Accurate estimations of the energy budget in lakes and reservoirs are important to obtain an indication of heating and cooling processes of the lake surface, as well as for calcu-lations of water availability. Methods that are commonly used consist of measuring and solving the energy fluxes at the lake surface assuming that kinetic and potential energy of the water body is negligible. If the heat transport through inflows and outflows are considerably smaller than the surface heat fluxes, especially during the dry period in the summer and autumn, the change in water heat storage, DG (J m2) can be written as:
DG @ [Rn– (lE + H)]Dt (1)
where Rn(W m2) is the net radiation, H (W m2) is the sensible heat flux, lE (W m2) is the latent heat flux, and Dt is the time step over which the heat storage change is determined. In many approaches, usually used in studies of short-term energy budget of soils, the DG term is negligible, but according to Tanny et al. (2008), in water bodies this term can have con-siderable impact. In lake studies, usually only the surface fluxes are measured, whereas the problem with DG is that measuring this very term might be a source of large calcula-tion errors (Stannard and Rosenberry 1991) and therefore results in an unreliable heat balance.
Many methods have been developed to estimate the terms of the energy balance. Since evaporation is considered as one of the main components of this budget (Gianniou and Antopoulos 2007), a multitude of methods exist to measure this 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 (Brutsaert 1982), 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 scale shorter 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 using
Distributed Temperature Sensing
T.H.M. van Emmerik
2*, A. Rimmer
1, Y. Lechinsky
1, K.J.R. Wenker
2, S. Nussboim
1, and N.C. van de Giesen
21Israel Oceanographic & Limnological Research Ltd, The Kinneret Limnological Laboratory.
2Delft University of Technology, Faculty of Civil Engineering and Geosciences, Section of Water Resources
Abstract
This 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 below the surface. Using a polyvinyl chloride hyperboloid construction, a floating standalone measuring device was developed. 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 resres-olution of 1 min. DTS measured the detailed variations in air and surface water temperature. The new method was tested in the deep Lake Kinneret (Israel) from 6 to 9 Oct 2011 and in the shallow Lake Binaba (Ghana) from 24 to 28 Oct 2011. With the developed method, it is possible to capture the heat storage change in the top water layer, and therefore verify the water surface heat balance on a time scale of 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 conditions in 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
Acknowledgments
This study was partly funded by the Friends of IOLR in the USA. The authors would like to thank Frank Annor from the Kwame Nkrumah University of Science and Technology for his dedicated help during the Binaba experiment and Stijn de Jong from Delft University of
Technology for his dedicated help and sense of humor during the Kinneret experiment. We would like to thank the two anonymous reviewers 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.
and
mining this term is important. Hence, to gain insight in the energy budget dynamics of lakes at short time scales, a method to take DG into account is required.
A new approach of measuring lake surface heat storage change will be presented. This new approach makes use of Dis-tributed Temperature Sensing (DTS). With a glass fiber-optic cable, high-frequency and high-resolution temperature mea-surements at the upper water layer (1 m) will be performed. At a 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 better verified.
The objective of this study is to test the newly developed measurement method by using it to verify the short time scale heat balance at the lake surface. The proposed measurement method was tested at two locations, Lake Kinneret (Israel) and Lake Binaba (Ghana). For Lake Kinneret, the results of the new measurements will be compared with the results of mea-surements using a thermistor chain that has a lower vertical resolution. 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 procedures
Energy balance theory
Sensible and latent heat fluxes
Using 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 single point over short time intervals (10 min). The general equa-tions for these calculaequa-tions are
a.
b.
c.
d.
e. (2)
Here Cp (J kg–1K–1) is the specific heat capacity of air; L Pis heat of vaporization of water; rais air density (kg m3); (T
S– Ta) is the gradient between water surface temperature and air tem-perature at standard height above the water (°C); (qS– qa) is the gradient between specific air humidity at the water surface
and at standard height (-); e is the partial pressure of water vapor in the air (mbar) calculated from the measured relative humidity (RH, %) and the Tetens equation ; P is the atmospheric pressure (mbar), CHW is the bulk transfer coeffi-cient (-), taking into account the roughness length of the lake surface, and U (m s–1) is the air velocity (ms–1)at a 10 m height above the lake surface.
Net radiation
The 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= aSWRSWin
RLW = aLWRLWin + BeTs4
where RLWin and RSWin are the measured incoming long and short wave radiation, respectively (W m–2). R
LWoutand RSWoutare the calibrated outgoing long and short wave radiation, respec-tively (W m–2). The parameters a
LW and aSW are calibrated reflection constants (-) for long- and short-wave radiation. Calibration can be done using measured net radiation. BeTs4is the emitted long-wave radiation from the lake surface (W m–2) calculated from the surface temperature Ts (°C), with the Boltzman constant B (W m–2K–) and the emissivity of the lake surface e (-), which is equal to the absorptivity (1 – aLW; Kirch-hoff’s law; see Stull 2000).
Heat storage change
The change in the heat storage of the water body (DG) can be determined by measurements of the lake’s temperature using a thermistor chain stretched throughout the water pro-file. The measurements can be taken at various time intervals depending on the time scale of the heat budget desired (e.g., hour, day, week, or month). The heat storage change can then be calculated by
(4)
where CPw(J kg–1K–1) is the specific heat capacity of water, Z m is the lake level (m), Zeis the lower level of heat measurements (m), Tw(z,t) is the water temperature measurement (°C) at depth z and time t, and rw(z,t) is the water density. The usage of DG within the calculations of short-term energy balance is not trivial because Zeshould be determined according to the degree of light penetration into the water profile. The radia-tion on the lake surface decreases with depth according to the Beer-Lambert law H= −CHWCPraU T
(
s−Ta)
LE= −CHWLPraU q(
s−qa)
q e P @0 622. × e RH e T airs K o = ×(
)
e T air T T s C o C o C o(
)
= ∗(
×)
+(
)
6 112 17 67 237 35 . . . exp e T airs C o(
)
DG=G t| 2−G t| 1 G t CPW W z t TW z t dz z Z z Z e m( )
=∫
== r( )
,( )
,l(z,t) = I0(t)exp(–Kdd) (5)
where I0is the global radiation absorbed by the water surface (Wm–2), t is the time (s), d is the depth (m), and K
dthe constant of radiation decrease with depth (m–1). In Lake Kinneret, typi-cally Kd0.4 (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 heat storage change integrated only for the top 10 m, which is suf-ficient to account for most of the adsorbed radiation.
Energy balance
Three 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 Research at the University of West Australia (Rayner 1980; Imberger and Patterson 1990); (2) AIR-SEA based on the Fairall TOGA COARE code version 2.0 (Fairall et al. 1996); (3) Empirically simpler algorithm based on Imboden and Wüest (1995), here referred to as the KLL algorithm. In all three algorithms the sensible heat flux H is related to the evaporative heat flux LE through the Bowen ratio. Latent and sensible heat fluxes were calculated at 10 min intervals. In all algorithms, net radiation was calculated directly from the radiation measurements and surface fluxes were calculated using the attributed algorithm of aerodynamic method. Energy balance of the upper 10 m of the epilimnion should take into account the heat transport to deep water layer. This component may take place as a result of molecular diffusion, wind-induced turbulence (‘turbulent diffusion’), or conductive heat transport that follows the cooling of the water at the lake surface during the night. In the 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 a short time periods (10 – 60 min), heat transport to deep water layers is negligible compared with the heat transport through the air-water interface.
With this assumption, heat storage change is mainly expected in the upper part of the epilimnion, from the lake surface to a depth slightly below the maximal penetration of radiation 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 monomictic lake located in the northern part of Israel (Fig. 1). It is the most important surface water resource in the country providing 35% of annual drinking water through the National Water Carrier (NWC) canal and local pumping. The average area of the 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 major inflow to the lake, whereas the water pumped into the NWC constitutes the major outflow. The lake is replenished during the colder rainy season, which lasts from around October to April.
The experiment was conducted during 6 to 9 Oct 2011. During this month, daily northwesterly wind, caused by the Mediterranean Sea breeze, usually peaks at 15:00 (Rimmer et al. 2009). Wind speed is typically of ~5-10 m s–1during the afternoon hours, and significantly lower (< 2 ms–1) between the hours 20:00 to 12:00 the following day. The relative
humidity is usually inversely correlated with the wind speed because the wind removes the wet air above the lake surface, bringing dry air from the land, reducing RH by ~ 20% above the lake surface. Air temperature fluctuates between 22 to 30°C. Together with reduced short wave radiation, the result is that the lake cools down during October. Typical water surface temperatures vary from ~28°C during the night to ~29°C in the afternoon. The thermocline depth (defined as the peak temperature gradient throughout the water profile) is located at ~20 m.
Lake Binaba (10.78°N, 0.48°W) is an artificial lake located in 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 supplying water 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 natural streams. The air temperature fluctuates between 24°C and 35°C, and the surface temperature varies from 28°C to 33°C.
Distributed temperature sensing
Previous studies have shown that DTS can be applied for many hydrological systems (Selker et al. 2006; Tyler et al. 2009). Lakes (Vercauteren 2009, 2011), estuaries (Henderson et al. 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 this study, 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 sent into the fiber and light scattered back to the DTS instrument is analyzed. The time of flight of the reflected pulse gives the place along the fiber from where the light was scattered back. Most light is reflected at the same frequency as the incoming light but some photons have a lower frequency (Stokes backscatter) and some photons have a higher frequency (anti-Stokes backscatter). Anti-Stokes depends strongly on the temperature of the scattering element, whereas Stokes hardly depends on temperature. By determining the ratio of Stokes and anti-Stokes backscatter, the temperature of the fiber can be determined. For a detailed description, see Tyler et al. (2009).
By using the Stokes/anti-Stokes ratio, one can correct for general extinction losses along the fiber. However, Stokes and anti-Stokes are not extinguished at the same rate, which can be especially troublesome where step losses occur. Such step losses 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 such differential losses. In addition, DTS instruments are
tempera-ture sensitive, and when there are large differences over the day, the standard parameters often have to be corrected. There are two calibration strategies, both making use of at least two independently 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 calicali-bration uses pulses that alternately enter the two ends of the same fiber, 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 homogenous stretches of fiber with calibration baths and corrects with an off-set and slope. Accuracy of the DTS depends on the quality of the instrument, the length of the cable, and the spatial and temporal integration intervals. After calibration, for a mea-surement using a 1000 m cable and integration times of 1 to 2 min, the standard deviation of the temperature was 0.1°C for the DTS systems used in these experiments.
1037 m cable was used in this research. The cable was a Simplex cable consisting of a tight buffered bend-tolerant multi-mode optical fiber, protected by Aramid yarn, enclosed in a white jacket (AFL). The cable had an outer diameter of 1.6 mm. 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 m and temporal averaging of 2 min per direction.
At each site, two calibration baths were used consisting of large insulated chests (“coolers”). One bath was filled with plain, unheated water and the other bath was filled with water that was heated to about 35°C. An air compressor (aquarium bubbler) was used to keep the water mixed and avoid stratifi-cation. The temperature in the baths was measured using two HOBO Tidbit Mini Underwater Temperature Data loggers (Onset Computer Corp.) per calibration bath. The Tidbits used a logging interval of 1 min.
Measurement setup
Meteorological measurements
These 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 station provides the following data at 10 min time intervals: Air tem-perature (°C) and relative humidity (%) are measured using a relative humidity and temperature probe model 43372C (R.M. Young), at ~3 m above water level. Net radiation (W m–2) was measured with a CNR4 net radiometer (Kipp and Zonen), at ~4 m above water level. Wind speed and direction were measured with a MA-05106 wind monitor (R.M. Young), at ~8 m above water level. Water surface temperature (Ts, °C) was measured by YOUNG platinum floating temperature probe model 41342, at a depth of ~5.0 cm. During part of the experiment this measurement was damaged, and therefore it was replaced by the temperature measurements of the upper thermistor in the chain (at depth of 20.0 cm; see below). The relation
between these two measurements is usually with good agree-ment (r2 > 0.99). In Lake Binaba no meteorological mea-surements were performed.
Thermistor chain measurements
Temperature profiles were measured in Lake Kinneret at Station A, using a Thermistor Chain (Precision Measurement Engineering Inc.), a single cable thermistor chain with 40 thermistors 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 2 m depth downward. Measurement time intervals were 10 min. Temperatures were measured with an error of 0.005°C. In Lake Binaba 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 to float freely, (3) measured temperature above and below the lake surface, and (4) minimized the effect of heating from radi-ation on the construction and the water around it. To meet all these requirements the fiber-optic cable was mounted on a PVC hyperboloid frame (Fig. 2a). Twelve PVC pipes (10 mm diameter) for the internal skeleton and 6 PVC pipes (25 mm diameter) for the outer mounting construction were used, from which all ends were closed. Buoyancy was gained because of the encapsulated air in the PVC pipes, brought to equilibrium with extra weights at the bottom of the frame. Because of the open construction, water was able to flow freely through the construction, preventing a temperature bias due to direct radiation heating of the water within the frame. The open construction maximized the flow of air and water around the setup, minimizing radiation absorption by the cable 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 the heating of the construction itself, white cables and light-col-ored PVC was used. Radiation absorption by a white DTS cable is assumed to be low. Radiation absorption has most influence when heat is transferred from the construction, on which the cable 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 absorption by PVC and hence the heat transfer from the PVC pipes to the cable. Measurements were conducted between 0.3 m above and 1.30 m below lake surface in both lakes (Fig. 2c,d). Since the resolution of DTS is limited (1.03 m for the Oryx and 2.03 m for the Halo), a high spatial resolution was gained by mounting the fiber-optic cable onto the construction in spi-rals (Fig. 2a). All 6 outer PVC pipes were threaded with 1.6 mm furrows, which guided the fiber-optic cable around the con-struction. The furrows were spaced 5 mm and the diameter of the 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 measurements are assumed to be point measurements. In total 837 meter of fiber-optic cable was used. For practical reasons, 40 m at the beginning and another 100 m at the end of the cable were used for calibration (Fig. 2b). The PVC construction was con-nected to anchors, which partly prevented the movement of the construction with surface waves. Since the construction was meant to measure air and water temperature, the depth of the lower part of the construction was measured. This was done 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
assumed to be fixed. However, this could not be verified throughout the experiment. A second pressure gauge mea-sured the barometric pressure at the lake surface. Using both pressure gauges, the location of the water-air interface could be determined relative to the construction.
Assessment
Meteorological measurements
In Fig. 3 wind speed, water surface and air temperature measurements in Lake Kinneret are presented, indicating that the meteorological conditions from 5 to 8 Oct 2011 were nearly similar. The temperatures of air followed a daily pattern with ~24°C at night and ~30°C at noon. The temperatures of the water surface followed with a significantly smaller ampli-tude with ~27.5°C at night and ~29°C at noon. A minimum wind speed of ~2 m s and a maximum wind speed of ~10 m s were measured in the night and afternoon (~15:00), respec-tively.
Heat balance calculations
The heat balance calculations (Fig. 4) indicate that the CWR and AIR-SEA algorithms result in nearly similar trends of surface heat fluxes, whereas the KLL algorithm results in minor differences from the other two. In all algorithms, radi-ation heats the upper water column during the day time while the wind cools down the lake surface during the afternoon through evaporation (latent heat flux). Wind also contributes some additional heat to the lake through sensible heat flux. During the nights, the lake is cooling down both by latent and sensible heat fluxes due to the lower air temperature com-pared with lake surface temperature. On average, the daily summary 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 are not considered as the most reliable approach for computing surface fluxes. However, the three algorithms were used here after the bulk transfer coefficient were tested, and the results of the algorithms were cross verified using other methods like long-term simultaneous energy + water balance and Pan A evaporation 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 in order to close the heat balance equation (Eq. 1), in the next section we will compare these results to the calculated heat storage change from measurements of water profile tempera-tures.
Temperature profiles in Lake Kinneret
Temperature measurements from 5 to 11 Oct 2011 for the entire water profile in Station A (0-40 m) using the thermistor chain 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 depth the epilimnion temperature is rather constant during the daily cycle, 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 tempertemper-ature contours 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-Fig. 4.Calculated heat balance components (W m–2), based on 10-min
interval measurements between 5 and 11 Oct 2011 using 3 algorithms: KLL, CWR, and AIR-SEA. Net radiation Rn, latent heat LE, sensible heat flux H and calculated residual DG, representing the lake heat storage change.
Fig. 3.Raw meteorological data: (a) Wind speed (m s–1) and (b) water
ture occur in a similar pattern from 6 to 9 Oct 2011. Further-more, the water-air interface, as calculated with the pressure logger measurements is shown. The rise of the water-air inter-face during the afternoon hours was when the construction was on average deeper in the water because of small surface wave’s fluctuations.
Despite calibration, a constant bias of ~0.5°C was detected between the temperature measured by DTS and the thermistor chain (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 of the raw signal. The bias depends on how the cable is applied in the field and/or mounted on the measurement setup. DTS measurements were corrected by subtracting this constant bias from its measurements for every depth, but were not corrected for the peak bias values at noon. In the following analysis the corrected DTS measurements were used.
The temperature time series for several depths (Fig. 8) demon-strates how the variations of temperature over time decrease with the depth. At 0.05 m below the surface, rapid temperature fluctuations 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, the temperature pattern is similar to that at the 0.05 m, although the peak is lower and the temperature changes smoother. At 10 m
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. The date on the horizontal axis indicates the start of that day (i.e., 00.00AM).
below surface temperature decreases gradually during the night and 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 temtem-perature measured in the uppermost part of the setup, varying from 0.3 m to 0.1 m above the lake surface (see upper part of Fig. 6). DTS surface temperature was determined by the temperature measured at the cable segment on the air-water interface. The DTS air tem-perature shows good correlation with the air temtem-perature mea-sured by the meteorological station (Fig. 9). The variations can be explained by the fact that the DTS measures at the air–water interface while the meteorological station measures 3 m above the surface. The water surface temperature also demonstrates relatively good correlation. The pattern of both DTS and the thermistor chain is similar. DTS however, shows more variation.
Heat storage change
Heat storage change, DG, in the top 10 m of the water pro-file (Fig. 10), was calculated using 3 methods: (1) According to Eq. 1, as the residual of the heat budget at the lake surface, referred to as DG1, with t = 10 min interval; (2) According to Eq. 4, using the thermistor chain measurements (DG2; t = 10 min); and (3) Same as 2, with DTS temperature at the top 1.5 m replacing the thermistor chain data (DG3; t = 10 min). The DG1time series is relatively smooth compared to the DG2and DG3. From 6 to 9 Oct, DG2and DG3are about the same. How-ever, around noon at 7 and 8 Oct 2011, the peaks of DG2and DG3deviate, probably as a result of the sensitivity of the DTS to the heating processes at the water surface. The latter can be observed as well in the total heat storage at the top 10 m, as shown in Fig. 11. The DTS is more sensitive to temperature change near the surface and hence the total measured heat stored in the lake is higher.
All measured energy fluxes are shown in Fig. 12. At times with high net radiation, the measured heat storage change is positive and high as well. During the afternoon hours, the latent heat flux increases, and together with a decreasing net radiation DG becomes negative. However, some fluctuations of DG are not compensated by other surface fluxes, meaning that there 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 DTS measurements slightly increase the correlation and therefore appear to improve the estimation of DG.
Temperature profile in Lake Binaba
According to the temperature profile measured with DTS in Lake Binaba from 24 to 27 Oct 2011 (Fig. 14), the air
tempera-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 the thermistor 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
ture varies between 24°C and 35°C. At night the air temperature is minimal and increases quickly during the day. The water sur-face temperature varies between 28°C to 33°C. Similarly to Lake Kinneret, during the night the water temperature is higher than air. The temperature of the lake surface usually increases simul-taneously with air temperature. During noon hours maximal air temperature and maximal temperature in the upper 0.2–0.3 m of the lake usually occur simultaneously. Wind speed was not measured, but only calm winds were observed during the exper-iment. Compared with Lake Kinneret, the water-air interface shows almost no fluctuations throughout the day, indicating that 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 upper layer (Fig. 15) suggests that part of these cooling hours is caused by internal cold waves from the lower parts of the lake. If this is the case, which we could not verify, the approach to determine DG as used for Lake Kinneret cannot be applied. The latter assumes daily temperature changes in the upper water layers to be caused by surface fluxes only, which is prob-ably not the case in Lake Binaba.
Discussion
DTS measurements
A bias between the DTS and the thermistor chain mea-surements was observed despite the fact that the DTS was
cali-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.
brated. Some 140 m of glass fiber-optic cable was used for cali-bration, using four Tidbit thermistors and two calibration baths with different temperatures (see “Methods” section). The observed bias can be separated into a part which remains con-stant during time, and a peak bias around noon. The concon-stant bias is a result of the measurement setup and can be corrected for. This was done for the heat balance calculations. We suggest that the peak bias probably indicates that direct radiation caused 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 calibration of 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 changes in the uppermost water layer. The overall patterns and values measured by DTS are almost similar to those measured by the thermistor chain (DG2). The DG3yield a slightly smoother pat-tern and is better correlated with the residual heat storage change (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 DG1reflects average changes in time of the meteorological measurements in the air, which are fast and integrated relatively smooth over time. The DG2and DG3, however, are the result of changes in the temperature of water currents. These currents are slow compared with the air, and therefore integrated with more fluctuations over a given time interval than DG1.
The bias of both DG2and DG3compared with the DG1 cal-culation seems to be especially large (up to ~300 W m2) and with more fluctuations during noon hours. It is suggested that this bias is mainly due to changes of temperature in water cur-rents. These currents are affected mainly by the relatively high wind speed and the high radiation at noon. We suggest that the same reasons are responsible for the difference between the patterns of (DG3) and (DG1) observed during the night hours with low net radiation and low wind speed. Usually dur-ing these hours DG1is small and smooth in time, whereas DG3 shows more variation. Still the accumulated DG is nearly the same for both DTS and the thermistor chain.
Energy balance
While the general pattern of all surface fluxes (Fig. 10) could be explained, some small variations in DG could not be com-pensated by other fluxes. Therefore the sum of all fluxes does not always sum to zero and at times, an energy flux excess or deficit is observed. These deficits can be explained both by physical reasons and by errors in determining DG. In the phys-ical part, we can take into account some of the energy sources or sinks that were considered as negligible, like the inflows and
outflows, some contribution of temperature from layers lower than 10 m below surface, and other natural or anthropogenic sources of energy that were not included in the energy balance. The other part of non-zero energy balance can be attributed to minor errors in the meteorological measurements, resulting different 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 as accurately as possible. Results from Fig. 9 showed that DTS captured the characteristic pattern and magnitude of the air temperature. However, besides the possible inaccuracy of the DTS, and its fluctuations in time, it should be considered that air temperature at the meteorological station was measured at 3 m above the lake surface. This can result in a deviation between air temperature measured by DTS and the meteoro-logical station.
Fig. 9 also showed reasonable patterns and magnitudes of the 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 the pressure gauge, resulting in a wrong estimation of the water-air surface. A second source of error is the inability of DTS to move in the vertical direction. Due to (small) waves, some cable 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 effect was observed in the results, allowing vertical movement could minimize 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 in Lake Kinneret follows a daily pattern, similar to the net tion and the air temperature. Around noon, both the net radia-tion and air temperature are at the peak, similar to that of the lake surface temperature. When net radiation and air tempera-ture decrease in the afternoon toward the night, so does the lake surface temperature. In Lake Binaba, the air temperature shows a similar pattern, but the lake temperature profile reveals that different mechanisms are occurring. After the peak air tempera-ture at noon, a sudden decrease in lake temperatempera-ture occurs, which appear to originate from lower layers of the lake. We sug-gest that it indicates a cooling process from internal waves and currents that bring cooler water to the upper layer.
In Lake Kinneret, a clear wind pattern was distinguished and caused pressure changes at the bottom of device. Around 15:00 wind speeds up to 10 m s–1were registered, causing sur-face waves, which influenced the temperature measured by DTS. Wind over Lake Binaba was calm, did not show clear pat-tern, and surface waves were minimal.
The presented temperature profiles showed that in shallow lakes, the energy balance approach that assumed no heat con-tribution from lower layers might not be applicable. Since the hypolimnion in Lake Kinneret is at low depths, internal waves have almost no influence on the temperature in the upper lay-ers on a daily basis. In Lake Binaba this is probably not the case. Temperature differences at the upper layer are not only caused by surface fluxes and hence a different approach should 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 and how temperature profiles change and how heat is transported throughout the day. Furthermore it is likely that energy is absorbed by the sediments at the bottom of the lake, since this is 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, the proposed method can be considered as easily applicable, sta-ble, and rigid. However, some minor improvements would be beneficial. First, the cables from the frame to the DTS and back ran freely through the water. To prevent cable breakage, it is recommended to protect the latter with, e.g., plastic tubes or buoys. Second, the setup should be allowed vertical move-ment to minimize the vertical movemove-ment of the cable into and out of the water.
Comments and recommendations
This DTS set-up was able to measure air and surface tem-perature with high resolution. Detailed variations throughout time 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 measurements than to those of the thermistor chain alone.
It is recommended to conduct more measurements of this type. Longer time series will give more insight in whether the observed heat storage change is representative for longer peri-ods. Furthermore, additional research in various types of lakes is suggested to test the proposed method and its applicability. Results from Lake Binaba showed that the energy balance approach used for Lake Kinneret is not applicable, due to the importance of heat transport from lower water layers. A similar, but deeper, setup covering the entire depth is recommended to reveal the energy transport mechanisms in shallow lakes.
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Submitted 20 June 2012 Revised 20 November 2012 Accepted 10 February 2013
