Diurnal and Seasonal Variations of Thermal Stratification ... · (Kalff, 2002; Wang et al., 2012)....

Diurnal and Seasonal Variations of Thermal Stratification and Vertical Mixingin a Shallow Fresh Water Lake

Yichen YANG12 Yongwei WANG13 Zhen ZHANG14 Wei WANG14 Xia REN13 Yaqi GAO13Shoudong LIU14 and Xuhui LEE15

1 YalendashNUIST Center on Atmospheric Environment Nanjing University of Information Science amp Technology Nanjing 210044 China2 School of Environmental Science and Engineering Nanjing University of Information Science amp Technology Nanjing 210044 China

3 School of Atmospheric Physics Nanjing University of Information Science amp Technology Nanjing 210044 China4 School of Applied Meteorology Nanjing University of Information Science amp Technology Nanjing 210044 China

5 School of Forestry and Environmental Studies Yale University New Haven CT 06511 USA

(Received June 21 2017 in final form November 18 2017)

ABSTRACT

Among several influential factors the geographical position and depth of a lake determine its thermal structure Intemperate zones shallow lakes show significant differences in thermal stratification compared to deep lakes Herethe variation in thermal stratification in Lake Taihu a shallow fresh water lake is studied systematically Lake Taihuis a warm polymictic lake whose thermal stratification varies in short cycles of one day to a few days The thermalstratification in Lake Taihu has shallow depths in the upper region and a large amplitude in the temperature gradientthe maximum of which exceeds 5degC mndash1 The water temperature in the entire layer changes in a relatively consistentmanner Therefore compared to a deep lake at similar latitude the thermal stratification in Lake Taihu exhibits smallseasonal differences but the wide variation in the short term becomes important Shallow polymictic lakes share thecharacteristic of diurnal mixing Prominent differences on the duration and frequency of long-lasting thermal strati-fication are found in these lakes which may result from the differences of local climate lake depth and fetch Aprominent response of thermal stratification to weather conditions is found being controlled by the stratifying effectof solar radiation and the mixing effect of wind disturbance Other than the diurnal stratification and convection therepresentative responses of thermal stratification to these two factors with contrary effects are also discussed Whensolar radiation increases stronger wind is required to prevent the lake from becoming stratified A daily average windspeed greater than 6 m sndash1 can maintain the mixed state in Lake Taihu Moreover wind-induced convection is detec-ted during thermal stratification Due to lack of solar radiation convection occurs more easily in nighttime than indaytime Convection occurs frequently in fall and winter whereas long-lasting and stable stratification causes lessconvection in summerKey words Lake Taihu thermal stratification solar radiation wind speed convectionCitation Yang Y C Y W Wang Z Zhang et al 2018 Diurnal and seasonal variations of thermal stratification

and vertical mixing in a shallow fresh water lake J Meteor Res 32(2) 219ndash232 doi 101007s13351-018-7099-5

1 Introduction

In many studies of lake temperature thermal stratifica-tion in the body of a lake has attracted widespread atten-tion Thermal stratification is a stable state in lakes thatcircumscribes the vertical transport of oxygen and other

dissolved gases limiting the supply of nutrients foraquatic organisms (Schadlow and Hamilton 1995)Plankton can be trapped in the surface layer where sun-light is abundant which increases the risk of water qual-ity problems such as algal blooms (Berger et al 2007Fonseca and de M Bicudo 2008) The stability of

Supported by the National Natural Science Foundation of China (41275024 41575147 41505005 and 41475141) Natural Science

Foundation of Jiangsu Province (BK20150900) Startup Funds for Introduced Talents of Nanjing University of Information Science ampTechnology (2014r046) Ministry of Education of China grant PCSIRT and Priority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD)

Corresponding author wywnuisteducncopyThe Chinese Meteorological Society and Springer-Verlag Berlin Heidelberg 2018

Volume 32 APRIL 2018

thermal stratification changes the chemical properties ofthe water body by affecting the exchange of chemicalelements between sediment and the water column (Gileset al 2016) The thermal structure of a lake not only in-dicates the response of the lake to atmospheric forcing(Oswald and Rouse 2004) but also plays an importantrole in changing the wind and fluxes to the atmosphereby controlling surface temperature (Liu et al 2015) andtherefore can be a useful variable for improving numeri-cal weather forecasts (Heo and Ha 2010)

The geographical position and depth of a lake directlyinfluence its vertical temperature distribution Simultan-eously the thermal stratification is controlled by severalexternal factors (Churchill and Kerfoot 2007) For in-stance salinity specific heat algal blooms turbidityheat flux and meteorological elements all contribute tothe characteristics of vertical temperature profiles (Fee etal 1996 Condie and Webster 2002 Zhao et al 2011Wang et al 2012 Wang et al 2014) For most deeplakes in the temperate zone greater heat storage leads tosustained stability which causes the temperature to varyover a long cycle (Kalff 2002) Hence although the gen-eral characteristics of temperature change in deep lakes isaffected by wind disturbances biological disturbancesand salinity (Wang et al 2014) temperature changes areprimarily due to seasonal differences in solar radiationthat is the dimictic type and the warm monomictic typeIn these two situations a dimictic lake shows a strongthermocline in the summer a frozen surface layer in thewinter and a homogeneous temperature in the spring andfall which is caused by overturning A warm monomic-tic lake shows only one overturning period between thefall and the spring and no ice cover exists in the winter(Kalff 2002 Wang et al 2012) In shallow lakes theheat storage is not large enough to maintain thermal strat-ification for more than 24 h (Kalff 2002) which leads torapid changes in the thermal structure In this processmeteorological elements heat transport at the surface ac-cumulation of algae and the height of submerged plantsare more influential (Zhao et al 2011 Cheng et al2016) Generally vertical mixing occurs in shallow lakesat nighttime (Deng et al 2013) As the change in depthgreatly influences the variation in thermal stratificationas well as its response to different factors the pattern ofstratification in shallow lakes must possess particularcharacteristics

To date studies of the characteristics of thermal strati-fication and the relevant physical and chemical pro-cesses in deep lakes are relatively mature (Michalski andLemmin 1995 Crawford and Collier 1997 Boehrer and

Schultze 2008 Pernica et al 2014) Current research onsimilar topics in shallow water involve mainly modelsimulations (Chu and Soong 1997 Farrow and Stevens2003) analyses of short-term cases (Tuan et al 2009Zhao et al 2012) mechanisms related to internal waves(Samal et al 2008) the vertical circulation that emergesduring upwelling (Godo et al 2001 Condie and Web-ster 2002) and the regulation of entrainment in a mix-ing water body (Chai and Kit 1991 Tuan et al 2009)However studies based on long-term data (longer thanone year) to characterize features of thermal stratifica-tion in shallow lakes are still limited

It is important to quantify the strength of stratificationby determining the mixed layer depth (MLD) The MLDcan be used to support the parameterization of surface-airexchanges processes in lakes (Sun et al 2007) Field ob-servations allow the performance of the MLD parameter-izations to be validated

At present there are two most practical techniques fordetermining the MLD the subjective method and the ob-jective method The former commonly involves the dif-ference criterion and the gradient criterion (Chu and Fan2011) which are concise and effective with an empiric-ally given threshold that varies with the environment ofthe lake Thus an optimal solution in the subjectivemethod is rarely found (Monterey and Levitus 1997)The latter commonly involves the curvature criterionwhich demands high vertical resolution because it calcu-lates the second derivative of the water thermal propertyNoisy data should be avoided when using the objectivemethod (Chu and Fan 2011) Kara et al (2000) pro-posed an optimal definition that can process temperatureprofiles with low resolution and to some extent solvesthe problem in selecting a best threshold after a rigorouscomparison between two independent datasets Anothernovel criterion called the maximum angle method pro-posed by Chu and Fan (2011) leads to good results byseeking the MLD based on profile angles However thatmethod has a stringent requirement for vertical resolu-tion

All of the existing criteria for determining the MLDhave their own advantages and limitations A simplifiedform of Kararsquos optimal definition was used in a shallowlake for a few days in the summer and a significant vari-ation in the MLD was obtained (Zhao et al 2012)However whether it can be applied to long-term re-search in Lake Taihu still needs confirmation

Lake Taihu is located in the urban agglomeration inthe Yangtze River Delta which has a dense populationLake Taihu is not only an important source of water and

220 Journal of Meteorological Research Volume 32

food supply but also affects the surrounding weather(Zhang et al 2017) The lake area is 2400 km2 and themean depth is 19 m with the northwest part deeper (ap-proximately 25 m) and the east part shallower (approx-imately 15 m Qin et al 2007 Lee et al 2014) Thisstudy is performed based on one year observed data inLake Taihu The following three scientific problems arediscussed (1) How does water temperature in LakeTaihu vary diurnally and vertically in different seasonsHow does the water temperature respond to variousweather characteristics (2) How should the thermalstratification in Lake Taihu be quantified Furthermorewhat are the main factors that control it How does thethermal stratification in Lake Taihu typically change withthese dominant factors under different conditions (3) AsLake Taihu is shallow what mechanism underlies theswitch of its thermal stratification (from being stable tobeing unstable)

The paper is organized as follows Section 2 intro-duces the observations from the Lake Taihu Eddy FluxNetwork in 2015 and associated data quality control to-gether with the method used to determine the MLD ofthe lake Section 3 presents the data analysis results withthe thermal structure and stratification of the lake andwind-induced convection being extensively discussedFinally conclusions are provided in Section 4

2 Data and methods

21 Sites and instruments

The data used here are from the Pingtaishan (PTS) sitein the Lake Taihu Eddy Flux Network in 2015 (Fig 1)

This site was established in June 2013 and is locatedclose to the center of the lake (312323degN 1201086degE)with an average water depth of 28 m The representedwater area is mesotrophic (Lee et al 2014) with relat-ively little photosynthetic activity (Hu et al 2011) Mac-rophytes are not common in this zone and are omitted inour research

The Lake Taihu Eddy Flux Network mainly includesthe eddy covariance (EC) system a four-way net radi-ation observation system an automatic weather stationand a water temperature gradient observation system(Fig 1) At the PTS site the automatic weather stationconsists of an air temperature and humidity probe (mo-del HMP155A Vaisala Inc Helsinki Finland) and ananemometer and wind vane (model 05103 R M YoungCompany Traverse City Michigan) A four-way net ra-diometer (model CNR4 Kipp amp Zonen B V Delft theNetherlands) systematically measures incoming and out-going radiation The water temperature gradient observa-tion system comprises a group of temperature probes(model 109-L Campbell Scientific) set at 02 05 10and 15 m below the surface and in the sediment beneaththe water column All the data noted above are recordedat 1 Hz and processed to average values over 30 min by adata logger (model CR1000 Campbell Scientific)

Moreover the historical meteorological data from theDongshan weather station (approximately 36 km fromthe PTS site) are adopted to combine the analysis withspecific weather features The weather is classified intoclear days (cloud amount le 3) overcast days (cloudamount ge 8) and cloudy days (3 lt cloud amount lt 8Qiu 2013)

Fig 1 (a) The location of the Lake Taihu Eddy Flux Network and (b) the instrument platform of the Pingtaishan (PTS) site The red star marksthe PTS site and the black dots mark the Meiliangwan (MLW) Dapukou (DPK) Bifenggang (BFG) Dongshan (DS) and Xiaoleishan (XLS)sites The Dongshan weather station (31deg04primeN 120deg26primeE) marked by the red triangle is distinguished from the DS site In addition to the automa-tic weather station and EC system mounted at 85 m a four-way net radiometer and rain gauge are installed Water temperature probes are set be-low the surface (Lee et al 2014)

APRIL 2018 Yang Y C Y W Wang Z Zhang et al 221

22 Data quality control

The data chosen from 1 January to 31 December 2015consist of air temperature wind speed water vapor pres-sure upward and downward longwave and shortwave ra-diation and the water temperature profile Data qualitycontrol methods are used to ensure good data quality Acomparison of five temperature probes at the same depthis performed periodically to obtain systematic errorsPeriods of instrument failure recorded on the field main-tenance log are excluded from post-field processing(Wang 2014) High failure rates appear in May JuneAugust and September In detail only 58 of data inMay are in good quality and this proportion is 70 inJune The water temperature probes failed completely inAugust and all profile data were rejected accordinglyThis problem was not fixed until mid-September whichinevitably caused the percent of passable data to be 43Except for the periods noted above the data quality inother months is good

To ensure that qualified data represent the features forthe entire year our investigation is performed with datafrom January April July and October which representthe seasonal features of winter spring summer and fallrespectively The quality of the data of air temperaturewater vapor pressure radiation and wind speed is verygood Only a few small gaps in air temperature data arefilled by linear interpolation Gaps in radiation data arefilled by the observations from other sites Gaps in windspeed data are filled by measurements from the EC sys-tem at the PTS site Those data from the EC system dur-ing the period from 30 min before precipitation to 30 minafter precipitation are rejected

23 Method to determine mixed layer depth

As a fresh-water body with extremely low salinityLake Taihu forms no barrier layer that indicates the dif-ference between the isothermal layer depth (ILD) and themixed layer depth (MLD) (Sprintall and Tomczak1992) Thus adopting a temperature-based criterion todetermine the MLD is convenient and reasonable As ob-jective methods require high vertical resolution in theprofile subjective methods are more suitable to the ob-servation system in the Lake Taihu Eddy Flux NetworkTwo subjective methods Kararsquos optimal definition andthe traditional difference criterion are compared to de-termine the more applicable one

Based on a subjectively determined temperature dif-ference ΔT Kararsquos optimal definition searches the mixedregion where the temperature difference between adja-cent layers is less than 01ΔT downward with a continu-

ously resetting reference temperature Tref The MLD willbe the depth where the temperature has changed by anabsolute value of ΔT from Tref This method adapts wellto various stratifications in oceans (Kara et al 2000) Inour profile system we set the initial Tref to be the temper-ature at the depth of 02 m

Based on the traditional difference criterion Tref is al-ways the surface temperature Therefore the MLD with atemperature Tb lower than the surface temperature by ΔTcan be determined accurately between depth intervals ascalculated in Eqs (1) and (2) below If no depth is foundfor the MLD it is set to the maximum depth which isalso applied in the optimal definition

Tb = Tsminus∆T (1)

MLD =TbminusTn

Tn+1minusTn(hn+1minushn)+hn (2)

where Ts refers to the surface temperature and is repres-ented by the temperature at 02 m depth and Tn and hnare the temperature and depth of layer n respectivelyAccording to Kara et al (2000) three values of ΔTmdash0805 and 02degCmdashare used in both criteria

The Kararsquos optimal definition which performs wellfor oceans gives two types of unreasonable MLD resultswhen processing weak and thin inversion layers at thesurface (Fig 2) First taking the period 20ndash28 July as anexample when the temperature difference of the inver-sion layer is smaller than ΔT the algorithm is unable tofind a place for Tb as the lower part of the lake is stillstratified As a result the MLD is improperly set to themaximum depth leading to a lack of MLD continuity intime Second the temperature difference of the inversionlayer is slightly larger than ΔT from 4 to 8 October Thisresult causes a low value of MLD although vertical mix-ing is still quite strong in the whole water column

Therefore although Kararsquos optimal definition is a rel-atively comprehensive method to determine the MLDthe traditional difference criterion gives more stable res-ults for Lake Taihu and is more suitable to use with bet-ter continuity and fewer errors

As the MLD also varies with the value of ΔT an ap-propriate ΔT should be ensured to objectively analyze thevariation trend of thermal stratification In the differencecriterion the MLD generally decreases as a lower ΔT ischosen (Fig 2) In some cases we find that thermal strat-ification (MLD lt maximum depth) does not appear withΔT = 05degC or ΔT = 08degC but occurs only when ΔT =02degC These typical cases are included in Fig 3 whereweak thermal stratification as a transition between stableand unstable state is highlighted by using ΔT = 02degC

Thus using ΔT = 02degC helps to detail the change pro-cess of thermal stratification quantitatively

Eventually the traditional difference criterion with ΔT= 02degC is applied in studying thermal stratification andvertical mixing processes in Lake Taihu

3 Results and discussion

31 General characteristics of thermal stratification

In terms of seasonal differences (Fig 4) the thermalstratification in the spring (April) is stronger than that in

Fig 2 Two typical differences between Kararsquos optimal definition and the traditional difference criterion The left panels show the MLD of thetwo methods from 20 to 28 July with ΔT set to (a) 08degC (b) 05degC (c) 02degC and (d) the coupled water temperature The right panels show theMLD of the two methods from 4 to 8 October with ΔT set to (e) 08degC (f) 05degC (g) 02degC and (h) the coupled water temperature In the le-gend the letters ldquoKarardquo and ldquoDifrdquo refer to the MLDs from the optimal definition and the difference criterion respectively The single blue line in(e f) indicates that equal values are determined by the two methods

Fig 3 Cases of water temperature and the MLD partly chosen from the daily patterns in which the wholly mixed state is shown with ΔT =08degC and ΔT = 05degC while thermal stratification is found with ΔT = 02degC on (a) 3 (b) 9 (c) 21 (d) 31 January and on (e) 2 April (f) 8 July(g) 12 July (h) 18 July and (i) 28 October The white line indicates the coupled MLD at ΔT = 02degC

the winter (January) which can be summarized by com-paring the vertical temperature difference in these twomonths Strong thermal stratification appears in the sum-mer (July) with a temperature gradient that stretches tothe bottom and lasts for more than 24 h (21ndash29 July)This effect probably results from strong solar radiation inthe summer and the sustained transport of heat flux at the

surface which allows continuous accumulation of en-ergy in the lake for a few days In the fall thermal strati-fication becomes weaker compared with that in otherseasons Although thermal stratification typically changeson a diurnal scale in Lake Taihu some seasonal differ-ences can still be found as a result of seasonal variationsin solar radiation

Fig 4 Continued on next page

The differences in stratification and mixing betweenshallow lakes and deep lakes can be shown on compar-ing Lake Taihu to a deep lake at similar latitude Deep

lakes commonly mix less frequently than shallow lakesThe type of mixing regime varies with latitude and cli-mate zone from warm monomictic lakes at low latitudes

Fig 4 (a1 b1 c1 d1) Temporal evolutions of solar radiation (Rsn net shortwave radiation) wind speed (Ws) and turbulent diffusivity (Kz) and(a2 b2 c2 d2) vertical distributions of water temperature in (a1 a2) winter (January) (b1 b2) spring (April) (c1 c2) summer (July) and (d1 d2)fall (October) The accompanying dominant weather characteristics are marked with black arrows and text CLR CLD and OVC denote cleardays cloudy days and overcast days respectively (Overcast or cloudy days are usually associated with weather systems such as cold fronts andtyphoons which bring precipitation and strong wind as well)

to dimictic lakes and cold monomictic lakes at relativelyhigh latitudes and to amictic lakes in polar regions(Lewis 1983) The thermal structure of Lake Qiandaohu(29deg22primendash29deg50primeN 118deg36primendash119deg14primeE) with a mean depthof 30 m and a lake area of 580 km2 was discussed byZhang et al (2014) It typically exhibits a thermocline asstratification the depth of which ranges from a fewmeters to tens of meters as the season changes By con-trast the thermal stratification in Lake Taihu always hasa shallow depth in the upper region As a warm mo-nomictic lake Lake Qiandaohu requires a one-year cyclefor the thermocline to change it maintains thermal strati-fication in the spring summer and fall and is mixed inthe winter In contrast Lake Taihu is a warm polymicticlake that except for rare examples of lasting stratifica-tion in the summer stratifies in the daytime and mixes atnight on the cycle of one day The thermocline in LakeQiandaohu possesses a temperature gradient within only1degC mndash1 whereas that in Lake Taihu usually exceeds 5degCmndash1 (30 April) The water temperature in Lake Qiandaohubecomes less sensitive to depth as depth increases andalmost no vertical gradient occurs in the bottom layerIn other words only the epilimnion layer in Lake Qi-andaohu is a good indicator of climate forcing In LakeTaihu a shallower depth allows faster transport of heatfrom the surface Although a vertical temperature gradi-ent develops due to the change of heating rate with depththe entire layer generally shows a consistent tendency ofrapid variation which resembles the epilimnion in deeplakes Accordingly compared to a deep lake whose ther-mal stratification changes depth thickness and strengthwith the seasons the thermal stratification in Lake Taihushows little seasonal differences but large variations inthe short term

Being the same as many other shallow lakes in tem-perate zone (Lewis 1983) Lake Taihu is classified as apolymictic lake that retains the feature of diurnal mixingFor instance the Lake Muumlggelsee which has a meandepth of 49 m and an area of 73 km2 located in thesoutheast of Berlin Germany is a shallow and polymic-tic lake with 793 of its stratification events shorterthan 1 day (Wilhelm and Adrian 2008) However thereare also some undeniable differences on thermal stratific-ation between Lake Taihu and Lake Muumlggelsee WhenLake Taihu has its rare continuous thermal stratification(longer than one week) only in summer Lake Muumlggelseeusually has its long-lasting stratification events more fre-quently (more than once per year in different seasons)and more durably (up to eight weeks) The greater depthless fetch and different local climate of Lake Muumlggelseemay account for its difference in thermal stratification

from Lake Taihu (von Einem and Graneacuteli 2010)

32 Representative response of thermal stratification todominant factors

Many factors affect the thermal stratification of a lakeFor the shallow Lake Taihu solar radiation and wind dis-turbance dominate the variations of thermal stratification(Fig 4)

On clear days strong thermal stratification is found ineach season (eg 4 and 11 January 22 28 and 30 April13 14 and 28 July and 22 October) Among these casesthe maximum vertical temperature difference reached8degC (30 April) and the minimum value was not lowerthan 2degC making the water column stable Howeverstrong stratification did not always occur on clear daysIn this situation the vertical temperature difference wasless than 2degC with weak thermal stratification (eg 19January 15 July and 15ndash17 October) or a wholly mixedstate (eg 21ndash23 January and 12 October) For instancealthough solar radiation was strong on 22 January a rel-atively high average wind speed of 583 m sndash1 resulted indynamic mixing that prevented a great vertical temperat-ure difference from occurring

With an extremely low temperature gradient thermalstratification hardly ever appeared on overcast days thatlacked solar radiation Even if the lake was slightly strati-fied due to the residual impact of previous days it rap-idly mixed to a homogeneous state (eg 12 January and3 July) due to dynamic mixing (wind disturbance) andthermal mixing (surface cooling)

Cloudy days are a transition between clear days andovercast days On these days strong thermal stratifica-tion was less developed (10 January) and the propor-tions of weak thermal stratification and mixed state weremuch higher than on clear days

Having contrary effects on a water body solar radi-ation (Rsn) and wind speed (Ws) are considered dominantfactors that control the change of thermal stratificationIn most cases (Fig 4) the prevalent diurnal stratificationresults from strong solar radiation in daytime making Kz(calculated from meteorological factors and water tem-perature) which represents the strength of turbulent mix-ing to be nearly zero in spite of the considerable windspeed (eg 20ndash24 October) The coupled diurnal mixinghappens after sunset when solar radiation has droppedSimultaneously Kz increases in nighttime indicatingprominent vertical convection In addition continuousperiod of high Kz exists when the wind is strong and thesolar radiation gets weak (eg 4ndash12 July) in which casesturbulent mixing is dominant enough that Kz never dropsto zero To consider further the monthly average Rsn and

Ws are calculated as seasonal thresholds We regard thecondition when the daily average Rsn is higher than thethreshold while the daily average Ws is lower than thethreshold as Type 1 Thus the contrary condition is Type2 when the daily average Rsn is lower than the thresholdwhile the daily average Ws is higher than the thresholdAll the cases that coincide with these two extreme typesare averaged to obtain a representative pattern of thethermal structure in the four seasons (Fig 5)

When Rsn is strong and Ws is weak (Figs 5andashd Type1) solar radiation becomes a dominant factor that dir-ectly leads to a low MLD in daytime in the four seasonsamong which spring and summer develop strongerthermal stratification than fall and winter The thermalstratification in summer declines with difficulty at night-time due to energy accumulation whereas it is mixedthoroughly at night in other seasons which is consistentwith the analysis in Section 31 When Rsn is weak andWs is strong (Figs 5endashh Type 2) wind speed becomesthe dominant factor The MLD reaches a high value in allfour seasons which means a wholly mixed state A weaktemperature inversion is found under Type 2 conditionsnear the surface due to heat loss from net radiation sens-ible heat and latent heat which are influential when littleenergy is supplied by Rsn In addition there is a slightlywarmer bottom region in spring fall and winter This ef-fect results from energy released by sediment as a heatsource In summer the sediment receives energy as aheat sink from the water column due to intense energyaccumulation thus no high-temperature zone is found

By utilizing relative MLD (RMLD) the thermal struc-

ture in Lake Taihu can be divided into three differentstates wholly mixed state nearly mixed state and strati-fied state (Fig 6) As concluded cases with thermalstratification mainly occupy the lower right regionwhich refers to Type 1 Most cases of wholly mixed stateare distributed in the upper left region which coincideswith Type 2 It is worth noting that the cases of nearlymixed state show positive correlations between Rsn andWs when Rsn is relatively high which cannot be founddue to few cases when both Rsn and Ws are lower Thisresult indicates that when Rsn increases Ws must be higherto offset the stronger stratifying effect to maintain thethermal structure As the nearly mixed state is a criticalcondition before the water column is wholly mixed itcan be inferred that when Rsn is higher a higher Wsthreshold is required to prevent the wholly mixed lakefrom stratifying From Fig 6 it can be seen that whenRsn is 100 and 200 W mndash2 the thresholds are approxim-ately 2ndash3 and 4ndash5 m sndash1 respectively when Rsn is higherthan 300 W mndash2 the threshold can exceed 6 m sndash1

33 Wind-induced convection

The concept of convection is usually used to describethe process whereby the gradient of the water propertydeclines with prominent vertical mixing during the cool-ing period of the water body However in Lake Taihu aspecific quick convection during the short cycle ofthermal stratification is found which is also controlledby Rsn and Ws

During the development and decline of thermal strati-fication four types of daily patterns are summarized

Fig 5 The average response of water temperature and MLD to (andashd) Type 1 (high Rsn and low Ws) and (endashh) Type 2 (low Rsn and high Ws) con-ditions at the PTS site in (a e) January (b f) April (c g) July and (d h) in 2015 The monthly average maximum depths are used in the fourseasons and the white line denotes the MLD

(Fig 7) When both Rsn and Ws are strong thermal strati-fication develops and then slowly decreases (Fig 7a)When Ws is dominantly high a mixed state lasts for theentire day (Fig 7b) However when Ws suddenly in-creases an existing stable thermal stratification is thor-oughly mixed in a short time with the MLD increasing tomaximum depth This phenomenon which occurs in bothdaytime (Fig 7c) and nighttime (Fig 7d) is here calledwind-induced convection

Furthermore the frequencies of mixing stratifyingand wind-induced convection as well as its prerequisitesare shown in Table 1 and specific data of wind-inducedconvection are recorded in Table A1 in the AppendixThe presence of solar radiation in daytime makes theconvection frequency far lower than in nighttime For ex-ample wind-induced convection appears in fall 17 timesat night but only twice in daytime Moreover the lowestMLD before convection and the lowest Ws during con-vection at night are clearly lower than those in the dayindicating that high Ws is not necessary for night convec-tion but stronger thermal stratification still can be turnedeven in this situation By contrast these prerequisites arestricter in daytime For example the lowest MLD beforeconvection in spring daytime is 1 m deeper than that innighttime but the required Ws is nearly twice as high asthat for night convection

Regarding seasonal differences Lake Taihu is whollymixed most frequently in winter (17 days) Wind-in-duced convection occurs in the day for the most times (6days) and the prerequisites for both the MLD and Ws arethe lowest (085 m and 243 m sndash1 respectively) TheMLD and Ws are also relatively low at nighttime (030 mand 241 m sndash1 respectively) This result means thatwinter is the most difficult season for thermal stratifica-tion to develop Although the lake is stratified it can beeasily mixed by wind In fall there are only a few daysof thorough mixing (7 days) while thermal stratificationis commonly seen (20 days) However wind-induced

Table 1 Number of wholly mixed days stratified days convection in daytime and convection in nighttime The lowest MLD before convec-tion and the lowest Ws during convection are also shown NoD denotes number of days

Season Whole mixing Stratification Convection in daytime Convection in nighttimeNoD Value NoD Value

Spring (31 days) 10 20 4 MLD 122 m 11 MLD 029 mWs 404 m sndash1 Ws 204 m sndash1

Summer (28 days) 4 24 1 MLD 233 m 4 MLD 078 mWs 446 m sndash1 Ws 391 m sndash1

Fall (27 days) 7 20 2 MLD 123 m 17 MLD 042 mWs 277 m sndash1 Ws 191 m sndash1

Winter (31 days) 17 14 6 MLD 085 m 7 MLD 030 mWs 243 m sndash1 Ws 241 m sndash1

Fig 6 Thermal stratification with different strengths and the corres-ponding Rsn and Ws The circle points refer to the wholly mixed statewith average RMLD of 100 The squares refer to the nearly mixedstate with average RMLD between 85 and 100 The triangles referto the stratified state with average RMLD lower than 85 All data ofRMLD Rsn and Ws here are chosen from daytime and are averaged todecrease the influence of extreme values (RMLD is the relative MLDwhich is the ratio of the MLD to the daily maximum depth)

Fig 7 Four typical cases for changes in water temperature and the MLD (a) thermal stratification slowly decreases on 23 April (b) no thermalstratification appears on 17 April (c) developed thermal stratification suddenly disappears in daytime on 18 January and (d) developed thermalstratification suddenly disappears in nighttime on 18 October The white line denotes the MLD

convection at night occurs the most often in fall (17days) with the lowest requirement for Ws (191 m sndash1)Therefore the daily cycle of the thermal structure is moreobvious in fall because the easily stratified water is usu-ally mixed at night For summer the lake is whollymixed on only 4 days Wind-induced convection is thehardest to induce as shown by the fewest times of con-vection whether in day (1 day) or night (4 days)Moreover its prerequisite values of the MLD and Ws arethe highest (233 m and 446 m sndash1 respectively in day-time and 078 m and 391 m sndash1 respectively in night-time) These values in spring are all at intermediatelevels Finally wind-induced convection prevails inwinter and fall but becomes rare in summer whenthermal stratification is easy to maintain

4 Conclusions

In this study the data from the PTS site in the LakeTaihu Eddy Flux Network in 2015 are used to analyzethe variation in thermal stratification and vertical mixingin Lake Taihu Stable thermal stratification is stronger inspring and summer than in winter but becomes weaker infall Compared to a deep lake at similar latitude LakeTaihu stratifies at a comparatively shallow depth that isalways in the upper region Its vertical temperature gradi-ent is greater (usually exceeds 5degC mndash1) and the vari-ation tendency of the entire layer is more uniformThermal stratification in Lake Taihu does not change ob-viously with seasons but varies greatly in the short term(one day to a few days) Therefore Lake Taihu should beclassified as a warm polymictic lake Many shallowploymictic lakes share the same characteristic of diurnalmixing However differences on thermal stratificationamong them are also prominent The duration and fre-quency of long-lasting (more than one week) thermalstratification vary with location and morphology whichin detail may be caused by different local climate lakedepth and fetch

Based on comparison between different MLD criteriathe traditional difference criterion with ΔT = 02degC isshown to be a more suitable method for determining theMLD in Lake Taihu especially when a weak temperat-ure inversion exists at the surface In this situation theMLD from Kararsquos optimal definition usually differs fromthe logical value by nearly 2 m

Weather conditions are influential Strong thermalstratification occurs more frequently on clear days thanon cloudy days When it is overcast the lake is almostmixed Indeed different weather conditions control thethermal structure of the lake mainly through solar radi-

ation (Rsn) and wind speed (Ws) which are the two dom-inant factors with totally contrary effects on thermalstratification The most direct results are the diurnal strat-ification and convection as well as the distinct patternsunder the combination of these two factors When highRsn corresponds to low Ws strong thermal stratificationappears in each season among which the lake is morestratified in spring and summer than in fall and winterWhen Rsn is low but Ws is high the lake is well mixed ineach season with a weak temperature inversion near thesurface In this case a warmer region at the bottom isalso found in spring fall and winter when sediment be-comes a heat source This effect cannot be seen in sum-mer due to heat accumulated in the water column Solarradiation and wind speed are positively correlated for thenearly mixed state When Rsn increases a higher Wsthreshold is required to maintain the mixed state Rsn val-ues of 100 and 200 W mndash2 need thresholds of approxim-ately 2ndash3 and 4ndash5 m sndash1 respectively When Rsn is higherthan 300 W mndash2 the threshold can exceed 6 m sndash1

In this study the PTS site is chosen because of itsgood water quality few macrophytes and more spaciousfetch Furthermore the effects of meteorological condi-tions are mainly discussed Future work should involveother zones in Lake Taihu to take into consideration thefactors such as plankton macrophytes and morphologyThus more comprehensive research can be performedMoreover it is undoubted that the Ws threshold in-creases with Rsn However only approximate values havebeen obtained to date because there are few cases foranalysis A specific and quantitative law must be foundbetween these factors

Prominent convection occurs in Lake Taihu due towind disturbance This effect occurs more easily at nightthan in daytime As the season with the least thermalstratification winter has the greatest tendency of convec-tion in daytime In fall thermal stratification and wind-induced convection are both common showing a typicaldaily cycle of thermal structure A stratified state is easyto maintain in summer and the prerequisites for MLDand Ws are the strictest thus the least number of convec-tion occurs in summer Generally convection results in asubstantial change in the thermal structure in a lake Indeep lakes convection chiefly results from seasonal vari-ations of thermal properties in the water (Socolofsky andJirka 2005) controlling the growth of algae and havinga great impact on substance distribution in the lake(Gonccedilalves et al 2016) However the diurnal convec-tion in shallow Lake Taihu is caused more by wind dis-turbance which may help in studies of algal blooms andthe uncertainty of flux in Lake Taihu similar to other

polymictic lakes (Wilhelm and Adrian 2008) We useonly the MLD to depict convection in one dimension Todeeply study the mechanism underlying convection theflow field and what affects it in three-dimensional spacemust be considered Therefore subsequent observational

and modeling studies are neededAcknowledgments I would like to express my heart-

felt thanks to all those who have helped me in this re-search

Table A1 This table records average Rsn Ws MLD and RMLD in daytime as well as the thermal stratification in each day in 2015 If a thermalstratification declines in the next day prior to the sunrise it is considered a mixing process for the previous day (days of wholly mixed state arenot included) The last two columns of the table show the MLD before and the Ws during wind-induced convection

Date (mthday) Rsn (W mndash2) Ws (m sndash1) MLD (m) RMLD () Start time End time MLD before convection Ws during convection12 32132 179 131 4827 1200 1930 13 25865 358 248 9162 1300 1500 141 40814 27860 108 046 1711 1100 2200 175 28518 29629 171 145 5459 1300 1730 030 25319 27674 229 220 8262 1300 1530 108 245110 28273 158 041 1547 1030 2300 119 241111 29896 108 028 1048 1030 2030 060 548117 30568 182 122 4608 1200 1730 046 515118 20173 459 243 9011 1300 1430 124 485119 33616 182 082 3102 1100 0000 141 546121 27552 666 241 9086 1000 1200 085 829124 24201 386 186 6990 1100 1530 091 569126 9932 251 251 9533 1500 1600 116 243131 27464 223 188 7188 1300 1800 148 49341 26866 599 178 6092 1600 162 73542 29979 756 245 8251 1200 1530 122 64744 15002 488 277 9375 1300 1430 186 40448 48192 163 116 3732 1030 0030 059 65149 30820 273 111 3471 1030 1830 129 460410 42051 090 079 2470 0930 2330 029 623411 46997 297 060 1885 0830 2330 169 443412 47340 311 102 3201 1030 1900 031 1233416 35488 581 212 6900 1000 1500 418 31353 234 089 2905 1100 419 26408 116 073 2409 2100 123 945421 48516 124 036 1174 0830 422 52878 199 038 1239 0830 0330 146 395423 50746 431 149 4945 1100 2330 220 361424 20494 097 049 1649 0900 425 49904 131 029 981 0100 164 204426 53908 397 073 2458 0900 1930 427 46094 501 276 9340 1330 1600 229 464428 48111 245 031 1054 0730 2130 135 1419430 53095 141 025 858 0730 2200 116 65071 38639 263 121 3388 1000 2400 72 32588 187 096 2678 0830 0300 73 25457 201 074 2071 0800 0130 77 19577 388 334 9355 1100 1300 233 44678 19846 350 292 8148 1100 1830 279 39279 21691 424 226 6219 1030 2100 234 689710 44843 673 175 4860 0900 2000 712 30011 720 327 8785 1500 2030 713 45030 199 039 1038 0800 714 39441 185 041 1089 715 42426 432 138 3659 716 20072 466 214 5734 2100 717 8565 663 359 9739 1100 1600 718 9596 307 253 6837 1030 0100 264 534719 18015 445 182 4947 0900 1900 078 770720 44649 147 117 3148 0700 721 25133 167 095 2565 722 42127 255 055 1501 723 10895 240 156 4238

to be continued

Appendix

REFERENCESBerger S A S Diehl H Stibor et al 2007 Water temperature

and mixing depth affect timing and magnitude of events dur-ing spring succession of the plankton Oecologia 150643ndash654 doi 101007s00442-006-0550-9

Boehrer B and M Schultze 2008 Stratification of lakes RevGeophys 46 RG2005 doi 1010292006RG000210

Chai A and E Kit 1991 Experiments on entrainment in an an-nulus with and without velocity gradient across the density in-terface Exp Fluids 11 45ndash57 doi 101007BF00198431

Cheng X Y W Wang C Hu et al 2016 The lakendashair ex-change simulation of a lake model over eastern Taihu Lakebased on the Endashε turbulent kinetic energy closure thermody-namic process Acta Meteor Sinica 74 633ndash645 doi 1011676qxxb2016043 (in Chinese)

Chu C R and C K Soong 1997 Numerical simulation of wind-induced entrainment in a stably stratified water basin J Hy-draul Res 35 21ndash42 doi 10108000221689709498642

Chu P C and C W Fan 2011 Maximum angle method for deter-mining mixed layer depth from seaglider data J Oceanogr67 219ndash230 doi 101007s10872-011-0019-2

Churchill J H and W C Kerfoot 2007 The impact of surfaceheat flux and wind on thermal stratification in Portage LakeMichigan J Great Lakes Res 33 143ndash155 doi 1033940380-1330(2007)33[143TIOSHF]20CO2

Condie S A and I T Webster 2002 Stratification and circula-tion in a shallow turbid waterbody Environ Fluid Mech 2177ndash196 doi 101023A1019898931829

Crawford G B and R W Collier 1997 Observations of a deep-mixing event in Crater Lake Oregon Limnol Oceanogr 42299ndash306 doi 104319lo19974220299

Deng B S D Liu W Xiao et al 2013 Evaluation of the CLM4Lake Model at a large and shallow freshwater lake J Hydro-

meteorol 14 636ndash649 doi 101175JHM-D-12-0671Farrow D E and C L Stevens 2003 Numerical modelling of a

surface-stress driven density-stratified fluid J Eng Math47 1ndash16 doi 101023A1025519724504

Fee E J R E Hecky S E M Kasian et al 1996 Effects oflake size water clarity and climatic variability on mixingdepths in Canadian Shield Lakes Limnol Oceanogr 41912ndash920 doi 104319lo19964150912

Fonseca B M and C E de M Bicudo 2008 Phytoplankton sea-sonal variation in a shallow stratified eutrophic reservoir(Garccedilas Pond Brazil) Hydrobiologia 600 267ndash282 doi101007s10750-007-9240-9

Giles C D P D F Isles T Manley et al 2016 The mobility ofphosphorus iron and manganese through the sediment-watercontinuum of a shallow eutrophic freshwater lake under strati-fied and mixed water-column conditions Biogeochemistry127 15ndash34 doi 101007s10533-015-0144-x

Godo T K Kato H Kamiya et al 2001 Observation of wind-induced two-layer dynamics in Lake Nakaumi a coastal la-goon in Japan Limnology 2 137ndash143 doi 101007s102010170009

Gonccedilalves M A F C Garcia and G F Barroso 2016 Morpho-metry and mixing regime of a tropical lake Lake Nova(Southeastern Brazil) An Acad Bras Cienc 88 1341ndash1356doi 1015900001-3765201620150788

Heo K-Y and K-J Ha 2010 A coupled model study on theformation and dissipation of sea fogs Mon Wea Rev 1381186ndash1205 doi 1011752009MWR31001

Hu W P S E Joslashrgensen Z Fabing et al 2011 A model on thecarbon cycling in Lake Taihu China Ecol Model 2222973ndash2991 doi 101016jecolmodel201104018

Kalff J 2002 Temperature cycles lake stratification and heatbudgets Limnology Inland Water Ecosystems J Kalff EdPrentice Hall Upper Saddle River N J 592 pp

Continued from Table A1Date (mthday) Rsn (W mndash2) Ws (m sndash1) MLD (m) RMLD () Start time End time MLD before convection Ws during convection724 22759 278 092 2491 725 30080 204 106 2912 726 40339 188 092 2527 727 42468 265 063 1727 728 53248 321 047 1319 108 5691 639 284 9266 1230 1400 150 7941010 33148 670 277 9004 1530 1730 150 7001011 41154 199 116 3763 1000 2000 140 3241012 39413 311 133 4344 1000 1830 189 3001013 37572 145 093 3049 1000 0500 138 1911014 17624 182 180 5902 1230 2100 169 3781015 37059 199 065 2150 0900 0100 042 4621016 33176 120 121 3981 0930 0100 148 2611017 40725 182 064 2125 0900 2330 108 5131018 38709 187 071 2360 0830 2100 086 4861019 37139 320 125 4178 1030 2200 228 5971020 34684 167 091 3055 1000 0100 1021 37713 170 085 2855 0900 2130 119 4821022 35433 161 063 2115 0930 2130 141 4831023 38010 216 081 2737 0930 0100 145 6061024 31515 259 095 3253 1030 2000 180 6401025 28778 317 169 5808 1130 1930 210 7501026 33336 354 171 5827 2130 2200 154 9901028 16996 241 256 8809 1000 1200 123 2771031 25560 296 245 8518 1500 1730 131 253

Kara A B P A Rochford and H E Hurlburt 2000 An optimaldefinition for ocean mixed layer depth J Geophys Res 105doi 1010292000JC900072

Lee X H S D Liu W Xiao et al 2014 The Taihu Eddy FluxNetwork An observational program on energy water andgreenhouse gas fluxes of a large freshwater lake Bull AmerMeteor Soc 95 1583ndash1594 doi 101175BAMS-D-13-001361

Lewis W M Jr 1983 A revised classification of lakes based onmixing Can J Fish Aquat Sci 40 1779ndash1787 doi 101139f83-207

Liu H Z J W Feng J H Sun et al 2015 Eddy covariancemeasurements of water vapor and CO2 fluxes above the Er-hai Lake Sci China Earth Sci 58 317ndash328 doi 101007s11430-014-4828-1

Michalski J and U Lemmin 1995 Dynamics of vertical mixingin the hypolimnion of a deep lake Lake Geneva LimnolOceanogr 40 809ndash816 doi 104319lo19954040809

Monterey G and S Levitus 1997 Seasonal Variability of MixedLayer Depth for the World Ocean NOAA Atlas NESDIS 14Washington DC US Government Printing Office 96 pp

Oswald C J and W R Rouse 2004 Thermal characteristics andenergy balance of various-size Canadian shield lakes in theMackenzie River Basin J Hydrometeorol 5 129ndash144 doi1011751525-7541(2004)005lt0129TCAEBOgt20CO2

Pernica P M G Wells and S MacIntyre 2014 Persistent weakthermal stratification inhibits mixing in the epilimnion ofnorth-temperate Lake Opeongo Canada Aquat Sci 76 187ndash201 doi 101007s00027-013-0328-1

Qin B Q P Z Xu Q L Wu et al 2007 Environmental issuesof Lake Taihu China Hydrobiologia 581 3ndash14 doi 101007s10750-006-0521-5

Qiu Y Y 2013 Numerical simulation study of the effect of un-derlying surface obstacles on observation environment Mas-ter Degree dissertation Nanjing University of InformationScience amp Technology China 53 pp (in Chinese)

Samal N R K D Joumlhnk F Peeters et al 2008 Mixing and in-ternal waves in a small stratified Indian lake Subhas SarobarMonitoring and Modelling Lakes and Coastal EnvironmentsP K Mohanty Ed Springer Publishing Berlin 91ndash100

Schadlow S G and D P Hamilton 1995 Effect of major flowdiversion on sediment nutrient release in a stratified reservoirMar Freshwater Res 46 189ndash195 doi 101071MF9950189

Socolofsky S A and G H Jirka 2005 Mixing in lakes andreservoirs Special Topics in Mixing and Transport Processesin the Environment S A Socolofsky and G H Jirka Eds

College Station TX Texas AampM University 230 ppSprintall J and M Tomczak 1992 Evidence of the barrier layer

in the surface layer of the tropics J Geophys Res 977305ndash7316 doi 10102992JC00407

Sun S F J F Yan N Xia et al 2007 Development of a modelfor water and heat exchange between the atmosphere and awater body Adv Atmos Sci 24 927ndash938 doi 101007s00376-007-0927-7

Tuan N V K Hamagami K Mori et al 2009 Mixing by wind-induced flow and thermal convection in a small shallow andstratified lake Paddy Water Environ 7 83ndash93 doi 101007s10333-009-0158-x

von Einem J and W Graneacuteli 2010 Effects of fetch and dis-solved organic carbon on epilimnion depth and light climatein small forest lakes in southern Sweden Limnol Oceanogr55 920ndash930 doi 104319lo20105520920

Wang M D J Z Hou and Y B Lei 2014 Classification ofTibetan Lakes based on variations in seasonal lake water tem-perature Chinese Sci Bull 59 4847ndash4855 doi 101007s11434-014-0588-8

Wang S X Qian B P Han et al 2012 Effects of local climateand hydrological conditions on the thermal regime of a reser-voir at tropic of cancer in southern China Water Res 462591ndash2604 doi 101016jwatres201202014

Wang W 2014 Energy budget at Lake Taihu and its response toclimate change PhD dissertation Nanjing University of In-formation Science amp Technology China 140 pp (in Chinese)

Wilhelm S and R Adrian 2008 Impact of summer warming onthe thermal characteristics of a polymictic lake and con-sequences for oxygen nutrients and phytoplankton FreshwBiol 53 226ndash237 doi 101111j1365-2427200701887x

Zhang L B Zhu J H Gao et al 2017 Impact of Taihu Lake oncity ozone in the Yangtze River Delta Adv Atmos Sci 34226ndash234 doi 101007s00376-016-6099-6

Zhang Y L Z X Wu M L Liu et al 2014 Thermal structureand response to long-term climatic changes in Lake Qian-daohu a deep subtropical reservoir in China Limnol Ocean-ogr 59 1193ndash1202 doi 104319lo20145941193

Zhao L L G W Zhu Y F Chen et al 2011 Thermal stratific-ation and its influence factors in a large-sized and shallowlake Taihu Adv Water Sci 22 844ndash850 (in Chinese)

Zhao Q H J H Sun and G W Zhu 2012 Simulation and ex-ploration of the mechanisms underlying the spatiotemporaldistribution of surface mixed layer depth in a large shallowlake Adv Atmos Sci 29 1360ndash1373 doi 101007s00376-012-1262-1

Tech amp Copy Editor Lan YI