environmental Conservation and New York State Department 

of Environmental Conservation, 2002). In 1992, the Lake 

Champlain long-term water-quality and biological monitoring 

project (LTMP) formalized an ongoing plan of data collection 

in 18 tributaries to the lake and at 15 lake stations (Lake 

Champlain Management Conference, 1996) to supplement 

collection of continuous records of streamflow on the 

18 tributaries at streamgages operated by the U.S. Geological 

Survey (USGS).

The LTMP collects water samples in tributaries that are 

analyzed for 23 chemical constituents and field parameters 

(Vermont Department of Environmental Conservation and 

New York State Department of Environmental Conservation, 

2012). Although monitoring for total phosphorus was the 

principal effort and concern, the samples also were analyzed 

for constituents that were judged by the Lake Champlain 

Basin Program Technical Advisory Committee to be the most 

meaningful for assessing the long-term effects of management 

actions and other changes in the environment. 

Earlier investigators have analyzed trends for various 

subsets of the water-quality data: total phosphorus concentrations in the lake and concentrations and fluxes in tributaries during 1990–2000 (Medalie and Smeltzer, 2004); total 

phosphorus concentrations in the lake and loading from 

tributaries during 1990–2008 (Smeltzer and others, 2009); 11 

physical, chemical, and biological properties in the lake generally during 1990–2009 (Smeltzer and others, 2012); and total 

phosphorus and total nitrogen concentrations and fluxes in the 

tributaries during 1990–2009 (Medalie and others, 2012).

Except for the last study mentioned in the preceding 

paragraph, estimates of fluxes and trends in water-quality 

data from tributaries have relied on regression-based 

statistical models like ESTIMATOR (Cohn, 2005) or Load 

Estimator (LOADEST; Runkel and others, 2004) that estimate 

constituent concentrations or flux on the basis of factors 

that may include discharge, time, season, or the squares of 

these terms. Concentrations or flux estimated using these 

models, which have been utilized for many years, may have 

been adjusted to remove the random effects of discharge 

(“flow-adjusted concentrations”). In 2010, the USGS 

developed a new method (WRTDS—Weighted Regressions 

on Time, Discharge, and Season) for estimating constituent 

concentrations and fluxes and for detecting trends in long-term 

water-quality datasets (Hirsch and others, 2010). WRTDS was 

designed to overcome shortcomings of traditional methods 

of regression analysis related to inflexible model constraints 

and to increase the amount of information that can be derived 

from long-term datasets. A recent publication that compared 

results from WRTDS with those from ESTIMATOR found 

that WRTDS provides estimates of concentration and flux that 

are more accurate and less biased than does ESTIMATOR; 

WRTDS also has an enhanced ability to determine changes 

in flux over time as a result of human activities in the basin 

(Moyer and others, 2012). 

To address the need to evaluate environmental waterquality changes with a flexible, state-of-the-art regression 

model, the USGS, in cooperation with the Vermont 

Department of Environmental Conservation, applied the 

WRTDS method to 21 years of streamflow and concentration 

data for total phosphorus, dissolved phosphorus, total nitrogen, 

and chloride in water samples collected from 18 tributaries 

to Lake Champlain. One purpose of this study was to 

provide annual estimates of concentrations and flux of total 

phosphorus, dissolved phosphorus, total nitrogen, and chloride 

for the Lake Champlain tributaries for calendar years 1990 

through 2011. This was accomplished by aggregating daily 

estimates of concentrations and flux for dissolved phosphorus 

and chloride and by updating estimated concentrations 

and flux of total phosphorus and total nitrogen previously 

published in Medalie and others (2012). A second purpose was 

to statistically relate basin characteristics to total phosphorus 

concentrations, flux, and trends.

This report provides analysis of 2 more years of data 

than did a previous investigation of concentrations and flux 

of total phosphorus and total nitrogen (Medalie and others, 

2012); includes statistical analysis for two new parameters 

(concentrations and flux of dissolved phosphorus and 

chloride); provides new interpretations regarding model 

bias and seasonal effects on concentrations and flux of total 

phosphorus; and describes results of tests of correlation 

between estimated annual phosphorus concentration, flux, 

and changes in concentration or flux during several time 

periods with a set of selected basin characteristics to determine 

whether any of those characteristics could be statistically 

related to the phosphorus data. Trends are presented as net 

changes in concentration and flux between 1990 and 2000 

(decade I), between 2000 and 2010 (decade II), and between 

1990 and 2010 (the full period of analysis). Note that the 

“period of analysis” from 1990 through 2010, selected for 

even decadal time intervals, differs slightly from the “period 

of record” (of available data) from 1990 to 2011. The first year 
Study Methods 3

for analyzing and reporting results of concentrations for total 

nitrogen was 1992. Categories of basin characteristics that 

were examined include physical and demographic properties, 

point sources of phosphorus, land use, and best-management 

practices (BMPs). The streamflow and surface-water quality 

of about 74 percent of the area of the Lake Champlain Basin is 

monitored by the data collected at 18 streamgages and waterquality sampling stations (fig. 1). Use of the term “basinwide” 

in the report refers to the 74 percent of the total drainage area 

that is monitored. 

Study Methods

Original data that may have been reported and (or) were 

stored in various formats and units in many cases required 

modifications in order to be useful for exploring water-quality 

trends at two subbasin scales within the Lake Champlain 

Basin. As described below, some digital geodatasets were 

combined or overlain and intersected using ArcMap software.

Assembling and Modifying Data

Water-quality data were collected, analyzed, and 

posted online by the Vermont Department of Environmental 

Conservation (VTDEC) as part of the Lake Champlain 

Long-Term Water Quality and Biological Monitoring Project 

(Vermont Department of Environmental Conservation and 

New York State Department of Environmental Conservation, 

2012). The number of samples collected at each monitoring 

station ranged from approximately 14 to 19 samples per 

year that were analyzed for total phosphorus and from 5 

to 16 samples per year that were analyzed for the other 

constituents. Streamflow at the 18 Lake Champlain tributary 

stations has been gaged continuously by the USGS, in 

cooperation with the VTDEC and the New York State 

Department of Environmental Conservation (NYSDEC), and 

is part of the National Water Information System network. 

Streamflow records at 10 of the streamgages, where data 

collection began on March 1, 1990, were extended 2 months 

back in time, and the record at one additional station was 

extended back 21 months, as previously described in Medalie 

and others (2012), to complete the 1990 calendar year record.

Data on basin characteristics were assembled from 

many different sources (table 1). Spatial data on populations 

by census block from the U.S. Census Bureau were intersected with subbasin boundaries in ArcMap to reformulate as 

populations by subbasins. A 2011 consultant’s report (Stone 

Environmental, Inc., 2011) indicated that hydrologic soil 

group, in particular group C and D soils (Natural Resources 

Conservation Service, 2007), was one of the top three factors 

driving the magnitude of phosphorus export (in both total and 

dissolved species) and the incidence of critical source areas. 

A general hypothesis, of whether the relation of the percent 

of agricultural land in the subbasin to phosphorus flux could 

be strengthened by combining it with hydric soils (saturated 

with water), was formulated from that report. This hypothesis 

was tested in a gross manner across the Lake Champlain Basin 

by creating a spatial layer from an overlay of the two types of 

information (land use is equal to agricultural and soil hydrologic group equal to C or D).

Statistical data that profile agricultural activities across 

the United States are reported at the county level by the 

U.S. Department of Agriculture (USDA) census of agriculture. 

The transformation of county-level census data to a dataset 

applicable to subbasins involved first a disaggregation of 

county data into pixels of agricultural land use and then 

an aggregation of pixels into subbasin areas. For the first 

step of disaggregation, a polygon spatial layer of all unique 

county/subbasin (CSUB) areas was created by overlaying the 

county spatial layer with the gaged subbasin spatial layer. A 

spreadsheet was then created that listed the number of pixels 

of agricultural land from the 1992 and 2001 land-use datasets 

in each CSUB area. The ratio of agricultural land in the 

CSUB area to agricultural land in the county was multiplied 

by the county census statistic. The agricultural statistics data, 

transformed to a CSUB basis, were aggregated up to subbasin 

areas by adding all values for the CSUB areas that belonged to 

each particular subbasin. 

Spreadsheets with data on agricultural best-management 

practices (BMPs) were obtained from the New York State 

Department of Agriculture and Markets and the Vermont 

Agency of Agriculture. Both states provided itemized lists of 

BMPs that included information about BMP type, implementation date, total cost, and subbasin location. Although different types and scales of BMPs would have different effects on 

the amount of phosphorus in runoff, substantiated information 

to quantify these effects is not available. Many other factors, 

including but not limited to proximity to streams, slope, and 

soil type, also contribute to BMP performance. Thus, associations between phosphorus trends and BMPs are provided for 

just two unambiguous measures of BMPs: the number implemented and the money spent on implementation (not including upkeep). Subbasin locations from the state agency data 

were provided at the HUC111 scale for New York State and 

the HUC14 scale for Vermont, and where possible, the data 

were reassigned to the HUC8 and HUC12 scales used in this 

report. BMP datasets were grouped by implementation date 

into two periods for correlation analysis—the entire period of 

available data (from 1995 through 2010) and the years before 

2000—to test whether there might be a delayed or lag effect 

between BMP implementation and water-quality response in 

the streams.

1

The USGS developed a system of nested hydrologic unit codes (HUCs) to 

organize hydrologic data across the United States into successively smaller 

basins, called “hydrologic units.” The designation HUC8, for example, means 

the 8-digit code used for hydrologic units at the subbasin level. As the HUC 

number increases, the size of the basin decreases. For example, HUC8 scale 

basins are larger than HUC12 scale basins.
4 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

Otter

Winooski

Lamoille

Missisquoi

Saranac

Ausable

Pike

Mettawee

Bouquet

Poultney

Lewis

Salmon

Little

Ausable

Little

Chazy

Putnam

LaPlatte

73°

45°

44°

74°

Lake

Champlain

0 10 20 KILOMETERS

0 10 20 MILES

EXPLANATION

New York

Vermont

UNITED STATES

CANADA

New England,Taconic

New England, Green Mountain

Tributary water-quality monitoring

 station and streamgage

Basin boundary

Subbasin boundary

Tributry basin and name.

 Green-shaded zone is 

 12-digit hydrologic unit 

 closest to monitoring station

EXPLANATION

Vermont State Plane Coordinate System

North American Datum 1983

Basin boundaries from 1:24,000-scale U.S. Department 

of Agriculture Natural Resources Conservation Service

watershed boundary dataset (WBD), 2003

Lake Champlain basin

Physiographic provinces

 (shown as dashed and

 colored lines) 

Great Chazy

Little

Otter

St. Lawrence Valley, Champlain

Adirondacks

Hudson

Otter

Figure 1. Lake Champlain Basin, physiographic provinces (inset), water-quality monitoring stations, tributary boundaries, and 

parts of tributaries that include only the 12-digit hydrologic unit closest to the monitoring station.
Study Methods 5

Table 1. Sources of data for basin characteristics that were tested for correlation with concentration and flux of total phosphorus for 

tributaries to Lake Champlain.

[km2, square kilometers]

Basin characteristic Source of data and citation for basin characteristic

Physical and demographic

Physiographic province Fenneman and Johnson, 1946

Population density, people per km2 U.S. Census Bureau (2001; Jen McCormick, written commun., 

June 11, 2012); Vermont Center for Geographic Information, 2012 Change in population density, people per km2

Point sources

Phosphorus flux from point sources Vermont Department of Environmental Conservation (Eric Smeltzer, 

written commun., June 7, 2012) Percent change in phosphorus flux from point sources

Land use

Percent or percent change in:

Urban land use including open land University of Vermont Spatial Analysis Laboratory, 2007 Agricultural land use

Agricultural land in basin that intersects hydric soils 

(type C or D)

University of Vermont Spatial Analysis Laboratory, 2007 and soils data 

(Natural Resources Conservation Service, variously dated)

Acres of land in farms

U.S. Department of Agriculture Census of Agriculture, 1987; 1992 and 

1997 (U.S. Department of Agriculture, 1999); 2002 and 2007 (U.S. 

Department of Agriculture, 2009)

Acres of cropland

Acres of corn for grain or seed

Acres of corn for silage

Acres of commercial fertilized

Number of milk cows

Best-management practices

Number of agricultural best-management practices implemented Vermont Agency of Agriculture (Jeffrey Cook, written commun., 

October 29, 2010) and New York State Department of Agriculture and 

Markets (Bob Brower, written commun., August 2, 2011) Money spent on agricultural best-management practices, dollars

Estimating Annual Average Concentration, 

Annual Flux, and Trends

The WRTDS method was used to estimate annual 

average concentrations of constituents and their annual flux 

(movement on a mass basis) and to determine trends in those 

factors (Hirsch and others, 2010). The method was developed 

by USGS to improve upon previous regression-based methods 

of estimating concentration and flux from a set of waterquality observations and continuous streamflow records for 

datasets that span at least 20 years. WRTDS has been applied 

to datasets from the Chesapeake Bay (Hirsch and others, 

2010; Moyer and others, 2012), the Mississippi River Basin 

(Sprague and others, 2011), and the Lake Champlain Basin for 

data through 2009 (Medalie and others, 2012). 

The WRTDS weighted regression model provides 

daily estimates of constituent concentration and flux in two 

ways (Hirsch and others, 2010). First, the software creates a 

3-dimensional matrix (with dimensions of time in years, time 

in months, and equal log-space increments of discharge) of 

weighted regression results that cover the time and stream 

discharge continuum of the dataset and then applies bilinear 

interpolation between matrix results to estimate concentration 

for every day in the entire period based on the given time and 

observed discharge. At each estimation point in the matrix, 

weights are assigned to every combination of observed concentration and discharge based on distance (in terms of time, 

season, and discharge) to the time and discharge at the estimation point. The idea is that observations close in time and with 

similar discharges to the estimation point will be weighted 
6 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

heavily, and observations that are very different in either time 

or discharge will have little or zero weight. The daily estimate 

of flux is calculated by multiplying the estimated concentration by the observed discharge (times a unit conversion factor). Estimates produced in this way (based on the observed 

daily discharge) are estimates of actual concentration or flux 

that occurred on a given day. 

The second method of estimating concentrations calculates, for every day in the record, the mean of 20 (this number 

represents the number of years of record; this example is for 

a 20-year record) interpolated estimates of concentration. The 

20 estimates for a specified date, for example July 1, 2001, 

are made with the 20 different observed discharges for that 

date (July 1) and the given date as the time variable (July 1, 

2001). The rationale is that any of those 20 July 1st discharges 

are equally likely to have occurred during the years of record. 

The mean of the 20 results provides the “flow-normalized” 

estimate of concentration for that day. The estimate of flownormalized flux for each day is the mean of the 20 estimates 

of flux generated by multiplying the 20 interpolated estimates 

of concentration times discharge. Flow normalizing provides estimates of concentration and flux that remove natural 

climate-related variability. Because it offers a depiction of 

water-quality conditions that is not obstructed by random 

noise, flow-normalized estimates can be used as a tool to 

evaluate progress and effectiveness (or lack thereof) of basin 

restoration activities. Daily estimates of concentration are 

averaged during a month or year to provide monthly or annual 

estimates, and daily estimates of flux are aggregated to form 

monthly or annual estimates.

Trend results from WRTDS are presented in terms 

of percent change for a user-defined period of time 

rather than a hypothesis test for significance. While 

many traditional multiple linear regression approaches 

(ESTIMATOR, LOADEST, FLUX (Walker, 1996)) allow 

for the determination of a trend and associated statistical 

significance, the ability of those trends to fully describe 

water-quality changes over time is limited because the 

forms are fixed and the trend models are monotonic. The 

weighting scheme used by WRTDS results in a flexible model 

that maximizes relevancy of information. For example, in 

traditional approaches, concentrations are predicted on the 

basis of solutions to equations that assign equal weights to 

all streamflow observations in the prediction window; in 

WRTDS, the models to predict concentrations are constructed 

using unequal weights of discharge, with greater weights 

assigned to discharge values closer in time (in years), 

discharge, and season to values to be estimated. Flexibility 

afforded by the weighted regression approach of WRTDS 

models the full range of observed discharges, which is not 

possible with traditional linear or log-linear regression models. 

In addition, the inability of traditional approaches to decouple 

concentration from flux trend (Moyer and others, 2012) 

artificially constrains those models. The WRTDS model was 

designed specifically to overcome these and other limitations.

A limitation of the WRTDS model was identified for 

two of the tributaries (Little Ausable and Poultney Rivers) 

where the sampled dataset did not include samples collected 

at the extremely high discharges that occurred during the 

period of record. Because concentrations at very high flows 

typically are among the highest in the water-quality record 

and can inordinately influence annual estimates, model results 

based on extrapolations far above the sampled range of 

discharge cannot be substantiated and therefore should not be 

used. For the Little Ausable and Poultney Rivers, estimated 

concentrations and fluxes were calculated using only the 

mean (concentration) or sum (flux) of daily values where the 

daily discharge was less than some designated value (near the 

highest discharge that was sampled: 530 cubic feet per second 

(ft3/s) for the Little Ausable River and 2,470 ft3/s for the 

Poultney River). Days with discharges above this designated 

value simply were omitted from the annual calculations 

for concentration and flux. Because high discharges were 

targeted for the collection of samples, the number of days with 

discharge that exceeds the designated discharge is very small 

(0.6 percent for the Little Ausable River and 0.3 percent for 

the Poultney River), and these exceeded discharges correspond 

to total flow volumes of about 10 percent for the Little 

Ausable River and 4 percent for the Poultney River of the total 

discharge over the period of record. For the Little Ausable and 

Poultney Rivers, annual estimates of concentration and flux for 

years with at least one daily discharge above the designated 

value are represented as “greater than” the value listed in 

appendix 1. This adjustment only affects the estimates of 

actual concentration, flux, or yield; since the flow-normalized 

estimates are based on discharge values integrated over the 

21 years of record, a very high discharge in one particular 

year would have minimal impact on the smoothed estimates. 

This approach is predicated on the idea that the data do not 

provide any reliable means for estimating concentrations or 

fluxes on these extreme high-discharge days. Any attempt to 

do so would be a substantial extrapolation beyond the data. 

Thus, the results reported simply describe inferences about 

water-quality conditions that have taken place below that 

discharge threshold. 

Another tool available as part of WRTDS to enhance 

model representation of the sample data is the ability to 

adjust weights of the variables in the regression. Weights are 

assigned to every combination of observed concentration and 

discharge based on distance (of time, season, and discharge) 

to the time and discharge at each estimation point. In WRTDS, 

weights are a function of the user-assigned half-window width. 

Although the default half-window widths of 10 years for time, 

2 logarithm cycles for discharge, and 0.5 year for season are 

adequate in most situations, diagnostic tools available as part 

of the WRTDS software have pointed to some cases in the 

Lake Champlain dataset where better model representations 

could be achieved by widening the half-window widths 

(appendix 2). Half-window widths that are widened result in 

greater weights for more observations, which has the effect of 

smoothing results and decreasing the magnitudes of the trends. 
Annual Average Concentration, Annual Flux, and Trends 7

Decisions about widening the windows were based on a 

subjective analysis using various graphical means to determine 

how much wider they needed to be to produce relatively 

smooth representations of relations between concentration and 

discharge (for a given time) or relations between concentration 

and time (for a given discharge). Thus, results produced by 

widening the half-window widths are conservative and serve 

to reduce the possibility of identifying a sizeable upward or 

downward trend when there is a paucity of data to support 

the trend. 

Determining the Relation Between Trends and 

Basin Characteristics

Many of these datasets were evaluated in two ways: as 

applicable to the whole subbasin (HUC8) and as applicable 

to just that part of the subbasin nearest the monitoring station 

(HUC12) to determine whether there were better relations for 

areas within the immediate vicinity of data collection. Basin 

characteristics were analyzed for correlations with total phosphorus concentrations and flux (appendix 6). The significance 

level of statistical tests was established as α = 0.10. Correlation for most analyses was calculated using jmp software (SAS 

Institute, Inc., 2010) by use of the nonparametric Kendall’s tau 

correlation coefficient, which was selected for its resistance 

to outliers (Helsel and Hirsch, 2002). Physiographic province, 

the only categorical (nonnumeric) independent variable, was 

evaluated using the nonparametric Kruskal-Wallis test (Helsel 

and Hirsch, 2002). For this test, each of the 18 major subbasins was assigned to one of three physiographic provinces and 

sections (appendix 6) in the Appalachian Highlands division: 

St. Lawrence Valley, Champlain; New England, Taconic; and 

New England, Green Mountain. For most of the correlation 

tests, there was no need to normalize flux by land area (by calculating yield) because the datasets consisting of percentages 

were already normalized. 

Calculating Flux Bias

WRTDS model fit is examined for each constituent 

of interest (dissolved and total phosphorus, total nitrogen, 

and chloride) for each tributary by plots of observed versus 

estimated concentration (appendix 4) and flux (appendix 7). 

Plots include the 1:1 reference lines, which would occur if 

all observed values were perfectly represented by the modeled, or estimated, values. Table 2 shows the flux bias statistic 

associated with appendix 7, computed as (mean (predicted 

flux) – mean (observed flux)) / mean (observed flux). A model 

that has no bias would have a flux bias statistic of 0. Using 

total phosphorus in the Great Chazy River as an example, the 

mean of the predicted fluxes is about 0.7 percent lower than 

the mean of the observed fluxes. Three of the models for total 

phosphorus (Saranac, Little Ausable, and Putnam) and one 

for dissolved phosphorus (Saranac) are moderately biased as 

indicated by a flux bias statistic of at least 10 percent (±0.1). 

The remaining 68 WRTDS models have minimal flux bias.

Table 2. Flux bias statistic comparing WRTDS1 regression 

model estimates with observed water-quality observations for 

total phosphorus, dissolved phosphorus, total nitrogen, and 

chloride for tributaries to Lake Champlain.

Tributary Total 

phosphorus

Dissolved 

phosphorus

Total 

nitrogen Chloride

Great Chazy -0.007 0.027 -0.002 -0.018

Little Chazy -0.014 -0.011 -0.013 -0.012

Saranac -0.281 -0.142 -0.024 -0.032

Salmon -0.052 0.012 -0.035 0.022

Little Ausable -0.100 -0.097 0.014 -0.017

Ausable 0.069 -0.037 -0.036 -0.016

Bouquet 0.087 0.068 0.085 -0.041

Putnam -0.133 -0.026 -0.066 -0.046

Poultney 0.023 -0.002 -0.020 -0.015

Mettawee 0.086 0.023 -0.009 -0.004

Otter -0.002 0.007 -0.038 -0.023

Little Otter 0.011 0.020 0.007 -0.026

Lewis -0.036 -0.083 -0.013 -0.008

LaPlatte 0.053 0.072 0.001 -0.003

Winooski 0.016 -0.003 -0.014 -0.028

Lamoille -0.082 0.015 -0.017 -0.023

Missisquoi 0.027 0.021 -0.025 -0.027

Pike 0.006 0.009 -0.062 -0.016

1

WRTDS is Weighted Regression on Time, Discharge, and Season.

Annual Average Concentration, Annual 

Flux, and Trends

Estimated annual average concentration, flux, and yield 

(flux divided by drainage area) for total phosphorus, dissolved 

phosphorus, total nitrogen, and chloride in tributaries to Lake 

Champlain from 1990 to 2011 are presented in appendix 1. 

The three types of estimates (concentration, flux, and yield) 

are shown for the two types of WRTDS output: those based 

on observed discharges and those based on flow-normalized 

data. The flow-normalized data listed in appendix 1 are shown 

as plots in appendixes 3 (concentration) and 8 (yield) for individual subbasins. Temporal trends are presented as changes in 

flow-normalized concentrations and flux for three time periods 

(decade I, decade II, and the period of analysis) in tables 3 and 

4. Figures 2 (flow-normalized concentrations) and 3 (flownormalized flux) illustrate annual percent changes listed in 

tables 3 and 4 for the two decades. For purposes of assigning 

tributaries to the eastern or western group, the Mettawee River 

is considered an eastern tributary because it is closest hydrologically to other tributaries in the eastern group.
8 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

Table 3. Net change in flow-normalized concentrations of total phosphorus, dissolved phosphorus, total nitrogen, and chloride in the 

[mgL, milligrams per liter; %/yr, percent per year; No., number]

Tributary name 

(and group)1

Change, 

1990–2000

Change, 

2000–2010

Change, 

1990–2010

Change, 

1990–2000

Change, 

2000–2010

Change, 

1990–2010

mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr 

Total phosphorus Dissolved phosphorus 

Great Chazy (W) 0.008 1.8 0.006 1.2 0.014 1.7 0.005 2.3 0.006 2.2 0.011 2.6 

Little Chazy (W) 0.010 1.0 0.005 0.4 0.015 0.8 0.013 1.6 0.009 0.9 0.022 1.4 

Saranac (W) 0.003 1.2 0.002 0.7 0.005 1.0 0.003 2.6 0.003 2.2 0.005 2.8 

Salmon (W) 0.003 1.1 0.002 0.8 0.005 1.0 0.002 2.0 0.002 1.2 0.004 1.8 

Little Ausable (W) 0.012 1.9 -0.008 -1.1 0.004 0.3 0.015 4.2 -0.014 -2.6 0.001 0.2 

Ausable (W) 0.002 0.9 0.000 0.1 0.003 0.6 0.002 2.1 0.002 1.6 0.003 2.1 

Bouquet (W) 0.008 2.6 -0.002 -0.5 0.006 1.0 0.004 4.3 0.002 1.8 0.006 3.6 

Putnam (W) 0.002 1.0 -0.000 -0.3 0.001 0.4 0.002 3.0 0.003 3.8 0.005 4.2 

Poultney (E) -0.000 -0.0 -0.003 -0.5 -0.003 -0.3 0.000 0.1 0.002 1.0 0.002 0.6 

Mettawee (E) 0.004 0.6 -0.004 -0.5 0.000 0.0 0.011 5.0 0.002 0.5 0.013 3.0 

Otter (E) -0.026 -2.3 -0.018 -2.2 -0.044 -2.1 -0.033 -4.8 -0.004 -1.1 -0.037 -2.8 

Little Otter (E) 0.003 0.3 -0.004 -0.3 -0.001 -0.0 -0.007 -1.1 0.002 0.3 -0.005 -0.4 

Lewis (E) 0.003 0.6 0.004 0.7 0.006 0.7 0.001 0.3 0.002 0.9 0.002 0.7 

LaPlatte (E) -0.225 -6.7 -0.025 -2.8 -0.249 -3.9 -0.168 -6.6 -0.031 -4.5 -0.199 -4.1 

Winooski (E) -0.004 -0.8 -0.001 -0.2 -0.005 -0.5 -0.001 -0.9 0.000 0.2 -0.001 -0.4 

Lamoille (E) 0.007 3.0 -0.003 -1.0 0.004 0.9 0.001 1.2 0.002 2.0 0.004 1.8 

Missisquoi (E) -0.001 -0.1 0.000 0.0 -0.000 -0.0 0.002 1.2 0.004 2.1 0.006 1.9 

Pike (E) -0.017 -1.5 -0.010 -1.0 -0.027 -1.2 -0.010 -1.6 -0.006 -1.1 -0.016 -1.3 

No. of no change 1 3 3 0 0 0 

No. of decreases 5 11 5 5 4 5 

No. of increases 12 6 10 13 14 13 

1

Tributaries are assigned to the western (W) or eastern (E) group, based on hydrologic connection.

2

The first year that samples were analyzed for total nitrogen was 1992.
Annual Average Concentration, Annual Flux, and Trends 9

monitored Lake Champlain tributaries for three time periods.

Change, Change, Change, Change, Change, Change, 

1992–20002 2000–2010 1992–2010 1990–2000 2000–2010 1990–2010

mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr mg/L %/yr

Total nitrogen Chloride

-0.08 -1.1 -0.07 -1.0 -0.15 -1.0 3.9 2.7 0.2 0.1 4.2 1.5

-0.01 -0.0 -0.05 -0.4 -0.05 -0.2 3.0 1.6 0.5 0.2 3.5 1.0

-0.01 -0.2 -0.14 -2.6 -0.15 -1.4 4.3 6.9 2.1 1.9 6.4 5.4

0.00 0.0 -0.14 -2.7 -0.14 -1.4 1.6 2.4 3.0 3.4 4.6 3.5

0.10 1.2 -0.08 -0.8 0.02 0.1 3.8 3.2 2.6 1.6 6.4 2.8

0.06 1.2 -0.15 -2.8 -0.09 -1.0 6.5 8.1 2.2 1.4 8.7 5.6

0.01 0.3 -0.15 -3.4 -0.13 -1.7 6.0 4.7 3.7 1.9 9.8 4.0

-0.05 -1.2 -0.08 -2.1 -0.12 -1.6 3.4 4.3 3.2 2.7 6.6 4.3

0.04 0.7 -0.08 -1.5 -0.04 -0.4 2.2 1.5 -0.4 -0.2 1.8 0.6

0.06 0.6 -0.22 -2.2 -0.16 -0.9 7.3 5.4 5.0 2.3 12.3 4.7

0.05 0.6 -0.13 -1.7 -0.09 -0.6 2.6 2.1 0.5 0.4 3.1 1.3

0.08 0.8 -0.03 -0.3 0.04 0.2 3.5 2.3 1.1 0.6 4.6 1.6

0.03 0.6 -0.05 -0.9 -0.02 -0.2 0.9 1.0 0.3 0.3 1.2 0.7

-0.15 -1.7 -0.26 -3.4 -0.41 -2.3 -6.5 -1.2 -18.5 -3.8 -25.0 -2.3

0.10 1.4 0.07 0.8 0.17 1.2 5.5 3.3 4.5 2.0 10.0 3.2

0.00 0.1 -0.04 -0.8 -0.04 -0.4 0.2 0.2 -0.2 -0.1 0.1 0.0

0.08 1.1 -0.09 -1.1 -0.01 -0.1 1.2 1.5 -0.6 -0.6 0.7 0.4

0.19 1.1 -0.03 -0.2 0.16 0.5 0.7 0.4 -2.8 -1.6 -2.1 -0.7

2 0 0 0 0 0

4 17 14 1 5 2

12 1 4 17 13 16
10 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

Table 4. Net change in flow-normalized fluxes of total phosphorus, dissolved phosphorus, total nitrogen, and chloride in the monitored 

[mt/yr, metric tons per year; %/yr, percent per year; No., number]

Tributary name 

(and group)1

Change, 

1990–2000

Change, 

2000–2010

Change, 

1990–2010

Change, 

1990–2000

Change, 

2000–2010

Change, 

1990–2010

mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr 

Total phosphorus Dissolved phosphorus 

Great Chazy (W) 1.0 0.4 -0.3 -0.1 0.7 0.1 1.6 1.4 2.0 1.6 3.7 1.7 

Little Chazy (W) 0.4 0.6 0.0 0.0 0.4 0.3 0.5 1.1 0.1 0.3 0.6 0.7 

Saranac (W) 3.1 1.2 2.6 0.9 5.7 1.1 2.7 3.0 3.3 2.8 5.9 3.5 

Salmon (W) 0.1 0.3 0.2 0.5 0.3 0.5 0.2 1.8 0.1 1.1 0.3 1.6 

Little Ausable (W) 0.3 0.7 -0.5 -1.0 -0.2 -0.2 0.3 1.2 -0.8 -2.9 -0.5 -1.1 

Ausable (W) 4.6 1.1 -2.3 -0.5 2.4 0.3 1.9 3.2 2.3 2.9 4.2 3.7 

Bouquet (W) 2.0 0.7 -2.0 -0.7 -0.0 -0.0 1.7 3.9 1.1 1.8 2.8 3.3 

Putnam (W) 0.1 0.3 -0.1 -0.6 -0.1 -0.1 0.1 2.5 0.2 3.2 0.3 3.4 

Poultney (E) 0.7 0.2 0.6 0.2 1.3 0.2 0.0 0.0 0.3 0.5 0.3 0.3 

Mettawee (E) 0.7 0.2 -3.2 -1.0 -2.5 -0.4 2.1 2.5 -0.3 -0.3 1.8 1.1 

Otter (E) -13 -1.1 -18 -1.6 -32 -1.3 -20 -3.3 -3.6 -0.9 -24 -2.0 

Little Otter (E) 1.1 1.3 0.2 0.2 1.3 0.8 -0.1 -0.1 0.2 0.4 0.1 0.1 

Lewis (E) 0.3 0.3 0.7 0.7 1.0 0.5 0.0 0.0 0.1 0.4 0.1 0.2 

LaPlatte (E) -5.6 -4.1 -1.2 -1.6 -6.8 -2.6 -4.9 -5.5 -1.1 -3.2 -6.0 -3.5 

Winooski (E) -11 -0.6 2.1 0.1 -9.2 -0.2 -3.1 -1.2 -0.5 -0.2 -3.6 -0.7 

Lamoille (E) 10 1.8 -5.7 -0.8 4.7 0.4 1.3 0.8 3.0 1.7 4.3 1.4 

Missisquoi (E) -13 -0.6 3.8 0.2 -9.4 -0.2 1.8 0.5 9.5 2.3 11 1.5 

Pike (E) -2.7 -0.6 3.3 0.9 0.6 0.1 -0.7 -0.5 -0.3 -0.2 -1.0 -0.3 

Total -21 -0.2 -20 -0.2 -42 -0.3 -15 -0.7 16 0.7 0.7 0.0 

West total 12 0.8 -2 -0.2 9 0.3 9 2.3 8.4 1.7 17 2.3 

East total -33 -0.5 -18 -0.3 -51 -0.4 -24 -1.3 7.4 0.4 -17 -0.5 

No. of no change 0 1 1 2 0 0 

No. of decreases 5 9 7 5 6 5 

No. of increases 13 8 10 11 12 13 

1

Tributaries are assigned to the western (W) or eastern (E) group, based on hydrologic connection.

2

The first year that samples were analyzed for total nitrogen was 1992.
Annual Average Concentration, Annual Flux, and Trends 11

Lake Champlain tributaries for three time periods.

Change, Change, Change, Change, Change, Change, 

1992–20002 2000–2010 1992–20102 1990–2000 2000–2010 1990–2010

mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr mt/yr %/yr

Total nitrogen Chloride

-35 -1.0 -39 -1.3 -73 -1.1 1,388 3.7 117 0.2 1,505 2.1

-0.7 -0.1 -4.4 -0.5 -5.1 -0.3 137 1.5 62 0.6 199 1.1

-5.9 -0.1 -120 -2.3 -126 -1.2 3,883 7.4 1,644 1.7 5,527 5.5

1.5 0.4 -9.7 -2.4 -8.2 -1.1 105 2.4 134 2.5 240 2.9

2.2 0.4 -7.4 -1.2 -5.2 -0.5 151 2.5 72 0.9 224 1.9

71 1.7 -138 -2.8 -67 -0.8 3,674 8.4 1,042 1.2 4,716 5.6

16 0.8 -68 -3.2 -52 -1.4 1,608 4.7 975 1.9 2,584 3.9

-3.4 -1.1 -5.4 -2.0 -8.9 -1.5 223 5.2 133 2.0 356 4.4

24 1.5 -20 -1.1 3.6 0.1 446 1.5 -52 -0.1 394 0.7

9.3 0.3 -69 -2.4 -60 -1.1 1,444 4.7 917 2.0 2,361 4.0

77 1.0 -178 -2.0 -100 -0.7 2,433 2.2 52 0.0 2,486 1.2

3.7 0.5 -4.8 -0.6 -1.1 -0.1 124 1.7 10 0.1 134 0.9

4.8 0.7 -4.3 -0.6 0.5 0.0 66 0.8 26 0.3 91 0.6

-7.1 -1.3 -15 -3.1 -22 -2.1 -93 -0.7 -315 -2.5 -408 -1.6

56 0.4 41 0.3 97 0.4 7,095 2.9 4,626 1.4 11,722 2.5

10 0.1 -59 -0.8 -49 -0.3 710 0.6 -448 -0.4 261 0.1

131 1.0 -106 -0.7 24 0.1 1,834 1.7 -1,296 -1.0 538 0.3

86 1.8 -20 -0.3 67 0.7 -66 -0.2 -639 -2.1 -706 -1.2

440 0.8 -826 -1.1 -386 -0.3 25,163 2.8 7,062 0.6 32,225 1.9

46 0.3 -391 -2.2 -345 -1.2 11,170 5.8 4,180 1.3 15,350 4.2

394 0.9 -435 -0.8 -41 -0.0 13,993 2.0 2,882 0.3 16,875 1.2

0 0 0 0 0 0

5 17 13 2 5 2

13 1 5 16 13 16
12 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

Total Phosphorus Dissolved Phosphorus

Total Nitrogen Chloride

-4

-2

0

2

4

from 1992 to 2000

-8

-4

0

4

8 from 1990 to 2000

-4

-2

0

2

4

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-9

-6

-3

0

3

6

9

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-8

-4

0

4

8

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-8

-4

0

4

8

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-8

-4

0

4

8 from 1990 to 2000

-9

-6

-3

0

3

6

9

from 1990 to 2000

Annual percent change in concentration Annual percent change in concentration 

Figure 2. Annual percent changes in flow-normalized concentrations of total phosphorus, dissolved phosphorus, total 

nitrogen, and chloride between 1990 and 2000 and between 2000 and 2010.
Annual Average Concentration, Annual Flux, and Trends 13

Dissolved Phosphorus

Chloride

Total Phosphorus

Total Nitrogen

-10

-5

0

5

10

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-10

-5

0

5

10

from 1990 to 2000

-4

-2

0

2

4

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-4

-2

0

2

4 from 1992 to 2000

-6

-3

0

3

6

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-6

-3

0

3

6 from 1990 to 2000

-6

-3

0

3

6

Great Chazy

Little Chazy

Saranac

Salmon

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

from 2000 to 2010

-6

-3

0

3

6 from 1990 to 2000

Annual percent change in flux Annual percent change in flux

Figure 3. Annual percent changes in flow-normalized fluxes of total phosphorus, dissolved phosphorus, total nitrogen, and 

chloride between 1990 and 2000 and between 2000 and 2010.
14 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

The graphs in appendix 8 illustrate the benefits of flow 

normalization in removing year-to-year variations in streamflow for assessing long-term trends in water quality. Extremely 

high streamflows occurred in 2011 throughout the basin; for 

instance, in the Winooski River, the annual mean streamflow 

for water year 2011 was the highest on record for the period 

from 1929 to 2011 (3,380 ft3

/s in 2011 compared to the longterm average of 1,801 ft3

/s) (U.S. Geological Survey, 2012). 

Because of these high streamflows, the 2011 estimates of 

actual yield (circles in the graphs in appendix 8) based on 

observed streamflows were all either the highest or among the 

highest of yields since 1990 for all four constituents. However, 

the solid lines of flow-normalized yields in the graphs, whose 

endpoints and mid-point were the values used in the trend 

calculations (for differences between 1990, 2000, and 2010), 

in most cases do not show a sharp upturn near the latter part 

of the record because of the effects of the flow normalization. 

It is useful to see it both ways: that estimates of actual loads 

(appendix 1) or yields (appendixes 1 and 8) were extremely 

high in 2011, as expected because of the extreme weather, and 

to see loads and yields in the context of long-term trends that 

are uninfluenced by extreme events. 

Total Phosphorus

For decade I, concentrations of total phosphorus 

increased in 12 tributaries, decreased in 5 tributaries, and did 

not change in 1 tributary (fig. 2; table 3; appendixes 1 and 

3). Those numbers almost completely reversed in decade II, 

when concentrations increased in 6 tributaries, decreased in 

11 tributaries, and did not change in 1 tributary. Improvements 

seen in the second decade did not compensate entirely for the 

larger increases during the 1990s; for the overall period of 

analysis, concentrations decreased in 5 tributaries, increased in 

10 tributaries, and did not change in 3 tributaries. The patterns, 

or directions, of change in total phosphorus flux were similar 

to those for concentration (fig. 3; table 4; appendixes 1 and 

8). For decade I, flux decreased in 5 tributaries and increased 

in 13 tributaries. For decade II, flux of total phosphorus 

decreased in nine tributaries, increased in eight tributaries, and 

did not change in one tributary. For the entire period of analysis, flux decreased in 7 tributaries, increased in 10 tributaries, 

and did not change in 1 tributary.

On a mass basis, each time period that was examined 

showed a basinwide decrease in flux of total phosphorus. The 

total annual decrease in total phosphorus flux for decade I 

was 21 metric tons (t). For decade II, the total annual decrease 

was 20 t, and for the entire period of analysis, the total annual 

decrease was 42 t (table 4). The flux of total phosphorus for 

the whole basin was dominated by flux from tributaries on the 

eastern side. For example, the reduction in flux in decade I 

primarily reflects flux decreases in Otter Creek and Missisquoi 

and Winooski Rivers (of 13, 13, and 11 metric tons per year 

(t/yr), respectively), all on the eastern side of Lake Champlain. 

Decade II saw slight reversals (increases) in flux in two of 

those tributaries, Missisquoi and Winooski Rivers. However, 

since these increases were very small, and Otter Creek 

continued with a large decrease in combination with decreases 

in several tributaries (that had shown increases in decade I), 

the net effect was a decrease in flux in decade II. Adding the 

effects over the two decades, the period of record showed 

a net decrease of 42 t/yr, composed of a 51 t/yr decrease 

from the eastern tributaries and a 9 t/yr increase from the 

western tributaries.

Normalizing the changes in concentration and flux (by 

expressing in terms of percent changes) provides a sense 

of the relative magnitude of change among the tributaries. 

Most of the annual changes in concentration and flux of total 

phosphorus for tributaries over the period of analysis were less 

than 1 percent (tables 3 and 4). The largest relative changes in 

flux in decade I were decreases in the LaPlatte River (6.7 and 

4.1 percent per year for concentration and flux, respectively) 

and increases in the Lamoille River (3.0 and 1.8 percent per 

year for concentration and flux, respectively). In decade II, the 

largest relative changes in flux were decreases in the LaPlatte 

River (2.8 and 1.6 percent per year for concentration and flux, 

respectively) and Otter Creek (2.2 and 1.6 percent per year for 

concentration and flux, respectively). The net change of all 

gaged tributaries for the period of record was a 0.3 percent per 

year decrease in flux.

Dissolved Phosphorus

The pattern of increases and decreases between decades 

did not shift as much for concentration or flux of dissolved 

phosphorus as it did for total phosphorus. More tributaries had increases than had decreases in concentrations and 

flux of dissolved phosphorus for all of the time periods. In 

decade I, concentrations of dissolved phosphorus decreased in 

5 tributaries and increased in 13 tributaries (table 3; fig. 2; and 

appendixes 1 and 3); in decade II, concentrations decreased 

in 4 tributaries and increased in 14 tributaries; and for the 

entire period, concentrations decreased in 5 tributaries and 

increased in 13 tributaries. The number of tributaries with flux 

that decreased was five for decade I and for the overall period 

of analysis (fig. 3; table 4; appendix 8). For decade II, flux 

decreased in 6 tributaries and increased in 12 tributaries. 

Thirteen tributaries had changes in concentrations that did 

not vary by more than 0.005 milligrams per liter between 

decades I and II.

In decade I, the total annual decrease in dissolved 

phosphorus flux was 15 t; this decrease was entirely offset 

in decade II with a total annual increase of 16 t, resulting 

in a total annual increase of 0.7 t from 1990 through 2010 

(table 4). The decade I decrease in flux of dissolved phosphorus was dominated by decreases in flux from tributaries on 

the eastern side of Lake Champlain, in particular, from Otter 

Creek (a decrease of 20 t/yr). Small relative increases in flux 

from all of the western tributaries had minimal effect on basinwide flux. In decade II, increases and decreases in dissolved 
Discussion of Trends 15

phosphorus flux were distributed among tributaries on both 

sides of the lake, with the largest increases seen in Missisquoi 

and Saranac Rivers (9.5 and 3.3 t/yr). Throughout the period 

of analysis, tributaries on the western side of the lake collectively increased by 17 t/yr, and tributaries on the eastern side 

collectively decreased by 17 t/yr, led by Otter Creek and the 

LaPlatte and Winooski Rivers (decreases of 24, 6.0, and 

3.6 t/yr, respectively). The effect of this net decrease was 

diminished by increases of 11 t/yr in the Missisquoi River and 

of 5.9 t/yr in the Saranac River.

While the magnitudes of many of the large annual percent 

changes in concentration and flux of dissolved phosphorus 

seen in decade I were diminished in decade II (tables 3 and 4), 

the number of increasing changes still was greater than those 

for decreasing changes. In decade I, the largest annual percent 

increase in concentration was in the Mettawee River. The largest increase in flux was in the Bouquet River, and the largest 

decrease in concentration and flux was in the LaPlatte River. 

In decade II, the largest annual percent increases in concentration and flux were seen in Putnam Creek, and the largest 

decrease was again in the LaPlatte River. 

Total Nitrogen

Concentrations of total nitrogen in decade I showed 

no change in 2 tributaries, decreasing concentrations in 

4 tributaries, and increasing concentrations in 12 tributaries 

(fig. 2; table 3; appendixes 1 and 3). An almost complete 

reversal in this pattern was seen in the data for decade II, 

when concentrations decreased in 17 tributaries and increased 

in just one. Concentration changes for the period of analysis 

showed 14 tributaries with decreasing concentrations of total 

nitrogen and 4 with increasing concentrations. The numbers 

of tributaries with either upward or downward trends in the 

flux of total nitrogen for the three time periods was similar 

to the pattern in the trends for concentration, with the flux 

in 17 of the 18 tributaries (all except Winooski) decreasing 

during decade II (fig. 3; table 4; appendixes 1 and 8). For the 

period of analysis, 13 tributaries showed decreases (table 4; 

appendix 8) in nitrogen flux. 

On a mass basis, the total annual increase in the flux of 

total nitrogen for decade I was 440 t. For decade II, the total 

annual decrease was 826 t, and for the period of analysis, the 

total annual decrease was 386 t (table 4). The largest increases 

in flux in decade I were in the Missisquoi and Pike Rivers (131 

and 86 t/yr, respectively). The largest decreases in mass flux 

in decade II were in Otter Creek and the Ausable River (178 

and 138 t/yr, respectively). In decade II, flux of total nitrogen 

decreased in all of the tributaries from the western side of 

Lake Champlain; the largest mass decreases were seen in the 

Saranac, Great Chazy, Ausable, and Bouquet Rivers on the 

western side, and also in Otter Creek and the Mettawee River 

on the eastern side of Lake Champlain. 

All of the increasing concentrations and fluxes of total 

nitrogen in decade I were relatively small; only five were 

more than 1 percent per year (but less than 2 percent per year). 

Percent changes in decade II were larger; the concentration 

in seven tributaries and the flux in eight tributaries decreased 

at least 2 percent per year. On a normalized basis, the largest increases in flux in decade I were in the Ausable and 

Pike Rivers (1.7 and 1.8 percent per year, respectively). The 

largest decreases in flux in decade II were in the Bouquet and 

LaPlatte Rivers (3.2 and 3.1 percents per year, respectively). 

Chloride

For decade I, concentrations of chloride decreased in 

1 tributary and increased in 17 tributaries. For decade II 

concentrations decreased in 5 and increased in 13 tributaries, 

and for the period of analysis, concentrations decreased in 

2 and increased in 16 tributaries (fig. 2; table 3; appendixes 

1 and 3). The summary for numbers of tributaries that had 

decreasing and increasing chloride flux and associated rates of 

change in flux (fig. 3; table 4; appendixes 1 and 8) is almost 

identical to the summary for chloride concentration. 

On a mass basis, the two tributaries with decreases in 

chloride for decade I and for the period of analysis were 

LaPlatte and Pike Rivers; for decade II, tributaries with the 

largest mass decreases were Missisquoi and Pike Rivers 

(table 4), and those with the largest normalized decreases were 

LaPlatte and Pike Rivers. For all three time periods, the largest contributors to the mass increase in chloride flux were the 

Winooski and Saranac Rivers. For decade I, the total annual 

increase in chloride flux was 25,163 t. For decade II, the total 

annual increase was 7,062 t, and for the period of analysis, 

the total annual increase was 32,225 t. Seventy-eight percent 

of the annual flux increase during the period of analysis was 

realized during decade I. The five tributaries that had decreasing concentration and flux of chloride between 2000 and 2010 

were all on the eastern side of Lake Champlain. Decreasing 

chloride fluxes were not seen in any tributaries on the western 

side of the lake for any of the three time periods analyzed.

Eleven of the increasing concentrations for decade I 

increased at rates greater than 2 percent per year. The highest 

rates of decrease of concentration and flux for both the 

separate decades and for the period of analysis were in the 

LaPlatte River. For decade II, the rates of increase generally 

decelerated; concentrations in only four of the tributaries 

with increasing concentrations increased at least 2 percent 

per year, and for the period of analysis, the greatest rates of 

increase, over 5 percent per year, were seen in the Ausable and 

Saranac Rivers.

Discussion of Trends

Because of the emphasis in the Lake Champlain 

Management plan on the goal of reducing phosphorus flux 

to the lake, the following discussion focuses on the trends in 

concentrations and flux of total and dissolved phosphorus. 
16 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

An important question is how to interpret the data in terms 

of measuring progress toward meeting the phosphorus 

reduction goals. A tool that provides information about the 

influence of particular seasons and discharges on positive 

and negative changes in total phosphorus concentrations 

between two selected years is illustrated and discussed. 

Additional discussion topics are the significance of the ratios 

of total phosphorus to dissolved phosphorus and trends in 

concentrations and fluxes of nitrogen and chloride.

Is Progress Being Made in Reducing 

Phosphorus?

Examination of data on the concentrations and flux of 

total phosphorus for the overall period of analysis showed 

that more tributaries had increasing than had decreasing 

concentration and flux. When the datasets for the two separate 

decades of record are compared, however, decade II shows 

that concentrations improved compared to those in decade 

I, in that a greater number of tributaries showed decreasing 

concentrations (10 decreases in decade II compared to 

5 decreases in decade I; fig. 2; table 3). The flux picture 

is more complex. As with concentrations, the number of 

tributaries with downward trends in flux was greater in decade 

II than in decade I (9 decreases in decade II and 5 in decade 

I) (fig. 3 and table 4); however, basinwide flux is an additive

property, unlike concentration, and the tendency for flux 

from a small number of tributaries to dominate the basinwide 

picture is important to note. In particular, although trends 

from two of the largest tributaries, Winooski and Missisquoi, 

have decreased over 21 years, they have increased in the most 

recent 11-year period. While the annual percent changes from 

these tributaries has been very small, their large areas translate 

to a large overall contribution on a mass basis. 

To put things in perspective, many of the changes in 

concentration and flux of these Lake Champlain tributaries 

have been very small, less than 1 percent per year. While most 

tributaries had increasing concentration and flux over the 

period of record, improvements were seen for a greater number of individual tributaries in decade II compared to decade 

I. In decade I, most of the western tributaries had increasing 

flux, and the eastern tributaries had decreasing flux, but the 

larger tributaries in the east dominated the basinwide decrease. 

In decade II, all of the western tributaries improved in both 

concentrations and flux compared to decade I, except Salmon 

River, whose flux increased. Flux in tributaries on the eastern 

side of the basin continued to decrease in decade II, although 

at a lower rate of change compared to decade I.

Influence of Season and Discharge on Changes 

in Total Phosphorus

The USGS software package that includes WRTDS2

offers additional tools that can be used to improve our 

understanding of water-quality responses to ecosystem and 

land-based processes. One such tool is the contour plot 

shown in figure 4 that depicts the difference in estimated 

total phosphorus concentrations for four representative 

rivers between two selected years, during the range of 

seasons and discharges, in order to demonstrate how the 

combination of various discharges and seasons influence the 

annual estimates. Similar plots of estimated total phosphorus 

concentrations for all 18 tributaries are in appendix 5. In 

figure 4 and appendix 5, pink areas show times of the year 

and discharges for which estimates of total phosphorus 

concentration increased between 1994 and 2010, with darker 

shades of pink indicating greater increases. Likewise, areas of 

blue shading indicate combinations of times of the year and 

discharges for which estimates of the concentrations of total 

phosphorus decreased, with darker shades showing greater 

decreases. Figure 4A shows that for the Saranac River, total 

phosphorus concentrations increased at all discharges during 

the spring and summer and at very low discharges through the 

winter. In the fall and winter at all but the lowest discharges, 

the concentrations decreased. Thus, concentrations of total 

phosphorus that increased in the Saranac River throughout the 

period of analysis were dominated by increases that occurred 

primarily in the spring and summer, especially at very high 

discharges in June and July and at very low discharges 

between March and June. Increased concentrations during 

periods of low flow throughout the year provide evidence 

of increases in point-source or groundwater sources of 

phosphorus, and increases during summer high flows suggest 

new or additional sources of seasonal nonpoint contamination. 

Even this kind of general information that provides some 

guidance on where the phosphorus in observed concentrations 

is coming from can be helpful to managers who are charged 

with designing treatments for reducing phosphorus inputs to 

tributaries or to Lake Champlain.

For the Mettawee River (fig. 4B), decreases and 

increases in estimated total phosphorus concentrations were 

evenly distributed throughout the year, but large decreases 

were estimated at very high discharges (generally above 

the 95th percentile of flow) for most parts of the year. 

Concentrations in Otter Creek (fig. 4C) decreased across all 

seasons and discharges except for increases during summer 

months at very high discharges (generally above the 95th 

percentile of flow). For the Missisquoi River (fig. 4D), 

decreases and increases in estimated total phosphorus 

concentrations were relatively evenly distributed throughout 

2

WRTDS is one component of an Exploration and Graphics for River 

Time-Series (EGRET) toolkit, a utility in R programming language to analyze 

long-term changes in water quality and streamflow (https://github.com/USGSCIDA/WRTDS/blob/master/README.md).
Discussion of Trends 17

-0.10

-0.05

0.00

0.05

0.10

50

100

200

500

1,000

2,000

5,000

10,000

20,000

-0.05

0.00

0.05

100

200

500

1,000

2,000

5,000

-0.10

-0.05

0.00

0.05

0.10

10

20

50

100

200

500

1,000

2,000

-0.04

-0.02

0.00

0.02

0.04

Jan. 1 Mar. 1 May 1 July 1 Sept. 1 Nov. 1 Jan. 1

Jan. 1 Mar. 1 May 1 July 1 Sept. 1 Nov. 1 Jan. 1

Jan. 1 Mar. 1 May 1 July 1 Sept. 1 Nov. 1 Jan. 1

Jan. 1 Mar. 1 May 1 July 1 Sept. 1 Nov. 1 Jan. 1

200

500

1,000

2,000

5,000

Discharge, in cubic feet per second

Months

Difference in concentration,

in milligrams per liter

EXPLANATION

A

B

C

D

Figure 4. The seasonal differences in estimated total phosphorus concentrations between 1994 and 2010 in the A, Saranac River, 

B, Mettawee River, C, Otter Creek, and D, Missisquoi River.
18 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

the year. The largest increases or decreases occurred at very 

high discharges, those above the 95th percentile, through most 

of the year. Graphs in appendix 5 show that increases and 

decreases in concentrations of total phosphorus between 1994 

and 2010 in all of the monitored Lake Champlain tributaries 

follow similar patterns as those described in figure 4: patterns 

in all the New York tributaries (Great Chazy, Little Chazy, 

Salmon, Little Ausable, Ausable, Bouquet, and Putnam) were 

similar to those in the Saranac River. The Lamoille River 

was similar to the Mettawee River, the Poultney and LaPlatte 

Rivers were similar to Otter Creek, and the Winooski River 

was similar to the Missisquoi River. The Pike River had 

a slight, fairly uniform decrease in concentrations of total 

phosphorus during most discharges and seasons, except for 

large increases at very high discharges in fall and winter. 

Little Otter and Lewis Creeks were characterized by increases 

in concentrations during the summer and fall and decreases 

during parts of the winter and spring.

Ratios of Dissolved to Total Phosphorus 

Concentration and Flux

Examination of the ratios of concentrations of dissolved 

to total phosphorus may provide some insight to the 

movement of phosphorus in the tributaries to Lake Champlain. 

Ratios of dissolved to total phosphorus concentration and flux 

for the tributaries essentially fall into one of three groups: 

the majority of phosphorus is in the dissolved state (the ratio 

is greater than 0.5), the minority of phosphorus is in the 

dissolved state (the ratio is less than 0.5), or about half of the 

phosphorus is dissolved. The fraction of total phosphorus 

that is not dissolved is in a particulate form. Examples from 

each of these groups are shown as graphs of concentration 

(fig. 5A) or flux (fig. 5B) of dissolved versus total phosphorus. 

Although some similar patterns of the ratios among tributaries 

are seen in figure 5, the similarities appear unrelated to 

geography or to have any other simple explanation. The 

interaction of several different processes that may influence 

this ratio makes it difficult to trace the evolution of any 

particular pattern. Areas saturated with orthophosphate (the 

degrees of saturation are indicated in fig. 5 by the distance 

that blue points plot below the 1:2 reference line), the primary 

dissolved form of phosphorus, as a result of over application 

of manure or other fertilizers can show increases in dissolved 

relative to total phosphorus, except in the presence of clays or 

iron oxides, which lead to adsorption or calcium carbonate, 

which in turn leads to mineralization (Domagalski and 

Johnson, 2012). In addition to soil chemistry reactions, some 

of the other processes that might increase the concentration 

of total phosphorus relative to that of dissolved phosphorus 

include plant uptake of dissolved phosphorus, streambank 

erosion, and erosion away from streams in areas dominated by 

overland flow. 

Trends in Total Nitrogen

Total nitrogen concentration and flux for most individual 

tributaries have decreased since 1990. What could be causing 

these large and fairly uniform decreases in total nitrogen? 

Some of the decrease could be related to the decrease in 

inorganic nitrogen loading from atmospheric deposition by 

about 0.08 kilograms per hectare per year between 1990 and 

2010, which has been documented at an observation station in 

the Lake Champlain Basin (National Atmospheric Deposition 

Program, 2012). There also could be some concurrent benefit 

from the implementation of agricultural BMPs in the Lake 

Champlain Basin, such as cattle exclusion from streams, 

erosion control, and waste storage. Although these BMPs 

are designed primarily to reduce phosphorus flux into the 

lake by runoff processes, and thus target the total rather than 

dissolved fraction of phosphorus, the focus on runoff could 

concomitantly be helping to reduce total nitrogen flux to 

streams. These BMPs also might be particularly effective 

in areas with impermeable soils and impermeable bedrock 

that contribute only small amounts of nitrate-containing 

groundwater to base flow (Spahr and others, 2010). In areas 

with greater groundwater contributions to base flow, such 

as agricultural areas with permeable soils, it is possible that 

BMPs or other processes that directly or indirectly induce 

denitrification have been effective in reducing nitrogen 

input to streams. Denitrification occurs in any setting where 

groundwater flow paths intersect reducing environments (those 

containing little or no free oxygen), including upland parts of 

aquifers, riparian (near stream) zones, and hyporheic (interface 

between groundwater and surface water along a stream) zones 

(Puckett, 2004).

Trends in Chloride

 Trends in concentrations and fluxes of chloride in the 

tributaries to Lake Champlain correspond, in most cases, 

with in-lake data for chloride concentrations presented in 

Smeltzer and others (2012). The only in-lake data that does 

not reflect inputs from its closest major contributing tributary 

is that for Shelburne Bay, which shows no overall trend in 

chloride concentration and flux between 2001 and 2011, 

while the LaPlatte River, which drains into Shelburne Bay, 

has a pronounced downward trend in chloride for that period, 

possibly related to a wastewater-treatment facility upgrade 

(Vermont Department of Environmental Conservation and 

New York State Department of Environmental Conservation, 

1998). Smeltzer and others (2012) suggest that the 30 percent 

decrease in winter road salt application in Vermont since 1999 

could feasibly account for the downward trends in chloride 

concentrations and flux in those parts of Lake Champlain 

that receive inflow primarily from tributaries draining from 

Vermont. The temporal and spatial pattern of decreasing 

chloride concentration and flux appears to support that 

hypothesis because in general, the chloride concentrations 
Discussion of Trends 19

A. ConcentrationB. Flux

0.050.040.030.020.010.00

0.009 0.010 0.011

Total phosphorus, in milligrams per liter Dissolved phosphorus, in milligrams per liter

Winooski annual FN concentration with 1:2 line 

(a similar pattern is seen in Ausable, Bouquet, Poultney, 

Mettawee, Otter, Lewis, Lamoille, and Missisquoi) 

0.250.200.150.100.050.00

0.07 0.08 0.09 0.10

Dissolved phosphorus, in milligrams per liter

Little Chazy annual FN concentration with 1:2 line 

(a similar pattern is seen in Little Ausable, Little Otter, and Pike)

0

4020

5.8 6.0 6.2 6.4

Total phosphorus, in metric tons

Dissolved phosphorus, in metric tons

Poultney annual FN flux with 1:2 line

(a similar pattern is seen in Great Chazy, Saranac, Salmon, Little Ausable, Ausable, Bouquet, Putnam, Mettawee, Otter, 

Lewis, Winooski, Lamoille, Missisquoi, and Pike)

840

12

3.5 4.0 4.5 5.0

Dissolved phosphorus, in metric tons

Little Chazy annual FN flux with 1:2 line

(no other tributary has a similar pattern)

0.030.020.010.00

0.004 0.008 0.012

Dissolved phosphorus, in milligrams per liter

Putnam annual FN concentration with 1:2 line 

(a similar pattern is seen in Great Chazy, Saranac, Salmon, 

and LaPlatte)

50

1510

4.5 4.6 4.7 4.8 4.9

Dissolved phosphorus, in metric tons

Little Otter annual FN flux with 1:2 line

(a similar pattern is seen in LaPlatte)

Figure 5. Patterns of the ratio of A, concentration and B, flux of flow-normalized dissolved phosphorus to flow-normalized total phosphorus for tributaries to Lake 

Champlain, from 1990 through 2011.
20 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

in Vermont tributaries (eastern side of Lake Champlain) are 

decreasing and in the New York tributaries (western side) 

are increasing in decade II3

. Note, however, that the New 

York tributaries have clearly improved in both chloride 

concentration and flux in decade II compared to decade I; that 

is, the increases in concentration in decade II are much less 

than the increases in decade I.

Relating Trends in Total Phosphorus to 

Basin Characteristics

A variety of basin characteristics were tested at two 

spatial scales for correlations with total phosphorus concentration and with flux. One scale was HUC8, which represents 

the entire subbasin for the major tributary (such as Winooski 

or Ausable), and the other was HUC12, the scale that represents a nested subdivision of the subbasin that was closest to 

the water-quality and streamflow monitoring station (fig. 1). 

Results of the correlation tests are presented in table 5. For 

most of the correlation tests, the time periods of the two data 

sets that were tested are the same or nearly the same, except 

for the category of BMPs where possible lag effects were 

tested. The lack of strong trends in total phosphorus for most 

of the tributaries over the time periods that were analyzed 

should be kept in mind during this discussion.

Physical and Demographic Factors

Physiographic province had a significant relation with 

phosphorus concentration and flux (table 5). As a static 

measure, population density was positively correlated with 

phosphorus flux at the HUC12 scale. The change in population density was not correlated with the change in phosphorus 

concentration or flux at any scale or time period. 

Point Sources of Phosphorus

Fluxes of total phosphorus from point sources decreased 

in all tributaries (except Bouquet River, where the Willsboro 

wastewater-treatment plant began operations in 1995) that 

reported fluxes between 1991 and 2011 (fig. 6). The largest 

point-source fluxes of total phosphorus in 1991 and 2000 

were in Otter Creek and the Winooski River (64.0 and 24.3 t, 

respectively, in 1991 and 13.9 and 16.1 t, respectively, in 

2000), but by 2011, the largest fluxes were in the Winooski 

and Saranac Rivers (7.7 and 3.7 t, respectively). During the 

1991 to 2011 time period, all tributaries except the Bouquet 

River saw point-source total phosphorus flux decreases of 

3

Tributaries in figures 2 and 3 are listed in downstream order number; the 

first eight tributaries are in New York, the next two drain area in both states, 

the next six are entirely in Vermont, the next drains areas in both Vermont and 

the Province of Quebec, and the last is entirely in Quebec.

between 58 (Saranac) and 99 percent (LaPlatte). Phosphorus 

flux decreased in the Bouquet River by 43 percent from 2000 

to 2011. Because locations of point sources were identified 

only to the HUC8 subbasin, correlations were not tested at 

the finer HUC12 scale. The decreases in point source fluxes 

from 1991 to 2011 correlated with decreases in phosphorus 

concentrations and flux in the tributaries for the same period 

(table 5). Fluxes from point sources in 2000 and in 2010 were 

strongly correlated with phosphorus flux in tributaries for the 

same years.

Given these reductions in point-source discharges in 

many of the Lake Champlain subbasins between 1991 and 

2011, it is worth assessing whether the reductions appear 

related to concurrent changes in concentrations of dissolved 

phosphorus, the form of phosphorus with greatest bioavailability (Ekholm and Krogerus, 1998), in the tributaries. 

Figure 7 shows that 38 percent of the variation in the changes 

of flow-normalized flux of dissolved phosphorus in tributaries 

is related to the variation in changes in total phosphorus flux 

from point sources. The point in the lower left corner of the 

graph represents data from the LaPlatte River Basin. 

Land Use and Agricultural Statistics

Runoff from agricultural land and urban land is estimated 

to contribute about 56 and 37 percent, respectively, of the 

nonpoint source of total phosphorus flux to Lake Champlain 

(Hegman and others, 1999). As a result, several State and 

Federal agricultural and stormwater initiatives are aimed at 

reducing runoff from these types of land uses. The collective 

effectiveness of these programs is an elusive metric at the 

basin scale because of complexities associated with multiple 

sources of phosphorus with different hydrological controls 

(Sharpley and others, 2009). Another difficulty with matching 

tributary concentrations of phosphorus with agricultural 

activities on the land is that many of the measures of activities 

are reported on a county rather than basin basis.

Yet, the countywide USDA census of agriculture data 

(U.S. Department of Agriculture, 2012) presents a comprehensive, detailed, consistent, and well documented picture 

of farming across the country every 5 years—all important 

characteristics of datasets if they are to be useful in exploring 

relations to trends. The agricultural statistics that were selected 

for exploring correlation tests against total phosphorus in the 

tributaries to Lake Champlain were acres of land in farms, 

acres of harvested cropland, acres of corn for grain or seed, 

acres of corn for silage or green chop, acres of land with applications of commercial fertilizer, and number of dairy cows in 

the tributary basins. 

Several land-use and agricultural statistics for the basins 

of the tributaries to Lake Champlain showed significant 

correlations with the phosphorus concentration or flux 

data (table 5). The percentages of agricultural land and of 

agricultural land that intersected hydric soils in year 2001 

were positively correlated with year 2001 phosphorus 
Relating Trends in Total Phosphorus to Basin Characteristics 21

Table 5. Basin characteristics that were tested for correlation with total phosphorus concentration and flux, and correlation test results for tributaries to Lake Champlain.

—Continued

[Supporting data are in appendix 6; HUC8, data pertain to drainage area from streamgage to entire 8-digit hydrologic unit basin; HUC12, data pertain to drainage area from streamgage to adjacent 12-digit hydrologic unit subbasin; τ, Kendall’s tau; --, not applicable; km2, square kilometers; bold values signify statistical significance for α = 0.10]

Watershed characteristic Year or range of years

Phosphorus concentration and flux Statistical test result for phosphorus concentrations and part of watershed Statistical test result for phosphorus flux and part of watershed

Year or range 

of years1

HUC8 HUC12 HUC8 HUC12

Kendall τ p-value Kendall τ p-value Kendall τ p-value Kendall τ p-value

Physical and demographic

Physiographic province2 -- ChiSquare = 4.8 0.092 -- -- ChiSquare = 6.2 0.045 -- --

Population density, people per km2 2000 2000 0.217 0.211 0.092 0.620 0.085 0.622 -0.417 0.024

Change in population density, people per 

square kilometer3

1990–2010 1990–2011 -0.072 0.677 -0.167 0.368 -0.046 0.791 0.050 0.787

2000–2010 2000–2011 -0.111 0.520 -0.233 0.207 -0.150 0.384 -0.167 0.368

Point sources

Phosphorus flux from point sources

2000 2000 -0.143 0.420 -- -- 0.683 0.000 -- --

2010 2010 -0.014 0.939 -- -- 0.597 0.001 -- --

Percent change in phosphorus flux from 

point sources

1991–2011 1991–2011 0.462 0.028 -- -- 0.487 0.020 -- --

2000–2011 2000–2011 0.026 0.903 -- -- 0.180 0.393 -- --

Land use

Percent or percent change in:

Urban land use including open land3 2001 2001 0.275 0.111 -0.147 0.402 0.146 0.403 -0.203 0.252

Agricultural land use3 0.555 0.001 0.409 0.019 0.535 0.002 0.428 0.015

Agricultural land in basin that intersects hydric soils (type C or D)3 0.573 0.002 0.400 0.026 0.526 0.004 0.420 0.021Acres of land in farms 1987–2007 1990–2007 0.338 0.053 0.244 0.174 0.298 0.087 0.362 0.043

1997–2007 1997–2007 0.020 0.910 0.044 0.805 0.163 0.344 0.206 0.249

Acres of cropland 1987–2007 1990–2007 0.320 0.064 0.237 0.187 0.216 0.211 0.267 0.137

1997–2007 1997–2007 0.236 0.172 0.199 0.266 -0.066 0.705 -0.111 0.536

Acres of corn for grain or seed 1987–2007 1990–2007 0.373 0.031 0.598 0.001 0.294 0.088 0.376 0.036

1997–2007 1997–2007 0.300 0.105 0.260 0.180 -0.033 0.857 -0.048 0.804

Acres of corn for silage 1987–2007 1990–2007 0.026 0.880 0.007 0.967 0.013 0.940 -0.022 0.902

1997–2007 1997–2007 0.137 0.426 0.185 0.303 -0.242 0.161 -0.244 0.174

Acres of commercial fertilized 1987–2007 1990–2007 0.137 0.426 0.081 0.650 0.033 0.850 0.037 0.837

1997–2007 1997–2007 -0.020 0.910 -0.059 0.742 0.177 0.307 0.044 0.805

Number of milk cows 1987–2007 1990–2007 0.112 0.519 0.118 0.510 0.086 0.622 0.074 0.680

1997–2007 1997–2007 0.177 0.307 0.191 0.284 -0.203 0.240 -0.206 0.249
22 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011 Table 5. Basin characteristics that were tested for correlation with total phosphorus concentration and flux, and correlation test results for tributaries to Lake Champlain. —Continued [Supporting data are in appendix 6; HUC8, data pertain to drainage area from streamgage to entire 8-digit hydrologic unit basin; HUC12, data pertain to drainage area from streamgage to adjacent 12-digit hydro- logic unit subbasin; τ, Kendall’s tau; --, not applicable; km2, square kilometers; bold values signify statistical significance for α = 0.10] Phosphorus con- Statistical test result for phosphorus Statistical test result for phosphorus centration and flux concentrations and part of watershed flux and part of watershed Year or range Watershed characteristic of years Year or range HUC8 HUC12 HUC8 HUC12 of years1 Kendall τ p-value Kendall τ p-value Kendall τ p-value Kendall τ p-value Best-management practices 1990–2011 -0.231 0.201 0.184 0.469 -0.245 0.173 0.138 0.587 1995–1999 Number of agricultural best-management 2000–2011 -0.275 0.127 -0.230 0.365 -0.290 0.107 -0.368 0.148 practices constructed or implemented 1990–2011 -0.229 0.201 0.200 0.421 -0.126 0.483 0.156 0.531 1995–2010 2000–2011 -0.170 0.343 -0.244 0.325 -0.170 0.343 -0.289 0.245 1990–2011 -0.339 0.070 -0.291 0.152 -0.390 0.037 -0.268 0.186 1995–1999 Money spent on agricultural best- 2000–2011 -0.271 0.148 -0.358 0.078 -0.203 0.278 -0.156 0.441 management practices, dollars 1990–2011 -0.332 0.064 -0.332 0.100 -0.214 0.232 -0.199 0.324 1995–2010 2000–2011 -0.229 0.201 -0.155 0.443 -0.185 0.303 0.044 0.826

1When a range of years is denoted, the variable tested for correlation was percent change between the range of years.2This is the only watershed characteristic which, because the variable is nominal (non-continuous), uses the Kruskal-Wallis statistical test instead of Kendall’s tau for correlation.3Correlation tests are with phosphorus yield rather than flux.
Relating Trends in Total Phosphorus to Basin Characteristics 23

0

10

20

30

Great Chazy

Little Chazy

Salmon

Saranac

Little Ausable

Ausable

Bouquet

Putnam

Poultney

Mettawee

Otter

Little Otter

Lewis

LaPlatte

Winooski

Lamoille

Missisquoi

Pike

Aggregate load, in metric tons per year 

1991

2000

2011

64

EXPLANATION

1991, 2000, and 2011.

Figure 6. Aggregate reported point-source fluxes of total phosphorus for the 18 monitored Lake Champlain tributaries in 

R2 = 0.38

-100

0

100

-100 -75 -50

Percent change in total phosphorus flux from point sources

Percent change in flow-normalized flux 

of dissolved phosphorus in tributaries

Figure 7. The relation between changes in flux of total phosphorus from point sources and in dissolved 

phosphorus from Lake Champlain tributaries from 1991 to 2011.
24 Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011

concentrations and yield at both the HUC8 and HUC12 

scales. The change in acres of land in farms between 1987 

and 2007 was positively correlated with the change in 

phosphorus concentration at the HUC8 scale and with the 

change in phosphorus flux at the HUC8 and the HUC12 

scales. At the HUC8 scale, the change in acres of cropland 

between 1987 and 2007 was positively correlated with 

changes in phosphorus concentration. At all scales and over 

a 20-year time period, the change in acres of corn for grain 

or seed was positively correlated with changes in phosphorus 

concentrations and yields. 

Best-Management Practices

Several significant negative correlations (and no positive 

correlations) were found between money spent on agricultural 

BMPs and changes in phosphorus concentration and flux 

(table 5). A negative correlation (for example, an increase in 

money spent on agricultural BMPs relates to a decrease in 

percent change of phosphorus concentration or flux) indicates 

a beneficial outcome that occurred synchronously with BMP 

implementation. Just as with other results presented, however, 

this does not necessarily demonstrate that BMPs are causing the reduction in phosphorus. Although the two metrics of 

agricultural BMP effectiveness used in this study (the number of BMPs implemented and the money spent on BMPs) 

are related, the finding of a number of significant results 

for money spent on BMPs and no significant results for the 

number of BMPs implemented indicates that projects that cost 

more money are more strongly related to a reduction in phosphorus (suggesting that perhaps money is well spent). 

At the HUC8 scale, the change in phosphorus concentration during the period of record was negatively correlated with 

money spent on agricultural BMPs from 1995 to 1999 and 

from 1995 through 2010. Also at the HUC8 scale, the change 

in phosphorus flux during the period of record was negatively 

correlated with money spent on BMPs from 1995 to 1999. The 

only significant correlation between phosphorus concentration or flux and BMPs at the HUC12 scale was negative for 

concentration from 2001 to 2010 and money spent from 1995 

to 1999. This latter correlation in addition to the incidence of 

several negative correlations for BMPs from 1995 to 1999 

and changes in phosphorus concentration and flux during the 

longer time period suggests perhaps a possible delay between 

the time of BMP implementation and observed phosphorus 

reductions in Lake Champlain tributaries.

Summary and Conclusions

The second decade of the record (from 2000 through 

2010) saw improvement (a decrease) in flow-normalized 

total phosphorus concentration and flux for most individual 

tributaries in the Lake Champlain Basin compared to the first 

decade (from 1990 through 2000). During the entire period 

of analysis (from 1990 through 2010), however, total phosphorus concentrations increased in most of the tributaries 

(10 increases and 5 decreases); similarly, the number of flux 

increases and decreases were 10 and 7, respectively. From 

1990 through 2000, the total change in flow-normalized total 

phosphorus flux was a decrease of 21 metric tons (t). From 

2000 through 2010, the total change was a decrease of 20 t, 

and overall from 1990 through 2010, the total change in flux 

was a decrease of 42 t. The basinwide flux picture across the 

two decades was first dominated by decreases in flux for Otter 

Creek and the Winooski and Missisquoi Rivers in decade I followed by the continued decrease in Otter Creek in decade II. 

Basinwide, dissolved phosphorus flux in the Lake 

Champlain Basin increased by 0.7 metric tons per year 

(t/yr) during the period of analysis (from 1990 through 

2010). Flux of dissolved phosphorus decreased in decade 

I, primarily because of the large decrease in Otter Creek of 

20 t/yr. In decade II, large increases seen in Missisquoi and 

Saranac Rivers (9.5 and 3.3 t/yr) contributed to the basinwide 

increase in flux of dissolved phosphorus of 16 t/yr. Throughout 

the period of analysis, tributaries on the western side of the 

lake collectively increased by 17 t/yr, and tributaries on the 

eastern side collectively decreased by 17 t/yr. The effect of 

this net decrease was diminished by increases of 11 t/yr in the 

Missisquoi River and of 5.9 t/yr in the Saranac River.

Total nitrogen concentrations and flux for most individual tributaries and for the aggregate Lake Champlain Basin 

improved during the period of analysis. Between 1992 and 

2010, flow-normalized total nitrogen flux decreased by 386 t 

(increase of 440 t between 1992 and 2000 and decrease of 

826 t between 2000 and 2010); concentrations decreased in 

14 tributaries, and flux decreased in 13 tributaries, with greater 

percent and absolute decreases generally for the western side 

of the lake. Between 2000 and 2010, decreases in concentration and flux were seen in 17 of the tributaries (Winooski was 

the exception), with the largest mass decreases in flux in Otter 

Creek and the Ausable River (-178 and -138 t/yr).

Large increases in flow-normalized chloride concentrations and flux that occurred between 1990 and 2000 shrank to 

small increases or decreases for individual tributaries between 

2000 and 2010. Between 1990 and 2010, total flow-normalized chloride flux increased by 32,225 t, with 78 percent 

of that increase realized during the first decade. During the 

21-year period of analysis, decreases in concentrations and 

flux of chloride were seen in two tributaries, the LaPlatte and 

Pike Rivers, both on the eastern side of the basin. During the 

11-year period between 2000 and 2010, decreases were seen 

in five of the tributaries for both concentration and flux, in all 

cases from tributaries on the eastern side of Lake Champlain, 

although the total flux increase had contributions from both 

sides of the lake. Chloride trend results are in general agreement with published in-lake chloride concentration data and 

may be reflecting a decrease in winter road salt applications in 

Vermont since 1999. 
References Cited 25

Contour plots were used to demonstrate how various 

combinations of discharges and seasons influenced the difference between two selected years (a measure of trend) of 

annual estimates of total phosphorus concentrations. Contour 

plots of the differences between 1994 and 2010 of estimated 

daily phosphorus concentrations showed that many of the New 

York or western tributaries to Lake Champlain had the greatest 

increases in total phosphorus during the summer at all discharges and the greatest decreases in total phosphorus during 

the fall and winter at medium or high discharges. Tributaries 

on the eastern side of the lake lacked a uniform pattern for any 

of the seasons.

Significant correlations were found between physiographic province and concentration and flux of phosphorus 

but not between any of the measures of population density and 

phosphorus. The decreases in point source fluxes from 1991 

to 2011 correlated positively with decreases in phosphorus 

concentrations and fluxes for the same period. Fluxes from 

point sources in 2000 and in 2010 were positively correlated with phosphorus flux for the same years. The percents 

of agricultural land and of agricultural land that intersected 

hydric soils in 2001 were positively correlated with 2001 

phosphorus concentrations and yield at the HUC8 scale, as 

well as at the finer HUC12 scale. The change in acres of land 

in farms between 1987 and 2007 was positively correlated 

with the change in phosphorus concentration at the HUC8 

scale and with the change in phosphorus flux at the HUC8 and 

the HUC12 scales. At the HUC8 scale, the change in acres 

of cropland between 1987 and 2007 was positively correlated with changes in phosphorus concentration. At all scales 

between 1987 and 2007, the change in acres of corn for grain 

or seed was positively correlated with changes in phosphorus 

concentrations and yields. 

There were no significant correlations between the 

number of best-management practices (BMPs) and phosphorus concentration or flux in the Lake Champlain tributaries. 

The change in phosphorus concentration during the period 

of record was negatively correlated with money spent on 

implementation of BMPs from 1995 through 1999 and from 

1995 through 2010 at the HUC8 scale. Also at the HUC8 

scale, the change in phosphorus flux during the period of 

record was negatively correlated with money spent on BMPs 

from 1995 to 1999. The finding that there are some significant 

results for money spent on BMPs and no significant results for 

the number of BMPs suggests that costlier projects might be 

related to a greater reduction in phosphorus. Significant negative correlations between BMP measures from 1995 to 1999 

and reductions in phosphorus concentration or flux during the 

period of record suggest a possible delay between the time of 

BMP implementation and observed phosphorus reductions in 

Lake Champlain tributaries.

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Appendixes 1–8

Appendix 1. Concentration, Flux, and Yield for Total and Dissolved Phosphorus, Total Nitrogen, 

and Chloride in 18 Monitored Tributaries of Lake Champlain for 1990 through 2011

Appendix 2. Half-Window Widths Used for the WRTDS Regression Model Estimates for 

Concentration and Flux of Total Phosphorus, Dissolved Phosphorus, Total Nitrogen, 

and Chloride for Tributaries to Lake Champlain

Appendix 3. Flow-Normalized Annual Average Concentrations of Total and Dissolved 

Phosphorus, Total Nitrogen, and Chloride for 18 Monitored Tributaries of Lake 

Champlain from 1990 through 2011

Appendix 4. Observed and Estimated Concentrations of Total and Dissolved Phosphorus, 

Total Nitrogen, and Chloride for 18 Monitored Tributaries of Lake Champlain from 1990 

through 2011

Appendix 5. Contour Plots of the Difference in Estimated Concentrations of Total Phosphorus 

Between 1994 and 2010 in the 18 Monitored Tributaries of Lake Champlain

Appendix 6. Data for Correlation Analysis Between Total Phosphorus Concentration and Flux 

and Basin Characteristics for 18 Monitored Tributaries of Lake Champlain from 1990 

through 2011

Appendix 7. Observed and Estimated Flux of Total and Dissolved Phosphorus, Total Nitrogen, 

and Chloride for the 18 Monitored Tributaries of Lake Champlain from 1990 through 

2011

Appendix 8. Yield of Total and Dissolved Phosphorus, Total Nitrogen, and Chloride for the 18 

Monitored Tributaries of Lake Champlain from 1990 through 2011
Prepared by the Pembroke and West Trenton Publishing 

Service Centers.

For more information concerning this report, contact:

Office Chief

U.S. Geological Survey

New England Water Science Center

New Hampshire-Vermont Office

331 Commerce Way, Suite 2

Pembroke, NH 03275

dc_nh@usgs.gov

or visit our Web site at:

http://nh.water.usgs.gov
Medalie—Phosphorus, Nitrogen, and Chloride in Tributaries to Lake Champlain, 1990–2011—Scientific Investigations Report 2013–5021