4. Physical and chemical features of Lake Limnopolar in three meteorologically contrasting summers
4.3.5. Heat content variation and thermal diffusivity in the lake during summer 2003-04
Along the 2003-04 summer, the thermal regime in Lake Limnopolar was more accurately measured using a chain of thermisthors. This installation provided a temporal resolution as high as one temperature value per 30 minutes (Fig. 4.23).
When measurements began at the end of December with the lake still covered by ice, the water column was almost thermally homogenous, with slightly warmer temperatures (~1ºC) at the bottom. From mid January, an evident inverse stratification built up. During this period, the colder water, close to 0ºC, was at the surface just under the ice, whereas the deepest layers were near 4ºC. Thus, through this timeframe, mainly when the ice was thinner and circulation increased in the lake, convective plumes migrated gradually through the water column, transporting heat downwards. This resulted in the progressive heating of the deep layers, beginning around mid January and continuing through the first week of February.
Finally, this gradual heating generated a temperature gradient between the surface and deep layers of approximately 3.5 ºC. This thermal discontinuity disappeared when the lake was entirely free of ice, which was accompanied by temperature fluctuations that followed the diurnal cycle. These changes in the thermal regime of the lake are also illustrated in the range of daily temperature variations, shown in figure 4.24. Here, it is observed that marked temperature changes occurred when the dam fractured over mid January, though mostly after the ice cover was thawed. This is in contrast with both the observed temperature changes at the end of December until the outlet opened, and those during mid January, when the water column maintained higher thermal stability.
During the austral summer, as a general trend, daily global radiation decreased with time due, in part, to the decrease in the illuminated hours of the day.
Another general trend was the occurrence of cloudy days, which were more frequent from the end of January. The net radiation arriving at the lake surface was estimated based on profiles of PAR and the regime of solar radiation obtained from the AMS.
Some previous considerations were made for calculations as follow. Given that the values of global radiation rendered by the AMS were in kJ m-2, they were transformed to calories (1 calorie equals 4.1868 joules). Following, we applied the percentages of light extinction obtained from the underneath PAR profiles to the global solar radiation data obtained from the AMS (Fig. 4.25). The percentage of light extinction for the different sampling dates was obtained using linear interpolation. Our calculations assume that the ice is an optically homogenous layer.
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We recognize the limitation of this procedure given that bands of ultraviolet and infrared radiation are less available below the ice and selectively absorbed by water.
As shown in figure 4.26, the lake generally gained heat as summer advanced, though the ice cover condition and some episodic events altered this trend. Hence, from last days of December to the second week of January, the heat content in lake remained stable at 100 Kcal m-3. The daily variation of heat content during this period was also the lowest for the overall times studied (Fig. 4.27). A slight increase in heat content occurred on the 6th of January, but it was lost again over the next few days. A more notable increase in the stored heat started just after this period, when the lake outlet opened (10th-13th Jan). Over the next 10 days, the lake ceased to gain heat appreciably despite the increase in incident solar radiation.
This situation remained somewhat stable until the last week of January. At this point, the heat content in the lake began to increase more steeply until it reached the highest values observed during the ice cover period (~650 Kcal m-3). This heat increase stored in the lake likely helped to melt the ice. As the ice melted, a notable decline in the heat content of the lake took place, and approximately 200 cal cm-3 were lost during the first days of February. This coincided with a decline in solar radiation. Therefore, although the light coming into the lake at this time was not impeded by ice during this time, the solar heating throughout the lake was on the order of that observed during January. Later, when the heat provided by solar radiation increased again, the lake started to gain heat until it reached values close to 800 cal cm-3.
Figure 4.23. Time-course of temperature regime in Lake Limnopolar during the summer 2003/2004 obtained from data of the thermistors chain.
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Figure 4.24. Isopleths of daily temperature variation in the water column of Lake Limnopolar during the summer 2003/2004.
Figure 4.25. Variations in the incident and below ice daily solar heating in Lake Limnopolar during summer 2003-04. The amount of light absorbed trough the ice was estimated based on the observed PAR attenuation by ice in the regular profiles performed in the lake. Data between different sampling dates were obtained by linear interpolation of data from the AMS.
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Figure 4.26. Box plots showing the evolution of the heat stored daily in Lake Limnopolar during summer 2003-04. The solid line inside the boxes indicates the median, the end of the boxes correspond to the interquartile range and the whiskers to 5% and 95% percentiles.
Figure 4.27. Daily heating rates in Lake Limnopolar during summer 2003-04.
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Using the continuous profiles of temperature recorded for summer 2003-04 we can estimate the thermal diffusion (KZ) in the water column. This was estimated by evaluating the first (time) and second (space) moments of the temperature changes. Given that both conductive and non-conductive heat transfer may occur, as discussed in more detail below, it may be most appropriate to consider the KZ as
“apparent” or “effective” thermal diffusivity. Otherwise, large differences were observed depending on the way in which the data set was calculated. If a least-squares polynomial interpolation is applied to the temperature data, then it produces incoherent results, indicating the need to use only the real data set rendered by thermisthors.
As shown in figures 4.28 and 4.29, the variation of the KZ coefficient estimated for Lake Limnopolar is a function of both depth and time. Table 4.4 and figure 4.30 show the means and dispersion for the measurements at different layers.
During the more quiescent period, just before the outlet damn break, KZ fell within the range of 0.8-3.3 x 10-5 m2 s-1. The higher values during this period were observed in December between 2 and 3 meters, and then they dropped progressively at these depths as increases occurred at the bottom. The deepening of this maximum of KZ
stopped by mid January, coinciding with the opening of the outlet.
After the partial lake drainage, values of KZ were at maximum, just above the pycnocline, and then plumes transporting heat downward were formed. Once the pycnocline was defined near the midpoint of the water column, more notable differences appeared for KZ between the upper and lower layers and demonstrated a clear dependence on water column stratification. KZ in the mixing layer were up to 3 x 10-5 m2 s-1, with maximum values just over the maximum of the N2 profile. In contrast, during this period apparent eddy diffusion below the pycnocline showed basal values around 1 x10-5 m2 s-1, the lowest observed during the entire period. The turbulence generated over this period via the downward transport of heat from the upper strata eroded the pycnocline, thus increasing the depth of the mixing layer.
This phenomenon is exemplified in figure 4.29, in which sinking in the N2 peak is observed from mid to late January (red points in the plot).
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Figure 4.28. Time-course evolution of the apparent eddy diffusivity at different layers of lake.
The slices between 1 and 3 meters and between 3 and 5 were respectively over and below the pycnoclyne.
Figure 4.29. Isopleths of eddy diffusivity (m2 s-l) in the portion of the water column from 1 to 4 of Lake Limnopolar. Points indicate the depth at which maximum stability occurred.
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Table 4.4. Mean and range of variation for the apparent coefficients of thermal diffusion (Kz) obtained at different layers of water column during summer 2003-04.
Layer n Mean SD Minimum Maximum
1-2 m Above the pycnocline
2046 2.00 x 10-5 1.14 x 10-5 6.31 x 10-6 7.91 x 10-5 2-3 m 2046 2.30 x 10-5 9.34 x 10-5 7.49 x 10-6 5.87 x 10-5 3-4 m Below the
pycnocline
2046 1.53 x 10-5 4.82 x 10-5 8.05 x 10-6 3.87 x 10-5 4-5 m 2046 1.29 x 10-5 4.50 x 10-5 3.42 x 10-6 3.18 x 10-5
Figure 4.30. Box-wisker plots showing the distributions of the calculated eddy diffusion coefficients (KZ) obtained for different layers of water column in Lake Limnopolar at summer 2003/04. The solid and dashed lines inside the boxes indicates median and mean respectively, the end of the boxes correspond to the interquartile range and the whiskers to 5% and 95%
percentiles.