Dynamics of water temperature and interfacial heat flux in lake ice and under-ice layers

Temperature is closely related to water density, which is the main factor of thermal stratification in lakes (Hall 1980). The stratification phenomenon of lakes and reservoirs under the vertical temperature gradient is of great significance in lake hydrodynamics, which not only affects the transportation and circulation of nutrients in water bodies but also determines the productivity level of water bodies and the seasonal succession of microorganisms such as phytoplankton to a certain extent (Bennett 1978).

During the freezing period, the direct exchange of gas and heat between the atmosphere and the lake is blocked by the ice cover. Consequently, no prominent vertical mixing occurs between the atmosphere and lake body, which affects the balance between the net output of the ecosystem and the respiration of the ecosystem, and determines the concentration of dissolved oxygen (DO) under the ice to a certain extent. Excessive consumption of DO will eventually lead to anoxia in the water under the ice, which may lead to the death of fish and benthic invertebrates (Obertegger et al. 2017).

Bilello (1967) conducted field experiments on a large number of lakes in the middle and high latitudes during the freezing period and found that after the formation of a permanent ice layer over a shallow lake in Michigan, most of the heat responsible for the melting of ice originated from the energy stored in underground soil in summer. Comparing the thermodynamic characteristics of lake ice between Great Slave Lake and Great Bear Lake, Rouse et al. (2008) found that the key factor affecting the change in frozen periods is the solar radiation absorbed by the lakes. Likens & Ragotzkie (1965) conducted an experiment using radioactive tracers in a small lake and identified organized vertical water circulation in the ice-covered lake and speculated the occurrence of similar vertical movements in other ice-covered lakes in temperate regions. In a study on a small shallow lake in Minnesota, Ellis et al. (1991) found that the water temperature distribution was relatively stable before ice sheet formed, but the temperature began to fluctuate under the ice cover and the water temperature increased. Compared with high-latitude lakes, lakes in China's cold regions are mostly located in the middle and low latitudes. Zhi et al. (2009) analyzed the data of total radiation, reflection, air temperature, water temperature, and ice thickness on the ice surface of Hongqipao Reservoir in Heilongjiang Province in winter and found that the peak time of daily near-surface ice temperature/air temperature ratio was 1.4 h behind the peak time of radiation. Song et al. (2019) and Cao et al. (2021) studied solar radiation, ice thickness, ice temperature, subglacial water temperature, and DO in subglacial water during the freezing period in Lake Wuliangsuhai and found that the amount of solar radiation controls photosynthesis under the ice. These studies have expanded our understanding of the evolution of ice and snow transmittance in temperate and arid regions and its role in lake ecology.

According to the above research, air temperature, lake ice temperature, and water temperature are important factors affecting the thickness of lake ice, and the heat transmission intensity at the interface of air–ice and ice–water determines the increase of ice thickness during the freezing period (Jie et al. 2021). Nevertheless, it is difficult to directly measure the change of heat flux at the ice–water interface, and it is usually calculated by referring to solar radiation, ice body, temperature change of water under ice, and hydrodynamic conditions (Aslamov et al. 2014a). Limited by the regional characteristics of lake ice, quantitative studies on the growth process of lake ice during the ice-covered period with sufficient internal temperature of ice and actual measured data of water body under ice are still relatively lacking (Kirillin et al. 2012).

To obtain a deeper understanding of the temperature dynamics during the ice growth period, Lake Wuliangsuhai, a shallow lake in the cold and arid region of China, was investigated from December 2016 to February 2017. By observing the increase rate of ice thickness, ice temperature, and longitudinal temperature of water under ice, this study estimated the heat flux at the ice–water interface, estimated the vertical diffusion of heat under ice, observed the influence of air temperature, wind speed and solar radiation on the longitudinal temperature profile, and explored the change characteristics of the ice thickness of shallow lakes in cold regions during the freezing period. Based on the results, the temperature dynamics of lakes during the freezing period were qualitatively evaluated, and the findings provide scientific support for the development and improvement of thermodynamic models of lake ice and water under ice during the freezing period.

In total, 21 temperature monitoring probes were installed (Figure 2). Specifically, 6 temperature probes were installed on the ice body at 4.5–29.2 cm, four temperature probes were installed in the freezing layer at 34.0–48.6 cm, and the remaining 11 temperature probes were installed in the water layer at 10 cm intervals from 58.3 to 156.0 cm (Figure 2(a)). The temperature probes measured instantaneous temperature every 10 min, and the average value of 1 h was taken and saved. This monitoring scheme can reduce the impact of sudden errors in a single measurement and solve the problem of excessive data storage. The data presented in the figure are not continuous, and abrupt changes and missing values appear due to power failure and maintenance issues with instruments.

The monitoring data of air temperature, ice temperature, and water temperature under the ice generally remained stable with time, and there was no prominent temperature rise in the water under the ice during the monitoring period, indicating that there was no interference of other thermal factors during the monitoring period, except for solar radiation. The temperature data used in heat flux calculation started from = 29.2 cm, and the sudden change of temperature occurred in the initial measurement stage (sensors h₅ and h₆).

where t is the time, z is the vertical distance to the ice surface (this vertical axis is positive downward), ξ(t) is the coordinate of the ice–water phase transition boundary, T(z, t) is the temperature, and k_i is the thermal conductivity of ice (2.24 W/(m² °C)) (Stefan 1891).

In the above formula, is the molecular thermal conductivity of water (0.569 W/(m² °C)), and is the temperature gradient.

For the entire research period, according to the change rate of ice thickness in Lake Wuliangsuhai, the period of ice growth was roughly divided into three stages (Figure 4). The first stage was called the rapid growth period, which lasted from 25 December 2016 to 26 January 2017. In this stage, ice thickness increased from 294.56 to 472.28 mm, at a rate of 5.60 mm/d, and the maximum change rate was 14.72 mm/d, which occurred on 29 December 2016. The second stage was called the stable growth period, which lasted from 27 January 2017 to 2 March 2017. In this stage, ice thickness increased from 474.3 mm to the maximum of 569.76 mm at a rate of 2.83 mm/d, which fluctuated within a certain range. The maximum change rate of 8.66 mm/d occurred on 30 January 2017. In the third stage, which is called the ablation period, the average change rate of ice thickness declined to −2.87 mm/d from 2 to 8 March 2017, indicating that the ice thickness was no longer increasing but rather exhibited a linear decreasing trend.

Similar to the change trend of ice body temperature, the corresponding change was observed in the temperature of the water body under the ice. Water temperature also exhibited distinct stratification from the upper layer to the lower layer. With the increase of water depth, the water temperature also increased considerably. In the freezing period, solar radiation acts as the main factor of water temperature stratification under ice. On 28 December, for example, the highest and lowest values of the upper water temperature were 1.71 and 1.18 °C, respectively. By 15 January, the highest and lowest values of the upper water temperature decreased to 0.61 and 0.07 °C, respectively. Under the influence of sediments, the fluctuation of water temperature at the water–sediment interface was weak, and the diurnal variation was not prominent, remaining at approximately 7 °C.

At the initial stage of instrument monitoring, the bottom ice body showed a temperature above 0 °C (Figure 9). This is because at the initial stage of the formation of the bottom ice layer, water remains in the ice, and the ice body structure is still unstable. Finally, the bottom ice body temperature was stable at the freezing point of approximately 0 °C. Similar to the surface ice temperature, the water temperature at the ice–water interface exhibited the same diurnal fluctuation as the surface ice temperature. This fluctuation spread from the ice–water interface to the water–sediment interface but gradually decreased with increasing depth.

In the stable growth period, and with the increase of water depth, the water temperature increased slowly. Taking 30 January as an example, the highest and lowest values of upper water temperature were −0.2 and −0.97 °C, respectively. By 23 February, the highest and lowest values were −0.4 and −0.78 °C, respectively.

The temperature change characteristics of the ice layer and water layer during ablation period are presented in Figure 8. With the increase of depth, the ice temperature began to rise. The diurnal fluctuation caused by the diurnal variation of incidence began to make the ice temperature gradually weaken with the increase of ice depth, and the diurnal temperature difference became progressively smaller. Since March, the ice body was melting, such that the ice temperature began to approach positive values (Figure 9). During daytime in the ice melting period, the melting of surface ice body is affected by the temperature rise. At this time, the temperature probe measured the temperature after the melting of the ice body. At night, the temperature begins to drop sharply again, and some melted water refreezes. During the ice melting period, temperatures above 0 °C were also recorded at 44 cm below the ice surface. After entering the ablation period, the fluctuation of water temperature under ice was significantly enhanced.

During the entire monitoring period, six temperature probes remained frozen in the ice from 26 December to 11 February. During this period, at least one temperature probe gradually recorded values lower than 0 °C with the increase of ice thickness. In other words, the probe was frozen in the ice. After 11 February, all the predesigned temperature probe Nos 1–10 were frozen in the ice body. Probe No. 11 started at 10 cm below the ice body and the remaining Nos 12–21 were still placed in the water body under the ice (Figure 2(a)). With increasing depth, the temperature of both the ice and water under the ice changed, and the fluctuation gradually decreased (Figure 9).

At about 17:00 h, the temperature of the upper ice reached the maximum value of −1.3 °C. After 17:00, the temperature of the upper ice began to decrease with the decrease of solar radiation and air temperature. At this time, the temperature inside the ice was −1.38 °C at 9 cm, and a ‘relatively hot middle layer’ appeared from the upper surface layer, which caused the temperature difference between the ‘relatively hot middle layer’ and the adjacent upper and lower ice layers over time. On 7 February, the temperature profile corresponded to the snow-covered period (Figure 10(c) and 10(d)). During the snow-covered period, with the change of air temperature, the diurnal variation characteristics of the upper ice temperature were similar to those of the snow-free period, both of which first increased and then decreased. However, the maximum monitored temperature of the upper ice layer was greater in the absence of snow than in the presence of snow, and the minimum value was greater in the presence of snow. In the presence of snow, the change of ice temperature in each period was relatively gentle, and the change trend was roughly the same. In the absence of snow, there was no ‘relatively cold middle layer’ and ‘relatively hot middle layer’. From the temperature profile of the underwater layer of the ice body with no snow cover on 3 February and the temperature profile of the underwater layer of the ice body with snow cover on 7 February, the temperature change trend can be estimated to be roughly the same between the snow-free period and the snow-covered period.

The daily variation range of the temperature of the ice and the water temperature under the ice body decreased prominently with increasing depth (Figure 13), and the surface ice body temperature was easily affected by solar radiation, driving the drastic fluctuation of the daily variation range of the surface ice body, with the highest above 12 °C and the lowest around 2 °C. The daily variation range of the middle ice body generally remained below 4 °C, and the daily variation range of the bottom ice body was the lowest within 1.5 °C. The daily variation of the interface water temperature was relatively large, but far less than that of the surface ice temperature, which was approximately 1.5 °C at most. The temperature of the middle water body was approximately 1 °C at most, and the temperature of the bottom water body was approximately 0.8 °C at most, which occurred during the ablation period.

As the monitoring instrument was placed in the ice body for a long time, the thickness of the ice body gradually increased, and the bottom of the ice body approached the monitoring probe, which was initially located in the water. We assume that the ice body was in a static state, and consider the ice body to approach the temperature probe with the probe moving to the ice–water interface. The temperature probe sequentially entered the buffer zone from the lower turbulent layer in the water body, then entered the laminar boundary layer at the ice–water boundary, and finally froze in the ice body.

Therefore, the heat flux density of the frozen temperature probe in the ice body was calculated from the average data of the time (100 min) corresponding to the position of the temperature probe: 1, 1.5, and 2 mm from the bottom of the ice body (see Table 1). Considering unstable influencing factors, when a single temperature probe passed through different horizontal planes in the laminar layer, the calculated gradient changes include the contribution of unstable conditions.

With the distance from the temperature probe to the ice surface as h_j, the freezing time t of the sensor, the average 100-min heat flux density q (W/m²) at the ice–water interface is calculated using formula (3), and the average daily heat flux density q (W/m²) at the ice–water interface is calculated using formula (2). is the growth rate of the ice sheet, and the heat flux density of the upper water body near the bottom of the ice is Q (W/m²).

The experimental data of daily average change of hydrothermal flux density were obtained using formula (2). From 27 December to 6 January, the temperature of the water layer in the ice body decreased with time (Figure 5), and the observed heat flux density gradually increased from 11.887 W/ to the maximum value of 24.15 W/⁠. After 7 January, the heat flux density determined using formula (2) changed from 0.25 to 16.83 W/m² (Table 1). The heat flux of the ice–water interface calculated using formula (3) was 0.24–24.14 W/⁠, and that of ice–water interface calculated using formula (3) was 1.73–19.6 W/⁠.Therefore, the variation range of heat flux calculated using different calculation methods were consistent (Figure 14).

The surface ice temperature exhibited prominent high-frequency fluctuation with changes in air temperature, and this high-frequency fluctuation was clearly attenuated in the middle and lower ice layers. The temperature changes in the middle and lower ice layers exhibited a lag effect relative to the high-frequency changes in the surface layer (Figure 9). The air temperature is high and the radiation is strong during the daytime, the surface ice body heats up rapidly, and the surface ice body temperature is higher than the middle ice body temperature, giving rise to the phenomenon of the ‘relatively cold middle layer’. With the increase of solar incidence, the temperature of surface ice will increase and vice versa. Our results are consistent with those of previous studies (e.g., Song et al. 2019; Cao et al. 2021). Because of the variation in incidence, the temperature of the ice body clearly changes between day and night, and in the same day, the temperature will show certain symmetry.

When the ice body is growing steadily during the period of no snow cover, the surface ice temperature rises rapidly at a much faster rate than that of other layers of the ice body. In the presence of short-term snow, the temperature change is gentler, which indicates that snow acts as a thermal insulation layer. The temperature fluctuation of the ice–water interface in the snow-free period is greater than that in the snow-covered period, and the bottom water body temperature in the snow-free period is approximately 0.3 °C higher than that in the snow-covered period.

With proceeding monitoring time, the thickness of the ice body becomes continuously increased. Under the observed ice growth rate, there was little difference in the time points when the temperature probes crossed different horizontal layers (Figure 14). In the ice growth stage, Q > q because of the exothermic process during the phase change of the ice–water interface, and the heat flux from the water under the ice to the ice was 11–23% of the heat flux inside the ice (Shirasawa & Leppäranta 2009). This means that if the heat flux at the ice–water interface is not considered in the calculation of the ice thickness increase, it is impossible to accurately calculate the dynamics of ice thickness change in Lake Wuliangsuhai.

During the system monitoring, the temperature of the water body under the ice caused the change of the heat flux density from the water body to the ice body. In this monitoring, the current meter was not used to monitor the water flow velocity under the ice body. Consequently, the change of the heat flux density from the water body to the ice body could not be confirmed as to whether it was related to the water flow velocity under the ice (Bogorodskii et al. 1974). According to the measurement results of South Baikal Lake in March 2012 using a Doppler profiler, the velocity of the water layer in an ice body varied from 0.001 to 0.006 m/s, indicating that the velocity of the water layer in the ice body will contribute to the change of heat flux from the water body to the ice body (Aslamov et al. 2014b).

• 1.

  With continued monitoring time, the ice body temperature exhibited distinct stratification from the upper layer to the lower layer, and the temperature showed an increasing trend from top to bottom. According to the diurnal variation, the increase of incident light increased upper layer temperature and vice versa. In the same time period, the temperature fluctuation showed a certain level of symmetry between daytime and nighttime. With high-frequency changes in incident light, the temperature of the upper ice body exhibited a similar high-frequency fluctuation, which gradually weakened with increasing depth.

• 2.

  The temperature of the upper layer of water under the ice body followed a similar diurnal variation law with that of the corresponding upper layer of the ice body. With increasing depth toward the water–sediment interface, the diurnal fluctuation of temperature gradually weakened. The diurnal variation of the water–sediment interface was relatively insignificant and the fluctuation was weak.

• 3.

  Ice temperature and water temperature under ice change significantly in temporal and space due to the influence of solar radiation, and the presence of snow affects the incoming solar radiation, thus affecting the ice temperature and under-ice water temperature.

• 4.

  Using this systematic monitoring equipment, the temperature gradient near the ice–water interface was measured for the first time. Two different calculation methods were employed to estimate the heat flux density from the ice body to the water under the ice. Although the results were affected by unstable conditions, the size of the temperature probe, and the thickness of the laminar layer, the variation ranges of heat flux density and heat flux density from the water body under the ice obtained using different calculation methods were generally consistent.

The authors would like to thank all the reviewers who participated in the review and MJEditor (www.mjeditor.com) for its linguistic assistance during the preparation of this manuscript.

This work was supported by the National Key Research and Development Program of China (2019YFC0409200); Inner Mongolia Autonomous Region Science and Technology Plan (2021GG0089); and National Natural Science Foundation of China (52060022).

X.S., S.Z., and B.S. guided and modified important research knowledge; G.L., H.Y., and S.W. made substantial contributions to the conception of research; J.H. was the main contributor to writing the manuscript, sorting and processing data. All authors have read and approved the final manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.