Mesocosm experiments identifying hotspots of groundwater upwelling in a water column by fibre optic distributed temperature sensing

Lacustrine groundwater discharge (LGD) can substantially impact ecosystem characteristics and functions. Fibre optic distributed temperature sensing (FO‐DTS) has been successfully used to locate groundwater discharge into lakes and rivers at the sediment–water interface, but locating groundwater discharge would be easier if it could be detected from the more accessible water surface. So far, it is not clear if how and under which conditions the LGD signal propagates through the water column to the water surface–atmosphere interface, and what perturbations and signal losses occur along this pathway. In the present study, LGD was simulated in a mesocosm experiment. Under winter conditions, water with temperatures of 14 to 16 °C was discharged at the bottom of a 10 × 2.8‐m mesocosm. Water within this mesocosm ranged from 4.0 to 7.4 °C. Four layers (20, 40, 60, and 80 cm above the sediment) of the 82 cm deep mesocosm were equipped with FO‐DTS for tracing thermal patterns in the mesocosm. Aims are (a) to test whether the positive buoyancy of relatively warm groundwater imported by LGD into shallow water bodies allows detection of LGD at the lake's water surface–atmosphere interface by FO‐DTS, (b) to analyse the propagation of the temperature signal from the sediment‐water interface through the water column, and (c) to learn more about detectability of the signal under different discharge rates and weather conditions. The experiments supported the benchmarking of scale dependencies and robustness of FO‐DTS applications for measuring upwelling into aquatic environments and revealed that weather conditions can have important impacts on the detection of upwelling at water surface–atmosphere interfaces at larger scales.

caused by industries such as electric power plants, which use water and discharge heated water into lakes and streams (Hung, Eldridge, Taricska, & Li, 2005;Shuster, 1986). In both cases, quantitative interpretations of warm water upwelling patterns are hampered by the lack of understanding of how the signal propagates from the sediment-water interface through the water column to the water surface-atmosphere interface and which perturbations and signal losses occur along this pathway. The present study will focus on LGD as an example of upwelling of warm water in lacustrine ecosystems during winter conditions due to its substantial impact on the ecosystem characteristics and functioning. LGD creates favourable habitats by affecting water chemical composition and temperature, supporting for instance the spawning of fish (Brunke & Gonser, 1997;Hayashi & Rosenberry, 2002). As climate warms, aquatic environments with strong GW influence are expected to support habitat stability and provide refuge for thermally stressed-aquatic species (Brabrand, Koestler, & Borgstrøm, 2002;Curry & Noakes, 1995;Hayashi & Rosenberry, 2002). Furthermore, detection of LGD is essential with respect to identifying it as a potential vector for pollution in aquatic ecosystems when GW quality is degraded (Nakayama & Watanabe, 2008). Despite the reported relevance of LGD on ecosystems, very little has been written about discharge of warm GW to lakes. Nearly all of the literature discusses discharge of cold GW to warm lakes, primarily because most of the research has been conducted during warm-water periods.
Relatively cold GW has a higher density than warm lake water and, thus, would not reach the water surface.
There are no detailed field observations of how warm water propagates through the water column and to the surface of the lake during winter conditions. We address this research gap by looking at trigger conditions that allow upwelling of LGD from the sediment-water interface to the water surface atmosphere interface. We consider the temperature difference required between GW and surface water (SW) as well as the influence of meteorological conditions and diurnal cycles.
The different temperatures of GW and SW might allow the detection of potential discrete areas of GW discharge to SW (Hare, Briggs, Rosenberry, Boutt, & Lane, 2015). Under the prerequisite of similar ion composition (which impacts water density), warm GW is less dense and more buoyant than cold SW, which allows upwelling of GW to the water surface. Thus, heat convection is augmented by density driven buoyant forces where warm GW discharges to cold SW. This process occurs during winter and early spring when SW is substantially colder than discharging GW and when the mixing is at a minimum at the lake surface (Hare et al., 2015;Lewandowski et al., 2013).
The basic concept of fibre optic distributed temperature (FO-DTS) technology is to analyse the temperatures monitored along specific distance intervals of a fibre optic cable based on (a) the travelling time of light in the optic fibre and (b) the temperature-dependent backscattering of light in the fibre (Selker, van de Giesen, Westhoff, Luxemburg, & Parlange, 2006). In this way, temperature can be monitored through the fibre optic cable up to a distance of several km, with spatial resolutions ranging from 0.3 to 4 m and measurement precision of 0.05 to 0.1°C when sampling over 30-s intervals (Hausner et al., 2011;Selker, Thévenaz, et al., 2006;van de Giesen et al., 2012).
Here, FO-DTS is placed in layers of a specific depth above the sediment-water interface, to provide high-resolution temperature data to quantify the incidence, frequency, persistence, and attenuation of warmer discharging GW that reaches the water surface.
The aim of this study is to show that during winter, the positive buoyancy of relatively warm LGD to cold SW will allow or enhance detection of GW at the water surface-atmosphere interface (the lake surface). To address this aim, a mesocosm was used as a model system.
Different layers of FO-DTS cable were deployed at different water depths to measure the temperature distribution. In addition, the following questions are addressed: 1. Which lake-internal upwelling patterns from the sediment-water interface through the water column to the water surface-atmosphere interface are caused by (simulated) LGD? 2. What are the intensities of (simulated) LGD at which GW signals can be identified at the water surface with FO-DTS?
3. What is the impact of weather conditions on detection of LGD at the water surface-atmosphere interface?
This paper addresses the research questions by (a) qualitative analysis of FO-DTS data, (b) statistical analysis of the FO-DTS data in order to describe temperature hotspots and significant spatial patterns across the water column, and (c) quantification of the effect of different weather conditions, injection rates, and the diurnal cycle on the net heat fluxes across the water surface (G, W m −2 ) as well as the energy change due to advective transport by the water inlet from the lake and the water outlet from the mesocosm (E adv in MJ) and the change of internal energy in the mesocosm (ΔE in MJ). Section 4 presents a conceptual model based on analyses and limitations of FO-DTS data. The conclusions of the paper will summarize briefly the findings on the different data analyses carried out, answering the three research questions.

| Experimental set up
The mesocosm is composed of two inlets and one outlet (see Figure 1).
Through one inlet water from Lake Müggelsee with a mean temperature of 4.7°C was discharged with a rate of 33 L min −1 . The inlet was open throughout the experiment in order to keep homogeneous and relatively constant water temperatures and water levels. The second inlet comprised a hosepipe that was deployed on the bottom of the mesocosm to provide the warm water (14-16°C measured at halfway between tap and mesocosm) injection. The hosepipe was insulated with insulation foam in order to reduce cooling of the injected water along the flow path from the tap (located in a building close to the mesocosm, 65-m distance).
A nozzle was connected to the end of the hose and covered with a bag (35 × 35 cm) filled with sediment in order to most realistically simulate discrete LGD at the sediment-water interface. Finally, an outlet on the opposite side to the cold water inlet assured a constant water level in the mesocosm of 0.82 m height. The outlet discharge rates varied from 34 to 48 L min −1 depending on the applied warm water injection rate.
An aluminium frame with dimensions: 4 m × 2 m and 1.5 m height was used to deploy the FO-DTS cable at different water depths ( Figure 1). The FO cable was installed in four layers at different heights: 20, 40, 60, and 80 cm (Layers 1, 2, 3, and 4, respectively) above the bottom of the mesocosm (Figure 1). The FO-DTS cable was routed back and forth across the aluminium frame in a rectangular grid formation so that 15 parallel reaches of the cable extended across each layer within the mesocosm. Temperatures were averaged over 12.5-cm intervals (sampling resolution) along the FO-DTS cable. We acknowledge that the presence of the FO cable may alter the flow of water and heat within the mesocosm; however, considering the cable volume (0.009%) compared to the water volume and the spacing between cables (at least 12.5 cm), the effect is probably minor.
From March 11, 2015, to March 27, 2015, seven 24-hr temperature datasets were obtained: one control dataset without warm water injection under overcast conditions; three datasets with 1 L min −1 injection rate, under clear, partly cloudy, and overcast conditions, respectively; two datasets with 5 to 5.5 L min −1 injection rate, under clear and overcast conditions, respectively; and finally, one dataset with 15 L min −1 injection rate under overcast conditions. Measurements were carried out using an ULTIMA-S DTS (SILIXA Ltd.) with a sampling resolution of 12.5 cm and spatial resolution of approximately 30 cm. DTS sampling resolution depends on the duration of each of the laser pulses sent by the DTS. For example, a DTS sending laser pulses of 10 ns has a sampling resolution of 1 m, the ULTIMA-S, with a sampling resolution of 12.5 cm, sends pulses of 1.25 ns. The spatial resolution refers to the distance between points along the FO cable located next to an abrupt change on temperature in a way that the point on the low side is not placed higher than 10% of the abrupt jump and the point on the high side is placed higher than 90% of the abrupt jump (Selker, Tyler, & Van de Giesen, 2014).
Five hundred metres of multimode FO cable from Silixa Ltd., were deployed for the experiments of this study. Using a multimode fibre allowed flexible bending and thus supported an adequate set up of the cable in the aluminium frame.

| Simulated upwelling flux rates versus rates reported in literature
The LGD rates used in the present study are based on measured flow rates in the tube (1 to 15 L min −1 ) used for injecting warm water into the mesocosm. The tube outlet is covered by a sand bag to simulate discrete LGD from sediments. An uncovered tube outlet might have caused a jet stream that would be quite unrealistic for LGD and therefore was avoided. The LGD rate can be referred to different areas: (a) the sand bag covering the tube outlet (35 × 35 cm) resulting in 8.2 to 122.4 L m −2 min −1 , (b) a square metre, that is, 1 to 15 L m −2 min −1 , and (c) the entire mesocosm (10 × 2.8 × 0.82 m) resulting in 0.036 to 0.536 L m −2 min −1 . The latter approach is often used in lake studies in which the total exfiltration is related to the entire lakebed.
The LGD rates applied in the present mesocosm experiment are at the upper end of LGD rates occurring in situ. Rosenberry, Lewandowski, Meinikmann, and Nützmann (2015) reviewed the international literature and report a median exfiltration rate of 0.74 cm day −1 (=0.005 L m −2 min −1 ) and a maximum of 745 cm day −1 (=5.2 L m −2 min −1 ).
The maximum of 745 cm day −1 is a point estimate based on seepage metre measurements (Kidmose, Engesgaard, Nilsson, Laier, & Looms, 2011). A high rate referred to the entire lake bed is reported by Piña-Ochoa and Lvarez-Cobelas (2009), which is 0.05 to 0.1 L m −2 day −1 .
For punctual focused LGD much higher rates are possible: For example, in Norrström and Jacks (1996) macropore GW discharge rates of 18 and 42 L min −1 are reported for areas of 0.0078 and 0.031 m 2 . More extreme examples can be found in natural thermal ponds or pools with hot springs with up to 800 L min −1 discharge rates (Haselwimmer, Prakash, & Holdmann, 2013). Intense warm water discharge might also be of anthropogenic origin such as sewage leakage from under water pipes (Apperl, Pressl, & Schulz, 2017).

| Measurement protocol and calibration
Once the FO cable was properly deployed onto the aluminium frame, the exact start and end positions of each cable line were identified. This was done by locally warming the cable at each bend, identifying the temperature peak on the data output graph, and noting the distance along the cable at this peak. This allowed locating of each of the four fibre optic layers, including their start and end points, as well as the beginning and end of each FO cable sequence.
Calibration of the FO-DTS by temperature offset correction was carried out using an external probe of the DTS device and FO cable reference sections within an isolated ice bath with a mix of ice and water that assured constantly 0°C. For the differential loss correction, the fixed value setting was chosen along the relatively short cable (500 m) without any splices. A default value of 0.255 dB/km was used as this value is the expected value for Corning ClearCurve™ OM3 fibre.
An alternate single-ended measurement set up was used with alternating monitoring direction of the light pulse sent from the DTS device. Measurements were averaged at 10-s intervals (integration time) in each direction. This means that the time interval between measurements from the same channel was 20 s.

| Data analyses and spatial statistics
All data analysis, including summarizing statistics for quantification of spatial patterns and statistical relationships of observed data within layers and between layers, was conducted in R and ArcGIS. The following spatial statistical metrics were quantified:

| Moran's I and Moran scatter plot of testing spatial autocorrelation
The Moran's I values were calculated as indicators of the degree of linear association between a value in a specific location (x-axis) and surrounding locations (y-axis). Moran's I scatter plots were used to visualize the type and strength of spatial autocorrelation of observed temperatures. The four quadrants of the Moran's I scatter plot indicate, from x-axis to y-axis: high-high and low-low quadrants contain values with positive spatial autocorrelation and high-low and low-high quadrants contain values with negative spatial autocorrelations. The Moran's I scatter plot displays a "spatially lagged" transformation of a variable (in y-axis) on the original spatial variable (in x-axis). In addition, the Moran's I scatter plot reports the summary of potential influential observations (highlighted in red diamond shape in Moran's I scatter plot) for the linear relationship between the data and the lag. Finally, the slope of the scatter plot indicates Moran's I values obtained and the overall spatial autocorrelation of the dataset (Anselin, 1996;Bivand, Pebesma, & Gómez-Rubio, 2013).

| Local indicators of spatial association maps
Local indicators of spatial association (LISA) have been calculated to identify significant spatial clusters or outliers that have been used in this study to highlight local hotspots of simulated warm water upwelling. The clusters and spatial outliers of LISA maps correspond to the four quadrants of the Moran's I scatter plots, providing a measure of clusters or outliers that are of statistical significance (Anselin, 1995).     In summary, significant spatial autocorrelations within each layer have been identified in all datasets. However, calculated Moran's I values vary depending on the injection rate of warm water, weather conditions, and the diurnal cycle (see Figure 5). This indicates that the strength of the spatial pattern within each layer also varies depending on the injection rates applied, the weather conditions, and the diurnal cycle.

| Preprocessing and sources of error
3.2.2 | Vertical spatial temperature patterns: Spatial correlation between layers

Spatial correlation between neighbouring layers
At high injection rates, the largest correlations between neighbouring layers occurred (Table S1). At lower injection rates, the correlation was usually much smaller and the largest correlation generally occurred between neighbouring layers. There are three exceptions where the largest correlations occurred between nonneighbouring layers: dataset 1 L min −1 , clear, daytime and 1 L min −1 , partly cloudy, day and night-time.
The reason might be that the extent of the spatial warm water pattern in Layers 1 and 3 is more similar than the observed pattern in Layer 2 (See Figures 4c and S1).
Measurements under clear sky conditions with an injection rate of 1 L min −1 showed a downward trend (from Layer 1 to 4) on spatial correlation coefficients calculated between neighbouring layers (1&2, 2&3, 3&4). When weather conditions were "partly cloudy" for 1 L min −1 , spatial correlation coefficients calculated between neighbouring layers showed an upward trend from Layer 1 to 3 (1&2 and 2&3) and the lowest value between the two uppermost layers (3&4). Finally, when weather conditions were overcast and injecting 1 L min −1 , it is possible to see that there was an upward trend (from Layer 1 to 4) on spatial correlation coefficients calculated between neighbouring layers (1&2, 2&3, 3&4), for example, from 0.415 to 0.815 during day.
The same upward trend was observed for an injection rate of

Spatial correlation between nonneighbouring layers
Highest spatial correlations calculated between nonneighbouring layers (1&3, 1&4, and 2&4) were found for 1 L min −1 under overcast conditions during night (0.681, 0.572, and 0.663, respectively) and Spatial correlation coefficients between Layers 1&3 generally increase from 1 to 15 L min −1 under overcast conditions. Spatial correlation coefficients between layers 1&4 and 2&4 generally increase from 1 to 5 L min −1 and considerably decrease at 15 L min −1 .
These observations agree with the change on the spatial pattern observed in Figure 3f, compared with the spatial patterns observed in Figures 3d and 3e. In Figure 3f, injected warm water flows straight up across Layers 1, 2, and 3. In Layer 4, injected warm water spreads all over the water surface. Low spatial correlation coefficients for 15 L min −1 between Layers 2&4 and 1&4 indicate differences of spatial patterns observed between Layers 1&4 and 2&4 in Figure 3f.  Three main findings can be listed from the calculation of spatial correlation coefficients between layers: • In general, overcast weather conditions result in higher spatial correlation coefficients between neighbouring layers and nonneighbouring layers.
• At 15 L min −1 , the uppermost layer (Layer 4) is spatially less correlated with the underlying layers than at 1 and 5 L min −1 under overcast conditions. These observations agree with the change on the spatial pattern observed in Figure 3f in comparison with the spatial patterns observed in Figure 3d,e.
• The diurnal cycle has an effect on spatial correlation coefficients calculated between layers. Layers within the water column show higher spatial correlation coefficients between them during night than during day for the same injection rates no matter of the weather conditions. However, for the uppermost layer (Layer 4) at the water surface-atmosphere interface, spatial correlation coefficients are lower for clear nights and generally similar or slightly higher for overcast nights.

| Net heat fluxes across the water surface, advective heat fluxes, and internal energy change
The effects of different weather conditions, different injection rates, and the diurnal cycle on the energy balance of the water column were quantified. This was done by quantifying the net heat fluxes across the

Net heat fluxes across the water surface (G)
Net heat fluxes across the water surface (G) during day and night are composed of net radiation (R n ), latent heat fluxes (phase transformation, λE), and sensible heat fluxes (H) with R n being the most important of the three (see Figure 7a,c,e,g,i,k,m). This indicates that the system gains and loses energy mainly by R n .
Net radiation (R n ) is composed of net shortwave radiation (R ns ) and net longwave radiation (R nl ). The net shortwave radiation (R ns ) is considered a heating term (during daytime) and the net longwave radiation (R nl ) is considered a cooling term (during day and night; Betts, 2015). Therefore, during daytime, calculated R n values are higher than during night for both clear and overcast weather conditions (Figure 7a, c,e,g,i,k,m). This is because during daytime, the surface cooling due to R nl is partly compensated by R ns (Betts, 2003(Betts, , 2015Betts, Desjardins, & Worth, 2013). In addition, during night, there is no shortwave radiation coming from the sun and the cooling term, R nl , will be the main component of the R n .
In On the other hand, during day and night, surface cooling to space due to R nl is lower under overcast weather conditions than under clear sky conditions (Betts, 2003(Betts, , 2015Betts et al., 2013). The smallest net heat fluxes across the water surface (G) occur under overcast conditions (see Figure 7a,g,k,m). For all datasets, during daytime measurements, the system gains energy mainly by E G and during night time measurements by E adv (Figure 7b,d,f, h,j,l). Only, for 15 L min −1 overcast weather conditions dataset, the system mainly gains energy by E adv during day and night due to the high amounts of injected warm water (Figure 7n) water will prevail across the water column and at the water surface due to: 1) less absorbed shortwave radiation at the water surface of the mesocosm (R ns ) and 2) less water surface cooling in the mesocosm due to R nl . During night-time, the heat signal of the injected warm water will prevail across the water column and at the water surface due to: 1) less water surface cooling in the mesocosm due to R nl and 2) energy gains in the mesocosm due to injected warm water.
Finally, spatial patterns of injected warm water, across the water column and at the water surface, observed in Figure 3a-c can be related to high and fast energy changes (ΔE) over time in the mesocosm, due to stronger net heat fluxes across the water surface (G) under clear sky during day and night, than under overcast conditions. In general, during daytime, the heat signal of the injected warm water is not detectable at the water surface, mainly due to high amount of absorbed shortwave radiation at the water surface (R ns ) during clear sky and to a less extent, due to water surface cooling in the mesocosm by R nl . During night, the heat signal of the injected the net radiation (R n ), which is the sum of net shortwave radiation (R ns ) and net longwave radiation (R nl ). The net radiation balance is driven by the diurnal cycle of the incident shortwave radiation (Betts, 2015). This means that the solar warming during daytime and the longwave cooling during night-time drive the diurnal cycles of air temperature and water surface temperature (Betts, 2015;Vercauteren et al., 2011) and, thus, impact on the detectability of the injected warm water temperature signal in the mesososm.
Furthermore, cloud cover is also a relevant regulator of the diurnal cycle of the net radiation balance (R n ; Betts, 2003Betts, , 2015Betts et al., 2013;Dai & Trenberth, 1999). Clouds decrease the incident shortwave radiation at the water surface and decrease the net surface cooling at the water surface because there is less R nl .
Therefore, the detectability of the injected warm water temperature signal in the mesocosm is decisively controlled by the diurnal cycle of the net radiation balance (R n ) and the cloud cover.
In order to illustrate the relevance of the diurnal cycle (day vs. night) of the net radiation balance (R n = R ns + R nl ) and cloud cover on the observed spatial patterns of the heat signal related to warm water injection and based on the results presented in this paper, a conceptual model for the spatial patterns observed under different weather conditions (clear, partly cloudy, and overcast), injection rates, and diurnal cycles (day vs. night) is suggested in Figure 9. due to the R n (=R ns + R nl ). During clear sky conditions during daytime, due to the higher solar warming (R ns ) at the water surface than during overcast weather conditions, the water surface is heated up. In consequence, the heat signal of the injected warm water at the water surface is mixed with the heated water surface due to solar warming.
On the contrary, during overcast weather conditions during daytime, calculated R n (see Figure 7) and solar warming due to R ns are lower.
In consequence, the heat signal of the injected warm water can be detected at the water surface (see Figure 9a).
During night, because there is no R ns , the main gains or losses of heat at the mesocosm's water surface are due to R nl . Both, during night and day, the degree of heat losses from the water surface depends on the presence of clouds at the sky (see Figure 9b). During clear sky conditions, the strength of R nl is higher than under overcast weather conditions. In consequence, during clear sky conditions at night, the mesocosm loses higher amounts of energy across the water surface-atmosphere interface than during overcast conditions. The heat signal of the injected warm water at the water surface is lost faster during clear sky conditions than during overcast conditions at night (Figure 9b).

| Application of FO-DTS for detection of LGD upwelling
FO-DTS has been used to detect GW discharge at the sediment-water interface in lakes (Blume et al., 2013;Liu et al., 2015;Tristram et al., 2015) and streams (Hare et al., 2015;Krause et al., 2012;Lowry et al., 2007). However, it had not yet been determined how the temperature signal propagates from the sediment-water interface through the water column up to the water surface-atmosphere interface and how the signal is affected by environmental parameters such as weather conditions (clear vs. overcast) and the diurnal cycle of net radiation. In Hare et al. (2015), FO-DTS measurements were compared with thermal infrared (TIR) measurements, which allowed the comparison of heat signals detected at the stream bed and at the water surface. Winter conditions were proven to be the best season to conduct these kinds of measurements. However, the characterization of weather and diurnal conditions that might have affected the upwelling patterns of the GW heat signal across the water column was not addressed until the present study. For instance, Liu et al. for correct interpretation that might present a real difficulty for any quantitative assessment. Therefore, it is essential to determine those parameters that may influence the temperature such as solar radiation and to make sure that the temperature variations of the lake as detected by the FO-DTS are mainly caused by GW discharge (Liu et al., 2015) as presented in this paper.

| Possible system interferences and uncertainties of the study 4.4.1 | Effect of wind and possible consequences
Wind is an important factor affecting lake SW temperatures and lake internal mixing (Pöschke et al., 2015). Wind promotes movement and mixing of SW bodies. The SW can be dragged by the wind from one shore of a lake to the other shore inducing downwelling of water in the water body on one side of the lake and at the same time water movement from the bottom of the lake upwards to the lake surface (mixing). This process, relevant in lake settings, is probably irrelevant in the small experimental mesocosm used in the present study. From the slice3D plots in Figure 3, there is no indication for a wind-induced circulation or mixing. Wind speeds during the experiments were generally low (ranging from 0.0045 to 2.1789 m s −1 ). Steep bank slopes reaching a height of 1 m above the water surface prohibited wind impacts on the water surface. Furthermore, due to the small size of the mesocosm, the wind fetch is short and a potential wind impact on the water surface is irrelevant. However, when transferring the results of the mesocosm experiment to a real lake setting, possible wind impacts should be taken into account.

| Thickness of water column in the present study
In the present study, the thickness of the water column is 0.82 m. The obtained conclusions could be directly transferred to shallow lakes not deeper than 1 m, shore areas of lakes not deeper than 1 m, and probably to shallow lakes with slightly larger depth. Because there is no thermal stratification within the water column of the mesocosm, the obtained results of the present study can only be transferred to cases where there is no thermal stratification.

| Possible effects of electrical conductivity of GW
The upwelling of the water injected at the mesocosm's bottom is driven by density differences of the injected water and the water in for the lake and 429 mg L −1 for the injected water, that is, there is a density difference of 60 mg L −1 between the two waters. Based on a mean mesocosm temperature of 4.7°C, the density of the water in the mesocosm is 0.999946 kg L −1 , and based on a mean temperature of 15°C of the injected water, the density is 0.999114 kg L −1 , that is, there is a density difference of 832 mg L −1 between the two waters.
Basically, the density difference due to the different ion composition of the two different waters, strengthen the temperature induced density difference. The combined effect of ion composition and temperature on the density difference between the two waters is 880 mg L −1 (calculation according to Dietz, Lessmann, & Boehrer, 2012) or 921 mg L −1 (calculation according to Boehrer & Herzsprung, 2010).
Therefore, the injected warm water should immediately rise upwards through the surrounding denser lake water via buoyancy.
During the short ascent, some mixing might have occurred and the contact with surrounding water resulted in some cooling of the injected warm water. Nevertheless, only in experiments during overcast conditions (Figure 3d-f), the injected warm water was still warmer than the rest of the water in the mesocosm when it reached the water surface and thus, floated on the top of the water body. From there, the warmer less dense water gradually spread as a plume on the water surface.
Low wind speeds, shallow water conditions, and density differences between simulated GW and SW might favour the upwelling of simulated GW discharge on the SW. However, in the present study, the main parameters controlling the detection of simulated GW on the water surface seem to be the net radiation balance (R n ) and the cloud cover during day and night-time measurements. Because the experiments have been carried out under specific conditions, the previous statements are only true in lake areas where the same conditions apply as in the mesocosm experiment during winter conditions. This study is a first attempt to simulate thermal patterns of discrete LGD in shallow lakes or close to lake shores. The mesocosm experiment and simulation of GW discharge is the first step in order to identify the main controlling parameters that favour detection of hotspots of LGD on the lake surface (mesocosm surface in this case).
We have decreased the amount of variables that impact LGD by simulating discrete GW discharge in a mesocosm. The mesocosm where the simulation has been performed intends to represent a small shallow area of a lake where GW exfiltration by LGD occurs. Thus, not all the influencing factors such as wind, waves, and vegetation that could be present under natural conditions have been considered.
However, GW discharge that is warmer than SW has been little studied relative to discharge of cold GW to warmer SW. Thus, by conducting studies during colder times of the year, scientist can make use of the conclusions presented here.

| CONCLUSION
The present study demonstrates that during winter conditions, the positive buoyancy of relatively warm water imported by simulated LGD into shallow water bodies (mesocosm used as model system) allows detection of LGD at the lake's water surface-atmosphere interface by FO-DTS. FO-DTS technology offers fine scale measurements with high temporal resolution and allows the observation of induced lake-internal upwelling caused by simulated LGD in a three-dimensional perspective.
In this manner, different lake internal upwelling patterns have been described from the sediment-water interface through the water column to the water surface-atmosphere interface caused by the injection of warm water at different rates, different weather conditions, and during the diurnal cycle. Simulated GW signals at the water surface were identified at all applied injection rates, from lowest 1 L min −1 to highest 15 L min −1 .
However, detection of simulated LGD at the water surface-atmosphere interface was mainly determined by the diurnal cycle of the net radiation balance (R n ) and the cloud cover.
Based on the results presented in this paper, overcast weather conditions and night-time measurements are recommended for tracing discrete warm water upwelling fluxes across the water column and at the water surface.