THERMAL STRATIFICATION OF WISCONSIN LAKES

RICHARD C. LATHROP AND RICHARD A. LILLIE Bureau of Research Wisconsin Department of Natural Resources

Abstract A model predicting summer temperature stratification in lakes utilizing lake surface area and maximum depth information was developed from vertical profile temperature and dissolved oxygen data collected on approximately 500 Wisconsin lakes. From the model, the number of stratified versus non-stratified lakes (natural and impoundments) was estimated for the 3,000 plus Wisconsin lakes with surface areas 25 acres (10 hectares) or greater. Statewide, about one-half of the lakes are predicted to be non-stratified. Impoundments, which represent about 16 per­ cent of the state's lakes, are about 86 percent non-stratified. Potential uses for the lake stratification model are noted.

INTRODUCTION sity differences between surface and bottom Thermal stratification in moderately deep waters become too great for the wind to temperate latitude lakes is a well docu­ maintain complete homoiothermy. Thermal mented phenomenon. Hutchinson (1957) stratification results with the establishment provides a thorough discussion of the con­ of an epilimnion (upper warm water, freely tributions of earlier researchers. Thermal circulating), hypolimnion (deep, cold, rela­ stratification results from density differences tively undisturbed water), and a zone of in lake water of varying temperatures (Birge, steep thermal gradient called the metalim­ 1916). After the winter ice melts, water nion (or thermocline). These regions exist temperatures increase above the point of throughout the summer months until fall, maximum density of 4 °C until maximum when the lake surface water cools sufficiently Wisconsin lake surface temperatures, gen­ to again equalize water density differences erally between 21 °-27°C (Wisconsin DNR, between top and bottom, thereby initiating Bureau of Research lake data files), are fall overturn. reached by mid-summer. The wind provides Shallow lakes exhibit complete mixing energy during the spring to circulate the regularly throughout the summer as the wind warming surface waters throughout the entire provides enough energy to destabilize the water column (spring overturn) maintaining minor density differences that develop be­ homoiothermal (uniform) lake tempera­ tween the surface and bottom as a result of tures. As water temperatures increase above surface warming on hot, calm summer days. 4°C, water density decreases, with each suc­ Certain lakes have sufficient depth to allow cessive degree of rising water temperature for temporary thermal stratification, which resulting in a greater decrease in water den­ persists until major weather systems with sity. Consequently, more wind energy is re­ high winds again cause complete mixing. quired to completely circulate the warmer These weather systems occur frequently lake surface waters with the cooler, more enough during the summer months in Wis­ dense bottom waters. consin (Stauffer, 1974) that these weakly In deeper lakes, as surface temperatures stratified lakes can be considered as non­ increase on calm, warm spring days, the den- stratified. Stratified lakes do not exhibit

90 1980] Thermal Stratification of Wisconsin Lakes 91 complete miXlng during the summer, al­ southern Wisconsin, they are also greatly though metalimnetic deepening, as a result affected by thermal stratification (Lillie and of these strong weather fronts, does occur Mason, in press). In general, southern (Stauffer, 1974). Wisconsin lakes are more fertile, and those Rigorous mathematical expressions have that stratify usually exhibit dissolved oxygen been developed to describe the heat flux pro­ depletion throughout the hypolimnion as a cesses of lakes that ultimately result in ther­ result of respiration and bacterial decompo­ mal stratification (see Hutchinson, 1957). sition of organic matter. The lack of oxygen Calculations based on various physical lake in the colder hypolimnion precludes the sur­ characteristics can describe the stability of vival of cold-water-adapted fish such as trout a lake, or the amount of work needed to since surface water temperatures are high cause a lake to destratify to a uniform tem­ where dissolved oxygen concentrations are perature. Lake depth is an important vari­ adequate. Other aquatic life such as bottom able in the calculation. However, the lake feeding insects and zooplankton are re­ depth required before thermal stratification stricted from the anoxic hypolimnion except develops varies greatly between individual for brief periods when certain species mi­ lakes as a function of lake surface area, ba­ grate into the hypolimnion. Northern Wis­ sin orientation relative -to prevailing winds, consin lakes are generally less fertile and lake depth-volume relations, protection by therefore in many cases do not undergo com­ surrounding topography and vegetation, and plete hypolimnetic oxygen depletion. Cold­ otherfactors (Wetzel, 1975). water-adapted fi sh do well in the hypolim­ Few generalizations about stratification nion of these lakes during the summer have been attempted for diverse groups of months when surface waters are too warm. lakes. Hutchinson (1957) noted that the The lack of oxygen in the hypolimnion of eddy diffusivity (related to the process of fertile lakes causes the hypolimnetic lake turbulent mixing) is greatest in the wind­ sediments to release such dissolved constitu­ swept epilimnion of large, exposed lakes. ents as inorganic phosphorus, ammonia, and Consequently, lakes of similar maximum hydrogen sulfide into the overlying water depths may be either stratified or non-strati­ throughout the summer stratification period fied, depending on their surface area. (Mortimer, 1941-1942). In shallow, fertile Ragotzkie (1978), using data from Wis­ lakes a significant amount of dissolved nu­ consin and central Canadian lakes, developed trients released from the lake sediments dur­ one of the first simple lake stratification ing periods of brief stratification can be models. Lake fetch (F) was used to predict transported by subsequent mixing to the sur­ the depth of the summer thermocline (Dth) face waters where high levels of algal pro­ for lakes having fetches from 0.1 to over 20 duction are maintained. km: Resuspension of sediments is another im­ portant effect of lake mixing. Shallow lakes continually resuspend nutrient rich sediments Summer stratification of a lake has a tre­ that contribute to increased nutrient concen­ mendous impact on the chemical constituent trations for algal growth. concentrations of each lake and a great in­ The combined result of sediment resus­ fluence on the lake's biological community pension and frequent stratification followed structure. Although Wisconsin lakes are very by lake mixing in shallow lakes results in diverse in their geochemical characteristics potentially high rates of internal nutrient (Poff, 1961 ) and watershed nutrient load­ recycling during the summer months. As a ings, particularly between northern and result, surface waters of non-stratified lakes 92 Wisconsin Academy of Sciences, Arts and Letters [Vol. 68 in Wisconsin generally show a net increase limited data could provide useful informa­ in total phosphorus concentration from tion for the classification process. spring to summer, while deep stratified lakes usually exhibit a net decrease in total phos­ METHODS phorus concentration (Lillie and Mason, in Data used in this report came from two press . Thermal stratification effectively sources: (1) vertical profile temperature creates a temporary nutrient barrier between and dissolved oxygen data on approximately the epilimnion and the hypolimnion, while 500 lakes 25 acres (1 0 hectares) or greater nutrients are being removed from the epilim­ in surface area, collected by the Wisconsin nion by sedimenting algae. The importance DNR, Bureau of Research; and (2) lake of this barrier varies between lakes as a func­ surface area and maximum depth informa­ tion of lake basin morphometry. tion on Wisconsin lakes 25 acres or greater The classification and inventory of lakes (data compiled by DNR Bureau of Fish in relation to their trophic status has been Management). The lake inventory data was emphasized increasingly in recent years by subdivided into natural lakes and impound­ state and federal agencies. Since thermal ments. stratification can significantly affect lake Decisions about the establishment of water quality and concomitant recreational thermal stratification are based on inspection potential of a lake, a model capable of pre­ of the temperature and dissolved oxygen dicting stratification in Wisconsin lakes from vertical profiles. Three main types of tern-

I I STRATIFIED WEAKLY STRATIFIED NON-STRATIFIED I TEMPERATURE (°C) 0 10 20 0 10 20 30 0 10 20 0 +-"----1--'--,-<>'-~· o+--,__--£_ _.___...._____,~:;;;0 0 -llf--'--"---

:J: -- Temperature 1- 15 0 +--~__,__.....__~.-/-, 0 Q.. w Aug. 3 / 0--0 Dissolved 0 / Oxygen / 0 20 5 I 0 I 0 I I ,.....0 251 1 10 -1---o..... -....., 0 5 10 0 5 10 15

DISSOLVED OXYGEN (mg/1}

Fig. 1. Temperature stratification patterns found in Wisconsin lakes. (Stratified = Lake Monona, Dane Co., Aug. 1, 1978; Weakly Stratified= Lake Waubesa, Dane Co., July 7 and Aug. 3, 1976; Non-stratified = Round Lake, Chippewa Co., July 15, 1975). 1980] Thermal Stratification of Wisconsin Lakes 93 perature profiles are found in Wisconsin would reduce the density differences between lakes (Fig. 1). The stratified lake has a dis­ the top and bottom waters sufficiently to al­ tinct epilimnion, metalimnion, and hypolim­ low complete vertical mixing. nion. The hypolimnion in the example is Consequently, any lake.s with mid-summer completely anoxic, indicating the absence bottom water temperatures above 20°C were of mixing with the epilimnion. The non-stra­ generally considered to be weakly stratified tified lake is homoiothermal; dissolved oxy­ and were combined with 1he more obvious gen concentrations demonstrate well-mixed non-stratified lakes for the purposes of this conditions. study. For the few lakes where stratification The weakly-stratified lake (Fig. 1) dem­ or lack of it was even more difficult to de­ onstrates the difficulty in deciding whether or termine, the authors assigned lakes to the ncit the lake is capable of developing perma­ appropriate category based on . their judg­ nent stratification throughout the summer ment about the influence of other factors af­ season (late June, July, and August). On fecting stratification, such as lake shape and July 7, the lake appears to be stratified and surrounding topography. dissolved oxygen depleted near the lake bot­ tom. However, on August 3, the temperature RESULTS AND DISCUSSION gradient is not as steep (with bottom tem­ Lake surface area and maximum depth peratures being more than 2°C higher) and information were plotted for all natural lakes dissolved oxygen concentrations are higher that could be classified as either stratified or in deeper waters, indicating that some recent non-stratified based on interpretation of the mixing has occurred. The July 7 data pro­ temperature and dissolved oxygen vertical vides a clue to the lake's ability to destratify; profile information (Fig. 2). A generally bottom water temperatures are almost 22°C. linear separation between the stratified and Any cooling and/or mixing of the lake's sur­ non-stratified lakes resulted from a logarith­ face waters as a result of a weather front mic presentation of lake area. Those lakes

STRATIFIED c•> -(I) 30 • """'Q) ••• • Q) .,. •• • -E • •• • ·' • - • -• ... .. 20 J:.__ .. Q.. w 0 0 10 ~ ::::> ~ X (O) <( I I I II I I I I II I I I I I I I II I ~ 10 100 1,000 10,000 LAKE AREA (hectares) Fig. 2. Lake stratification model for Wisconsin lakes. 94 Wisconsin Academy of Sciences, Arts and Letters [Vol. 68 lying close to the stratification/non-stratifi­ This model allowed for the prediction of the cation interface (Fig. 2) represented border­ number of stratified versus non-stratified line cases, with stratified lakes having less lakes for Wisconsin from surface water in­ stability when in close proximity to the inter­ ventory data. As the model was based only face. Many of the non-stratified lakes near on lakes with surface areas 25 acres ( 10 the interface were weakly stratified. hectares) or greater and because smaller Impoundments plotted in this same man­ lakes may be heavily influenced by surround­ ner showed somewhat similar results, how­ ing topography, the model was only applied ever a few anomalies were noted. In some to the 3,000 plus Wisconsin lakes in this size cases stable ·temperature stratification oc­ range. Impoundments and also lakes with cured in small, relatively shallow depressions high color were included in the data set. The near the spiHways of dams where there was number of poor predictions was relatively no circulation and warmer surface waters small. were passing over the spillway. A number of Since the mathematical expression was de­ impoundments (and a few natural lakes) re­ veloped using a data set from Wisconsin ceive large river discharges in relation to lakes, application of the model to other their volume and thereby experience a physi­ areas of the country may result in inaccurate cal flushing which precludes the establish­ stratification predictions because of differ­ ment of thermal stratification. Lack of strati­ ences in basin configuration, climate, or fication in Wisconsin impoundments with other factors. However, lakes in the upper high flushing rates was found in depths up to Midwest should be reliably predicted by the 22 meters. Because of these abnormal strati­ model. fication characteristics impoundments were The lake stratification model, when com­ excluded from the development of the final pared to the model developed by Ragotzkie. stratification model (Fig. 2). However, the (1978), produced corresponding results. model should be applicable to most im­ poundments. Color, caused by dissolved humic sub­ stances, is one important variable affecting NATURAL LAKES the depth of thermocline development in all NORTH ERN ( NL) lakes. The increased absorptive capacity of REGION colored water restricts penetration of radi­ \ ant energy. Consequently, colored lakes fre­ quently have shallower epilimnions and nar­ rower thermoclines than clear-water lakes (Wisconsin DNR, Bureau of Research lake data files) . Because of the linear separation ·between stratified and non-stratified lakes, a simple NL-~ IMP-~ mathematical model was developed to pre­ b-;'o"t='-F=-F-'1 """ (!)- IMp dict lake stratification based on maximum SOUTHWEST/ SOUTHEAST depth and lake area: REGION CEN TRAL REGION Maximum Depth (meters) - 0.1 Fig. 3. Regional stratification characteristics of Wisconsin natural lakes and impoundments. (Num­ Log1o Lake Area (hectares) ber of lakes proportional to area of circle; Strati­ fied lakes = solid area, Non-stratified lakes= open > 3.8 - Lake should be stratified area). 1980] Thermal Stratification of Wisconsin Lakes 95

His equation predicted the top of the thermo­ the southwest region. Impoundments com­ cline, whereas the line drawn in Figure 2 prise less than 16 percent of the total num­ would correspond approximately to the bot­ ber of Wisconsin lakes 25 acres or greater. tom of the thermocline. Consequently, Ra­ The number of impoundments is similar in gotzkie's equation for lakes between 10 and all three regions. Most lakes in the northern 20,000 hectares (after fetch was converted region are natural; impoundments represent to circular lake area) when plotted was only about 8 percent of the total number. somewhat parallel to our line in Figure 2, Impoundments constitute about 75 percent but at shallower depths for corresponding of all lakes found in the southwest region. lake areas. As lake area increased, the two There are few natural lakes in southwestern models predicted a more extensive thermo­ Wisconsin since that area was not covered cline; this is consistent with observational by the Wisconsonian ice (Martin, 1965). data on Wisconsin lakes (Wisconsin DNR, Slightly more than one-half of Wisconsin's Bureau of Research lake data files) .. lakes with surface areas of 25 acres or For identification of lake stratification greater are predicted by the lake stratifica­ characteristics Wisconsin is divided into tion model to be non-stratified throughout three regions (Fig. 3). The southwest region the summer (Fig. 3). About 26 percent of generally coincides with the Western Upland the impoundments are predicted to be non­ Geographical Province of Martin (1965), stratified, compared to only 45 percent of part of which includes the Driftless or un­ the natural lakes. glaciated area. The topography is highly dis­ Impoundments are 80, 93, and 84 percent sected with few natural lakes present. The non-stratified in the northern, southeast cen­ northern region includes a maJority of the tral and southwest regions, respectively. The state's lakes; these are characterized by low high percentage of non-stratified impound­ alkalinity (Lillie and Mason, in press) as ments is not surprising since they represent a result of the igneous bedrock geology (Han­ shallow lakes on dammed rivers. Natural son, 1971; Poff, 1961). The southeast central lakes are predicted to be 55 and 58 percent area of the state generally has lakes of higher stratified in the northern and southeast cen­ alkalinity and poorer water quality than tral regions, but only 22 percent stratified northern lakes; this is particularly true in the in the unglaciated southwestern region. southern part of the southeast central region Striking water quality differences have (Lillie and Mason, in press). Separation been noted between stratified and non-strati­ of the state into distinct regions based on fied lakes. From data collected on approxi­ county lines is arbitrary, but lake inventory mately 500 lakes throughout the state, aver­ information was available on a county basis. age summer secchi disc (water transparency) The bedrock and surficial geology each indi­ readings were 2.8 and 1.5 meters for strati­ cate much more complex regional distinc­ fied and non-stratified lakes, respectively tions. (Wisconsin DNR, Bureau of Research, un­ Natural lakes and impoundments are un­ published data). Differences in water trans­ evenly distributed throughout the three state parency were related to greater concentra­ regions (Fig. 3). Approximately 75 percent tions of chlorophyll (algal biomass) and of Wisconsin's 3,000 plus lakes of 25 acres higher turbidity in nonstratified lakes. ( 10 hectares) or greater surface area are lo­ The lake stratification model has poten­ cated in the northern region of the state. The tially important applications for the classifi­ southeast central region has roughly 20 per­ cation of Wisconsin lakes. The combined cent of Wisconsin lakes in this size range, effect of generally poorer water quality in and the remaining 5 percent are located in non-stratified lakes resulting from greater

' 96 Wisconsin Academy of Sciences, Arts and Letters [Vol. 68 efficiencies in internal nutrient recycling, lakes that are currently experiencing a high coupled with the large number of non-strati­ rate of in-filling and sediment deposition. fi ed lakes in Wisconsin, necessitates careful Finally, a stratification model similar to selection of lakes as candidates for limited the one presented here may be developed to non-point pollution control efforts. Lakes predict the depth of the epilimnetic/ metalim­ that are chosen for programs designed to netic boundary. This depth could be used to restrict nutrient inputs, which are often ex­ calculate the lake bottom area exposed to pensive, should possess characteristics that wind mixing, thus providing an index of po­ would indicate a high probability of water tential internal nutrient recycling, as well as quality response (improvement or long-term information useful for calculating total lake protection), thereby ensuring a high benefit sedimentation rates. This model, coupled to cost ratio. Temperature stratification with other lake morphometric data, may al­ would seem to be a very important charac­ so help to refine existing lake eutrophication teristic in lake selection. models that relate external phosphorus load­ The thermal stratification model has other ings to in-lake water quality. potential uses in water resource management activities. The model may be useful for the LITERATURE CITED initial selection of •lakes capable of support­ Birge, E. A. 1916. The work of the wind in ing cold water fi sheries, particularly in north­ warming a lake. Trans. Wis. Acad., Sci., ern regions where hypolimnetic dissolved Arts, Lett. 18, Part II: 341-391. Hanson, G. F. 1971. Geologic map of Wiscon­ oxygen concentrations are likely to be ade­ sin. Wis. Geol. and Nat. Hist. Survey, Madi­ quate. The model can also serve as a guide son, 1 p. to lake managers conducting dredging proj­ Hutchinson, G. E. 1957. A Treatise on Lim­ ects. By predicting lake depths needed for nology. I. Geography, Physics, and Chem­ the development of ·thermal stratification, istry. John Wiley & Sons, Inc., New York, dredging can be planned to reduce internal 1015 pp. nutrient recycling in fertile lakes. The strati­ Lille, R. A. and J. W. Mason (in press). Lim­ fication model could also be used in the de­ nological characteristics of Wisconsin lakes. sign of impoundments for -the above reasons Wis. Dept. Nat. Resources Tech. Bull. or to maximize sediment trap efficiency. Martin, L. 1965. The Physical Geography of Other more theoretical uses of the tem­ Wisconsin. University Wisconsin Press, Mad­ ison, 608 pp. perature stratification model may have man­ Mortimer, C. H. 1941-1942. The exchange of agement implications. The sediments contain dissolved substances between mud and water a history of the lake's development, and lakes in lakes. J. Ecology 29:280-329; 147-201. of certain depths may have accumulated suf­ Poff, R. J. 1961. Ionic composition of Wiscon­ ficient bottom sediments over time to con­ sin lake waters. Wis. Dept. Nat. Resources, vert the lake from stratified to non-strati­ Fish Mgmt. Misc. Rept. No. 4, 20 pp. fied. Probable trophic changes in the lake Ragotzkie, R. A. 1978. Heat budgets of lakes. may be deduced by interpretation of differ­ Ch. 1 in Lerman, A. (ed.) Lakes: Chemistry, ences in the physical and chemical sediment Geology, Physics. Springer-Verlag, New characteristics. Differences in the biological York. 363 pp. Stauffer, R. E. 1974. Thermocline migration­ remains present, above and below the sedi­ algal bloom relationships in stratified lakes. ment depth where the lake should no longer Ph.D. Thesis. Water Chemistry Program, be stratified, also provide clues. Such inter­ Univ. Wisconsin, Madison, 526 pp. + App. pretation might allow the prediction of pro­ Wetzel, R. G. 1975. Limnology. W. B. Saun­ jected water quality changes in stratified ders Co., Philadelphia, 743 pp.