Convective Heat Transfer of Spring Meltwater Accelerates Active Layer Phase Change in Tibetan Permafrost Areas

Convective Heat Transfer of Spring Meltwater Accelerates Active Layer Phase Change in Tibetan Permafrost Areas Yi Zhao, Zhuotong Nan, Hailong Ji, Lin Zhao Key Laboratory of Ministry of Education on Virtual Geographic Environment, Nanjing Normal 5 University, Nanjing, 210023, China Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, China School of Geographical Sciences, Nanjing University of Information Science & Technology, Nanjing 210044, China 10

The inputs of the SHAW model consist of three types of data: (1) meteorological driving data including air temperature, relative humidity, wind speed, precipitation, density of new snow, and shortwave 145 radiation; (2) soil moisture content and soil temperature data as initial states and lower boundary conditions; (3) characteristic parameters of canopy, snow, soil residue and soil column at the study site.

Design of the control experiment
The SHAW model incorporates the CHT processes of the liquid and vapor flux in the energy budget equation, which makes it possible to portray complete water-heat interactions frequently occurring in the 150 freezing and thawing periods in permafrost regions. In this study we designed a control experiment containing three scenarios for representing full presence, partial presence and complete absence of liquid CHT in the model by modifying the model codes. We used the same forcing data at a typical permafrost https://doi. org/10.5194/tc-2021-191 Preprint. Discussion started: 30 August 2021 c Author(s) 2021. CC BY 4.0 License. site, the TGL, to drive the models. The impacts of liquid CHT on active layer dynamics are quantified by the differences in soil temperature and moisture content by contrasting the results from the three 155 scenarios.
The control experiment consists of three scenarios: 1. Control: in this setup the original SHAW model is applied to the TGL site and the simulated results serves as a baseline to contrast with the results of other scenarios. Confined within the physical limits, the soil parameters associated with each layer were calibrated to best match the 160 observed soil temperatures and moisture contents at various depth, i.e., 0.05 m, 0.1 m, 0.4 m, 1.05 m and 2.45 m. The same calibrated soil parameter values are used in the other two scenarios to maintain consistency throughout the experiment. CHT (NoSurf): CHT between the ground surface and the soil is not considered in this setup. For this purpose, the codes related to liquid water CHT from the ground surface layer 165 to the top soil layer (0.00 m) as described in the second term on the left hand side of the Eq. 1 were disabled in the SHAW model. By contrasting the results of this setup with that of Control, the effects of the infiltrative convective heat could be quantified.

No CHT (NoConv):
This setup completely eliminates the liquid water CHT, that is, both the infiltrative convection from the surface to the top soil and the heat transfer associated with the 170 liquid water migration within the soil layers are not considered. All codes related to the second term on the left hand side of Eq. 1 were disabled. By contrasting Control-NoConv with Control-NoSurf, the impacts of CHT relating to vertical advection within soil layers will be determined.
Note, in the NoSurf and NoConv setups, we only removed heat fluxes and the exchanges associated with the water movement, and still retained liquid water fluxes that is necessary to maintain the water balance 175 in each soil layer. In the SHAW model, we found the simulated direction of vapor flux did not match the real vapor cycle, so the vapor-related convection keeps intact in the three setups to exclude the impacts of vapor CHT in this analysis. The three scenarios were simulated with the same upper/lower boundary conditions, meteorological forcing data, initial states and calibrated parameters. Thus, the resultant differences obtained between NoSurf/NoConv and Control simulations represent the impacts of liquid 180 CHT occurrences in discrete places. Greater simulated soil temperatures of Control than those of the https://doi. org/10.5194/tc-2021-191 Preprint.  other two scenarios signify a positive thermal impact of CHT on the active layer, and it is a negative impact if they are lower.

Experimental area and data
A typical permafrost site, the TGL site, was chosen for the investigation due to its detailed observations 185 of the active layer. The TGL site is situated on a southwest-facing slope elevated at 5100 m a.s.l. in the Tanggula mountains on the eastern QTP, with latitude 33°04′ N and longitude 91°56′ E. The local vegetation is sparse alpine meadow with a coverage fraction of about 30~40%. The soils are mainly composed by loamy sand (sand content>70%). The annual mean of air temperature is about -4.9 °C . The active-layer thickness (ALT) is measured as about 3 m (Xiao et al., 2013).The annual precipitation is 190 about 400 mm and it mostly concentrates in the months from May to September, accounting for 92% of the whole year.
The installed instruments include an automatic weather station, which measures air temperature, wind speed and direction, humidity, shortwave/longwave radiation (upward and downward), air pressure, snow depth, and precipitation, and an active-layer monitoring system, which measures soil temperatures 195 and moisture contents at the depths of 0. 05, 0.10, 0.20, 0.40, 0.70, 1.05, 1.30, 1.75, 2.10, 2.45 and 2.80 m below the surface. The time series of observed half-hourly air temperature, relative humidity, wind speed, precipitation and shortwave radiation from 2008 to 2010, collected from the automatic weather observation station measured at 2-m height at the TGL site, were used to drive the SHAW model running at a time step of one hour. The observed daily soil temperature and unfrozen water content (UWC) at 200 0.05 m, 0.1 m, 0.4 m, 1.05 m and 2.45 m depth during the same period, collected from the active layer monitoring system, were used to calibrate and validate the SHAW model.

Model settings
Driving data. In addition to the hourly meteorological data from the TGL site, the inputs to the SHAW model also include the snow density of each new snowfall event. We set them as zeros and let the model 205 estimate it based on the air temperature at the time.
Soil column stratification. The soil column was stratified into 13 layers corresponding to the observation depths in the TGL site, including five layers (centered at 0.00, 0.02, 0.05, 0.1 and 0.2 m) as https: //doi.org/10.5194/tc-2021-191 Preprint.  at the depth of zero as the interface between atmosphere, vegetation and soils. The shallow depths were tightly discretized in order to accommodate rapid hourly variations in soil temperature and moisture near the ground surface.
Boundary conditions. The SHAW model depends on accurate lower boundaries usually specified at a shallow depth to enable a precise simulation of the coupled water-heat exchange processes (Chen et al., 215 2019). In this study, the observations at the 2.8 m depth close to the active layer bottom were provided as the lower boundaries. The observed daily soil temperatures at this depth constrain heat fluxes through the lower boundary interface. The lower boundary of the soil moisture contents (both ice and unfrozen water contents) was determined by the model following an empirical equation in relation to soil temperature by confining the maxima of liquid water equivalent to 0.25 m 3 /m 3 occurring in summer. 220 Initial conditions and spin up. For all the setups, initial soil temperature and soil moisture profiles were generated with three decades' spinning up with repeating forcing data from 2008-2010, until the differences in soil temperature and moisture content are narrowed to be less than 0.1 °C and 0.01 m 3 /m 3 , respectively, between the last cycle and penultimate cycle at the same date for all soil layers. The eventual soil temperature and moisture profiles were provided to each scenario simulation as the initial states. were used to quantify the model performance: where and are the observed value and simulated value in the time step ; ̅ is the mean of the observations in the entire period; and is the total number of time steps. 240 Table 1 shows the vertical discretization of the TGL soil profile and some of the important soil parameters associated with each layer. The volumetric percentages of sand, silt and clay and the bulk density were measured and the other four parameters, i.e., saturated hydraulic conductivity, air-entry potential, 245 saturated volumetric moisture content, and pore-size distribution index, were obtained by calibration.   During the thawing period in spring each year, the observed temperatures (Figure 1a-e) rapidly increased from the negative to the positive, but the simulated soil temperatures exhibited an obvious, prolonged 275 duration of the zero-curtain effect, which delayed warming of soil temperature for days. The effect was especially strong in 2009. The formation of zero-curtain is a joint result of multifaceted thermal processes including evapotranspiration, phase change, thermal conduction and convection during the freezing and thawing periods (Outcalt et al., 1990), and is more obvious during the thawing periods than freezing periods (Jiang et al., 2018). The overestimation of the zero-curtain duration in the SHAW simulation is 280 primarily related to the irrational vapor movement and simplified ice-liquid phase change process.

Model evaluation
In January 2010, overestimation of soil temperature was observed throughout the entire soil column   Figure 3b and c, which exhibit the differences in soil temperature between the Control and the two scenarios partially (NoSurf) or fully (NoConv) ignoring consideration of CHT in the model. However, 295 in the same periods of 2009, no noticeable temperature differences were simulated between Control and NoSurf for the entire soil column, and only slight differences between Control and NoConv in the middle depths. Because the vapor convection has not been modified, those effects solely come from the partial or full presence of CHT due to surface infiltration and vertical advection within the soil column. The soil temperature differences were also noticeable at shallow depths in January 2010 (Figure 3b and c), when 300 the soils at those depths were frozen. This phenomenon was in line with the occurrence of extra snowmelt events in this period as shown in Figure 2. It suggests that CHT could also take place in freezing periods provided that liquid pore water migrates in response to external air temperature changes in these periods. Figure 3b and c, the occurrence of CHT were more and more delayed with soil depth with the most delayed taking the lowest place. The shallow depths are characterized with long thawing periods 305 spanning from later spring to summer with large thermal gradients and active water migration between soil layers, so that CHT in those depths considerably impacts the thermal regime. Conversely, in deep depths where the temperature gradient and water motion are relatively modest, the thermal effects of CHT are much smaller. The differences between the Control and NoConv (Figure 3c) are more evident than those between the Control and NoSurf (Figure 3b) in particular at the shallow and middle depths, 310

As shown in
indicating that the CHT process within the soils influences the soil thermal regime as well, although its effect is not as strong as those due to infiltration from the surface .
During melting periods in spring when air temperature is higher than soil temperature, meltwater infiltrates into the soils along with warmer water temperature and warms the soils, as manifested by higher simulated soil temperatures in Control than either NoSurf or NoConv. However, in Figure 3 temperature difference between soil layers. If the fluxes move from a higher temperature layer to a lower temperature layer, the low-temperature layer is heated up, and vice versa. It is interesting that in 320 comparison to Control-NoSurf (Figure 3c), more negative differences (in blue) exist in Control-NoConv ( Figure 3c). It implies the liquid migration within the soils is more frequent to exert cooling effects on the thermal regimes than the surface infiltration.  pattern of UWC is also different from the pattern of soil temperature in the same year (Figure 3b, c) where no occurrences of temperature difference are observed in the shallow depths. It implies due to relatively smaller water migration magnitudes during the melting period of this year compared to the neighbouring years, CHT promotes only the phase change, producing more liquid water from ice, but is unable to perceptibly increase soil temperature.

Shallow depths 345
By contrasting the results in the shallow depths of NoSurf and NoConv with Control, the effects of CHT were quantified as shown in Figure 5 and Apart from the heating effect imposed, an opposite, cooling effect is observed in the shallow depths, indicated as negative differences in Figure 5a and Figure 6a. It reduced soil temperature by up to -5 °C in some specific durations during the melting period in spring and the freezing period in fall by contrasting the results of Control with NoSurf and NoConv. The cooling effect is mainly related to upward water flow driven by hydraulic gradient in the melting periods and negative temperature 365 differences between the low-temperature surface and the high-temperature soils when infiltration happens.
We already draw the finding from Figure 3 that more cooling effects were introduced by the convective processes within the soils than those due to infiltration. It becomes more obvious by comparing Figure   6a showing Control-NoConv with Figure 5a showing Control-NoSurf.. Moreover, Figure 6a  It was not the same in 2009 spring, when a prolonged zero-curtain period was simulated and water flow in soils was suppressed. As a result, marginal effects of CHT were observed over this period. 380 In the summer when the zero-curtain has completely ended, the soils held a relatively stable soil moisture content. In this period, liquid water mainly percolated through the soils at a slow rate. The rate could sometimes reach half of the peak liquid flux in spring melting at its maximum. However, only a small increase of about 0.1 to 0.5 °C in soil temperature, or approximately 10% of the heating effect in spring, could be caused by convective heat accompanying with water migration. 385

Middle depths 400
Differing from the strong effects at the shallow depths, the effects of CHT on thermal and hydrological regimes at the middle depths of the active layer are not so much pronounced, as shown in Figure 7 and Another notable dissimilarity to the shallow depths is the apparent incoincidence between the occurrences of CHT and the peaks of water migration at the middle depths. When the vertical advection 415 occurs within the middle depths, the small amount of inputting heat along with the advection can hardly satisfy the consumption of ongoing phase change, which requires a large amount of heat, and thus usually impossible to directly increase soil temperature of the lower layer. However, this process alters the thermal gradients of the soil column, which gradually influencing the total thermal regime. This is a delayed and slow responses, resulting in asynchronous occurrences of spikes in temperature and water 420 fluxes as shown in Figure 7 and Figure 8.

Deep depths 430
The thermal impacts of CHT were minimal at the deep depths as shown in Figure 9a and Figure 10a. Accordingly, the water flow rarely occurred at the 2.45 m depth (Figure 9b and Figure 10b), with a frequency much less than that at the shallow and middle depths. The soil temperature in many thawing periods remained at zero degree (Figure 9c and Figure 10c). According to the study of Romanovsky and Osterkamp (2000), CHT associated with advection of unfrozen pore water no longer impacts soil 435 temperature when the ambient soils hold a temperature close to the frozen point same as the migrating liquid. The existence of temperature gradient between depths is a prerequisite for inducing thermal impacts of CHT. In the deep depths, however, soil temperature slightly fluctuates throughout a year and only tiny differences in temperature from that of advective unfrozen water has produced. Therefore, some marginal temperature differences (less than 0.5 °C ) were observed in this study by comparing

Twofold thermal impacts of convective heat transfer
This study has investigated two types of liquid CHT, i.e., the one due to infiltration from surface snow melt or rainfall and the other occurring within the soil column driven by hydraulic gradient, using a numerical modelling approach. During the thawing periods, soil temperature generally has a declining 455 trend from the surface downward and along the depth. Thus, the infiltrative water moves downward with warmer temperature and imposes a heating effect on the soils passing through, likely to accelerate the process of phase change, especially in the later spring. This mechanism can explain some observations that sudden warming events occurred at certain depths during the spring melting periods as reported in the previous study (Hinkel et al., 2001). 460 However, CHT also probably produces a cooling effect within the active layer. The actual role of CHT at specific time depends on the direction of the liquid flow and the temperature difference along the flow path at that time. In the case that air temperature and surface temperature rapidly drop to below the subsurface soil temperature, the water flow from the ground surface to the soil layer may reduce soil temperature, as demonstrated in our contrasting experiments where soil temperature in Control, which is 465 with full consideration of CHT, was simulated to be lower than that in NoSurf, which ignores infiltrative convective heat, at the shallow depths (0-0.2 m) in some periods. The other cause of cooling is related to upward water migration, such as return flow simulated in the SHAW model, in the thawing period, when the lower depth is colder than the upper depth in the soils. By contrasting Control-NoSurf with Control-NoConv, we found many cooling events occurring at the middle depths (0.4-1.3 m) within the soils and 470 are associated with the upward water migration driven by hydraulic gradient, resulting in higher simulated soil temperature simulated in NoConv (which completely removes the CHT process) than in Control. Some previous studies (Gao et al., 2020;Li et al., 2016) has reported that the melting occurring at the permafrost table provides water supply to the upper depths. The consequent impacts on the thermal and hydrological regimes of the entire active layer caused by the upward liquid movement also have been 475 reported (Chen et al., 2019;Cui et al., 2020). Our study strengthens those existing studies by quantifying and explaining such effects from a modelling perspective. In addition, Kurylyk et al. (2016) mentioned the potential thermal impact coming from lateral discharges in permafrost regions in spite of relatively https: //doi.org/10.5194/tc-2021-191 Preprint. Discussion started: 30 August 2021 c Author(s) 2021. CC BY 4.0 License. less magnitude. Unfortunately, it is not investigated in this study because the one-dimensional SHAW model ignores lateral water migration from the perimeter into the soil column due to soil anisotropy, and 480 it may lead to some uncertainty regarding to the simulation of water flux within the active layer.
Summer rainfall is believed to have an important role in modulating the thermal regime in the active layer (Wright et al., 2009;Zhang et al., 2021). Kane et al. estimated heat transfer due to the rainwater infiltration into the shallow layer may be twice more than the conductive heat. Rachlewicz and Szczuciński (2008)also postulated that non-conductive heat due to rainwater infiltration is particularly 485 important for the thermal regime in the upmost soil about 5 cm deep. However, this study shows the effects of CHT due to rainfall in summer were much less in magnitude than in the spring melting periods ( Figure 5a). In Figure 5b, the downward water fluxes (shown as positive values) responded well to the summer rainfalls in the near surface ground, whereas the impacts on soil temperature (Figure 5a) in this depth induced by CHT are minimal. Those findings are not contradicted each other. The summer rainfall 490 has multifaceted non-conductive effects, including cooling the topsoil due to amplified evapotranspiration from the ground surface, modifying the soil properties such as thermal capacity and conductivity by adding more liquid water into the soils, rapidly transporting external heat to the soils through percolation, and providing heat to the melting process occurring at the freeze-thaw front as a heat source when additional liquid water accumulates above the front (Zhang et al., 2021). In this study, 495 hydraulic and hydrological functions of precipitation are the same in the scenarios, therefore, only the effect of rapid transportation of external heat down to the soils are connected to the CHT process under investigation, which was found to be of less importance among the multiple effects brought by the summer rainfall.

Effects of soil moisture migration in late spring 500
In permafrost regions, soil moisture migration within the active layer is a major form to support CHT.
The liquid water migration at the shallow depths occurred most frequently during the spring melting periods as simulated, transporting considerable heat to the low-depth soils and inducing remarkable thermal impacts on soil temperature in line with these water migration events. Measurements of UWC at some typical permafrost sites indicate that during late spring when ground ice melts, the UWC rapidly 505 rises to the highest before gradually dropping back to the field capacity till summer (Boike et al., 1998). Before thaw begins, excessive ground ice accumulates at the shallow layers due to lowered soil permeability in the freezing process that inhabits the upper liquid water from percolating into the depth, and the presence of potential gradient between the freezing front that continues to move downward and the underlying unfrozen layer. The segregation potential of frozen soil drives the liquid flux moving 510 upward to the front. As a consequence, the shallow frozen layers tend to hold excessive ice content much more than the liquid equivalent can be held (i.e. field capability) in the melting soil (Perfect and Williams, 1980;Chen, 1982). SHAW considers the decrease in permeability due to growth of soil ice, but ignores the mechanism of segregated ice. Despite this flaw, at the beginning of thaw, nearly saturated liquid water can be simulated and the portion beyond the field capacity moves downward or upward as return 515 flow. It explains the formation of frequent and intense water migration occurring in the late spring, which makes strong CHT possible in those specific depths and periods.

Limitations
Existing observation-based studies indicate the unfrozen pore water can still migrate under the capillary force and van Der Waals force, even when the soil is completely frozen (Fisher et al., 2020;Kane and 520 Stein, 1983). The SHAW model is in theory unable to simulate this process in the completely frozen periods. Therefore, the discrepancies in simulated soil temperature in January 2010 are actually linked to the extra snowmelt calculated as illustrated in Figure 2. Those snowmelt affects the temperature on the surface (0.0 m) and consequently creates a temperature gradient by which the thermal regime at the shallow depths is affected via conduction as depicted in Figure 3b and c. 525 The SHAW model assumes that the direction of vapor flux is the same with the liquid water and adopts a simplified consideration of air flow in the soils. It may lead to miscalculate the vapor convection.
According to previous studies (Li et al., 2010;Yu et al., 2020), the evapotranspiration together with the CHT due to vapor flow plays an important role in the near surface soils in the thawing periods. Apart from the convective effect, air fluxes passing through the soils may also alter thermal properties such as 530 freezing point (Ming et al., 2020) or infiltration rate (Prunty and Bell, 2016). Such oversimplified assumptions in SHAW are possible factors contributing to a prolonged zero-curtain period in the simulation. In addition, SHAW permits long term coexistence of mixed solid-liquid state in the physics.
In reality, the inhomogeneity in soil property and the interference of surrounding conditions usually make https://doi.org/10.5194/tc-2021-191 Preprint. Discussion started: 30 August 2021 c Author(s) 2021. CC BY 4.0 License. it hard to maintain a long-term coexistence (Akyurt et al., 2002). In wake of the weaknesses in physics 535 implemented in the SHAW model, we focused on investigating the role of CHT due to infiltration and liquid migration through the soils while maintaining the rest all the same in the scenarios for comparison.
By subtracting the results from the two scenarios with modified models from that of the control scenario with the original model, the uncertainties associated with those weaknesses will be reduced to the greatest extent and the findings are thus more reliable. 540 The SHAW model implements a special Newton-Raphson procedure to solve energy and mass balance equations, in which automated division of finer time steps is invoked if the solution is not satisfactory.
In this process of iterating over finer time steps, high quality upper and lower boundaries are necessary to maintain a high simulation accuracy (Chen et al., 2019;Flerchinger, 1991). However, as a byproduct of this process, the importance of conduction resulting from the boundaries are amplified as the extra 545 iterations proceed and as a consequent, the effects of nonconductive heat transfer are likely to be underestimated.

Conclusions
This study utilized SHAW model in a typical permafrost distributed area, the Tanggula site at the eastern Qinghai-Tibetan Plateau, to explore and quantify the effects of liquid CHT on the active layer thermal 550 regime. By modifying the SHAW model, we set up a control experiment consisting of three scenarios representing the cases with full, partial or no consideration of CHT in the SHAW model. The following conclusions have been concluded: (1) The SHAW model demonstrated good performance in simulating soil temperature and moisture dynamics in the active layer. The NSE for the simulated temperature and moisture content in most of soil 555 layers exceed, respectively, 0.7 and 0.45 in both calibration and validation periods.
(2) Liquid CHF is most likely to occur during the later spring and summer on the QTP when the frozen ground at the shallow (0-0.2 m) and middle (0.4-1.3 m) depths had completely thawed. The infiltrative snowmelt and precipitation from ground surface into the active layer is the major form of CHT in permafrost regions. Only minimal influences of convective heat were found in freezing periods. 560 (3) In the shallow depth (0.0 m to 0.4 m), CHT is more active in the spring melt period than in summer.
During the melting period in spring, the differences in soil temperature simulated with or without https://doi. org/10.5194/tc-2021-191 Preprint.