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 80 percent of the watershed is forested; the remainder consists of wetlands, small lakes, agricultural land, residential development, and roads.
Figure 1. Location of Kirby Lake in relation to its watershed and tributary-monitoring sites. (45 Kb image)
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.
Figure 2. Water depth, and locations of piezometers and water-sampling sites at Kirby Lake. (25 Kb image)
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.
DS = (PPT + SWIn + GWIn) - (Evap + SWOut + GWOut),
where DS 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 domestic-well 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.
Figure 3. Daily precipitation at, and lake stage of, Kirby Lake. (15 Kb image)
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). Precipitation 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.
Figure 4. Inflows and losses of water, in acre-feet, for Kirby Lake, November 1, 1995 through October 31, 1996. (12 Kb image>
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.
Figure 5. Diagrammatic hydrogeologic section of Kirby Lake showing relation of lake to ground water. (17 Kb image>
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 greater-than-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.
One method of classifying a lake's condition or productivity is by computing water-quality indices based on Secchi depths, and, on near-surface 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 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 being moderately nutrient enriched (mesotrophic) and being heavily nutrient enriched (eutrophic).
Figure 6. Trophic-state indices for total phosphorus, chlorphyll a, and Secchi depth for Kirby Lake. (11 Kb image)
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.
Figure 7. Section showing distibution of dissolved oxygen concentration in Kirby Lake, March 13 - 14, 1996. Trace of section showin in figure 2. (12 Kb image)
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. (15 Kb image)
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.
By W.J. Rose and D.M. Robertson
Holmstrom, B.K., Olson, D.L., and Ellefson, B.R., 1997, Water resources data-Wisconsin, 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 Water-Resources Investigations Report 91-4125, 28 p.
U.S. Geological Survey, Wisconsin District Lake-Studies Team, 1997, Water-quality 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.
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