Convective heat transfer (CHT) is one of the important processes that
control the near-ground surface heat transfer in permafrost areas. However,
this process has often not been considered in most permafrost studies, and
its influence on freezing–thawing processes in the active layer lacks
quantitative investigation. The Simultaneous Heat and Water (SHAW) model,
one of the few land surface models in which the CHT process is well
incorporated into the soil heat–mass transport processes, was applied in
this study to investigate the impacts of CHT on the thermal dynamics of the
active layer at the Tanggula station, a typical permafrost site on the
eastern Qinghai–Tibet Plateau with abundant meteorological and soil
temperature and soil moisture observation data. A control experiment was carried
out to quantify the changes in active layer temperature affected by vertical
advection of liquid water. Three experimental setups were used: (1) the
original SHAW model with full consideration of CHT, (2) a modified SHAW
model that ignores CHT due to infiltration from the surface, and (3) a
modified SHAW model that completely ignores CHT processes in the system. The
results show that the CHT events occurred mainly during thaw periods in
melted shallow (0–0.2 m) and intermediate (0.4–1.3 m) soil depths, and their
impacts on soil temperature at shallow depths were significantly greater
during spring melting periods than summer. The impact was minimal during
freeze periods and in deep soil layers. During thaw periods, temperatures at
the shallow and intermediate soil depths simulated under the scenario
considering CHT were on average about 0.9 and 0.4
Permafrost is defined as the ground that remains frozen consecutively for more than 2 years (Zhao et al., 2010) and is mainly distributed at high latitudes and cold alpine areas, such as the Antarctic, Arctic, and Qinghai–Tibet Plateau (QTP) (Zhang et al., 1999). Given the current warming trends in most of the Earth's permafrost areas (Biskaborn et al., 2019), significant changes in permafrost dynamics are likely to occur, and the local ecosystem and environment have already been seriously influenced by regional hydrological and thermal changes caused by permafrost degradation (Cheng and Wu, 2007; Jin et al., 2009; Jorgenson et al., 2001; Tesi et al., 2016). It is thus very essential to understand thoroughly the thermal and hydrological processes in the soil in frozen ground regions.
It is generally recognized that ground heat transfer is more than a single
heat conduction process controlled by upper and lower boundary conditions
but a complex system that accounts for both conductive and non-conductive
heat transfer (Kane et al., 2001; Putkonen, 1998). Non-conductive heat
processes refer to all those heat transfer processes that can significantly
impact the thermal regime but are not explicitly described by heat conduction
theory, including the following: (1) latent heat exchange, (2) vapor convective heat
transfer (CHT) caused by vapor pressure gradients or thermal gradients
(Cahill and Parlange, 1998), and (3) CHT due to infiltration of snowmelt water
and rainwater from the surface and due to advection within soils (Scherler et
al., 2011; Woo et al., 2000). Despite the predominance of thermal conduction
in permafrost regions, the role of non-conductive processes on the
freeze–thaw cycles of the active layer cannot be ignored (Kane et al.,
2001). Vapor fluxes between soils due to temperature and pressure gradients
(Cahill and Parlange, 1998; Halliwell and Rouse, 1987) and soil moisture
evaporation (Roth and Boike, 2001; Shen et al., 2015) usually exert a
cooling effect on soil thermal regimes which is used to protect engineering
infrastructure from frost heave damage in permafrost regions (Cheng, 2004;
Cheng et al., 2008). Migration of liquid water can usually be forced by
gravitational, pressure, or osmotic pressure gradients in soils during thaw
periods. During spring snowmelt and summer rainfall, a rapid temperature
increase of about 2 to 4
Understanding the impact of CHT on frozen ground is important for the accurate simulation of ground temperature and associated hydrology in permafrost regions in the context of global climate warming. Although some convective heat effects have been observed, they are often produced by simultaneous processes such as heat conduction, advection and convection, and phase changes. In situ instrumentation is still limited to accurately measuring key thermal and hydrological soil variables. It is challenging to isolate the sole impacts of CHT from the totality of heat transfer processes in the soil (Hasler et al., 2008; Pogliotti et al., 2008).
Physically explicit numerical models are effective tools for isolating the impact of a single process from the overall system. These models could provide information that is otherwise impossible through observation techniques. Most existing land surface models such as Noah land surface model (LSM) and Community Land Model (CLM) only account for heat conduction and phase change in the energy budget despite their extensive use in modeling processes in cold regions (Gao et al., 2019; Guo and Wang, 2013; van der Velde et al., 2009; Wu et al., 2018). Neglecting the CHT mechanism in these models generally leads to increased uncertainty due to physical inadequacies. The demand for complete modeling of permafrost changes has therefore recently prompted interest in the development of simulation tools for coupled heat transport and variable hydrological processes to account specifically for CHT. A number of traditional schemes for soil heat transport have been further developed with enhanced vapor and/or liquid CHT processes and have been shown to be effective in cold regions (He et al., 2018; Kurylyk et al., 2014; Wang and Yang, 2018). Furthermore, researchers have recently begun to formulate soil heat and water transport processes within a three-dimensional framework to provide a more reasonable physical expression for vertical and horizontal heat and mass transport (Orgogozo et al., 2019; Painter et al., 2016). By using these advanced models, the role of CHT on the permafrost thermal regime, especially the vapor CHT, was provisionally explained. Wicky and Hauck (2017) developed a numerical model considering air flow in permafrost talus slopes and revealed the pronounced seasonality of the air flow cycle on talus slopes and considerable seasonal differences in the effects on soil temperature. Yu et al. (2018, 2020) quantified the thermal responses to different types of vapor migration associated with evaporation and air flow, respectively. Luethi et al. (2017) estimated the heat transfer efficiency of vapor and liquid convection. However, relatively few studies have examined liquid CHT processes in a permafrost context. Kurylyk et al. (2016) developed a three-dimensional coupled soil heat and water model to investigate the effects of runoff on soil temperature. Recently, M. Zhang et al. (2021) quantified the energy flux of infiltrative CHT during a summertime rainfall event and reported that the thermal impacts of CHT were not pronounced compared to other energy transfer pathways. While their studies improve our understanding of the role of CHT in altering permafrost thermal dynamics, they focused on specific permafrost conditions or single events, and the established methods were difficult to transfer to other regions with conditions dissimilar to those in these study regions.
The Simultaneous Heat and Water (SHAW) model is one of the well-known one-dimensional coupled hydraulic–thermal models that integrates mass and energy transfer processes of the atmosphere–vegetation–soil continuum into a simultaneous solution (Flerchinger and Saxton, 1989a). The SHAW model is one of the few land surface models (LSMs) that considers the detailed physics of the interrelated mass and energy transfer mechanisms, including precise convective heat transport processes of liquid water and vapor (Kurylyk and Watanabe, 2013), making it advantageous for demonstrating the important interactions between soil water dynamics and frozen soil thermal regimes in permafrost regions (Flerchinger et al., 2012). In addition, SHAW applies a special iteration scheme in which a time step is subdivided into multiple sub-time steps to control the error from the previous step in solving the mass and energy balance and to strictly enforce the mutual coupling of the hydrological and thermal processes (Flerchinger, 2000). The SHAW model has many applications in permafrost regions, including the studies of permafrost hydrological and thermal processes (Chen et al., 2019; Cui et al., 2020), permafrost evolution (Wei et al., 2011), and frozen ground responses to climate and land ecosystem changes (Huang and Gallichand, 2006; Kahimba et al., 2009; Link et al., 2004; Zuo et al., 2019). Previous studies have indicated that SHAW can simulate the dynamics of soil temperature, soil moisture (Flerchinger and Pierson, 1997), and the freeze–thaw cycles (Flerchinger and Saxton, 1989b) that occur repeatedly in the active layer with good accuracy. The fine consideration of CHT processes, the mutual coupling of hydrothermal processes, and the broad applicability render the SHAW model capable of investigating the impacts of CHT on permafrost thermal regimes.
Therefore, this study uses the SHAW model to quantify the impacts of liquid CHT on the soil temperature and moisture in the active layer through numerical modeling at a typical permafrost site, i.e., the Tanggula (TGL) site on the QTP, China. The SHAW model was modified to exclude the CHT processes, and then control experiments were implemented to simulate comparative scenarios with or without CHT included in the model. This enables precise and separate quantification of the thermal impacts of liquid CHT from different sources such as precipitation infiltration, snowmelt, and ground ice melt, which has never been accomplished in previous studies. The specific objectives are (1) to illustrate the characteristics of CHT events in time and depth, (2) to quantify the sole impacts of liquid CHT on the thermal regime of the active layer, and (3) to elucidate the interplay of heat and soil moisture during the freezing–thawing process in the active layer.
The SHAW model was developed to simulate heat, water, and solute transfer
within a one-dimensional profile which includes the effects of plant cover,
snow, dead plant residue, and soil. The model stratifies the soil column into
soil layers. For each soil layer, the net energy budget is equal to the sum
of conductive heat flux, CHT from liquid and vapor migration, latent heat
from water phase change, and temperature change. The one-dimensional energy
balance equation for each layer is
The diffusion equation for the soil moisture of each layer is
The SHAW model incorporates the CHT processes of the liquid and vapor flux into the energy conservation equation, making it possible to portray complete water–heat interactions that frequently occur in the freezing–thawing processes in permafrost regions. In this study, we designed a control experiment with three scenarios to represent the full presence, partial presence, and full absence of liquid CHT in the model by modifying the model codes. The same forcing data at a typical permafrost site, i.e., the TGL, and the same parameter values were used for the three modified models. The impacts of liquid CHT on the active layer dynamics are quantified as differences in soil temperature and moisture content by contrasting the results of the three scenarios.
The control experiment consists of three scenarios.
Note that in the NoSurf and NoConv setups, we removed only the heat fluxes
and exchanges associated with water movement and retained water movement
itself, which is necessary to maintain the water balance in each soil layer.
In the SHAW model, we found that the simulated direction of vapor flux did
not match well the real vapor cycle, so the convection associated with the
vapor remained intact in the three setups to exclude the impacts of vapor
CHT in this analysis. The resulting differences between the NoSurf/NoConv
and Control simulations, each configured by the same model settings
including the same meteorological forcing data, lower boundary conditions,
and calibrated parametric values, thus reflect the effects of liquid CHT on
the active layer dynamics. Higher simulated soil temperatures in the Control
than in the other two scenarios imply a positive thermal impact of CHT on
the active layer, and if lower, a negative one. We defined a CHT event as a
ground temperature deviation of more than 0.1
A typical permafrost site, the TGL site on the QTP, was selected for this
study because of long-term, quality-assured observations of the active layer
and deep permafrost in parallel with meteorological observations at high
temporal resolution. Due to the ideal representativeness to
elevation-controlled permafrost on the QTP, this site has been widely used
for alpine permafrost research such as permafrost hydrothermal
characteristics (Li et al., 2019), permafrost response to climate change
(Zhu et al., 2017, 2021), and permafrost process modeling (Hu
et al., 2015; Li et al., 2020). The TGL site (
Air temperature and precipitation
Installed instruments include an automatic weather station that measures air
temperature, wind speed and direction, humidity, shortwave and longwave
radiation (upward and downward), air pressure, snow depth, and
precipitation, as well as an active-layer monitoring system that measures soil
temperatures and moisture contents at the depths of 0.05, 0.1, 0.2, 0.4,
0.7, 1.05, 1.3, 1.75, 2.1, 2.45, and 2.8 m below the surface. The time series
of half-hourly air temperature, relative humidity, wind speed, precipitation,
and shortwave radiation at 2 m collected by the automatic weather station
at the TGL site from 2008 to 2010 were used to run the SHAW model with a
time step of 1 h (Fig. 1a). In the SHAW model, precipitation is
assumed to be snowfall when air temperature is below 1
In addition to the hourly meteorological data from the TGL site as driving data, 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 estimate them based on the air temperature at the time.
The soil column was stratified into 13 layers corresponding to the observation depths at the TGL site, including five layers (centered at 0.00, 0.02, 0.05, 0.10, and 0.20 m) as shallow depths, five layers (centered at 0.40, 0.50, 0.70, 1.05, and 1.30 m) as intermediate depths, and three layers (centered at 1.75, 2.10, and 2.45 m) as deep depths. The SHAW model defines a special soil layer at the depth of zero that accounts for heat and water exchange at the interface between the plant residue layer and the soil. The shallow soil depths were densely discretized to accommodate rapid hourly variations in soil temperature and moisture near the ground surface. Table 1 shows the vertical discretization of the TGL soil profile and the measured volumetric fractions of sand, silt, and clay and the bulk density for each layer.
The SHAW model depends on accurate lower boundaries, which are usually
specified at a shallow depth to allow accurate simulation of coupled
water–heat exchange processes (Chen et al., 2019). In this study,
observations at a depth of 2.8 m near the bottom of the active layer were
set as lower boundaries. The observed daily soil temperatures at this depth
constrain the heat fluxes through the lower boundary. The lower boundary of
soil moisture content (both ice and UWC) was determined by the model
following an empirical equation as a function of soil temperature by
confining the liquid water equivalent maxima of 0.25 m
For all scenarios, initial soil temperature and soil moisture profiles were
generated with a three-decade spin-up using forcing data cycling from
2008 to 2010 until differences in soil temperature and moisture content are
reduced to less than 0.1
According to a previous study at the same TGL site (Liu et al., 2013), the
SHAW model with the default parameter values simulated surface energy fluxes
and soil temperatures well, except for soil moisture, which was seriously
underestimated. We calibrated the four main hydraulic parameters (Table 1),
i.e., saturated hydraulic conductivity, air-entry potential, saturated
volumetric moisture content, and pore-size distribution index, relating to
soil moisture in the model, while keeping the other soil parameters as
default values. Data from 2008–2009 were used for calibration and 2010 for
validation. The model was run with an hourly time step, and the results were
then aggregated to a daily scale to facilitate comparisons and analyses. The
ranges of hydraulic parameter values were roughly determined with reference
to previously studies (Chen et al., 2019; Liu et al., 2013; Wu et al.,
2018). To find the best parameter combination and measure model uncertainty,
1000 independent parameter combinations were randomly generated by the Latin
hypercube sampling method in conjunction with the a priori ranges. We
restricted the values of sampling parameters in adjacent layers to assume
that adjacent soil layers have similar textures. Then the 1000 combinations
were used to drive the model one by one, and their outputs were compared and
evaluated to determine the optimal parameter values for each soil layer. Two
metrics, including the Nash–Sutcliffe efficiency coefficient (NSE) and root
mean square error (RMSE), were used to quantify the performance of the
parameter combinations:
The most optimal parameter values from the 1000 combinations, as presented in Table 1, were consistently applied to all three scenarios designed in Sect. 2.2 to eliminate the influence of parameter values on the inter-scenario comparison.
Key soil parameter values for the TGL soil profile:
Figure 2 shows the SHAW simulations of soil temperature (left panels) and
UWC (right panels) with the most optimal parameters and the observations at
depths of 0.05, 0.1, 0.4, 1.05, and 2.45 m at the TGL site, as well as the
95PPU of model outputs as determined by all 1000 random parameter
combinations. Overall, both the 95PPUs and the optimal outputs confirm a
good capability of the SHAW model to simulate the complex freezing and
thawing processes in the active layer given reliable lower boundaries.
Seasonal variations in both soil temperature and soil moisture in the active
layer of the TGL were successfully captured. The 95PPUs of soil temperature
associated with the 1000 parameter combinations are narrow in band and cover
the observations well at each depth, indicating the good performance and low
uncertainty of the SHAW model in modeling soil temperature at the TGL site.
According to our experiments, saturated hydraulic conductivity is the most
important parameter that affects the simulated soil temperature. Although
the 95PPUs of the simulated UWC also roughly cover the observations, a wide
band and overestimation at 0.4 and 1.05 m depths relative to the
observations indicate a large uncertainty in simulating UWC and call for a
necessary parameter calibration. Saturated hydraulic conductivity and
saturated volumetric moisture content were identified as the most important
parameters controlling simulated UWC and were treated carefully. At the
intermediate depths where low liquid contents were observed, optimal
parameter values are picked from the random parameter combinations for these
layers that both simulate lower UWC and ensure good accuracy of the
simulated soil temperature. The simulated soil temperatures with the optimal
parameter combination were in particularly good agreement with the observed
temperatures at the TGL site during both the calibration and validation
periods (Fig. 2). Specifically, the NSE values between the simulated and
observed soil temperatures are above 0.70 in most soil layers in both
periods, except for the value at 1.05 m depth in the validation period,
and are highest (up to 0.90) in the shallow layers. The RMSE values for soil
temperature decrease with soil depth because there is less interannual
variation in the deep layers than in the shallow layers. Despite the
relatively lower performance in UWC, simulation of UWC with optimal
parameters still produced NSE values greater than 0.42 in all soil layers
and RMSE values of about 0.05 m
Simulated (solid lines) and observed (dashed lines) daily soil
temperature (ST; left panels) and unfrozen water content (UWC; right
panels) at 0.05
During the spring thaw period in each year, the observed temperatures (Fig. 2a–e) increased rapidly from the negatives to the positives, but the simulated soil temperatures exhibited an obvious prolonged duration of the zero-curtain effect, which delayed the warming of soil temperature by days. Accordingly, the 95PPUs of the simulated soil temperatures from 1000 random parameter combinations also exhibited larger intervals in spring thaw periods than in other seasons. This effect was especially strong in 2009. The formation of zero curtain is a joint result of multifaceted thermal processes including evapotranspiration, phase change, heat conduction, and convection during freeze and thaw periods (Outcalt et al., 1990) and is more obvious during the thawing process than the freezing process (Jiang et al., 2018). The overestimation of the zero-curtain duration in the SHAW simulation is primarily related to the irrational vapor motion and simplified phase change between ice and liquid.
In January 2010, an overestimation of soil temperature was observed throughout the entire soil column (Fig. 2a–e). However, this phenomenon did not occur in the same month in 2008 and 2009. It is certain that the observed discrepancies result from unusually warm air temperature (Fig. 3). These anomalies also caused additional snowmelt events with ca. 0.5 mm of snow water equivalent in this month (Fig. 3).
Unusual warm air temperature in January 2010, presumably related to overestimation of modeled soil temperature that month, and simulated hourly snowmelt, also influenced by air temperature. The dates (month/day) at the top of the figure indicate when the snowmelt events occurred.
The simulations of hourly soil temperature under the Control scenario using the original SHAW model with full CHT processes included are shown in Fig. 4a. The differences in the soil temperature profiles between the Control and the two other scenarios, i.e., partial (NoSurf) or full (NoConv) exclusion of CHT in the model, are presented in Fig. 4b and c, respectively, which depict the distribution patterns of CHT occurrence in time and depth, as well as the intensity of soil temperature variations due to CHT. The effects of CHT appeared primarily in the thaw periods of 2008 and 2010, as shown in Fig. 4b and c, and resulted in a pronounced increase in soil temperature. However, during the same periods of 2009, no noticeable temperature differences were simulated between Control and NoSurf for the entire soil column, and only minor differences were simulated between Control and NoConv at intermediate depths. Since vapor convection was not altered, those effects were due entirely to the partial or complete presence of CHT due to surface infiltration and vertical advection within the soil column. The differences in soil temperature were noticeable even at shallow depths in January 2010 (Fig. 4b and c), when soils at those depths were frozen and impermeable. This phenomenon coincided with the occurrence of extra snowmelt events during this period, as shown in Fig. 3. Although snowmelt did not infiltrate into the underlying impermeable soil layers, it moved downward into the uppermost soil layer (0.00 m) during these periods. In the Control scenario, the sensible convective heat flux due to percolation of snowmelt water altered the temperature of the uppermost soil layer and consequently the temperature gradient there. These temperature perturbations were then transmitted to the near-surface soil layers by conduction. In the other two scenarios, in which the CHT process at the ground surface was excluded from the model, the same amount of snowmelt water was transported to the top soil layer, but no convective heat was transferred and thus no thermal disturbance occurred in the shallow soil layers as in the Control, as manifested in the temperature deviations in the shallow layers when contrasting the scenarios. It suggests that CHT could also have indirect thermal impacts during freeze periods, provided that snowmelt occurs during these periods in response to changes in air temperature.
As shown in Fig. 4b and c, the occurrence of CHT became increasingly delayed with increasing soil depth, with the largest delay occurring at the deepest location. The shallow depths are characterized with long thaw periods spanning from late spring to summer, with large thermal gradients and active water migration between soil layers so that CHT at those depths has considerable impacts on the thermal regime. In contrast, the thermal effects of CHT are much smaller at deeper depths, where the temperature gradient and water motion are relatively modest. The differences between the Control and NoConv (Fig. 4c) are more evident than those between the Control and NoSurf (Fig. 4b) in particular at the shallow and intermediate depths, suggesting that the CHT process within the soil also influences the soil thermal regime, although its effect is not as strong as that due to infiltration from the surface.
During spring thaw periods when air temperature is higher than ground temperature, snowmelt infiltrates and warms soils with warmer water temperature, as manifested by higher simulated soil temperatures under Control than under NoSurf or NoConv. However, Fig. 4 also shows the moments when the simulated temperature is lower under the Control scenario than under NoSurf and NoConv, signifying the existence of a cooling effect of CHT, although this cooling effect is much weaker than the heating effect. The culprit is the direction of convective flux, as well as the temperature difference between soil layers. When the flows move from a higher temperature layer to a lower temperature layer, the low-temperature layer is heated, and in the reverse direction, the high-temperature layer is cooled. It is interesting to note that compared to Control–NoSurf (Fig. 4c), there are more negative differences (in blue) in Control–NoConv (Fig. 4c). It implies liquid migration within the soil has more frequent cooling effects on the thermal regimes than surface infiltration.
Simulated hourly ground temperature profiles under the Control
scenario
The UWC differences between the scenarios (Fig. 5) are comparable to soil temperature differences in both space and time. The effects occurred mainly in thaw periods and were attenuated with increasing depth. In late spring 2009, patterns of UWC differences differ markedly from those in the same months of adjacent years (Fig. 5b, c). The 2009 differences are confined to shallow depths, whereas in adjacent years the differences penetrate most soil depths. The 2009 pattern of UWC also differs from the soil temperature pattern in the same year (Fig. 4b, c), in which no temperature differences are observed at shallow depths. This suggests that due to relatively less water migration during the thaw period, CHT only promotes phase change and produces more liquid water from ice this year compared to neighboring years but is unable to noticeably increase soil temperature.
Simulated hourly unfrozen water content (UWC) profiles under the
Control scenario
As shown in Fig. 4a, CHT processes have very non-uniform thermal effects at different soil depths. Therefore, to illustrate the inconsistent impacts of CHT at depth and to identify the driving factors, three specific soil layers, i.e., the layer centered at 0.05 m depth closest to the ground surface and for which observations are available, the layer at 1.05 m depth, which is at the middle depth of the entire active layer, and the layer at 2.45 m adjacent to the bottom of the active layer, were selected to represent the shallow (0–0.2 m), intermediate (0.4–1.3 m), and deep depths (deeper than 1.75 m), respectively, where very different impacts of CHT were observed.
By contrasting the hourly results at the shallow depths of NoSurf and NoConv
with those of the Control, the effects of CHT were quantified, as shown in
Figs. 6 and 7. The patterns are similar for all shallow depths
(above 0.2 m). Generally, the effects of CHT on the thermal regime are
strong at the shallow depths, as shown by the soil temperature differences
at 0.05 m depth in 2008 and 2010 obtained from both Control–NoSurf and
Control–NoConv (Figs. 6a and 7a). In the figures, positive
differences in soil temperature represent the heating effects of CHT at the
shallow depths, while negative values represent the cooling effects. The
convective heat estimated in Control acts as an extra heat source during the
spring melting periods when CHT occurred – the source that not only provided
heat for the phase changes from ice to water but also warmed the soils and
caused an average increase in soil temperature of about 0.9
Apart from the imposed heating effect, an opposite cooling effect is
observed at shallow depths, indicated as negative differences in Figs. 6a
and 7a. Soil temperature decreased by an average of
Figure 4 already shows that more cooling events were triggered by convective processes within the soils than by infiltration. It becomes even clearer by comparing Fig. 7a showing Control–NoConv with Fig. 6a showing Control–NoSurf. Table 2 shows that there are 1757 cooling events in the comparison between Control and NoConv but only 1195 between Control and NoSurf. Moreover, Fig. 7a contains more nonzero values than Fig. 6a. This is plausible because the results of Control–NoConv include the entire impact of CHT, whereas Control–NoSurf includes only a portion of the surface infiltration.
The peaks of liquid water migration in the 0.05 m layer are shown in Figs. 6b and 7b, in which positive values indicate downward flows and negative values upward flows. The downward flows are related to snowmelt events as shown in Figs. 6b and 7b, where only those simulated under Control are shown because the snowmelt events under the three scenarios are nearly identical. It indicates that infiltration of snowmelt is the major source of downward liquid flow during spring. Nevertheless, as the ambient temperature rises, the underlying frozen ground begins to thaw at depth (Fig. 4b), and ground ice melt also partially contributes to the liquid flux. It is difficult to distinguish which fraction of the flux comes from snowmelt and which from ground ice melt. Thus, we used the total liquid flows instead of snowmelt volume to examine the relationship between soil water migration and CHT. Liquid water migration correlates the occurrence of CHT very well (Figs. 6a and 7a). During the zero-curtain durations in 2008 and 2010, soils were repeatedly frozen and thawed. Liquid water migration became more frequent after soils were completely thawed and soil moisture content began to increase. At this time, CHT became more active at this depth. The situation was different in the spring of 2009, when a prolonged zero-curtain period was simulated and water flow in the soils was suppressed. As a result, only marginal effects of CHT were observed during this period.
In summer, when the zero curtain had completely disappeared, the soils had a
relatively stable soil moisture content. In this period, liquid water
percolated mainly through the soils at a slow rate. The rate could sometimes
reach half of the maximum liquid flux during the spring thaw. However, only
a small increase in soil temperature of about 0.1 to 0.5
Hourly soil temperature, water flux, and UWC at 0.05 m depth,
representative of shallow depths, simulated under NoSurf and Control during
the 2008–2010 thaw periods. From top to bottom are as follows:
Hourly soil temperature, water flux, and UWC at 0.05 m depth
simulated under NoConv and Control during the 2008–2010 thaw periods. From
top to bottom are as follows:
The numbers of occurrences of heating and cooling CHT events and the
average temperature deviations caused by CHT at 0.05, 1.05, and 2.45 m depths
at TGL. The deviations of 0.1
In contrast to the strong effects at shallow depths, the effects of CHT on
thermal and hydrological regimes are not as pronounced at the intermediate
depths of the active layer, as can be seen in Figs. 8 and 9, which
show the hourly results at 1.05 m depth, because water migration was
inactive at these depths. However, the characteristics of the occurrences
were similar to those at the shallow depths despite the weaker values.
Temperatures at these depths averaged 0.43
Another notable dissimilarity to shallow depths is the apparent incongruity between the occurrence of CHT and peak water migration at intermediate depths. When vertical advection occurs at the intermediate depths, the small amount of heat along with advection can hardly satisfy the consumption of ongoing phase change, which requires a large amount of heat, and thus it is usually not possible to directly increase soil temperature of the lower layer. However, this process alters the thermal gradients in the soil column, which gradually affects the total thermal regime. This is a delayed and slow response that results in asynchronous spikes in temperature and water fluxes, as shown in Figs. 8 and 9.
Hourly soil temperature, water flux, and UWC at 1.05 m depth, representative of intermediate depths, simulated under NoSurf and Control during the 2008–2010 thaw periods. The same notations as in Fig. 6 are applied.
Hourly soil temperature, water flux, and UWC at 1.05 m depth simulated under NoConv and Control during the 2008–2010 thaw periods. The same notations as in Fig. 7 are applied.
The thermal impacts of CHT were minimal at the deep depths, as shown in
Figs. 10a and 11a and Table 2. Accordingly, water flow occurred
infrequently at a depth of 2.45 m near the bottom boundary of the active layer
(Figs. 10b and 11b), with a much lower frequency than at the shallow
and intermediate depths. Soil temperature remained at 0
Hourly soil temperature, water flux, and UWC at 2.45 m depth, representative of the deep depths, simulated under NoSurf and Control during the 2008–2010 thaw periods. The same notations as in Fig. 6 are applied.
Hourly soil temperature, water flux, and UWC at 2.45 m depth simulated under NoConv and Control during the 2008–2010 thaw periods. The same notations as in Fig. 7 are applied.
This study has investigated two types of liquid CHT, i.e., the one due to
infiltration from surface snowmelt or rainfall and the other occurring
within the soil column due to hydraulic gradient, using a numerical
modeling approach. During thaw periods, soil temperature generally declines
from the surface downward and at depth. Thus, infiltrative water moves
downward at warmer temperatures and exerts a heating effect on the soils
it passes through, likely increasing soil temperature and accelerating the
process of phase change, especially in the late spring. Previous studies
have also observed some CHT effects due to the anomalous fluctuations in
soil temperature during the periods when snowmelt or rainfall infiltrates
into the soil. Kane et al. (2001) and Hinkel et al. (1996) reported the
step-like increase in near-surface temperature by 2 to
4
However, CHT also likely has a cooling effect within the active layer. The actual role of CHT at a given time depends on the direction of the liquid flow and the temperature difference along the flow path at that time. When the air temperature and surface temperature drop rapidly below the subsurface soil temperature, water flow from the ground surface into the soil layer can reduce the soil temperature, as demonstrated in our contrasting experiments in which the soil temperature in Control, which fully accounts for CHT, was lower than that in NoSurf, which ignores infiltrative convective heat, at the shallow depths (0–0.2 m) in some time periods. The other cause of cooling is related to upward water migration, such as the return flow simulated in the SHAW model during the thaw period when the lower depth is colder than the upper depth in the ground. By contrasting Control–NoSurf with Control–NoConv, we found many cooling events occurring at intermediate depths (0.4–1.3 m) within the soils and associated with upward water migration driven by the 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) have reported that the melting occurring at the permafrost table provides water supply to the upper depths. Effects on the thermal and hydrological regimes of the entire active layer due to the upward liquid movement have also been reported (Chen et al., 2019; Cui et al., 2020; Rowland et al., 2011). Our study strengthens those existing studies by quantifying and interpreting such effects from a modeling perspective.
To ensure that the experiment at TGL was not an exception, we performed a
similar simulation (spanning 2015–2018) at another permafrost site (coded
QT08) near the town of Wudaoliang alongside the Qinghai–Tibet highway to
verify the bidirectional thermal impacts of CHT. Since hourly meteorological
observations are not available for QT08, we extracted the atmospheric
forcing at the corresponding point from a reanalysis dataset with a
resolution of 0.1
Summer rainfall was believed to play an important role in modulating the thermal regime in the active layer (Wright et al., 2009; G. Zhang et al., 2021). While Rachlewicz and Szczuciński (2008) postulated that non-conductive heat due to rainwater infiltration was particularly important for the thermal regime in the uppermost soil at about 5 cm depth, Kane et al. (2001) estimated that the CHT due to heavy precipitation likely doubled conductive heat. However, this study shows the effects of CHT due to summer rainfall were much less than during spring thaw periods (Fig. 6a). In Fig. 6b, downward water fluxes (shown as positive values) respond well to summer rainfall in the near-surface ground, while the impacts on soil temperature (Fig. 6a) at this depth due to CHT are minimal. Those findings are not in conflict. Summer precipitation has multifaceted non-conductive effects, including cooling the topsoil through enhanced evapotranspiration from the ground surface, modifying soil properties such as heat capacity and conductivity by adding more liquid water to the soil (Zhou et al., 2021), rapidly transporting external heat to the soil through percolation, and providing heat for the melting process occurring at the freeze–thaw front as a heat source when additional liquid water accumulates above the front (G. Zhang et al., 2021). In this study, hydraulic and hydrological functions of precipitation are the same in the scenarios; therefore, only the effect of rapid transportation of external heat into the soils is associated with the CHT process under investigation, which was found to be of less importance among the diverse effects of summer precipitation. The same weak significance of CHT associated with summer rainfall is also reported by M. Zhang et al. (2021), in which the positive energy flux of rainfall convection into soil layers was low, in contrast to other negative energy fluxes due to increased soil evaporation and latent heat, as well as decreased soil conductivity due to growing soil moisture.
Snowmelt is a main component of spring infiltration that causes CHT from the ground surface and warms the underlying soil layers, as evidenced by both our study and the observation-based studies mentioned above. Normally, as air temperature warms, snowmelt is accompanied by the thawing of the soil, allowing meltwater to freely infiltrate into the soil. This is the main form of snowmelt-induced CHT. However, as shown in our contrasting experiments, the soil temperature of the Control scenario differs from that of the NoSurf and NoConv scenarios even during the periods when no vertical water flux occurs in these layers. This suggests that snowmelt could also have an indirect influence on the soil without explicit infiltration. For example, some snowmelt events took place in January 2010 (Fig. 3) possibly due to a transient increase in air temperature or shortwave radiation, resulting in temperature differences between Control and NoSurf/NoConv at shallow depths (Fig. 4). However, snowmelt could not infiltrate because the ground was still in an impermeable, frozen state at this time. We assume that in this case the temperature at the ground surface was affected by the convective heat carried with snowmelt, although snowmelt can only move downward through the snowpack and reach the ground surface before it drains laterally, which then affects the thermal gradient at shallow depths. Thus, the altered temperature at the ground surface was spread to the lower layers by the changed thermal gradient. Not coincidentally, we also measured some CHT-induced soil temperature changes at intermediate depths, but at the same time no corresponding convective fluxes were observed, which we believe is also part of the indirect convective heat influence exerted from other depths to this depth by conduction. Although this type of heat transfer is accomplished through heat conduction, it is still essentially an indirect convection-induced heat transport.
Moreover, percolation of liquid water within snow leads to a complex spatial
redistribution of snow depths and densities, which strongly regulates the
ground temperature and the active layer thickness in snowpack areas (Magnin
et al., 2017). Zweigel et al. (2021) have reported that redistribution of
snow, taking into accounts snow water percolation, increased ground surface
temperature by 1–2
In permafrost regions, soil moisture migration within the active layer is a major form supporting CHT. Liquid water migration at shallow depths occurs most frequently during spring thaw periods, transporting considerable heat into soils and producing notable thermal effects on soil temperature parallel to these water migration events. Measurements of UWC at some typical permafrost sites indicate that UWC rises rapidly to the highest in late spring as the ground ice in the active layer melts before gradually falling back to field capacity by summer (Boike et al., 1998). Before the thaw begins, excessive ground ice is present in the shallow layers because soil permeability is reduced during the freezing process, preventing the upper liquid water from percolating to depth, and because a potential gradient exists between the constantly downward migrating freezing front and the underlying unfrozen layer. The segregation potential of frozen ground drives the liquid flux upward to the front. As a consequence, the frozen shallow layers tend to hold excessive ice content much more than the liquid equivalent can be held (i.e., field capability) in the melting soil (Cheng, 1983; Perfect and Williams, 1980). SHAW accounts for the decrease in permeability due to growth of ground ice but ignores the mechanism of segregated ice. Despite this deficiency, nearly saturated liquid water can be simulated at the onset of the thaw, and the fraction in excess of field capacity moves downward or upward as return flow. This explains the emergence of the frequent and intense water migration in late spring, which makes strong CHT possible at those specific depths and times.
In addition, Kurylyk et al. (2016) mentioned the potential thermal impacts caused by lateral discharges in permafrost regions, which are relatively small. 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, which may lead to some uncertainty in simulating water flow within the active layer. Recently, three-dimensional LSMs have emerged as found in the recent literature (Endrizzi et al., 2014; Painter et al., 2016; Rogger et al., 2017). Those models couple both horizontal and vertical thermal and hydrological processes at the surface–subsurface and have obvious advantages over one-dimensional models in terms of the physical basis for studying surface–subsurface water migrations and the thermal consequences on permafrost. Although current observations on the QTP cannot meet high data and parameter demands of three-dimensional models, this provides another direction for CHT studies on the QTP.
CHT is a rapid thermal exchange process that generally occurs at hourly intervals and is influenced by soil moisture, so hourly data of high quality are used for the study of CHT. However, due to the harsh natural environment and cumbersome transport, we are unable to obtain a large amount of long-term, high-quality climate and permafrost observation data from multiple sites. Though we have conducted a 3-year long-term experiment at the TGL site that included 2 years of significant CHT impacts (2008 and 2010) and 1 year of relatively weak impacts, which could support investigation of interannual differences of CHT and the associated influencing factors, we still face the lack of high-quality data to enable a spatial and longer investigation into the CHT impacts. The good news is that some new observation sites have been deployed during the ongoing campaign of the second Tibet expedition (Chen et al., 2021), and the data situation for CHT studies is improved.
Existing observation-based studies indicate that the unfrozen pore water can still migrate under the capillary force and van Der Waals force, even when the ground is completely frozen (Fisher et al., 2020; Kane and Stein, 1983). The SHAW model is theoretically unable to simulate this process during the completely frozen periods. It also assumes that the direction of vapor flux is the same as that of the liquid water and adopts a simplified formulation of air flow in soils. This may bias the calculation of vapor convection. According to previous studies (Li et al., 2010; Yu et al., 2020), evapotranspiration, together with CHT due to vapor flow, plays an important role in near-surface soils in thaw periods. Apart from the convective effect, air fluxes passing through soils may also alter thermal properties such as 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 the long-term coexistence of mixed solid–liquid state in physics. In reality, it is hard to maintain a long-term coexistence due to the inhomogeneity of soil properties and the interference of environmental conditions (Akyurt et al., 2002). In this study, we subtract the results of the two scenarios with modified models from those of the control scenario with the original SHAW model, the uncertainties associated with these weaknesses are largely reduced, and the results are thus more reliable.
The SHAW model implements a special Newton–Raphson procedure to solve energy and mass balance equations, in which automated division into finer time steps occurs 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 high simulation accuracy (Chen et al., 2019; Flerchinger, 1991). However, a byproduct of this process is that the importance of heat conduction arising from the boundaries is amplified as iterations proceed, and as a consequence, the effects of nonconductive heat transfer are likely to be underestimated. Therefore, in the TGL application, the inaccurate lower boundary conditions for the SHAW model, particularly soil moisture, which is subject to appreciable measurable errors, also adversely affected the accuracy of the simulation at depth.
In this study, the SHAW model was applied to a typical permafrost area, the
Tanggula site on the eastern Qinghai–Tibet Plateau, to explore and quantify
the effects of liquid CHT on the active layer thermal regime. By modifying
the SHAW model, we conducted 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 were drawn.
The SHAW model performed well in simulating soil temperature and
moisture dynamics in the active layer. The NSE values for the simulated
temperature and moisture content in most soil layers exceed 0.70 and 0.45 in
both calibration and validation periods, respectively. Liquid CHT is most likely to occur on the QTP in late spring and summer
when frozen ground is fully thawed at shallow (0–0.2 m) and intermediate
(0.4–1.3 m) depths. The infiltrative snowmelt and precipitation from the
ground surface into the active layer is the main form of CHT in permafrost
regions. Only minimal influences of convective heat were observed during
freeze periods due to some incidental snowmelt events in winter. At shallow depths (0.0 to 0.4 m), CHT is more active during the spring
thaw period than in summer. During the spring thaw period, the differences
in soil temperature simulated with or without considering CHT had a wide
range from CHT has proven bidirectional thermal impacts on the active layer
temperature, although the heating effect predominates in an annual
freeze–thaw cycle on the QTP. During spring thaw periods, it was simulated
that the soil temperature was on average about 0.9
Site QT08 was set up in 2009 to monitor water and heat dynamics in the
active layer and is located at 35.22
Based on the borehole information, the soil column was stratified into nine
layers (centered at 0.00, 0.02, 0.07, 0.13, 0.23, 0.39, 0.66, 1.11, and 1.84 m) with discrete soil texture types. The values for the vegetation and soil
parameters were determined by the lookup table provided with the Noah land
surface model as in our previous work (Wu et al., 2018). For the remaining
parameters, the default values of the model were used. Since hourly
meteorological data are not available for this site, we extracted the
meteorological forcing at the corresponding point from the gridded China
Meteorological Forcing Dataset (CMFD) with a resolution of 0.1
The Control and NoConv scenarios were simulated at QT08 using the original SHAW model and the modified model (with CHT removed), respectively. The occurrences of heating and cooling events of CHT were counted and analyzed following Eq. (12).
The numbers of occurrences of heating and cooling CHT events and
the average temperature deviations caused by CHT at 0.07, 0.66, and 1.84 m
depths at the QT08 site. The deviations of 0.1
The simulation results at QT08 clearly reflect the bidirectional thermal
impacts of CHT, although the model was not carefully configured, for
example, as it used coarse-resolution forcing data and uncalibrated
parametric values for all soil layers. The role of CHT at QT08 was primarily
to warm the ground during the spring thaw period, along with a small number
of cooling effects (Fig. A1). The magnitude of CHT-induced soil
temperature deviations at QT08 (mean about 0.2
Simulated ground temperature profiles at QT08 under the Control
scenario
Validation of simulation results at different depths at QT08
against the observed daily soil temperatures during 1 January 2015 to
31 December 2018 for
The source codes of the Simultaneous Heat and Water (SHAW) model are available
on the USDA Agricultural Research Service website
(
ZN and LZ conceived and conceptualized the idea; YZ and ZN developed the methodology; YZ, ZN, and HJ performed the analyses; ZN and LZ acquired the funding and provided the resources; ZN supervised the study; YZ wrote the draft version; and ZN, YZ, and HJ reviewed and edited the writing.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors thank the National Cryosphere and Desert Data Center for providing data and the USDA Agricultural Research Service for providing the model. The authors are especially grateful to Tonghua Wu and Jianzong Shi from the Cryosphere Research Station on the Qinghai–Tibet Plateau, CAS, for providing observed soil temperature and moisture content data at the Tanggula site and the QT08 site.
This research has been supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (grant no. 2019QZKK0905-08) and the National Natural Science Foundation of China (grant nos. 41931180 and 41971074).
This paper was edited by Ylva Sjöberg and reviewed by Elchin Jafarov and one anonymous referee.