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Accurate estimations of the energy budget in lakes andreservoirs are important to obtain an indication of heatingand cooling processes of the lake surface, as well as for calcu-lations of water availability. Methods that are commonly usedconsist of measuring and solving the energy fluxes at the lakesurface assuming that kinetic and potential energy of thewater body is negligible. If the heat transport through inflowsand outflows are considerably smaller than the surface heatfluxes, especially during the dry period in the summer andautumn, the change in water heat storage, DG (J m2) can bewritten as:

DG @ [Rn – (lE + H)]Dt (1)

where Rn (W m2) is the net radiation, H (W m2) is the sensibleheat flux, lE (W m2) is the latent heat flux, and Dt is the timestep over which the heat storage change is determined. Inmany approaches, usually used in studies of short-term energybudget of soils, the DG term is negligible, but according toTanny et al. (2008), in water bodies this term can have con-siderable impact. In lake studies, usually only the surfacefluxes are measured, whereas the problem with DG is thatmeasuring this very term might be a source of large calcula-tion errors (Stannard and Rosenberry 1991) and thereforeresults in an unreliable heat balance.

Many methods have been developed to estimate the termsof the energy balance. Since evaporation is considered as oneof the main components of this budget (Gianniou andAntopoulos 2007), a multitude of methods exist to measurethis term, e.g., evaporation pans (Ponce 1989), eddy correla-tion techniques (Assouline and Mahler 1993; Tanny et al.2008; Ikebuchi et al. 1988), aerodynamic methods (Brutsaert1982), long-term water heat balance methods (Winter 1981;Assouline 1993), and partial heat balance methods (the Pen-man-Monteith equation, Allen et al. 1998). According to Stan-nard and Rosenberry (1991), the value of DG at a time scaleshorter than one day is often very large. Because DG is a sig-nificant part of the energy budget at short time scales, deter-

Measuring heat balance residual at lake surface usingDistributed Temperature SensingT.H.M. van Emmerik2*, A. Rimmer1, Y. Lechinsky1, K.J.R. Wenker2, S. Nussboim1, and N.C. van de Giesen2

1Israel Oceanographic & Limnological Research Ltd, The Kinneret Limnological Laboratory.2Delft University of Technology, Faculty of Civil Engineering and Geosciences, Section of Water Resources

AbstractThis research presents a new method to verify the measurements of surface fluxes and the heat balance at a

lake surface, by means of Distributed Temperature Sensing (DTS) measurements from 0.5 m above to 1.5 m belowthe surface. Using a polyvinyl chloride hyperboloid construction, a floating standalone measuring device wasdeveloped. Being an open construction, it is almost insensitive to direct radiation. With this construction, a spi-ral-shaped fiberoptic cable setup was created that obtained temperature measurements with a vertical spatial res-olution of 0.0002 m and a temporal resolution of 1 min. DTS measured the detailed variations in air and surfacewater temperature. The new method was tested in the deep Lake Kinneret (Israel) from 6 to 9 Oct 2011 and inthe shallow Lake Binaba (Ghana) from 24 to 28 Oct 2011. With the developed method, it is possible to capturethe heat storage change in the top water layer, and therefore verify the water surface heat balance on a time scaleof several minutes. Furthermore, a comparison was made between the measured temperature profiles of the air-water interface in Lake Kinneret and Lake Binaba. It was shown that the usage of DTS measurements for the ver-ification of surface energy balance was applicable for Lake Kinneret, but probably not suitable for the conditionsin the shallow Lake Binaba. In the latter, heat storage changes near the lake surface were not only caused by sur-face energy fluxes, but by internal heat waves and currents that bring cooler water to the upper layer.

*Corresponding author: E-mail: T.H.M.vanEmmerik@student.tudelft.nl

AcknowledgmentsThis study was partly funded by the Friends of IOLR in the USA. The

authors would like to thank Frank Annor from the Kwame NkrumahUniversity of Science and Technology for his dedicated help during theBinaba experiment and Stijn de Jong from Delft University ofTechnology for his dedicated help and sense of humor during theKinneret experiment. We would like to thank the two anonymousreviewers for their useful comments that improved the manuscript.

DOI 10.4319/lom.2013.11.79

Limnol. Oceanogr.: Methods 11, 2013, 79–90© 2013, by the American Society of Limnology and Oceanography, Inc.

LIMNOLOGYand

OCEANOGRAPHY: METHODS

mining this term is important. Hence, to gain insight in theenergy budget dynamics of lakes at short time scales, amethod to take DG into account is required.

A new approach of measuring lake surface heat storagechange will be presented. This new approach makes use of Dis-tributed Temperature Sensing (DTS). With a glass fiber-opticcable, high-frequency and high-resolution temperature mea-surements at the upper water layer (1 m) will be performed. Ata short time scale, this is where heat storage changes most.Furthermore, with the measured heat storage change, the esti-mations for sensible heat and latent heat flux can be betterverified.

The objective of this study is to test the newly developedmeasurement method by using it to verify the short time scaleheat balance at the lake surface. The proposed measurementmethod was tested at two locations, Lake Kinneret (Israel) andLake Binaba (Ghana). For Lake Kinneret, the results of the newmeasurements will be compared with the results of mea-surements using a thermistor chain that has a lower verticalresolution. The results of the DTS measurements are demon-strated at four day campaign (6 to 9 Oct 2011). For Lake Bin-aba, only the results of DTS measurements during a four-day(24 to 27 Oct 2011) experiment will be presented.

Materials and proceduresEnergy balance theory

Sensible and latent heat fluxesUsing the aerodynamic method (Brutsaert 1982), the sensi-

ble and latent heat fluxes are calculated through mea-surements of air temperature, water surface temperature, rela-tive humidity, and wind speed above the lake water surface.These fluxes and the energy balance are calculated at a singlepoint over short time intervals (10 min). The general equa-tions for these calculations are

a.

b.

c.

d.

e. (2)

Here Cp (J kg–1 K–1) is the specific heat capacity of air; LP isheat of vaporization of water; ra is air density (kg m3); (TS – Ta)is the gradient between water surface temperature and air tem-perature at standard height above the water (°C); (qS – qa) is thegradient between specific air humidity at the water surface

and at standard height (-); e is the partial pressure of watervapor in the air (mbar) calculated from the measured relativehumidity (RH, %) and the Tetens equation ; P is theatmospheric pressure (mbar), CHW is the bulk transfer coeffi-cient (-), taking into account the roughness length of the lakesurface, and U (m s–1) is the air velocity (ms–1)at a 10 m heightabove the lake surface.

Net radiationThe net radiation Rn is computed from meteorological

monitoring. It can either be measured directly, or partly mea-sured and partly calculated with the relation:

Rn = RSWin – RSWout + RLWin – RLWout (3)

RSWout = aSW RSWin

RLW = aLW RLWin + BeTs4

where RLWin and RSWin are the measured incoming long andshort wave radiation, respectively (W m–2). RLWout and RSWout arethe calibrated outgoing long and short wave radiation, respec-tively (W m–2). The parameters aLW and aSW are calibratedreflection constants (-) for long- and short-wave radiation.Calibration can be done using measured net radiation. BeTs

4 isthe emitted long-wave radiation from the lake surface (W m–2)calculated from the surface temperature Ts (°C), with theBoltzman constant B (W m–2 K–) and the emissivity of the lakesurface e (-), which is equal to the absorptivity (1 – aLW; Kirch-hoff’s law; see Stull 2000).

Heat storage changeThe change in the heat storage of the water body (DG) can

be determined by measurements of the lake’s temperatureusing a thermistor chain stretched throughout the water pro-file. The measurements can be taken at various time intervalsdepending on the time scale of the heat budget desired (e.g.,hour, day, week, or month). The heat storage change can thenbe calculated by

(4)

where CPw (J kg–1 K–1) is the specific heat capacity of water, Zm

is the lake level (m), Ze is the lower level of heat measurements(m), Tw(z,t) is the water temperature measurement (°C) atdepth z and time t, and rw(z,t) is the water density. The usageof DG within the calculations of short-term energy balance isnot trivial because Ze should be determined according to thedegree of light penetration into the water profile. The radia-tion on the lake surface decreases with depth according to theBeer-Lambert law

H C C U T THW P a s a= − −( )r

LE C L U q qHW P a s a= − −( )r

qe

P@

×0 622.

e RH e T airs Ko= × ( )

e T airT

Ts C

o Co

Co( ) = ∗

×( )+( )

6 11217 67

237 35.

.

.exp

e T airs Co( )

DG G t G t= −| |2 1

G t C z t T z t dzPW W Wz Z

z Z

e

m

( ) = ( ) ( )=

=

∫ r , ,

van Emmerik et al. Measuring lake heat balance residual using DTS

80

l(z,t) = I0(t)exp(–Kdd) (5)

where I0 is the global radiation absorbed by the water surface(Wm–2), t is the time (s), d is the depth (m), and Kd the constantof radiation decrease with depth (m–1). In Lake Kinneret, typi-cally Kd 0.4 (m–1) (Yacobi 2006), which means that less than 1%of the radiation penetrates to a depth larger than 10 m. There-fore, the 10-min heat balance can be expressed with the heatstorage change integrated only for the top 10 m, which is suf-ficient to account for most of the adsorbed radiation.

Energy balanceThree algorithms of the aerodynamic methods based on

Eqs. 1-3 were applied during this study (see also Rimmer et al.2009). (1) CWR – developed by the Center of Water Researchat the University of West Australia (Rayner 1980; Imbergerand Patterson 1990); (2) AIR-SEA based on the Fairall TOGACOARE code version 2.0 (Fairall et al. 1996); (3) Empiricallysimpler algorithm based on Imboden and Wüest (1995), herereferred to as the KLL algorithm. In all three algorithms thesensible heat flux H is related to the evaporative heat flux LEthrough the Bowen ratio. Latent and sensible heat fluxes werecalculated at 10 min intervals. In all algorithms, net radiationwas calculated directly from the radiation measurements andsurface fluxes were calculated using the attributed algorithmof aerodynamic method. Energy balance of the upper 10 m ofthe epilimnion should take into account the heat transport todeep water layer. This component may take place as a resultof molecular diffusion, wind-induced turbulence (‘turbulentdiffusion’), or conductive heat transport that follows thecooling of the water at the lake surface during the night. Inthe case of our experiment, we will show that small continu-

ous cooling occurred during time at a depth of 10 m, how-ever, based on the minor temperature changes at that depth,and similar to Rimmer et al. (2009) we assumed that for ashort time periods (10 – 60 min), heat transport to deep waterlayers is negligible compared with the heat transport throughthe air-water interface.

With this assumption, heat storage change is mainlyexpected in the upper part of the epilimnion, from the lakesurface to a depth slightly below the maximal penetration ofradiation into the lake water (Eq. 5) and therefore, heat stor-age change may be calculated as the residual of the heat bal-ance (Eq. 1).Lake description

Lake Kinneret (32.78°N, 35.59°E) is a natural monomicticlake located in the northern part of Israel (Fig. 1). It is the mostimportant surface water resource in the country providing35% of annual drinking water through the National WaterCarrier (NWC) canal and local pumping. The average area ofthe lake surface is 166 km2, the average volume is 4100 Mm3,the average annual available water is ~370 Mm3, and the aver-age residence time is ~8-10 years. The Jordan River is the majorinflow to the lake, whereas the water pumped into the NWCconstitutes the major outflow. The lake is replenished duringthe colder rainy season, which lasts from around October toApril.

The experiment was conducted during 6 to 9 Oct 2011.During this month, daily northwesterly wind, caused by theMediterranean Sea breeze, usually peaks at 15:00 (Rimmer etal. 2009). Wind speed is typically of ~5-10 m s–1 during theafternoon hours, and significantly lower (< 2 ms–1) betweenthe hours 20:00 to 12:00 the following day. The relative

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Fig. 1. Left: Bathymetric map of Lake Kinneret with depth in meters, TA is meteorolgical station. Right: Map of Lake Binaba.

humidity is usually inversely correlated with the wind speedbecause the wind removes the wet air above the lake surface,bringing dry air from the land, reducing RH by ~ 20% abovethe lake surface. Air temperature fluctuates between 22 to30°C. Together with reduced short wave radiation, the result isthat the lake cools down during October. Typical water surfacetemperatures vary from ~28°C during the night to ~29°C inthe afternoon. The thermocline depth (defined as the peaktemperature gradient throughout the water profile) is locatedat ~20 m.

Lake Binaba (10.78°N, 0.48°W) is an artificial lake locatedin northern Ghana (Fig. 1). The average area of the lake sur-face is 4.5 km2. The average lake depth is only 3 m with a max-imum depth of 7 m. Lake Binaba is considered a small reser-voir, used as a form of infrastructure for the provision of water.A natural stream has been dammed, storing and supplyingwater for domestic use and small-scale irrigation in the vicin-ity of Lake Binaba. The rainy season lasts from April to Sep-tember, during which the lake is fed by runoff via naturalstreams. The air temperature fluctuates between 24°C and35°C, and the surface temperature varies from 28°C to 33°C.Distributed temperature sensing

Previous studies have shown that DTS can be applied formany hydrological systems (Selker et al. 2006; Tyler et al.2009). Lakes (Vercauteren 2009, 2011), estuaries (Henderson etal. 2009), soils (Jansen et al. 2011; Sayde et al. 2010; Steele-Dunne et al. 2010), streams (Selker et al. 2006; Vogt et al.2010; Westhoff et al. 2007, 2011), groundwater (Lowry et al.2007; Schuetz and Weiler 2011), and atmosphere (Keller et al.2011) have been monitored using various DTS setups. In thisstudy, we expand these applications by using DTS for the mea-surement of the heat balance residual.

DTS uses Raman spectrometry to determine the tempera-ture of a fiber optic cable. A brief laser pulse (5-20 ns) is sentinto the fiber and light scattered back to the DTS instrumentis analyzed. The time of flight of the reflected pulse gives theplace along the fiber from where the light was scattered back.Most light is reflected at the same frequency as the incominglight but some photons have a lower frequency (Stokesbackscatter) and some photons have a higher frequency(anti-Stokes backscatter). Anti-Stokes depends strongly onthe temperature of the scattering element, whereas Stokeshardly depends on temperature. By determining the ratio ofStokes and anti-Stokes backscatter, the temperature of thefiber can be determined. For a detailed description, see Tyleret al. (2009).

By using the Stokes/anti-Stokes ratio, one can correct forgeneral extinction losses along the fiber. However, Stokes andanti-Stokes are not extinguished at the same rate, which canbe especially troublesome where step losses occur. Such steplosses may be caused by splices, loose connectors, sharp bends,and other stress on the fiber. To obtain good absolute mea-surements, one needs in-field calibration to correct for suchdifferential losses. In addition, DTS instruments are tempera-

ture sensitive, and when there are large differences over theday, the standard parameters often have to be corrected. Thereare two calibration strategies, both making use of at least twoindependently monitored temperature baths. The first strat-egy was used at Lake Binaba and is called double-ended cali-bration (Van de Giesen et al. 2012). Double-ended calibrationuses pulses that alternately enter the two ends of the samefiber, which allows for correction of different Stokes and anti-Stokes attenuation. The second strategy was used at Lake Kin-neret and is called single-ended calibration (Hausner et al.2011). For single-ended calibration, one brackets homogenousstretches of fiber with calibration baths and corrects with anoff-set and slope. Accuracy of the DTS depends on the qualityof the instrument, the length of the cable, and the spatial andtemporal integration intervals. After calibration, for a mea-surement using a 1000 m cable and integration times of 1 to 2min, the standard deviation of the temperature was 0.1°C forthe DTS systems used in these experiments.

1037 m cable was used in this research. The cable was aSimplex cable consisting of a tight buffered bend-tolerantmulti-mode optical fiber, protected by Aramid yarn, enclosedin a white jacket (AFL). The cable had an outer diameter of 1.6mm. The DTS instrument used at Lake Kinneret was an Oryx(Sensornet), with spatial samples averaging of 1.03 m and tem-poral averaging of 1 min. At Lake Binaba, the Halo DTS Sensor(Sensornet) was used, with a sampling resolution of 2.03 mand temporal averaging of 2 min per direction.

At each site, two calibration baths were used consisting oflarge insulated chests (“coolers”). One bath was filled withplain, unheated water and the other bath was filled with waterthat was heated to about 35°C. An air compressor (aquariumbubbler) was used to keep the water mixed and avoid stratifi-cation. The temperature in the baths was measured using twoHOBO Tidbit Mini Underwater Temperature Data loggers(Onset Computer Corp.) per calibration bath. The Tidbits useda logging interval of 1 min.Measurement setup

Meteorological measurementsThese measurements were taken from the meteorological

station A, located at the center of Lake Kinneret (32.82°N,35.60°E, Fig. 1), at an elevation of –210 m ASL. The stationprovides the following data at 10 min time intervals: Air tem-perature (°C) and relative humidity (%) are measured using arelative humidity and temperature probe model 43372C (R.M.Young), at ~3 m above water level. Net radiation (W m–2) wasmeasured with a CNR4 net radiometer (Kipp and Zonen), at ~4m above water level. Wind speed and direction were measuredwith a MA-05106 wind monitor (R.M. Young), at ~8 m abovewater level. Water surface temperature (Ts, °C) was measuredby YOUNG platinum floating temperature probe model41342, at a depth of ~5.0 cm. During part of the experimentthis measurement was damaged, and therefore it was replacedby the temperature measurements of the upper thermistor inthe chain (at depth of 20.0 cm; see below). The relation

van Emmerik et al. Measuring lake heat balance residual using DTS

82

between these two measurements is usually with good agree-ment (r2 > 0.99). In Lake Binaba no meteorological mea-surements were performed.

Thermistor chain measurementsTemperature profiles were measured in Lake Kinneret at

Station A, using a Thermistor Chain (Precision MeasurementEngineering Inc.), a single cable thermistor chain with 40thermistors along the cable at depth of (0.20, 0.50, 0.75, 1.00,1.25, 1.50, 2.00) m in the top 2 m and 1.00 m interval from 2m depth downward. Measurement time intervals were 10 min.Temperatures were measured with an error of 0.005°C. In LakeBinaba no thermistor chain measurements were performed.

Distributed fiber-optic temperature sensing (DTS)For this study a special measurement setup was constructed

(Fig. 2) that (1) had a high spatial resolution, (2) was able tofloat freely, (3) measured temperature above and below thelake surface, and (4) minimized the effect of heating from radi-ation on the construction and the water around it. To meet allthese requirements the fiber-optic cable was mounted on aPVC hyperboloid frame (Fig. 2a). Twelve PVC pipes (10 mmdiameter) for the internal skeleton and 6 PVC pipes (25 mmdiameter) for the outer mounting construction were used,from which all ends were closed. Buoyancy was gainedbecause of the encapsulated air in the PVC pipes, brought toequilibrium with extra weights at the bottom of the frame.Because of the open construction, water was able to flow freelythrough the construction, preventing a temperature bias dueto direct radiation heating of the water within the frame. Theopen construction maximized the flow of air and wateraround the setup, minimizing radiation absorption by thecable itself (Suarez et al. 2011). As suggested by Suarez et al.(2011), DTS applications might be sensitive to radiation

absorption when exposed to natural radiation. To prevent theheating of the construction itself, white cables and light-col-ored PVC was used. Radiation absorption by a white DTS cableis assumed to be low. Radiation absorption has most influencewhen heat is transferred from the construction, on which thecable is mounted, to the cable. Therefore, the amount of mate-rial used to the frame was minimized. Furthermore, the con-tact surface between cable and PVC pipe was minimized.Implementing both measures decreased radiation absorptionby PVC and hence the heat transfer from the PVC pipes to thecable. Measurements were conducted between 0.3 m aboveand 1.30 m below lake surface in both lakes (Fig. 2c,d). Sincethe resolution of DTS is limited (1.03 m for the Oryx and 2.03m for the Halo), a high spatial resolution was gained bymounting the fiber-optic cable onto the construction in spi-rals (Fig. 2a). All 6 outer PVC pipes were threaded with 1.6 mmfurrows, which guided the fiber-optic cable around the con-struction. The furrows were spaced 5 mm and the diameter ofthe frame was ~0.8 m, creating a vertical spatial resolution of~0.002 m in Lake Kinneret and ~0.004 m in Lake Binaba.Given the limited diameter of the frame, the measurementsare assumed to be point measurements. In total 837 meter offiber-optic cable was used. For practical reasons, 40 m at thebeginning and another 100 m at the end of the cable wereused for calibration (Fig. 2b). The PVC construction was con-nected to anchors, which partly prevented the movement ofthe construction with surface waves. Since the constructionwas meant to measure air and water temperature, the depth ofthe lower part of the construction was measured. This wasdone by installing a pressure data logger (Schlumberger Ltd.)that measured the pressure at the deepest point of the con-struction with time intervals of 1 min. The pressure gauge was

van Emmerik et al. Measuring lake heat balance residual using DTS

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Fig. 2. (a) Schematic overview of a vertical profile of the measurement setup: half with and half without cable; (b) DTS.

assumed to be fixed. However, this could not be verifiedthroughout the experiment. A second pressure gauge mea-sured the barometric pressure at the lake surface. Using bothpressure gauges, the location of the water-air interface couldbe determined relative to the construction.

AssessmentMeteorological measurements

In Fig. 3 wind speed, water surface and air temperaturemeasurements in Lake Kinneret are presented, indicating thatthe meteorological conditions from 5 to 8 Oct 2011 werenearly similar. The temperatures of air followed a daily patternwith ~24°C at night and ~30°C at noon. The temperatures ofthe water surface followed with a significantly smaller ampli-tude with ~27.5°C at night and ~29°C at noon. A minimumwind speed of ~2 m s and a maximum wind speed of ~10 m swere measured in the night and afternoon (~15:00), respec-tively.Heat balance calculations

The heat balance calculations (Fig. 4) indicate that theCWR and AIR-SEA algorithms result in nearly similar trends ofsurface heat fluxes, whereas the KLL algorithm results inminor differences from the other two. In all algorithms, radi-ation heats the upper water column during the day time whilethe wind cools down the lake surface during the afternoonthrough evaporation (latent heat flux). Wind also contributessome additional heat to the lake through sensible heat flux.During the nights, the lake is cooling down both by latent andsensible heat fluxes due to the lower air temperature com-pared with lake surface temperature. On average, the dailysummary of DG at this time of the year (October) is negative,

indicating that this is the time of the year when the lake sur-face is at the peak of its cooling process.

Aerodynamic methods with bulk transfer coefficient arenot considered as the most reliable approach for computingsurface fluxes. However, the three algorithms were used hereafter the bulk transfer coefficient were tested, and the resultsof the algorithms were cross verified using other methods likelong-term simultaneous energy + water balance and Pan Aevaporation measurements (see Rimmer et al 2009).

Given that the heat storage change (DG) in Fig. 4 is calcu-lated as the residual of the meteorological components inorder to close the heat balance equation (Eq. 1), in the nextsection we will compare these results to the calculated heatstorage change from measurements of water profile tempera-tures.Temperature profiles in Lake Kinneret

Temperature measurements from 5 to 11 Oct 2011 for theentire water profile in Station A (0-40 m) using the thermistorchain are presented in Fig. 5. Four sections with different tem-peratures can be distinguished. In the upper layer (0 – ~5 m),the temperature varies on daily basis. From 5 to 15 m depththe epilimnion temperature is rather constant during the dailycycle, thus justifying our assumption that heat transfer to lay-ers deeper than ~10 m is negligible. From 15 to 26 m the met-alimnion is distinguished by the sharp drop in water temper-ature with depth, and fluctuations of the temperaturecontours due to internal waves, whereas from 26 to 40 m(hypolimnion) the temperature is constantly relatively cold,with minimal changes over time.

The temperature profile obtained by the DTS mea-surements is presented in Fig. 6. Daily variations of tempera-

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Fig. 4. Calculated heat balance components (W m–2), based on 10-mininterval measurements between 5 and 11 Oct 2011 using 3 algorithms:KLL, CWR, and AIR-SEA. Net radiation Rn, latent heat LE, sensible heat fluxH and calculated residual DG, representing the lake heat storage change.

Fig. 3. Raw meteorological data: (a) Wind speed (m s–1) and (b) watersurface and air temperature (°C), from 5 to 12 of Oct 2011.

ture occur in a similar pattern from 6 to 9 Oct 2011. Further-more, the water-air interface, as calculated with the pressurelogger measurements is shown. The rise of the water-air inter-face during the afternoon hours was when the constructionwas on average deeper in the water because of small surfacewave’s fluctuations.

Despite calibration, a constant bias of ~0.5°C was detectedbetween the temperature measured by DTS and the thermistorchain (Fig. 7). The bias was similar at all depths and in time,excluding noon hours on 8 and 9 Oct 2011 when values were

significantly higher. The 0.5°C is an error after calibration ofthe raw signal. The bias depends on how the cable is appliedin the field and/or mounted on the measurement setup. DTSmeasurements were corrected by subtracting this constant biasfrom its measurements for every depth, but were not correctedfor the peak bias values at noon. In the following analysis thecorrected DTS measurements were used.

The temperature time series for several depths (Fig. 8) demon-strates how the variations of temperature over time decreasewith the depth. At 0.05 m below the surface, rapid temperaturefluctuations can be observed during the night and a large tem-perature peak was measured during noon. At a depth of 1.25 m,the temperature decreases gradually at night. During the day, thetemperature pattern is similar to that at the 0.05 m, although thepeak is lower and the temperature changes smoother. At 10 m

van Emmerik et al. Measuring lake heat balance residual using DTS

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Fig. 7. Bias of DTS compared with thermistor chain measurements.

Fig. 6. Temperature in Lake Kinneret measured by DTS, including water-air interface, from 6 to 9 Oct 2011.

Fig. 5. Temperature profile of Lake Kinneret from 5 to 12 Oct 2011. Thedate on the horizontal axis indicates the start of that day (i.e., 00.00AM).

Fig. 8. Temperature of Lake Kinneret at different depths.

below surface temperature decreases gradually during the nightand just slightly increases during the day.

Air and water surface temperature measured by the meteor-ological station and DTS are illustrated in Fig. 9. DTS air tem-perature was determined by using the temperature measuredin the uppermost part of the setup, varying from 0.3 m to 0.1m above the lake surface (see upper part of Fig. 6). DTS surfacetemperature was determined by the temperature measured atthe cable segment on the air-water interface. The DTS air tem-perature shows good correlation with the air temperature mea-sured by the meteorological station (Fig. 9). The variations canbe explained by the fact that the DTS measures at theair–water interface while the meteorological station measures3 m above the surface. The water surface temperature alsodemonstrates relatively good correlation. The pattern of bothDTS and the thermistor chain is similar. DTS however, showsmore variation.

Heat storage changeHeat storage change, DG, in the top 10 m of the water pro-

file (Fig. 10), was calculated using 3 methods: (1) According toEq. 1, as the residual of the heat budget at the lake surface,referred to as DG1, with t = 10 min interval; (2) According toEq. 4, using the thermistor chain measurements (DG2 ; t = 10min); and (3) Same as 2, with DTS temperature at the top 1.5m replacing the thermistor chain data (DG3 ; t = 10 min). TheDG1 time series is relatively smooth compared to the DG2 andDG3. From 6 to 9 Oct, DG2 and DG3 are about the same. How-ever, around noon at 7 and 8 Oct 2011, the peaks of DG2 andDG3 deviate, probably as a result of the sensitivity of the DTSto the heating processes at the water surface. The latter can beobserved as well in the total heat storage at the top 10 m, asshown in Fig. 11. The DTS is more sensitive to temperaturechange near the surface and hence the total measured heatstored in the lake is higher.

All measured energy fluxes are shown in Fig. 12. At timeswith high net radiation, the measured heat storage change ispositive and high as well. During the afternoon hours, thelatent heat flux increases, and together with a decreasing netradiation DG becomes negative. However, some fluctuations ofDG are not compensated by other surface fluxes, meaning thatthere is an energy surplus or deficit (see discussion chapter).

Fig. 13 shows that DG3 (calculated using DTS) and DG1 (cal-culated from heat balance Eq. 1) are correlated with R2 = 0.83.Compared with DG1 – DG2 correlation (calculated from ther-mistor chain measurements), which have R2 = 0.81, the DTSmeasurements slightly increase the correlation and thereforeappear to improve the estimation of DG.Temperature profile in Lake Binaba

According to the temperature profile measured with DTS inLake Binaba from 24 to 27 Oct 2011 (Fig. 14), the air tempera-

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Fig. 9. Air and surface temperature measured by DTS and meteorologi-cal station at Lake Kinneret.

Fig. 10. Heat storage change calculated (DG1), measured using thethermistor chain (DG2) and using the DTS (DG3) at Lake Kinneret.

Fig. 11. Heat storage G (J m–2) calculated from 10 m depth using DTS+ thermistor chain and using the thermistor chain alone at Lake Kinneret.

ture varies between 24°C and 35°C. At night the air temperatureis minimal and increases quickly during the day. The water sur-face temperature varies between 28°C to 33°C. Similarly to LakeKinneret, during the night the water temperature is higher thanair. The temperature of the lake surface usually increases simul-taneously with air temperature. During noon hours maximal airtemperature and maximal temperature in the upper 0.2–0.3 mof the lake usually occur simultaneously. Wind speed was notmeasured, but only calm winds were observed during the exper-iment. Compared with Lake Kinneret, the water-air interfaceshows almost no fluctuations throughout the day, indicatingthat indeed surface waves were very small.

Since Lake Binaba is a shallow lake (maximum 7 m depth),

the pattern of intrusion of lower temperatures to the upperlayer (Fig. 15) suggests that part of these cooling hours iscaused by internal cold waves from the lower parts of the lake.If this is the case, which we could not verify, the approach todetermine DG as used for Lake Kinneret cannot be applied.The latter assumes daily temperature changes in the upperwater layers to be caused by surface fluxes only, which is prob-ably not the case in Lake Binaba.

DiscussionDTS measurements

A bias between the DTS and the thermistor chain mea-surements was observed despite the fact that the DTS was cali-

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Fig. 12. Surface energy fluxes of Lake Kinneret.

Fig. 13. Measured (DG3) versus calculated (DG1) heat storage change.

Fig. 14. Temperature measured in Lake Binaba by DTS, including water-air interface, from 24 to 27 Oct 2011.

Fig. 15. Air and surface temperature measured by DTS at Lake Binaba.

brated. Some 140 m of glass fiber-optic cable was used for cali-bration, using four Tidbit thermistors and two calibrationbaths with different temperatures (see “Methods” section). Theobserved bias can be separated into a part which remains con-stant during time, and a peak bias around noon. The constantbias is a result of the measurement setup and can be correctedfor. This was done for the heat balance calculations. We suggestthat the peak bias probably indicates that direct radiationcaused the cable to warm up independently from the environ-mental temperature, and hence increasing its measured tem-perature. It is therefore advised to use two levels of calibrationof the DTS setup when it might be affected by direct radiation:once with the calibration bathes, and once with standard ther-mistors located at predefined points along the cable.Heat storage change in the upper layer

The results of DG analysis using DTS measurements (DG3,Fig. 10) give some insight into the daily temperature changesin the uppermost water layer. The overall patterns and valuesmeasured by DTS are almost similar to those measured by thethermistor chain (DG2). The DG3 yield a slightly smoother pat-tern and is better correlated with the residual heat storagechange (DG1). Whereas this result is statistically insignificant,it can probably be explained by the fact that DTS senses tem-perature changes in the upper 0.2 m layer at higher resolution,with as much as 100 measuring points closer to the water sur-face than the first thermistor.

It is generally suggested that DG1 reflects average changes intime of the meteorological measurements in the air, which arefast and integrated relatively smooth over time. The DG2 andDG3, however, are the result of changes in the temperature ofwater currents. These currents are slow compared with the air,and therefore integrated with more fluctuations over a giventime interval than DG1.

The bias of both DG2 and DG3 compared with the DG1 cal-culation seems to be especially large (up to ~300 W m2) andwith more fluctuations during noon hours. It is suggested thatthis bias is mainly due to changes of temperature in water cur-rents. These currents are affected mainly by the relatively highwind speed and the high radiation at noon. We suggest thatthe same reasons are responsible for the difference betweenthe patterns of (DG3) and (DG1) observed during the nighthours with low net radiation and low wind speed. Usually dur-ing these hours DG1 is small and smooth in time, whereas DG3

shows more variation. Still the accumulated DG is nearly thesame for both DTS and the thermistor chain.Energy balance

While the general pattern of all surface fluxes (Fig. 10) couldbe explained, some small variations in DG could not be com-pensated by other fluxes. Therefore the sum of all fluxes doesnot always sum to zero and at times, an energy flux excess ordeficit is observed. These deficits can be explained both byphysical reasons and by errors in determining DG. In the phys-ical part, we can take into account some of the energy sourcesor sinks that were considered as negligible, like the inflows and

outflows, some contribution of temperature from layers lowerthan 10 m below surface, and other natural or anthropogenicsources of energy that were not included in the energy balance.The other part of non-zero energy balance can be attributed tominor errors in the meteorological measurements, resultingdifferent DG than the measured value (DG1).Water surface and air temperatures

To determine the sensible and latent heat fluxes, tempera-tures of the air and at the wet surface have to be measured asaccurately as possible. Results from Fig. 9 showed that DTScaptured the characteristic pattern and magnitude of the airtemperature. However, besides the possible inaccuracy of theDTS, and its fluctuations in time, it should be considered thatair temperature at the meteorological station was measured at3 m above the lake surface. This can result in a deviationbetween air temperature measured by DTS and the meteoro-logical station.

Fig. 9 also showed reasonable patterns and magnitudes ofthe water surface temperature. Because the temporal resolu-tion of DTS is higher, it captured more changes in temperature(which were averaged by the meteorological measurement).There are however two sources of errors in the measured sur-face temperature. The first source of error is the possible inac-curate measurement of the water-air interface with the pres-sure gauges. Currents and waves might have moved thepressure gauge, resulting in a wrong estimation of the water-air surface. A second source of error is the inability of DTS tomove in the vertical direction. Due to (small) waves, somecable segments are continuously submerging and emerging,which could result in a temperature drop caused by evapora-tion on the cable surface. Although no clear cold bias effectwas observed in the results, allowing vertical movement couldminimize this potential effect.Lake Kinneret versus Lake Binaba

The DTS temperature profiles of Lake Kinneret and Lake Bin-aba show some clear differences. First, the lake temperature inLake Kinneret follows a daily pattern, similar to the net radia-tion and the air temperature. Around noon, both the net radia-tion and air temperature are at the peak, similar to that of thelake surface temperature. When net radiation and air tempera-ture decrease in the afternoon toward the night, so does the lakesurface temperature. In Lake Binaba, the air temperature showsa similar pattern, but the lake temperature profile reveals thatdifferent mechanisms are occurring. After the peak air tempera-ture at noon, a sudden decrease in lake temperature occurs,which appear to originate from lower layers of the lake. We sug-gest that it indicates a cooling process from internal waves andcurrents that bring cooler water to the upper layer.

In Lake Kinneret, a clear wind pattern was distinguishedand caused pressure changes at the bottom of device. Around15:00 wind speeds up to 10 m s–1 were registered, causing sur-face waves, which influenced the temperature measured byDTS. Wind over Lake Binaba was calm, did not show clear pat-tern, and surface waves were minimal.

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The presented temperature profiles showed that in shallowlakes, the energy balance approach that assumed no heat con-tribution from lower layers might not be applicable. Since thehypolimnion in Lake Kinneret is at low depths, internal waveshave almost no influence on the temperature in the upper lay-ers on a daily basis. In Lake Binaba this is probably not thecase. Temperature differences at the upper layer are not onlycaused by surface fluxes and hence a different approachshould be used to verify the energy budget.

For shallow lakes, it would be interesting to measure a tem-perature profile over the entire depth. This will reveal if andhow temperature profiles change and how heat is transportedthroughout the day. Furthermore it is likely that energy isabsorbed by the sediments at the bottom of the lake, since thisis situated at most 7 m below surface level.DTS measurement setup

Results obtained by the DTS measurement setup show con-sistency in time. The frame had sufficient buoyancy and sta-bility to keep floating on the same level with the same orien-tation of the cables relative to the lake surface. In general, theproposed method can be considered as easily applicable, sta-ble, and rigid. However, some minor improvements would bebeneficial. First, the cables from the frame to the DTS and backran freely through the water. To prevent cable breakage, it isrecommended to protect the latter with, e.g., plastic tubes orbuoys. Second, the setup should be allowed vertical move-ment to minimize the vertical movement of the cable into andout of the water.

Comments and recommendationsThis DTS set-up was able to measure air and surface tem-

perature with high resolution. Detailed variations throughouttime were registered.

As a result of this study, more insight was gained to the pat-tern of heat storage change in Lake Kinneret water surface.Patterns in observed DG with DTS were closer to the values cal-culated from the residual of the meteorological measurementsthan to those of the thermistor chain alone.

It is recommended to conduct more measurements of thistype. Longer time series will give more insight in whether theobserved heat storage change is representative for longer peri-ods. Furthermore, additional research in various types of lakes issuggested to test the proposed method and its applicability.Results from Lake Binaba showed that the energy balanceapproach used for Lake Kinneret is not applicable, due to theimportance of heat transport from lower water layers. A similar,but deeper, setup covering the entire depth is recommended toreveal the energy transport mechanisms in shallow lakes.

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Submitted 20 June 2012Revised 20 November 2012Accepted 10 February 2013

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