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

Figure 1. Location of Kirby Lake

in relation to its watershed and

tributary-monitoring sites.

Fact Sheet FS-066-98

Hydrology, Water Quality, and Phosphorus Loading of Kirby

Lake, Barron County, Wisconsin

Introduction

In 1992, residents near Kirby Lake, located about five miles northwest

of Cumberland, in Barron County, Wisconsin, formed the Kirby Lake

Management District. The Lake District immediately began to gather

information needed for the preparation of a comprehensive lake-management plan that would be used to protect the natural and recreational assets

of the lake. The Lake District completed a land-use inventory of the

watershed and an evaluation of available lake water-quality data. The

land-use data were used to assess the potential contribution of nutrients

to the lake from the watershed. The evaluation of lake water-quality data,

which were collected as part of the Wisconsin Department of Natural

Resources (WDNR) Self-Help Monitoring Program, indicated the lake

has relatively good water quality. Before a comprehensive lake-management plan could be prepared, however, a better understanding of several

aspects of the lake and its surroundings was needed. To address those

aspects—including the definition of the lake’s hydrology and the principal sources of nutrients, and the relation of the lake’s water quality to

nutrient loading—the U.S. Geological Survey, in cooperation with the

Lake District and the WDNR (through a Lake Management Planning

Grant), conducted a study of Kirby Lake and its watershed. This Fact

Sheet presents the results of that study.

The Lake and its Watershed

Kirby Lake has a surface area of 92 acres, a maximum depth of 19 feet,

and an average depth of 8 feet (Wisconsin Department of Natural

Resources, 1995). The area and depth of the lake vary, however, with

changes in lake stage, which in turn depends on inflow and outflow of

water. Water enters Kirby lake from precipitation, numerous small,

intermittently flowing tributaries, and ground-water inflow. The lake’s

outlet stream flows only intermittently, and water is lost primarily

through outflow to ground water or through evaporation.

The watershed of Kirby Lake (fig. 1) has a total area of 1,070 acres,

although part of this area is made up of depressions that do not normally

drain to the lake. Some of these depressions overflow after prolonged

periods of above-normal precipitation and drain to Kirby Lake. About 60

percent of the watershed is forested; the remainder consists of wetlands,

small lakes, agricultural land, residential development, and roads.

An aeration system was installed in the lake in 1989. The system is

operated during winter to keep a small part (less than one acre) of the lake

free of ice, which prevents oxygen depletion and the resulting fish kills.

Data Collection

Data used to describe the lake’s hydrology, water quality, and sources

of phosphorus were collected during the period from November 1, 1995

to November 6, 1996. Lake water-quality properties were measured eight

times at as many as six sites in the lake (fig. 2). At all sites, depth profiles

of water temperature, dissolved oxygen, specific conductance, and pH

were measured. Water samples were collected at these sites at either or

both near-surface (1.5 ft below surface during open water or just below

ice during ice cover) or near-bottom (1.5 ft above bottom) depths. Nearsurface water samples from the deepest part of the lake (Site 1 in fig. 2)

were analyzed for concentrations of total phosphorus (an indicator of

nutrient availability) and chlorophyll a (an indicator of algal population),

EXPLANATION

Lake-watershed boundary

Tributary-monitoring site

 and identifier

Outlet

Land use/land cover 

Forest

Wetland

Barren land

Grassland

Agriculture

45°36'53"

45°35'38"

92°05'00" 92°03'45"

0 .25 .50

0 .25 .50

MILES

KILOMETERS

G

Location of Kirby Lake in

Barron County

WISCONSIN

Kirby Lake

Cty Hwy H

4th Street

Kirby Lake

B A

C

D

E

F

G

H I

J

K

L
Figure 2. Water depth, and locations of piezometers and water-sampling

sites at Kirby Lake.

Figure 3. Daily precipitation at, and lake stage of, Kirby Lake.

Figure 4. Inflows and losses of water, in acre-feet, for Kirby Lake,

November 1, 1995 through October 31, 1996.

and, during ice-free periods, Secchi depths (an indicator of water clarity)

were also measured. In May 1996, when the lake was completely mixed,

near-surface water from Site 1 was also analyzed for dissolved nitrite plus

nitrate, total ammonia plus organic nitrogen, and chloride and nearbottom water from this site was analyzed for total phosphorus. Water

samples were collected and depth-profile measurements were made at the

other five sites (Sites 2–6, fig. 2) in January and March 1996 to assess the

conditions under the ice. Selected near-surface and near-bottom samples

from Sites 2–6 were analyzed for total phosphorus to define vertical and

areal differences in concentration. All water samples were analyzed by

the Wisconsin State Laboratory of Hygiene. Additional phosphorus,

chlorophyll a, and Secchi-depth data for 1992–95 were provided by the

WDNR (Danny Ryan, written commun., 1997). Data collected during

this study were published in two reports (Holmstrom and others, 1997;

U.S. Geological Survey, Wisconsin District Lake-Studies Team, 1997).

 Phosphorus input to the lake from surface runoff was determined by

analyzing water samples collected from the tributaries shown in figure 1

during periods of snowmelt and storm runoff. The amount of phosphorus

delivered to the lake by each tributary was calculated by multiplying the

flow-weighted phosphorus concentration by the estimated runoff volume.

Hydrology

The hydrology of Kirby Lake can be described in terms of components

of its water budget. The water budget for the lake may be represented by

the equation,

∆S = (PPT + SWIn + GWIn) – (Evap + SWOut + GWOut),

where ∆S is the change in the volume of water stored in the lake during

the period of interest and is equal to the sum of the volumes of water

entering the lake minus the sum of the volumes of water leaving the lake.

Water enters the lake as precipitation (PPT), surface-water inflow (SWIn),

and ground-water inflow (GWIn). Water leaves the lake as evaporation

(Evap), surface-water outflow (SWOut), and ground-water outflow (GWOut).

The change in the lake volume was determined from data obtained at

a continuously recording lake-stage gage installed in the southwestern

bay of the lake (fig. 2). Precipitation was measured at the same site by use

of an automatic-recording rain gage, and manually measured by Warren

Cook, at his residence on the southeastern side of the lake (fig. 2). All of

the other components of the lake’s water budget were estimated using

data from nearby sites or by solving for them as unknowns (residuals) in

the budget equation when all of the other components in the equation

were known or approximated. Surface-water inflow was estimated by an

analysis of precipitation data and intermittently measured flow at the 12

tributary sites (fig. 1). Ground-water inflow was estimated using measurements of water levels in small-diameter piezometers (wells) installed

at 10 sites around the lake (fig. 2) and from information from domesticwell construction reports. Ground-water outflow was assumed to be

constant throughout the year, and was estimated in September, when

surface-water inflow and outflow were known to be zero. During this

time, ground-water outflow was the only unknown variable in the

equation. Evaporation from the lake was estimated on the basis of

evaporation-pan data from a weather station at St. Paul, Minnesota, in

conjunction with lake/pan evaporation coefficients of 0.7–1.19. With all

the other variables known or estimated, surface-water outflow then was

calculated with the equation except when it was known to be zero—when

the lake stage was lower than the outlet level.

Precipitation during the study and the preceding year was greater than

normal and was the predominant source of inflow (57 percent of the total

inflow) to Kirby Lake during the study (figs. 3 and 4). Precipitation

measured at the lake during the study period (39.00 inches) was 18

percent, or 5.87 inches, greater than the 1961–90 average at Cumberland

(National Oceanic and Administrative Administration, 1996). Precipita15

15

45°36'15"

45°35'57"

92°04'23" 92°03'45"

EXPLANATION

Line of equal depth, 5 foot intervals

Trace of section shown in figure 7

Lake water-quality sampling site and identifier

Recording lake-stage gage and rain gage

Manually read precipitation gage

Piezometer

0 .125 .25

0 .125 .25

MILES

KILOMETERS

5

5

5

5

5

10

10

15

1

1

2

3

3

4

5

6

A

A'

A'

A

4th Street

N D J F M A M J J A S O

1995 1996

7.5

9.5

8.0

8.5

9.0

LAKE STAGE,

IN FEET

N D J F M A M J J A S O

1995 1996

0

3

1

2

PRECIPITATION,

IN INCHES

Intermittently measured stage

Continuously measured stage

Precipitation

309

(57%)

Surface-water inflow

229

(43%)

Evaporation

219

(34%) Ground-water

outflow

163

(25%)

Surface-water outflow

269

(41%)

INFLOWS LOSSES
Figure 5. Diagrammatic hydrogeologic section of Kirby Lake showing

relation of lake to ground water.

tion at Cumberland during the four months preceding the study (July–

October, 1995) was 22.77 inches, or 47 percent greater than normal for

that period.

Lake stage fluctuated from a minimum of 7.61 ft (relative to an

arbitrary datum) to a maximum of 9.24 ft (fig. 3). Lake stage at the end

of the study was 1.19 ft lower than at the start of the study.

The lake’s water budget (summarized in fig. 4) is for a “wet period”

and probably does not represent years with normal or less than normal

precipitation. The lake stage was high and most tributaries to the lake

were flowing at the start of the study, owing to the excess precipitation

in the preceding four months. Most surface-water inflow (about 94

percent) occurred during four months—November 1995, and April–

June 1996. About half of all of the surface-water inflow came from the

watershed above monitoring Site G, which drains most of the lake’s

watershed west of Fourth Street (fig. 1).

Ground-water inflow during the study period was assumed to be zero,

because water levels measured in the near-lake piezometers indicated

that water generally was flowing from the lake into the ground. Water

levels in two domestic wells near the south side of the lake indicated the

lake is hydraulically perched about 70 feet above the regional water table

(fig. 5). Small local areas, however, may have occasional subsurface

seepage to the lake, but their significance in the lake’s water budget is

thought to be negligible.

During the study, most of the water lost from the lake was from

surface-water outflow, which accounts for about 41 percent of all losses

(fig. 4). Evaporation and ground-water outflow accounted for 34 percent

and 25 percent of all losses, respectively. Losses of water exceeded

inflows, resulting in a 1.19 ft lowering of lake stage during the study. Lake

stage and surface-water outflow were influenced by vegetation and

activity of beavers in the lake’s outlet channel, which winds through a

marsh at the southwestern end of the lake. Beaver dams in the outlet

channel in October through November 1995 contributed to the greaterthan-normal lake stage at the start of the study period.

After an extended period of below-normal precipitation, such as the

1987–89 drought, Kirby Lake would likely have almost no surface-water

inflow or outflow. Lake stages during 1987–89 were reported to be 3 to

5 ft lower than during the study year (Michael Boland, Kirby Lake

District, oral commun., 1995). During these years, almost all water

inflow would have been precipitation, and water losses would have been

through evaporation and ground-water outflow.

Lake-Water Quality

The pH of water in Kirby Lake ranged from 5 to 6, and specific

conductance ranged from 20 to 30 microsiemens per centimeter. The low

pH and specific conductance values support the conclusion that groundwater inflow to the lake is negligible and direct precipitation on the lake

surface is the main source of inflow. A low chloride concentration of 0.9

milligrams per liter (mg/L) indicates there is little influence on the lake

from road salting or septic systems, which are common sources of

chloride.

One method of classifying a lake’s condition or productivity is by

computing water-quality indices based on Secchi depths, and, on nearsurface concentrations of chlorophyll a and total phosphorus developed

by Carlson (1977) and modified by Lillie and others (1993). These three

indices are related to each other in complex ways that differ seasonally and

among lakes. Secchi depths during the study ranged from 5.6 to 6.6 ft;

concentrations of chlorophyll a ranged from 4.3 to 7.4 micrograms per

liter; and concentrations of total phosphorus ranged from 0.023 to 0.042

mg/L. The trophic-state indices computed for Kirby Lake during this

study year and the preceding four years are shown in figure 6. All three

indices show the lake to be near the margin between moderately nutrient

enriched (mesotrophic) and heavily nutrient enriched (eutrophic).

Figure 6. Trophic-state indices for total phosphorus, chlorophyll a, and

Secchi depth for Kirby Lake.

At the beginning of winter, concentrations of dissolved oxygen were

about 11 mg/L, or near saturation, throughout the lake. The concentrations of dissolved oxygen decreased as winter proceeded, however, even

with the use of the aerator. The distribution of dissolved oxygen throughout the lake during late winter is shown in figure 7. The aerator significantly influenced the concentrations of dissolved oxygen and mixing

patterns throughout most of the lake, except in the northwestern bay. The

main effect of the aerator was to mix the water column in the main body

of the lake. This area of the lake remained oxygenated, but concentrations

of dissolved oxygen became low by late winter. The aerator had little

influence on the deep water in the northwestern bay, where water below

the sill depth (the shallowest depth separating the bay from the main body

of the lake) became almost devoid of oxygen.

Phosphorus Budget

Sources of phosphorus to Kirby Lake include the inflowing streams

and precipitation. Phosphorus concentrations in the streams varied only

slightly either seasonally or from site to site. The average, flow-weighted

concentration of total phosphorus from 43 samples collected at the 12

sampling sites was 0.073 mg/L; the maximum concentration was 0.169

Water table

Perched 

water table Typical 

domestic

well Zone of low permeability

Sandy material

Observation well

Direction of ground-water flow

Screened interval of well

Water level measured in well

EXPLANATION

1992 1993 1994 1995 1996

0

100

20

40

60

80

TROPHIC-STATE INDEX

Total phosphorus

Chlorophyll a

Secchi depth

Eutrophic

Mesotrophic

Oligotrophic
For more information, please contact:

District Chief

U.S. Geological Survey

8505 Research Way

Middleton, WI 53562

(608) 828-9901

www: http://wwwdwimdn.er.usgs.gov

U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet FS-066-98

Design and illustrations: Aaron Konkol and Michelle Greenwood

GIS support: David Saad

Banner graphic: Karen Lonsdorf

mg/L and the minimum concentration was 0.019 mg/L. The concentration of phosphorus in precipitation was assumed to be 0.007 mg/L, a value

used by Rose (1993) for a study of Balsam Lake in nearby Polk County,

Wisconsin. The total estimated external input of phosphorus to the lake

(fig. 8) was about 51 pounds, of which 88 percent was transported by the

inflowing streams. The watershed contributing to the tributary on the

southwestern side of the lake (Site G) accounted for 46 percent of total

phosphorus input. Evaluation of internal inputs of phosphorus from lake

sediments was beyond the scope of this study.

Approximately 35 percent of the total phosphorus input to the lake was

exported through the lake’s outlet. Phosphorus not lost through the outlet

remained in the lake water or was deposited in the bed sediment of the

lake, with a small unknown amount discharged with ground-water

outflow.

Conclusions

During the study period, which was wetter than normal, the principal

source of water to Kirby Lake was from direct precipitation and the

principal loss was from surface outflow; during a closer-to-normal year,

however, the primary losses of water would be through evaporation and

ground-water outflow. The main external source of phosphorus to the

lake was from surface runoff, most of which was from the single largest

tributary draining the western part of the lake’s watershed. Kirby Lake’s

trophic state is classified between mesotrophic and eutrophic. The

aerator, which is operated only during the winter, keeps part of the lake

free of ice and the water oxygenated and well mixed, except in the

northwestern bay of the lake.

By W.J. Rose and D.M. Robertson

References Cited

Carlson, R.E., 1977, A trophic state index for lakes: Limnology and Oceanography, v. 22, p. 361–369.

Holmstrom, B.K., Olson, D.L., and Ellefson, B.R., 1997, Water resources dataWisconsin, water year 1996: U.S. Geological Survey Water-Data Report

WI-96-1, 464 p.

Lillie, R.A., Graham, Susan, and Rasmussen, Paul, 1993, Trophic state index

equations and regional predictive equations for Wisconsin Lakes: Wisconsin

Department of Natural Resources Management Findings No. 35, 4 p.

National Oceanic and Atmospheric Administration. 1996. Climatological data—

Wisconsin: Asheville, N. C., National Climatic Data Center, published

monthly [variously paged].

Rose, W.J., 1993, Water and phosphorus budgets and trophic state, Balsam

Lake, northwestern Wisconsin, 1987–89: U.S. Geological Survey WaterResources Investigations Report 91-4125, 28 p.

U.S. Geological Survey, Wisconsin District Lake-Studies Team, 1997, Waterquality and lake-stage data for Wisconsin lakes, water year 1996: U.S.

Geological Survey Open-File Report 97-123, 134 p.

Wisconsin Department of Natural Resources, 1995, Wisconsin Lakes: Wisconsin Department of Natural Resources, PUB-FM-800, 182 p.

Figure 8. Phosphorus inputs to Kirby Lake from tributary-monitoring sites

and precipitation, November 1, 1995 through October 31, 1996. Total

inputs were 51 pounds.

Figure 7. Section showing

distribution of dissolved oxygen

concentration in Kirby Lake,

March 13–14, 1996. Trace of

section shown in figure 2.

3.6

3.0

2.0

1.0

0.0

DISTANCE FROM THE NORTHWEST SHORE, IN FEET

0 500 1000 1500 2000 2500 3000 3500 4000

0

2

4

6

8

10

12

14

16

DEPTH, IN FEET

3.0

Aerator Aerator

3.0

2.0

Ice Ice

3.0

A A'

DISSOLVED OXYGEN CONCENTRATION,

IN MILLIGRAMS PER LITER

Site A

13%

Site B

4.1%

Site C

.4%

Site D

10.0% Site E

6.4%

Site F

3.9%

Site G

46%

Sites H-L

4.7%

Precipitation

12%