thermal structure and energy budget in a small high

879Rodríguez-Rodríguez et al.—Physical limnology in a high mountain lake

Thermal structure and energy budget in a small high mountain lake:La Caldera, Sierra Nevada, Spain

MIGUEL RODRÍGUEZ-RODRÍGUEZUniversity Pablo de OlavideCarretera de Utrera Km. 1Seville 41013, Spainemail: [email protected]

ENRIQUE MORENO-OSTOS

INMACULADA DE VICENTE

LUIS CRUZ-PIZARROWater Research InstituteUniversity of GranadaC/ Ramón y Cajal s/nGranada 18071, Spain

SERGIO LUIZ RODRIGUES DA SILVA*

University Santa CecíliaRua Oswaldo Cruz no. 266Santos SP 11045–907, Brasil

*Present address: Water Research Institute,University of Granada, C/ Ramón y Cajal s/n,Granada 18071, Spain.

Abstract This work examines the diel change ofenergy storage and its associated patterns of thermalstratification during the ice-free period in a highmountain lake (La Caldera Lake, Sierra Nevada,Spain), in response to meteorological conditions.Bihourly data have been implemented to a standardmethodology of surface heat exchange calculationsin lakes. Strong variations have been observed on thediverse components of the energy budget at differ-ent time scales, ranging from diel to seasonal. Ad-ditionally, time-series analyses have been applied toreveal the underlying periodicities involved in rela-tion to the different variables studied. The resultsobtained from this study provided realistic

conditions for the environmental modelling of suchprocesses, which are very sensitive in time scale.

Keywords energy budget; diel variations; time-series analysis; high mountain lake

INTRODUCTION

High mountain lakes have traditionally been ofparticular interest to researchers, because they aresubjected to extreme meteorological conditions.Physical processes have a major influence on theorganisation and dynamics of the biological com-munities in these systems. In Spain, the scarcenessof natural lakes confers supplementary importanceon high mountain lakes as they offer opportunitiesfor conducting basic limnological research.

This work examines the diel change of energystorage and its associated patterns of thermalstratification during the ice-free period in a highmountain lake (La Caldera, Sierra Nevada, Spain)in response to meteorological conditions with a finetemporal resolution (2 hourly). Related publicationsconducted to study the lake’s heat budget at suchhigh temporal resolution (Frempong 1983) are onlyconfined for 24-h periods. There is, however, anextensive limnological literature available based ondaily, seasonal, and annual observations (Hutchinson1957; Elder et al. 1974; Schmid et al. 2003). One ofthe main objectives of this study is to obtain the heatbalance of the lake over a complete ice-free period(74 days) to reveal the magnitude of the differentcomponents of the heat balance equation at such afine temporal resolution.

The surface heat balance of a lake is governed byshort-wave and long-wave radiations, latent heat andsensible heat flux, and by energy associated with theinflows and outflows (Henderson-Sellers 1986). Inthis study various terms of heat balance weremeasured either directly or by evaluating empiricalformulations from the available data. The currentequations for the estimation of some componentsfrom meteorological observations (Armengol et al.

M03053; Online publication date 24 November 2004Received 16 September 2003, accepted 14 June 2004

New Zealand Journal of Marine and Freshwater Research, 2004, Vol. 38: 879–8940028–8330/04/3805–0879 © The Royal Society of New Zealand 2004

880 New Zealand Journal of Marine and Freshwater Research, 2004, Vol. 38

2000a) are reliable for short periods, so it is expectedthat the present budget approximates the processesof energy balance for the lake. Finally, statisticaltime-series analyses (cross-correlation technique)were performed to describe the mechanismsinvolved in the stratification-destratificationprocesses of the lake.

One of the main purposes of the present study isto apply an appropriate temporal scale to improvethe accuracy of surface heat exchange models inlakes.

METHODS

Study siteLocated in the Sierra Nevada National Park(Southern Spain) at an elevation of 3050 m, LaCaldera Lake is one of the highest permanent waterbodies in the Iberian Peninsula (Fig. 1). The lake iscovered by ice from November until mid July. Itoccupies a glacial cirque and rests above

Fig. 1 Bathymetry and location of La Caldera Lake, Sierra Nevada, Spain showing the Loma de Dílar weatherstation.

permotriassic and paleozoic materials, which havesuffered a notable metamorphism, and among whichmicaschists along with quartzites prevail (Cruz-Pizarro & Carrillo 1996). The substratum isimpervious, so very little or no infiltration isexpected to enter the lake. As the snow precipitation

Table 1 Some morphometric parameters from LaCaldera Lake (redrawn from Cruz-Pizarro & Carrillo1996), Sierra Nevada, Spain.

Length (m) 201Mean width (m) 115Max. depth (m) 14Mean depth (m) 4.60Relative depth (%) 6.63Centre of gravity (m) 3.00Area (m2) 23070Volume (m3) 107600Evolution of volume 1.22Catchment area (m2) 180000Perimeter (m) 595Evolution of perimeter 1.1


in its catchment area (18 ha) is the main water input,it does not have visible inlets or outlets. Table 1shows its main morphological parameters. It may beassumed that because of the shape and slope of thecatchment area practically all the precipitationeventually reaches the lake. It has a subcircular form(evolution of perimeter = 1.1) and it is relatively deep(14 m max.) in relation to size. The relative depth,which gives the maximum depth as a percentage ofthe diameter of a theoretical circle of equal surfacearea, is 6.63% (Cruz-Pizarro & Carrillo 1996), closeto that estimated in one of the most oligotrophic lakes(Crater Lake: 7%). The shape of the basin is similarto a cone with the maximum depth being displacedin west-north-west direction toward its steepest wall.Thermally the lake is considered as a temperatesubpolar dimictic lake with periods in which thetemperature of the surface waters are above 4°C.During the ice-free period, the lake undergoesprogressive warming and cooling, with the formergenerally being quicker and more persistent. Theheat absorbed on the surface is rapidly transmitteddownwards by wind stress, owing to the limitedmechanical resistance to the mixing of the watercolumn.

The lake water is highly transparent, more than10% of photosynthetic active radiation (PAR, 400–700 nm) reaches the bottom (Carrillo et al. 2002) andthe Secchi disk visibility is generally over 10 m(Cruz-Pizarro et al. 1998).

The plankton community is rather simple. Thephytoplankton is mainly dominated by flagellates(Chrysophyceae and Dinophyceae) and byCyanophyceae species (Cyanarcus sp.). Other algaegroups (mainly green algae and diatoms) are muchless abundant (Carrillo et al. 1995). Mixodiaptomuslaciniatus and Hexarthra bulgarica dominate thezooplankton. Particularly noteworthy is the absenceof a littoral rooted vegetation as well as fishes.

Energy budget termsAll the terms in the following heat balance equationare considered in relation to a unit area of the lakesurface and expressed as cal cm–2 h–1 (1 cal cm–2 h–1

= 4.19 10–4 J m–2 h–1 = 11.63 W/m–2).

Qsa + Qla – Qle – Qsh – Qt ± Qec = 0

where: Qsa = incident solar (short-wave) radiationabsorbed; Qla = long-wave radiation absorbed; Qle= long-wave radiation emitted; Qsh = sensible heatflux (convection); Qt = change in storage of thermalenergy; and Qec = energy used for evaporation/condensation.

Heat fluxes resulting from biological and chemicalreactions and heat exchange with bottom sedimentswere neglected because of the morphology of the lakebasin and time scale under consideration. There are nostreams flowing into or from La Caldera Lake (see Fig.1), therefore, the net energy advected by this processis not considered in the above equation. Groundwaterrecharge or discharge was considered negligible asmentioned earlier. All the meteorological data wereobtained bihourly from the Loma de Dílar weatherstation (Fig. 1).

Qsa = Incident solar (short-wave) radiation absorbed

The short-wave radiation absorbed by La CalderaLake was computed according to empirical relationsin the absence of direct measurements. The incidentsolar radiation absorbed by the lake surface is in theregion of the spectrum between 0.3 and 3 mm. Themain factors affecting this variable are the surfacealbedo and the cloud cover, both reduce thetheoretical total incident solar radiation (Qso). In thisstudy, Qso was obtained by the cosine method(Heerman 1985) which is a function of altitude (z),julian day (J), latitude (L) and a constant (C = 2.92):Qso = (31.54–0.274L + 0.0007813z) (1)

+(–0.2986 + 0.2678L + 0.0004102z) cos(2p(365–C)–1)

Taking (1) into account,Qsa= Qso (1–A) f(C’) (2)

where f(C’) = (1–0.507C’0.967) (3)C’ being the measured cloud cover (0 = clear sky and1 = total cloud cover). The albedo,(A) = a0/(a0 + sin f) (4)when a0 is a function of the cloud cover and theJulian day (J):a0 = 0.02 + 0.01 (0.5 – C’)[1 – sin ((p ((J–81)(183)–1))] (5)

the solar zenith angle (f) was obtained using anequation which is a function of the solar declination(Burman & Pochop 1994) and the average daily solarangle in late afternoon. To obtain Qsa bihourly valuesthe result was distributed over the 24-h period usingthe hourly solar zenith angle (fh). Detailedinformation about the methodology can be found inRodríguez-Rodríguez (2002).

Qla = Long-wave radiation absorbed

This component of the energy budget can be definedas the incoming atmospheric long-wave radiation. Itcomes principally from water vapour, cloud droplets,carbon dioxide, and ozone and is absorbed by thesystem. In this example the radiation is a function


of the air temperature and was computed accordingto empirical relations:

Qla = (1 – A) s T4a e0 f(C’) (6)

The above equation is the Stefan-Boltzmannequation modified by several environmental factors.Here Ta = absolute air temperature (°K), s = theStefan-Boltzmann constant (5.57¥10–8 Wm–2¥K–4),and e0 = the atmospheric emissivity, computedfollowing Idso (1981):

e0 = 0.723 + 4.19¥10–4 ea exp (1500(Ta)–1) (7)

where ea is the water vapour pressure in theatmosphere (%), calculated from Richard’s (1971)equation.

Qle = Long-wave radiation emitted

Bihourly values of long-wave radiation emitted fromthe lake were computed taking into account thatwater radiates as a grey body rather than as a blackone. Thus:

Qle = s T4w ew (8)

where emissivity (e) = 0.96, and Tw is the absolutesurface water temperature determined at a depth of0.5 m. Therefore, this term can be considered as anapproximation of the lake surface temperature, andthis was also used to calculate the surface saturationwater vapour pressure.

Qec = Energy used for evaporation/condensation

Latent heat flux is the result of heat budget itself asit measures the energy resulting from evaporation/condensation processes. The sign indicates theenergy transfer, being negative if evaporation pre-dominates and vice versa. Empirical approximations(Colomer et al. 1996; Armengol et al. 2000a) wereused to compute this term of the heat budget:

Qec = – fe (ew – ea) (9)

where fe is an empirical transfer function (Colomer& Casamitjana 1993; Armengol et al. 2000b) basedon the air and water temperatures and the wind speed(u12) 12 m above the ground (m/s):

fe = 4.8 + 1.92 u12 + (Tw – Ta) (10)

ew and ea are the partial vapour pressure in the waterand in the atmosphere, respectively, and werecalculated using Richards’ equation (Rodríguez-Rodríguez 2002).

Qsh = Sensible heat flux (convection)

The sensible heat flux is the energy flux resultingfrom molecular and turbulent conduction when there

is a movement of the fluid (i.e., wind stress). Again,empirical relations were used to compute thisvariable:

Qsh = – 0.63 fe (Tw – Ta) (11)

where the constant 0.63 is Bowen’s ratio (mbar K–1).

Qt = Change in storage of thermal energy

The total heat content (change in storage) of thewater column was quantified following the equation(Wetzel 1991):

Qt =1

00

At A hz z z

z

zm

Â (12)

where Qt = change in heat content of the lake in calcm–2 h–1, A0 = lake area (cm2), z0 = surface of thelake, zm = maximum depth of the lake, tz = averagetemperature in °C of a unit layer of water of thicknesshz in cm, with the midpoint at depth z, and Az = thearea at depth z in cm2. Volume in cm3 was thenmultiplied directly by temperature in °C to obtaincaloric content. The hypsographic curve of CalderaLake was used to obtain Az. Information on thetemperature at different depths (tz) in the lake wastaken from a series of submerged thermistors, eachconnected by its own cable. These temperatureprobes encompassed 15 depths from 0.5 m to11.7 m, with a constant interval of 80 cm betweenthe probes. The thermistor chain was attached to afixed buoy in the deepest point of the lake, and thebihourly temperature data (maximum error in thereadings was ± 0.05°C) were stored in a SquirrelGrant data logger.

There are many equations available for theestimation of these heat fluxes, especially for the Qsa(2), Qec (9), and Qsh (11) (Henderson-Sellers 1986);choosing another equation may easily result in adifference of 1.7–4.3 cal cm–2 h–1 (i.e., 20–50 W m–2)in the heat flux estimate (Schmid et al. 2003).Nevertheless, the results provided using thesetechniques are in accordance with previous studiesin lakes very similar to La Caldera (Catalán 1988;Armengol et al. 2000a).

Mixing and stability termsStability was calculated using SisDel 1.4, a computerapplication developed to automate calculations ofthermal stability and mixing in lakes (Rodrigues daSilva et al. 2003). To calculate stability, the Idso(1981) methodology was implemented in theapplication:


S = 1

00

AA z zz z

z

zm

( – ) ( – )r r rÂ (13)

where rz = density (g cm–3) at depth z, r = averagedensity resulting if the lake is mixed to isothermconditions, and zr = depth at which the water columnhave r density before mixing. The square of Brunt-Väisälä (N2) frequency was also computed to studythe mixing processes (Reynolds 1984). Waterdensity was calculated, in both instances, as afunction of the water temperature using theKrambeck equation:r = 0.999869 + 6.67413¥10–5T – 8.85556¥10–6T2

+ 8.23031¥10–8T3–5.51577¥10–10T4 (19)where T is the water temperature (in °C).

Mixed Layer Depth (MLD, cm) was approxi-mated in physical terms following Reynolds (1984)density gradient criteria.

Statistical methodsIn this paper, cross-correlation analysis was used toexplore the response of water column stability andmixed layer depth to short-term variations in windspeed and lake heat content. Two items of infor-mation emerge from such an analysis: the strengthof the relationship between the two compared series,and the lag or offset in time between them at theirposition of maximum correspondence (Davis 1986).

The time-series software formed part of theStatistica for Windows package supplied by StatSoft,Inc. (1997) and we used cross-correlation plots todisplay the correlations between the time series overa selected range of time differentials (lags).

RESULTS AND DISCUSSION

The thermal response of the lake to the diel variationsin meteorological conditions was examined over aperiod of 74 days (from July to September 1990, seeFig. 2). To show and discuss the results we haveselected three well defined thermal phases: strati-fication (from July 9 to July 17), late stratification(from July 18 to August 15), and post-stratification/overturn (from August 16 to September 20). Here,thermal stratification is defined as a temperaturedifference greater than 1.5°C between surface andbottom waters (Frempong 1983).

During the stratification phase there was a strongperiodic variation in the incident short-waveradiation, with maximum values c. 83.4 cal cm–2 h–1

Fig

. 2T

herm

al r

espo

nse

of th

e la

ke to

die

l var

iatio

ns in

met

eoro

logi

cal c

ondi

tions

dur

ing

the

ice-

free

per

iod

in L

a C

alde

ra, S

ierr

a N

evad

a, S

pain

(fr

om 9

Jul

yto

20

Sept

embe

r). A

, Str

atif

icat

ion

(9–1

7 Ju

ly);

B, l

ate

stra

tific

atio

n (1

8 Ju

ly to

15

Aug

ust)

; and

C, p

ost-

stra

tific

atio

n (1

6 A

ugus

t to

20 S

epte

mbe

r).


at 1200 h (15 July). Diel variations of air temperaturegenerally followed that of solar radiation, althoughthe maximum temperature lagged c. 2 h behind thatof radiation (12.5°C at 1400 h on 15 July). Theaverage value of air temperature during this phasewas 11.1°C and the range was 19.2°C (4.6–23.8°C).Diel cooling and heating effects were also observedin the surface water temperature, its maximumlagged behind that of the air temperature by 2 h; theaverage value of surface water temperature during

stratification was 14.3 and the range was 6.1°C(17.8–11.7°C). Wind speed exhibited considerablediel variations, the highest speed values occurred at1200–1400 h, 5 and 6 m s–1, respectively (Fig. 3). Theaverage value of wind speed during stratification (9–17 July) was 4.9 m s–1, but a small-scale windy period(from 0400 to 1800 h on 14 July) with an average windspeed of 13.6 m s–1 led to the gradual extension of thewarmer surface water to greater depths, and decreasedthe water column stability (Fig. 9C).

Fig. 3 Diel variations in short-wave radiation, meteorological conditions, and stability in the 0–10 m water columnduring the stratified phase. A, 10 July 1990; and B, 16 July 1990.


Fig. 4 Diel variations in short-wave radiation, meteoro-logical conditions, and stability in the 0–10 m water col-umn during the late-stratification phase. A, 2 August 1990;and B, 3 August 1990.

Meteorological conditions during the late strati-fication phase (18 July–15 August) varied from thosemeasured during the stratification phase, especiallyin the incident short-wave radiation and wind speed.Average incident short-wave radiation was 24.7 calcm–2 h–1 whereas, in the former phase it was closeto 30 cal cm–2 h–1. The average wind speed was4.2 m s–1, but the hourly values reached to 7 m s–1

on several occasions (Fig. 4). Variations both in theaverage water and average air temperatures valueswere not significant from those in the stratificationphase remaining at 14.5°C and 11.7°C, respectively.

The incident short-wave radiation during the poststratification phase (16 August–20 September), withan average value of 18.9 cal cm–2 h–1, had anapparently inappreciable effect on the diurnal heatingeffect of the water temperature, which remainednearly constant. From Fig. 5 (15 and 16 September)it can be observed that the short-wave radiation islow because of the cloud cover; therefore, diurnalstratification of the upper water layers is notproduced, and the stability remains zero all throughthe day. Wind speed hourly values were high duringthis phase (note the different scale for y axis in Fig.5) and consequently the average value was more thantwice that of the previous phase (8.5 m s–1).

Water column stability during the three periods(Fig. 9C) varied substantially as a consequence ofthe interaction between different factors mentionedabove, specially the incident short-wave radiationand wind speed. In the stratification phase theaverage value for this index was 18.8 g cm cm–2,reaching almost 40 g cm cm–2 at 1600 h on 11 July.During the late stratification phase the averagestability of the 0–10 m water column was 7.37 g cmcm–2, reaching its maximum value between 1200 and2000 h as a consequence of the heating of the upperwater layers because of incident solar radiation. Thewater column temperature during the mixing phase(average stability of 2.5 g cm cm–2) was completelyhomogeneous on some days (Fig. 5) because ofdecreasing incident short-wave radiation. Usually,during this phase, water column stratification valueswere over 1 g cm cm–2 between 1200 and 1600 h.Nevertheless, we have found an unexpected vari-ability in this general trend; accordingly we havemeasured in certain moments during the stratifi-cation phase lower stability values than in the latestratification one. This local stability minimum wasclosely related to a reduction in the incident short-wave radiation and possibly to wind stress (Fig. 3, 4).

Square of the Brunt-Väisälä frequency for the 6selected days of the three thermal phases can be seen

in Fig. 6. The thermocline was situated at a depth of6 m at the beginning of the stratifications phase anddeepens afterwards to 9 m (2 August). The formationof secondary shallow thermoclines during daytimecontribute to increment the total stability of the watercolumn (see Fig. 3 and 6 during the stratification


phase). Stability increments during the post-stratification phase are related to the heating of thewater surface as can be observed in Fig. 6E.

Energy budgetThe energy budget of the lake was computed for thecomplete period studied. Diel changes that occurredin the previously selected days are illustrated in Fig.7; meteorological conditions and Qsa which pre-vailed in those days are described above. The long-wave radiation absorbed and emitted, latent andsensible heat fluxes, and the total amount of energyinvolved in the budget (Qt) are also shown in Fig. 7.The fluxes of incoming and outgoing long-waveradiation were fairly uniform, with a small increaseduring the diurnal heating period. Average absolutevalues of Qla were lower than that of Qle, c. 21 calcm–2 h–1 and –32 cal cm–2 h–1 respectively. Theemitted component constituted the largest singleterm in the energy budget, and the computed valueswere very similar over the three periods, –32 calcm–2 h–1 during the stratification, –32.03 cal cm–2 h–1

during the late stratification, and –31.58 cal cm–2 h–1

during the post-stratification period (values given asan average). Average values calculated for Qec weresimilar, c. –1.3 cal cm–2 h–1 during the three studiedperiods. In Fig. 7 it can be observed that at certainperiods, this component denoted some decays, forexample, during the late stratification period. In Qsh,the major energy lost to the atmosphere occurredduring the post-stratification period (mean = –5.67cal cm–2 h–1) and the minor energy lost occurredduring the late stratification period (mean = –2.78cal cm–2 h–1). Diel changes in Qec and Qsh areillustrated in Fig. 7; an increment in the net loss ofthermal energy to the atmosphere was observedduring midday because of evaporative processes anda major net loss of thermal energy during the nightbecause of wind action; however, both processesresulted in nocturnal cooling of the surface water andthe breakdown of thermal stratification in the upperlayer through convective processes.

The consequence of the net energy exchangewithin the lake’s surface resulted in changes in theheat storage (Qt), determined directly from thermis-tors data, which fits a sinusoidal curve. Although thenet energy results show a slight decreasing tendency,the heat storage increased until the later part ofAugust. This behaviour could be explained by theinitial thermal conditions of the system, just after themelting of the ice cover. On a daily basis, the systemwas losing energy to the atmosphere during night andearly morning, and gaining thermal energy duringthe sunlight period of the day. However, in cloudyand windy periods the lake could be losing thermalenergy during the whole day, for example, see Qshin Fig. 7; on 16 September 1991 the lake has not

Fig. 5 Diel variations in short-wave radiation, meteoro-logical conditions, and stability in the 0–10 m water col-umn during the post-stratification phase. A, 15 September1990; and B, 16 September 1990.


Fig. 6 Diel variations in the Brunt-Väisälä frequency (s–2 10–3) at different depths in: A, 10 July 1990; B, 16 July1990; C, 2 August 1990; D, 3 September 1990; E, 15 September 1990; and F, 16 September 1990. Depths in cm.

received any positive thermal energy, and lost anamount of –248.51 cal cm–2 to the atmosphere.

An average value of 5.8 cal cm–2 h–1 wascomputed for the imbalance, that is the result of the


Fig. 7 Diel changes in the different components of the heat budget during: A, B, the stratification phase; C, latestratification; and D, post-stratification.

application of the energy budget equation (Qsa + Qla– Qle – Qsh – Qt ± Qec = imbalance). This can beattributed to different circumstances, such as theadvection of warmer water to the sampling site, anincorrect estimation of terms in the budget equationsas mentioned in Methods (Schmid et al. 2003), orto the conduction of thermal energy through thebottom sediments, a term neglected in the equationbecause of the morphology of the lake (Hutchinson1957).

The contribution of each of these components tothe total heat budget can be seen in Fig. 8 and in

Table 2, the net long-wave radiation (resulting fromthe calculation Qla – Qle) has no pronounced effecton diel fluctuation or on energy storage, because itwas fairly constant during the study period.However, it plays an important role in the overallenergy budget. On the other hand, short-wave solarradiation determines the fluctuations on the dielcycle and also plays a major role in the total energybudget. The contribution of sensible heat loss is highduring the post-stratification period (see Table 2)when maximum temperature gradients exist betweenthe warm surface water and overlying cold air.


Fig. 8 Diel variations in the components of the energy budget equation in cal cm–2 h–1. (Qsa, incident solar (short-wave) radiation absorbed; Qla, long-wave radiation absorbed; Qle, long-wave radiation emitted; Qsh, sensible heatflux (convection); Qec, energy used for evaporation/condensation; Qt, change in lake storage of thermal energy (calcm–2).) A, stratification (9–17 July); B, late stratification (18 July to 15 August); and C, post-stratification (16 Augustto 20 September).

Table 2 Average heat budget result (cal cm–2 h–1) in La Caldera Lake, Sierra Nevada, Spain for the three entireperiods.

Phases Qsa Qla Qle Qec Qsh Qt Imbalance

Stratification 29.24 21.32 –32.00 –1.39 –3.34 0.27 13.56Late stratification 24.74 21.09 –32.03 –1.13 –2.78 3.72 6.10Post-stratification 18.97 20.92 –31.58 –1.29 –5.66 –3.58 4.80% stratification 40 34 33.5 36 28 3 55% late stratification 34 33 33.5 30 24 50 25% post-stratification 26 33 33 34 48 47 20

Additionally, wind speed was very high during thisperiod. This fact and the minor short-wave radiationincome to the lake’s surface towards the end of

September results in a rapid loss of heat storage inthe water column as can be seen in Fig. 8, and fromthe complete isothermal conditions (zero stability)


depicted in Fig. 9C. Finally, the contribution of theevaporation/condensation term (Qec) was found tobe generally small in the overall energy budget (Fig.8).

Comparable results on the surface heat exchangefor the ice-free period were found on a weekly scalein Estany Redó, a high mountain lake of the CentralPyrenees similar to La Caldera Lake (Catalán 1988).Thus, the average solar radiation (Qsa) received fromthaw to mid August (1985) on that system was 2907–3489 cal cm–2 h–1 (i.e., 250–300 W m–2) and in LaCaldera Lake the total amount was 3491 cal cm–2 h–1

from 18 July to 15 August 1990. Similar results wereobtained for the other periods (mid August–September) and for the different components of theheat budget.

Time-series analysesFigure 9 represents the evolution of wind speed (A),air temperature (B), thermal stability (C), and mixedlayer depth, or MLD, (D) during the study period(bihourly data). There is a marked increasing trendin late summer wind speed, whereas air temperaturebecomes lower. Thermal stability reflects both theeffects of heat energy and wind kinetic energy overthe lake. As a consequence, stability depicts adramatic reduction along the study period, as MLDgets deeper values and finally reaches the bottomdepth at the beginning of September. Isolatedreductions in MLD associated with very low windspeed and high air temperature conditions weredetected in July and August. This situation iscoincident with the formation of secondary shallowthermoclines.

Cross-correlation analyses allow a better andmore accurate description of the processes involvedin the evolution of stability and MLD along the studyperiod, and their underlying periodicities. A strongand statistically significant (95% confidence) cross-correlation coefficient between wind speed andthermal stability time series is shown in Fig. 10A. Italso reveals a marked 12 h periodicity in such aninteraction. On the other hand, under the adopteddata logging frequency, the maximum response ofthe stability to changing wind speed is detected 2 hlagged (note that each lag in the cross-correlogramrepresents 2 h in the time series). Inversely, windspeed and MLD time series cross-correlogram (Fig.10B) depicts a strong direct and statistically sig-nificant cross-correlation coefficient. As happenedwith stability, changes in wind speed have theirmajor detected impact on MLD after 2 h. Althoughthis cross-correlation function shows a quite constant

pattern it is possible to detect a slight 12 h periodicityin the process.

As shown above, stability is also related to thechange in heat storage of the lake. The higher Qtvalues result in higher stability values. This relation-ship is demonstrated in Fig. 10C. It represents thecross-correlogram between Qt and stability timeseries. This cross-correlation function shows amarked periodicity of 12 h. However, it is importantto note that stability responses to changes in Qt areagain not immediate, but lagged by 2 h (see Fig.10C).

As a common feature, this analysis demonstratesthat the evolution of stability and MLD in La CalderaLake depicts a marked 12 h periodicity, which ismainly related with daily changes in the energybudget described in previous sections. Additionally,it also reveals that (under the adopted data-loggingfrequency) the response of the lake thermal structureto wind events (i.e., stability decreasing and MLDincreasing) becomes maximum after a 2 h lag. Aneven more accurate analysis (using data collectedhourly or at even higher frequencies) would obtaina more realistic description of the time-scalesinvolved in the short-term influence of meteoro-logical forcing over the lake thermal structure. It isalso remarkable that diel correspondence is greatestin those processes directly involving water columnstability (Fig. 10A,C). By contrast, the effect of windover MLD (Fig. 10B) shows only a slight dielcorrespondence and a more constant effect at longertime-scales. This is a consequence of the relativelymore unpredictable character of wind speed in thishigh mountain area, whereas the slight dielperiodicity in this interaction is basically a reflectionof the water column stability behaviour.

SUMMARY

As Legendre & Demers (1984) pointed out, theprecise knowledge of the temporal scales governingthe physical processes in the lake is of majorimportance to the proper understanding of thephysical-biological coupling and its relevance for theecosystem structure and dynamics. Diel energyfluxes from and to the lake determine the thermal/density stratification which, in turn, is the majorcontrolling factor in the dynamics of planktoncommunity. In this paper we have described dielenergy fluxes in La Caldera Lake during the ice-freeperiod at a very fine time scale; the results obtained


Fig. 9 Time series showing: A,wind speed (m s–1); B, air tempera-ture (°C); C, water column stabil-ity (g-cm cm–2); and D, mixed layerdepth (cm).

are a useful contribution because very little infor-mation is available at such a time scale for highmountain lakes. As the heat exchange from the water

surface to the atmosphere is both positive and nega-tive during a 24-h period, this kind of environmentalmodel has to be applied with hourly data. Recent


Fig. 10 Cross-correlograms. A,wind speed-water column stability;B, wind speed-mixed layer depth;C, energy stored-water column sta-bility.


studies on energy budget models have used monthlyor daily data (Catalán 1998; Schmid et al. 2003) butnot bihourly or higher frequency data. The time-series analyses also provided a high resolutiondescription of the physical processes occurring in thelake and its coupling with meteorological conditions.Further research involving biological variables isneeded to properly characterise the coupling ofphysical and biological variables in La Caldera Lake.

ACKNOWLEDGMENTS

We thank Professor R. Morales from the University ofGranada for field assistance in the collection of watertemperature data and Professor J. Armengol from theUniversity of Barcelona for collaboration in the devel-opment of the thermal balance methodology applied toLa Caldera Lake. We also thank two anonymous refereesfor their constructive comments on a previous version ofthis manuscript. This study was partly funded by theProject CICYT NAT91–0570 and EC-LIFE (ContractLIFE 93/UK/3167). Miguel Rodríguez-Rodríguez andEnrique Moreno-Ostos were supported by two Ministryof Education, Culture and Sports fellowships andInmaculada de Vicente was supported by a Ministry ofScience and Technology grant.

REFERENCES

Armengol, J.; Comerma, M.; García, J. C.; Romero, M.;Rodríguez, J. J.; Vidal, A. 2000a: Contribució alconeixement de l’ecologia acuática de l’embassa-ment de Sau. Evolució de l’embassament al 1999.Quaderns Aigües Ter LLobregat 3: 1–97.

Armengol, J.; Comerma, M.; Garcia, J. C.; Picón, A.;Romero, M.; Vidal, A. 2000b: Contribució alconeixement de l’ecologia aquàtica del’embassament de Sau. Evolució de l’embas-sament als anys 1995, 1996 i 1997. QuadernsAigües Ter LLobregat 2: 1–109.

Burman, R.; Pochop, L. O. 1994: Evaporation, evapotrans-piration and climatic data. Developments in at-mospheric science. New York, Elsevier. 278 p.

Carrillo, P.; Reche, I.; Sánchez-Castillo, P.; Cruz-Pizarro,L. 1995: Direct and indirect effects of grazing onthe phytoplankton seasonal succession in anoligotrophic lake. Journal of Plankton Research17: 1363–1379.

Carrillo, P.; Medina-Sánchez, J. M.; Villar-Argaiz, M.2002: The interaction of phytoplankton and bac-teria in a high mountain lake: importance of thespectral composition of solar radiation. Limnologyand Oceanography 47(5): 1294–1306.

Catalán, J. 1988: Physical properties of the environmentrelevant to the pelagic ecosystem of a deep high-mountain lake (Estany Redó, Central Pyrenees).Oecologia Aquatica 9: 89–123.

Colomer, J.; Casamitjana, X. 1993: A model to calculatesurface energy fluxes from routine meteorologi-cal data. Application to Lake Banyoles. Proceed-ings of the International Association of Theoreticaland Applied Limnology 25: 88–90.

Colomer, J.; Roget, E.; Casamitjana, X. 1996: Daytimeheat balance for estimating non-radiative fluxesof Lake Banyoles, Spain. Hydrological Processes10: 721–726.

Cruz-Pizarro, L.; Carrillo, P. 1996: A high mountainoligotrophic lake (La Caldera, Sierra Nevada,España). In: Cruz San Julian, J.; Benavente, J. ed.Wetlands, a multiapproach perspective. Granada,University of Granada. Pp. 111–130.

Cruz-Pizarro, L.; Conde-Porcuna, J. M.; Carrillo, P. 1998:Diel variations in the egg ratio of Hexarthrabulgarica in the high mountain lake La Caldera(Spain). Hydrobiologia 387/388: 295–300.

Davis, J. C. 1986: Statistics and data analysis in Geology.2nd ed. New York, John Wiley & Sons. 646 p.

Elder, B.; Davies, J. 1974: Preliminary energy budget ofLake Ontario for the period May through Novem-ber 1972. (IFYGL). Proceedings of the 17th Con-ference of Great Lakes Research, InternationalAssociation of Great Lakes Research. Pp. 713–724.

Frempong, E. 1983: Diel aspects of the thermal structureand energy budget in a small English lake. Fresh-water Biology 13: 89–102.

Heerman, D. F. 1985: Evapotranspiration in irrigationmanagement. Proceedings of the National Con-ference on Advances in Evapotranspiration. ASAEPublication. Pp. 323–334.

Henderson-Sellers, B. 1986: Calculating the surface en-ergy balance for lake and reservoir modelling: areview. Reviews of Geophysics 24(3): 625–649.

Hutchinson, G. E. 1957: A treatise on limnology. Vol. I.Geography, physics and chemistry. New York,John Wiley.

Idso, S. B. 1981: A set of equations for full spectrum and8–14 um and 10.5–12.5 µm thermal radiationfrom cloudless skies. Water Resources Research17(2): 295–304.

Legendre, L.; Demers, S. 1984: Towards dynamic bio-logical oceanography and limnology. CanadianJournal of Fisheries and Aquatic Sciences 41: 2–19.

Reynolds, C. 1984. The ecology of freshwaterphytoplankton. Cambridge, Cambridge Univer-sity Press. 284 p.


Richards, J. M. 1971: A simple expression for the satura-tion vapour pressure of water in the range –50 to140°C. Journal of Physics. D: Applied Physics 4:15–18.

Rodrigues da Silva, S. L.; Cruz-Pizarro, L.; Moreno-Ostos, E. 2003: SisDel 2.4. Sistema ParaDeterminación de Estabilidad Térmica en Lagos.Software. Spain, Instituto del Agua, University ofGranada.

Rodríguez-Rodríguez, M. 2002: Contribuciónhidrogeológica y limnológica a la caracterizaciónambiental de zonas húmedas de Andalucía orien-tal. Unpublished PhD thesis, University of Gra-nada, Spain. 205 p.

Schmid, M.; Lorke, A.; Wüest, A.; Halbwachs, M.;Tanyileke, G. 2003: Development and sensitivityanalysis of a model for assessing stratificationand safety of Lake Nyos during artificialdegassing. Ocean Dynamics 53: 288–301.

StatSoft, Inc. 1997: STATISTICA for Windows (Com-puter Program Manual). United States, Tulsa,Oklahoma.

Wetzel, R. G.; Likens, G. E. 1991: Limnological Analy-ses. 2nd ed. New York, Springer-Verlag. 391 p.

thermal structure and energy budget in a small high

Documents