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A Simple Model for Predicting the Date of Fall Turnover in Thermally Stratified Lakes Gertrud K Nurnberg Limnology and Oceanography Vol 33 No 5 Sep 1988 pp 11901195 Stable URL http1inksjstororgsicisici002435902819880929333A53C11903AASMFPT3E20CO3B2D Limnology and Oceanography is currently published by American Society of Limnology and Oceanography Your use of the J STOR archive indicates your acceptance of J STOR39s Terms and Conditions of Use available at httpwwwjstororgabouttenns html J STOR39s Terms and Conditions of Use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the J STOR archive only for your personal noncommercial use Please contact the publisher regarding any further use of this work Publisher contact information may be obtained at httpwwwjstororgjoumalslimnochtml Each copy of any part of a J STOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission The J STOR Archive is a trusted digital repository providing for longterm preservation and access to leading academic journals and scholarly literature from around the world The Archive is supported by libraries scholarly societies publishers and foundations It is an initiative of J STOR a notforprofit organization with a mission to help the scholarly community take advantage of advances in technology For more information regarding J STOR please contact supportj stororg httpwwwjstororg Thu Sep 13 133810 2007 1190 1987 15N and 13C abundances in the Antarctic Ocean with emphasis on the biogeochemical struc ture of the food web DeepSea Res 34 829 841 WALSH J J T E WHITLEDGE J E O REILLY W C PHOEL AND A F DRAXLER 1987 Nitrogen cy cling on Georges Bank and the New York shelf A comparison between wellmixed and seasonally Limnol 0cean0gr 335 1988 1 190 1 195 1988 by the American Society of Limnology and Oceanography Inc Notes strati ed waters p 234 246 In R H Backus ed Georges Bank Mass Inst Technol Submitted 22 December I 98 7 Accepted 23 March 1988 Revised 6 May 1988 A simple model for predicting the date of fall turnover in thermally strati ed lakes Abstract The date of fall turnover can be pre dicted from average midsummer hypolimnetic temperature in acidic and nonacidic lakes in cen tral Ontario The prediction of fall turnover date is improved by inclusion of two further indepen dent variables mean depth 2 and adjusted lat itude for altitude in a global data set ranges of 2 11 86 m adjusted latitude 38 6 5 The models explain 67 80 of the variance of fall turnover date and are potentially useful in the design of monitoring programs and for predicting impacts of anthropogenic activities that in uence lake thermal budgets eg diversion for cooling waters or damming of cold in ows Fall turnover is an important event in di and monomictic lakes The onset of iso thermal conditions after summer strati cation usually leads to an even distribution of chemical and biological constituents throughout the water column so that sur face waters become enriched in nutrients and trace elements from the hypolimnion eg Niimberg 1984a 1985 If the date of fall turnover is early productivity may be Acknowledgments I acknowledge the provision of data for Ontario lakes by the Ontario Ministry of the Environment MOE and the Ontario Ministry of Natural Resources I am especially indebted to Norm Yan Peter Dillon Bruce LaZerte and Bernie Neary of the MOE in Dorset On tario and Don McQueen of York University Two anonymous reviewers helped improve the manuscript I was supported by a postdoctoral fellowship from the Natural Sciences and Engineering Research Coun cil of Canada enhanced by the nutrient increase but if turnover is late and light and temperature conditions are too low for algal growth the entrained nutrients are eventually lost through the out ow Because of the lack of strati cation representative sampling dur ing this period is simple no pro le required and facilitates the design of synoptic lake surveys eg US EPA 1986 Fall turnover may be predicted from de tailed mechanistic models that are based on eddy diffusion or mixed layer theory and simulate strati cation cycles in single lakes eg HendersonSellers 1983 1984 but there is no model that predicts fall turnover dates from easily obtainable characteristics of a wide range of lakes In attempts to create such a model the in uence of several vari ables on the date of fall turnover has been investigated geographical location lati tude and altitude of the lake both of which in uence mixing states of lakes Lewis 1983 morphometric characteristics eg mean depth which is correlated with the rate of hypolimnetic entrainment into the epilim nion Blanton 1973 maximum depth the ratio of mean to maximum depth as a mea sure of the shape of the lake basin the pos sibility of meromixis calculated from max imum depth and lake area Berger 1971 and major effective fetch distances exposed to the two major wind directions conduc tivity to detect any differences between soft and hardwater lakes average epilimnetic Notes Table 1 Characteristics of the three data sets Data sets World Southern wide Ontario Acxd Number of Data pairs 92 172 40 Lakes or basins 56 44 9 Years per lake min max 1 5 1 10 2 11 summer temperature an indicator of weather conditions during spring and sum mer and hypolimnetic average summer temperature a variable that integrates spring mixing conditions and the summer thermal regime of the lake Early observations suggested that lakes with very low hypolimnetic temperature turned over later than lakes with higher hy polimnetic temperature even if the latter lakes were in more southern and warmer climates Niimberg 19841 It takes longer for the epilimnion to reach the lower hy polimnetic temperature in lakes that de stratify late Low hypolimnetic temperature is often found in northern lakes after spring turnover the temperature remains low es pecially in deep lakes or lakes with low transparency eg lakes rich in humic acids or chlorophyll wherein solar radiation fails to penetrate to the hypolimnion On the other hand shallow lakes or lakes with high transparency such as occurs in severely acidi ed lakes Y an 1983 can have comparably high hypolimnetic temperature in summer This paper introduces a model for pre dicting fall turnover date from the variables described here First geographically and morphometrically similar lakes of southern Ontario were investigated Then the model was expanded to lakes from North America and Europe for generalization and was also tested on acidic lakes The latter test should determine if the relationship applies to lakes with unusually elevated hypolimnetic tem peratures because of high transparency In an attempt to explain residual variation I examined annual and meteorological vari ations in the southern Ontario data set Data stem from lakes of a single region in southern Ontario from lakes across North America and Europe from the literature and from acid lakes located near Sudbury 1191 Ontario Data tables are available on re quest Average July and August temperatures 1 3 m above the bottom served as the pre dictor variable hypolimnetic tempera ture and the date of complete fall turnover as the dependent variable fall turnover date Weekly to monthly data from at least one season of lakes or distinct lake basins were used Table 1 Lake averages of 1 10 yr were calculated for the Ontario lakes to evaluate the effect of more constant lake characteristics eg lake area fetch and conductivity on the prediction of fall tum over Latitude and altitude were converted into a joined term adusted latitude latad latd latx a 100 X alt 1 where latx represents latitude in decimal degrees and ax is the factor which converts 100 m of altitude alt m into degrees of latitude at a given latitude x interpolated from Lewis 1983 The possibility of meromixis pm was cal culated for the southern Ontario lakes from maximum depth zmax m and lake surface area A m2 when pm gt 1 lake is possibly meromictic Berger 1971 pm ZmaxAquot 2 Effective fetch m was determined from the weighted sum of the length of open water in the main wind direction wind coming from 300 NW and in the next most fre quent wind direction from 130 SE for the southern Ontario lakes Directions were determined from daily wind records of the three fall seasons 1982 1984 at a location within 100 km of most of the southern On tario lakes Ranges and medians of mean and max imum depth adjusted latitude hypolim netic temperature and date of fall turnover vary in the different data sets Table 2 Regressions of fall turnover dates on aver age hypolimnetic temperatures of July and August were highly signi cant for the On tario lake data set Fig 1 and for all data sets after logarithmic transformation to sta bilize the variance of the data sets on acidic Fig 2 and worldwide lakes Fig 3 Slopes and intercepts were not signi cantly differ 1192 325 21Nov 300 27 Oct 275 2 Oct Date of Turnover day of the year 5 1o Hypolimne ric Temperature C Fig 1 Regression of fall turnover dates left axis number of days since 1 January on average hypolim netic temperature for southern Ontario lakes fall tum over 352 23 68 O35temp SE r2 070 n 172 P lt 00001 ent Table 3 The similarity of the rela tionship for the acidic lakes Fig 2 and severely acid lakes subset of Fig 2 means that the model seems to be applicable to lakes with elevated hypolimnetic tempera ture resulting from higher transparency Conductivity as an indicator of density and the degree of hardness in the nonacidic southern Ontario lakes had no effect on the temperature fall turnover relationship in the data set of annual averages of Ontario lakes median 311 range 21 450 umhos cm measured at 25 C Although singlevariable models with hy polimnetic temperature as the predictor are sufficient for the acidic and nonacidic On tario data set tested by stepwise regression ranges in depth and adjusted latitude are Notes U 316 12 Nov L D gt O C L 3 39 282 9 Oct 0 O D 4 U D 251 8Sep I m 1 1 I 56 100 178 Hypolimne ric Temperature C Fig 2 Regression of fall turnover dates as Fig 1 on average hypolimnetic temperature after logarithmic transformations for acidic lakes D slightly acidic pH 55 7 I severely acidic pH lt 55 The regression line for all data combined is logturnover 333 59 54 059logtemp SE r2 069 n 40 P lt 00001 small a threevariable model is more ap propriate for predicting fall turnover in lakes worldwide According to stepwise regres sion a level to enter a variable 015 the best prediction can be achieved by using mean depth and adjusted latitude in addi tion to hypolimnetic temperature SE logtumover date 262 032 0116 0017log hypolimnetic temperature 0042 0009log 2 0002 0000latad n 89 r2 0668 P lt 00001 The depen dence of fall turnover date on mean depth and adjusted latitude for the worldwide lakes can be determined from the signi cant in creases in r2 from 047 to 061 to 067 upon addition of temperature mean depth and adjusted latitude to the model Table 2 Ranges medians of several variables for the different data sets 2 mean depth zmax maximum depth latad adjusted northern latitude Eq 1 temp average hypolimnetic temperature for July and August Data sets Southern Variable Worldwrde Ontario Acrd z 11 86064 25 22080 38 14176 2m 42 281148 75 61204 95 51215 Latad 387 64850 460 47947 465 49148 Temp 36 18575 38 13559 50 20090 Date 25 Aug 29 Dec19 Oct 17 Sep3 Dec9 Nov 27 Aug 26 Nov7 Oct Days 237 363292 260 337313 239 330280 Number of days smce 1 January Notes U 355 21 Dec L Q 3 316 12 Nov C L 3 v 282k 9 Oct 0 4 U D 251 8 Sep U U U l l l 4 32 56 100 178 Hypolimne c Temperature C Fig 3 Regression of fall turnover dates as Fig 1 on average hypolimnetic temperature after logarithmic transformation of both variables for European and North America lakes logturnover 262 0017 0168 0019logtemp r2 047 n 92 P lt 00001 The relationship can be observed in more detail in the residual plots of the mono variable model with hypolimnetic temper ature as the sole predictor Fig 3 vs mean depth Fig 4A or adjusted latitude Fig 4B To determine the effect of lake morphom etry or wind exposure I examined effective fetch 34l 3388 m lake surface area 4 975 ha and the possibility of meromixis 034 148 in the data set on lake averages of the Ontario lakes No signi cant in u ence on the overall temperature tumover relationship was detectable however step wise regression and correlation analysis with the residuals Considering that absorbed heat of the lake surface during summer could in uence the turnover date I included epi limnetic temperature average for July and August l9 249 C in the stepwise regres sion of the Ontario lakes data set without however improving the relationship 1193 Further residual analysis on all the re ported models gave no indication of vio lations of any assumptions ie normality no correlation of the residuals with esti mates or predictor variables no in uential outliers based on the Cook s statistic and no correlation between the independent variables The reported models were built with data from lakes of the northern hemisphere only To see if the relationships are applicable in the southern hemisphere I examined 1 2 yr of data from nine New Zealand lakes latad 398 469 S The model on logarith mic transformed data with average hypo limnetic temperature of the austral summer 5 l7 C January February and mean depth 1 1 44 m as predictors was also sig ni cant r2 060 n 11 P lt 0026 but the parameter values differed from those of the model on the northern lakes These de viations can be expected since the dates were not corrected for the southern hemi sphere Despite the high signi cance of the regres sions 20 3 3 of the variance in date of fall turnover remains unexplained Since year toyear variation of date of turnover can be high in the same lake eg Fig 5 annual climatic variations could account for the re sidual deviations Therefore the regression of turnover date on hypolimnetic temper ature of the data set with many annual ob servations of nonacidic Ontario lakes in a small region Fig 1 was examined further For these lakes morphometry latitude and altitude are very similar and the residuals of the regression model were not correlated with z or latad It can be assumed that any weather pattern that might lead to unusual turnover dates would be similar in all these neighboring lakes for that year Indeed 17 of the variance of the residuals is explained by year as an independent discrete vari Table 3 Regression models which predict date of fall turnover from hypolimnetic temperature after loga rithmic transformation for the data sets P lt 00001 in all cases SE in parentheses Data set Intercept Slope n r2 Worldwide 2620017 01680019 92 047 Southern Ontario 26 1 0006 01540008 172 068 Mean 2610010 01560012 44 080 Acid 2640017 0 1970018 40 077 Lake averages of the southern Ontario data set 1194 Notes 005 A B U U B U D D q n a 035 D E1 U can u g a U a U u an DE 0 u g cu Dun U 396 an El U El oz 0 u OED 35 I 9 an 53 DD 0 7 H u 3935 U m an a E 3 t q u g u D a 0 gang a u U u U u H a B U u u u n 03905 a o05L E U u U l u l l l I a I 1 10 100 40 50 60 Mean Depth m Adiusted Latitude Fig 4 A Residuals observed predicted of the univariate regression model of Fig 3 vs mean depth r2 021 n 89 P lt 00001 B Residuals of the bivariate regression model including logarithmic transformed mean depth as second predictor variable vs adjusted latitude Eq 1 r2 013 n 89 P lt 0001 able P lt 0001 n 172 Similarly AN COVA indicates that 6 of the total vari ance can be explained by year To see if weather can account for the year toyear variation I compared wind speed data available for 3 yr to the average re siduals of the date of turnover model per year Of the recorded years 1984 had fall wind speeds of only 70 of the usual av erage speed The standardized residuals for 1984 are signi cantly higher than usual 0480 t 0191 n 22 C t SE which indicates late observed fall turnover Con cordance of residuals and wind speed pro vides circumstantial evidence for the an nual weather effect Maximum hours of sunshine for the years 1976 1984 for the fall months September October Novem ber are not signi cantly correlated with the residuals paired nonparametric tests and correlations between standardized average residuals and solar hours of average or in dividual fall months In this data set annual variation prob ably due to annual differences in weather and therefore not predictable can explain 17 of the residual variation Part of the residual variance might also be due to the lack of precise data in all data sets About half of the pro le data are avail able only in monthly intervals in the fall and interpolations might have falsely esti mated the real turnover date It is also pos sible that a hypolimnetic temperature of a period more important to the strati cation cycle eg the hydrological year rather than the arbitrarily chosen months of July and August or average temperature integrated over the whole hypolimnion instead of dis tinct depths would give better results Us ing calendar months and a xed location of the hypolimnion avoids the need of any more speci c information however such 330 26 Nov 320 i16 Nov Date of Fall Turnover l l l 76 80 84 Year Fig 5 Ten years of observed A and predicted O from linear model for Ontario lakes fall turnover dates as Fig 1 for Chub Lake Ontario Notes as dates of spring turnover iceout or hy polimnetic volume The observed magnitude of the squared correlation coef cient 067 080 ap proaches those of the best models linking stability and entrainment rate 071 Blan ton 1973 and thermocline depth and fetch 073 Arai 1981 085 Patalas 1984 085 for large and deep Ontario lakes for the Ra gotzkie 1978 model Zimmerman et al 1983 The cited models appear to be less general than the models developed here for example models predicting thermocline depth from fetch do not apply to acid lakes Y an and Miller 1984 The present model can be used to predict future changes in the date of fall turnover of a lake or reservoir due to temperature changes in the hypolim netic in ow eg after application as a cool ing water for hydroelectric power The strong correlation of the date of fall turnover and average midsummer hypolim netic temperature means that hypolimnetic temperature effectively integrates physical factors like watershed and lake morphom etry and weather conditions Many of these factors though conceptually the cause of varying fall turnover dates appear to be nonsigni cant when singled out Gertrud K Nu39rnbergl Faculty of Science York University Downsview Ontario M3J 1P3 1 Mailing address Ministry of the Environment PO Box 39 Dorset Ontario POA 1E0 1195 References ARAI T 1981 Climatic and geomorphological in u ences on lake temperature Int Ver Theor An gew Limnol Verh 21 130 134 BERGER F 1971 Zur Morphometrie der Seebecken Carinthia 11 Spec Issue 31 29 39 BLANTON J O 1973 Vertical entrainment into the epilimnia Of strati ed lakes Limnol Oceanogr 18 697 704 HENDERSONSELLERS B 1983 1984 Development and application Of USED A hydroclimate lake strati cation model Ecol Model 21 233 246 LEWIS W M JR 1983 A revised classi cation of lakes based on mixing Can J Fish Aquat Sci 40 1779 1787 Ni39IRNBERG G K 1984a The prediction of internal phosphorus load in lakes with anoxic hypolimnia Limnol Oceanogr 29 111 124 39 1984b The availability Of phosphorus from anoxic hypolimnia to epilimnetic plankton PhD thesis McGill University 240 p 1985 Availability Of phosphorus upwelling from ironrich anoxic hypolimnia Arch Hydro biol 104 459 476 PATALAs K 1984 Midsummer mixing depths Of lakes Of different latitudes Int Ver Theor Angew Limnol Verh 22 97 102 RAGOTZKIE R A 1978 Heat budgets Of lakes p 1 19 In A Lerman ed Lakes chemistry geol ogy physics Springer US ENVIRONMENTAL PROTECTION AGENCY 1986 Characteristics of lakes in the eastern United States V 1 US EPA600486007a 136 p YAN N D 1983 Effects Of changes in pH on trans parency and thermal regimes Of Lohi Lake near Sudbury Ontario Can J Fish Aquat Sci 40 621 626 AND G E MILLER 1984 Effects Of deposition Of acids and metals on chemistry and biology of lakes near Sudbury Ontario p 243 282 In J Nriagu ed Environmental impacts Of smelters Wiley ZIMMERMAN A P K M NOBLE M A GATES AND J E PALOHEIMO 1983 Physicochemical typol ogies Of southcentral Ontario lakes Can J Fish Aquat Sci 40 1788 1803 Submitted 28 August I 987 Accepted 22 March I 988 Revised 10 June I 988
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