Published March 14, 2019

Original Research

Core Ideas Simulation of Soil Freezing and Thawing • The SHAW model was used to simu- for Different Groundwater Table Depths late the freeze–thaw process during freeze–thaw periods. Junfeng Chen,* Xuguang Gao, Xiuqing Zheng, • It revealed the effects of Chunyan Miao, Yongbo Zhang, Qi Du, and Yongxin Xu and groundwater table depth on soil freezing and thawing. During freeze–thaw periods, the transformation between phreatic water and • The frost depth and accumulated soil water will change the soil hydrothermal properties and affect the soil freez- negative soil surface temperature ing and thawing in shallow groundwater areas. The purpose of this study was to relationship was determined. determine the effect of four different groundwater table depths (GTDs) and two soil textures on the process of soil freezing and thawing during two successive freeze–thaw periods using the Simultaneous Heat and Water (SHAW) model. The results show that the frost depth was the maximum when the GTD was 1.0 m, and the maximum frost depths of sandy loam and fine were 97.6 and 98.9 cm, respectively. When the GTD was larger than 1.5 m, the maximum frost depth decreased with an increase in GTD, and the maximum frost depth of the soil pro- file was more sensitive to changes in the air temperature. The frost depth of the soil profile was linear with the square root of the accumulated negative soil sur- face temperature (ANST) under different GTDs. The ANST was influenced by the phreatic evaporation, and the soil freezing rate increased with an increase in GTD under the same ANST. This research is significant for the rational development of soil water and heat resources and the study of soil water–heat transfer in shallow groundwater areas.

Abbreviations: ANST, accumulated negative soil surface temperature; GTD, groundwater table depth; SHAW, Simultaneous Heat and Water.

Soil freezing and thawing is a common natural phenomenon in seasonally frozen and areas. China has the third largest area of frozen soil in the world, and the soils are affected by seasonal freezing and thawing in northern China. In shallow ground- J. Chen, X. Gao, X. Zheng, C. Miao, and Y. water areas, the transformation between phreatic water and soil water is extremely strong Zhang, College of Water Resources and Engi- during the seasonal freeze–thaw period. Soil freezing will cause shallow groundwater to neering, Taiyuan Univ. of Technology, Taiyuan 030024, China; C. Miao, First Hydrogeology migrate into the soil profile, resulting in redistribution of soil moisture (Chen et al., 2018; and Engineering Geology Team of Shanxi Miao et al., 2017). Thus, the soil hydrothermal properties are changed and then affect Province, Taiyuan 030024, China; Q. Du, Taigu Water Balance Experimental Field, Bureau of the soil freezing and thawing. Not only does freeze–thaw action change the physical and and Water Resources Survey of chemical properties of soil (Dagesse, 2010; Özgan et al., 2015; Sheng et al., 2015), but it Shanxi Province, Taigu 030800, China; Y. Xu, also affects the soil erosion resistance and has a significant impact on the water and heat Dep. of Earth Sciences, Univ. of the Western Cape, Private Bag X17, Bellville, Cape Town balance in the soil (Guo et al., 2011a; Zhao et al., 2013). Therefore, study of the freezing 7535, South Africa. *Corresponding author and thawing process in soil is important for the rational development of soil water and ([email protected]). heat resources, agricultural production, and project construction. The freeze–thaw cycle of soil is the result of complex effects of meteorological and Received 20 Aug. 2018. environmental conditions on the heat flux of surface water. For many years, investigators Accepted 7 Jan. 2019. have conducted a great deal of research on the effects of snow cover (Iwata et al., 2010; Ling and Zhang, 2003; Osokin et al., 2000; Qiang et al., 2018; Zhang, 2005; Zhou et al., 2013), Citation: Chen, J., X. Gao, X. Zheng, C. Miao, Y. Zhang, Q. Du, and Y. Xu. 2019. Simulation meteorological factors (Frauenfeld and Zhang, 2011; Guo and Wang, 2014; Hirota et al., of soil freezing and thawing for different 2006; Jafarov et al., 2013; Wang et al., 2015, 2016), topography (Ling et al., 2012; Gao et groundwater table depths. Vadose Zone J. 18:180157. doi:10.2136/vzj2018.08.0157 al., 2016; Lin et al., 2010; Yi et al., 2014), and pore size (De Kock et al., 2015; Starkloff et al., 2017; Watanabe and Kugisaki, 2017) on the soil freezing and thawing process during the seasonal freeze–thaw period. The soil freezing and thawing process has been studied by monitoring methods (Kimball et al., 2004; Kong et al., 2014; Naeimi et al., 2012; Sun © 2019 The Author(s). This is an open access article distributed under the CC BY-NC-ND license et al., 2012; Wu et al., 2016b) and numerical models (Gens et al., 2009; Kojima et al., (http://creativecommons.org/licenses/by-nc- nd/4.0/). 2013; Mironov and Karavaysky, 2015; Semenova et al., 2014). Rasmussen et al. (2018)

Vadose Zone Journal | Advancing Critical Zone Science calibrated CoupModel to simulate permafrost temperature at two necessary to strengthen the research on the influence of ground- sites with different snow depths on the delta in the Zackenberg water on the process of soil freezing and thawing. Valley, northeastern Greenland. Younes et al. (2015) simulated The freeze–thaw cycle in the soil is a complex process accom- wintertime soil temperature, soil frost depth, and snow depth for panied by heat conduction, phase change of water, solute migration, a 14-yr period in a highland area of Iran using CoupModel. To pre- and other physical, chemical, and mechanical effects. Thus, various dict water migration in freezing soil, Ming et al. (2016) presented models have been used to simulate and monitor the soil freezing a water migration model that introduced the concept of a migra- and thawing process in many studies. Flerchinger and Saxton tion potential. Kelleners (2013) developed a new numerical model (1989) and Flerchinger (1991) established a coupled model of to calculate coupled water flow and heat transport in seasonally water and heat transfer in frozen soil based on the principle of frozen soil and snow. The freezing and thawing status of the soil conservation of mass and energy, the SHAW (Simultaneous Heat as well as the freezing and thawing process mainly depends on and Water) model, which is a systematically effective model for the soil temperature and the soil water content. Ding et al. (2000) simulating soil freezing and thawing. The SHAW model has been established the relationship between freeze–thaw depth and soil verified to accurately simulate the soil freezing depth, the effect of temperature in soil freeze–thaw cycles based on experimental water and solution on winter freezing, and the effect of solutes on data from the Tibetan Plateau region and found that the maxi- soil freezing (Chen et al., 2015; Corrao et al., 2017; Fu et al., 2016; mum freeze–thaw depth and freeze–thaw time for different frost Gosselin et al., 2016; Li et al., 2012, 2013; Liu and Shao, 2015). depths is determined by the surface soil temperature. Frauenfeld Guo et al. (2011a, 2011b) simulated the surface flux of the Naqu et al. (2004) used observational data of soil temperatures at 211 BJ station using the SHAW model and found that the daily freez- sites to assess the characteristics of soil depth changes in Russia ing–thawing process in shallow soils affected the surface energy from 1956 to 1990. flux, and this effect was greater during the freezing process than The freezing and thawing of soil is essentially the freez- the thawing process. Kojima et al. (2013) proposed a sensible heat ing and thawing of water in the soil medium, that is, the phase balance method to determine the soil freeze–thaw rate by using the change process of the pore water. The difference in soil water SHAW model to simulate the soil freezing and thawing process. content will directly affect the degree and intensity of soil freez- Throughout the current research, significant progress has been ing. Kozlowski and Nartowska (2013) simulated the variation in made in the monitoring methods and numerical simulations of the the unfrozen water content in representative bentonites during soil freezing–thawing process during the freeze–thaw period, and freeze–thaw cycles. By studying the freezing and thawing charac- the SHAW model has been mainly used to simulate heat, water, teristics of three kinds of soils. Tian et al. (2014) found that the and solute transfer within a one-dimensional profile that includes change in unfrozen water content in soil lags behind the change the effects of plant cover and snow. An inadequate understanding in soil temperature. of the effects of GTD on the soil freezing and thawing process As a source of soil water, the groundwater has an important during seasonal freeze–thaw period promoted this study. influence on soil water variations and soil evaporation, especially The objectives of this study were to: (i) use the SHAW model in shallow groundwater areas. Frequent fluctuations of ground- to simulate the freezing and thawing process of soils during two water would aggravate soil salinization in arid and semiarid areas successive freeze–thaw periods; (ii) investigate the characteristics where soil evaporation is strong (Ibrahimi et al., 2014). Wu et al. of soil freezing and thawing under four different GTDs (0.5, 1.0, (2016a) studied the evaporation of frozen and thawed soil under 1.5, and 2.0 m) and two different soil textures (sandy loam and fine different GTDs by field soil column experiments and revealed sand) during two successive freeze–thaw periods; and (iii) reveal the influence of GTD on water and salt transport in frozen and the effects of soil texture and GTD on the soil freezing and thaw- thawed soil. Sun et al. (2011) described the entire process of ing process and determine the relationship between the frost depth soil water movement in seasonally frozen unsaturated zones by and the ANST. analyzing the interrelationship between freeze–thaw action and groundwater level. The soil moisture content in the unsaturated 66 zone at different groundwater table depths is quite different. The Field Test Conditions shallower the groundwater table depth was, the earlier a high- Experimental Site moisture zone formed and with a higher soil moisture content The field experiments were conducted at the Taigu Water (Miao et al., 2017). The effect of groundwater on soil moisture Balance Experimental Field located in the east of the Jinzhong content in the root zone depends on the GTD (Chen and Hu, basin (37°26¢ N, 112°30¢ E), Shanxi Province, China. The eleva- 2004), and shallower groundwater tables lead to upward capil- tion of the experimental site is 777.0 m and the GTD is 25.0 m. lary fluxes over parts of the central and southern La Plata basin, With a typical continental semiarid climate, the annual average which leads to an increase in simulated moisture in the root zone temperature is 9.9°C (1954–2010) and the average annual precipi- (Martinez et al., 2016). Groundwater has an important effect on tation is 415 mm. The annual average frost-free period is about soil moisture variation, while soil moisture variations are closely 200 d (Miao et al., 2017), and the maximum frost depth in history related to the process of soil freezing and thawing. Therefore, it is was 92 cm in 1960. The variation curves of solar radiation and

VZJ | Advancing Critical Zone Science p. 2 of 14 Fig. 1. Curve of daily average air temperature and solar radiation dur- Fig. 2. Curve of soil freezing and thawing process at the experimental ing the test periods (a) from 1 Nov. 2004 to 31 Mar. 2005, (b) from 1 station during the test periods (a) from 1 Nov. 2004 to 31 Mar. 2005, Nov. 2005 to 31 Mar. 2006, and (c) from 1 Nov. 2006 to 31 Mar. 2007. (b) from 1 Nov. 2005 to 31 Mar. 2006, and (c) from 1 Nov. 2006 to 31 Mar. 2007.

daily average air temperature for the experimental station during Measurements the test periods are shown in Fig. 1, and the soil freezing and thaw- The ground meteorological monitoring projects at the experi- ing process at the experimental station during the test periods is mental station are: air temperature, solar radiation, precipitation, shown in Fig. 2. The field soil maximum frost depth was 52 cm wind speed, relative humidity, snow depth, atmospheric pressure, on 11 Jan. 2006 at the experimental station with a GTD of 25.0 m vapor pressure, soil temperature, and frozen soil depth. The obser- (the influence of the GTD can be ignored), and the soil began vation time was 8:00 AM and 8:00 PM each day, and the solar to thaw in early February and thawed completely in mid-March radiation was observed at 8:00 AM, 11:00 AM, 2:00 PM, and (Chen et al., 2018). 5:00 PM each day.

VZJ | Advancing Critical Zone Science p. 3 of 14 Soil water content and soil temperature monitoring under dif- For each node solved in the freeze–thaw soil, the net energy flux ferent phreatic water depths were performed by a lysimeter system into each layer is equal to the temperature increase in the system (Fig. 3). The monitoring period was three freeze–thaw periods and the sum of the latent heat of the water phase change, so the from 1 Nov. 2004 to 31 Mar. 2005, 1 Nov. 2005 to 31 Mar. 2006, energy equation for vertical one-dimensional motion is and 1 Nov. 2006 to 31 Mar. 2007. The GTDs were 0.5, 1.0, 1.5, æö¶ ¶¶ç T ÷ (qTL ) and 2.0 m, which were constant during the freeze– thaw peri- çKcs ÷-rLL + S = ¶¶zzèøç ¶ z ods. The soils were a sandy loam and a fine sand, and the main [2] ¶T ¶q æö¶r ¶q parameters are shown in Table 1. The soil moisture content in the C-r LLi +ç v + v ÷ s ¶if ¶ vèøç ¶¶÷ lysimeter system was monitored with a neutron probe, and the soil t t tz temperature was monitored by thermistor sensors (resistance error where K is hydraulic conductivity of unsaturated soil (m s−1); y was 0.5 W). Soil water content and soil temperature were monitored is soil matric potential (m); qL, and qi are volumetric liquid water 3 −3 synchronously. The monitoring time was 8:00 AM on the 1st, 6th, content and volumetric ice content of the soil layer (m m ); rL −3 11th, 16th, 21st, and 26th of each month. The depth of the moni- and ri are the density of water and ice (kg m ); Dv is the effective 2 −1 toring point is shown in Table 2. vapor diffusion coefficient through soil (m s ); Ks is the soil ther- −1 −1 mal conductivity (W m °C ); Cs is the volumetric heat capacity of the soil (J m−3 °C−1); U is a source–sink term for water flux 66Method 3 −3 −1 −3 (m m s ); S is a source–sink term for heat flux (W m ); Lf is Basic Theoretical Equation of the SHAW Model −1 the latent heat of fusion (kJ kg ); Lv is the latent heat of vaporiza- −1 −3 Vertical One-Dimensional Hydrothermal tion (kJ kg ); rv is the vapor density of the air space (kg m ); and Migration Balance Equation −2 −1 qv is water vapor flux (kg m s ). Assuming that the ice and soil particles are not flowing, and Because of the existence of a soil matrix potential, soil water considering the effect of water vapor transmission on the water– exists in equilibrium with ice when the soil temperature drops heat balance, the vertical one-dimensional motion equilibrium below 0°C. Thus, a relation between ice content and temperature equation for soil moisture is must therefore be defined before the latent heat of fusion can be determined. The total potential of the soil water with ice present is éùæö æö ¶qL r ii rq ¶ ¶y1 ¶ ¶rv ÷ + =êúK( q)ç +-1÷ ç DU÷+ [1] controlled by the vapor pressure over ice and is given by the freez- ¶ r ¶ ¶êúçèø ¶÷ r¶çèøv ¶÷ tLL tz ëû z zz ing point depression equation:

Fig. 3. Schematic diagram of the lysimeter.

Table 1. Main physical parameters of soils in the lysimeter system. Silt Sand Soil texture (<0.002 mm) (0.002–0.02 mm) (>0.02 mm) Avg. particle size Max. capillary height Specific yield ­———————— % (w/w) ———————— mm cm m3 m−3 Sandy loam 16.4 27.5 56.1 0.13 185 0.08 Fine sand 7.3 7.5 85.2 0.20 77 0.12

VZJ | Advancing Critical Zone Science p. 4 of 14 Table 2. Monitoring depth of soil moisture and soil temperature during surface (°C), Ta is air temperature (°C), and gH is the resistance freeze–thaw periods. to convective heat transfer from the surface of the system profile −1 Groundwater table (s m ); and G can be determined as depth Monitoring point depths TTLS- m cm Gk=- s [7] ZL 0.5 0, 10, 20, 40, 50 1.0 0, 10, 20, 40, 60, 80, 90, 100 where TL is the temperature of the soil at the measurement refer- 1.5 0, 10, 20, 40, 60, 80, 90, 100, 120, 140, 150 ence depth ZL (°C). 2.0 0, 10, 20, 40, 60, 80, 90, 100, 120, 140, 160, 180, 200 Lower boundary conditions. The lower boundary is the phreatic surface, which is the boundary between the saturated zone and the unsaturated zone. The soil temperature and moisture content are relatively stable. When the simulation is calculated, it is directly specified based on the actual measured value without L æöT ÷ j= f ç ÷ [3] the need for model estimation. ç ÷ gTèøk SHAW Model Inputs where j is the total water potential (m), Tk is the absolute tempera- ture (°C), T is the freezing temperature of water (°C), and g is the The SHAW model requires inputs of initial soil profile acceleration due to gravity (m s−2). moisture content, initial soil profile temperature, meteorological The soil temperature defines the soil matric potential, and element data, and simulation site general information and soil then the water content is determined according to the soil water characteristics. The meteorological elements of the upper bound- characteristic curve. If the total water content is known, ice con- ary are input by day, and the initial temperature, moisture content, tent and the latent heat term can be determined. and profile distribution conditions of the soil layer at the lower boundary are input with the observation value of the daily time Boundary Conditions step. The general information of the simulation site is: geographi- Upper boundary conditions. The upper boundary condi- cal location 112°30¢ E, 37°26¢ N; elevation 777.0 m; ground slope tion is the water–heat exchange interface between the soil system 3%; albedo of the dry soil surface 0.25; and albedo of the wet soil and the atmosphere. It controls the hydrothermal characteristics surface 0.35 (Li et al., 2012). of the soil. The exchange between longwave radiation and solar radiation absorbed by the surface soil as well as the water–heat 66 exchange between the ground and the gas are the inputs of the Results and Discussion dynamic process of the hydrothermal migration of the soil system. Model Calibration and Verification The interrelated energy and water fluxes at the surface boundary SHAW Model Calibration are computed from weather observations of air temperature, wind The soil characteristic parameters that were calculated based speed, relative humidity, and solar radiation. The equation of sur- on the average particle size, dry bulk density, and particle size face heat flow considered for the latent heat and vaporization latent composition were input into the SHAW model. Based on the heat generated during freezing and thawing is experimental data from November 2004 to March 2005, and comparing the simulated and measured values of soil tempera- R= H ++ G LE [4] Nv ture and soil water content, the parameter was repeatedly adjusted. −2 where RN is net all-wave radiation (W m ), H is sensible heat flux For model calibration, the calibrated soil characteristic hydraulic −2 −2 (W m ), G is soil heat flux (W m ), and LvE is latent heat flux parameters are as shown in Table 3. −2 −1 (W m ), where Lv is the latent heat of evaporation (J kg ) and E is the total evapotranspiration from the soil surface and plant SHAW Model Validation −2 −1 canopy (kg·m s ); RN can be determined as Based on the measured data of soil temperature during the freeze–thaw period from 2005 to 2006, the measured and simu- R= R(1 -a) + RL - [5] N s ts lated soil temperatures of the fine sand with a GTD of 0.5 and −2 where Rs is total solar radiation (W m ), a is the albedo of the 1.0 m on 1 Jan. 2006 and the sandy loam with a GTD of 1.5 and −2 soil surface, Ls is net longwave radiation (W ·m ), and Rt is atmo- 2.0 m on 1 Mar. 2006 were compared. As shown in Fig. 4, the spheric longwave radiation (W·m−2); H can be determined as variation trend of the measured and simulated soil temperature was basically the same in general, and the difference between TT- Hc=r sa [6] the measured and simulated values decreased with the increase aa g H of depth. There was a large difference between the measured −3 where ra is the density of air (kg m ), ca is the specific heat capac- and simulated values of the surface soil temperature because −1 −1 ity of air (J kg °C ), Ts is the temperature of the exchange the soil temperature at the surface is greatly variable during the

VZJ | Advancing Critical Zone Science p. 5 of 14 day and is greatly influenced by the exchange of water and heat 2.0 m on 1 Mar. 2006 were compared. As shown in Fig. 5, the between the ground and the air. The simulation of soil tem- measured values of soil moisture content were basically the same perature in the deep soil is close to the measured values (Fig. 4c as the simulated values, and the simulated values were close to and 4d). When the soil depth was <60 cm, the error between the measured values, indicating that the simulation results of the the measured and simulated soil temperatures was larger (Fig. SHAW model had a certain degree of credibility. 4b–4d), which was mainly related to the soil heat flux, which The degree of agreement between the simulated value and the fluctuated with time. measured value can be quantitatively analyzed based on the root Based on the measured soil water content data during the mean square error (also called the standard error), RMSE: freeze–thaw period from 2005 to 2006, the measured and simu- n 1 ˆ 2 lated soil water content of the fine sand with a GTD of 0.5 and RMSE=-å(YYii) [8] 1.0 m on 1 Jan. 2006 and the sandy loam with a GTD of 1.5 and n i=1

Table 3. Calibrated soil characteristic hydraulic parameters at groundwater table depths (GTDs) from 0.5 to 2.0 m. Sandy loam Fine sand Simulated Pore size Saturated Saturated Pore size Saturated Saturated hierarchical distribution Air entry hydraulic moisture distribution Air entry hydraulic moisture GTD node depth index potential conductivity content index potential conductivity content m m m cm h−1 m3 m−3 m cm h−1 m3 m−3 0.5 0 4.15 −0.31 0.17 0.48 2.92 −0.22 0.66 0.41 0.1 4.1 −0.32 0.17 0.48 2.92 −0.22 0.66 0.41 0.2 4.1 −0.32 0.18 0.48 2.9 −0.23 0.67 0.41 0.4 4.0 −0.32 0.18 0.52 2.9 −0.23 0.67 0.49 0.5 4.0 −0.32 0.19 0.52 2.9 −0.23 0.68 0.51 1.0 0 4.15 −0.31 0.17 0.45 2.92 −0.20 0.66 0.41 0.1 4.1 −0.32 0.17 0.45 2.92 −0.20 0.66 0.41 0.2 4.1 −0.32 0.17 0.45 2.91 −0.21 0.67 0.45 0.4 4.0 −0.32 0.18 0.48 2.91 −0.21 0.67 0.45 0.6 3.9 −0.33 0.19 0.48 2.91 −0.21 0.67 0.45 0.8 3.8 −0.33 0.19 0.51 2.9 −0.22 0.68 0.50 1.0 3.8 −0.33 0.2 0.52 2.9 −0.22 0.68 0.51 1.5 0 4.15 −0.30 0.17 0.40 2.92 −0.20 0.66 0.41 0.1 4.1 −0.31 0.17 0.45 2.92 −0.20 0.66 0.41 0.2 4.1 −0.31 0.17 0.45 2.91 −0.21 0.67 0.41 0.4 4.0 −0.31 0.18 0.45 2.91 −0.21 0.67 0.41 0.6 3.9 −0.31 0.19 0.48 2.91 −0.21 0.67 0.45 0.8 3.9 −0.32 0.19 0.48 2.9 −0.22 0.68 0.45 1.0 3.9 −0.32 0.2 0.48 2.9 −0.22 0.68 0.45 1.2 3.8 −0.32 0.2 0.50 2.9 −0.22 0.68 0.50 1.5 3.8 −0.32 0.2 0.52 2.9 −0.23 0.68 0.51 2.0 0 4.15 −0.31 0.17 0.40 2.92 −0.20 0.66 0.41 0.1 4.1 −0.32 0.17 0.45 2.92 −0.20 0.66 0.41 0.2 4.1 −0.32 0.17 0.45 2.91 −0.21 0.67 0.41 0.4 4 −0.32 0.18 0.45 2.91 −0.21 0.67 0.41 0.6 3.9 −0.32 0.18 0.45 2.91 −0.21 0.67 0.41 0.8 3.9 −0.33 0.18 0.48 2.9 −0.22 0.68 0.45 1.0 3.9 −0.33 0.18 0.48 2.9 −0.22 0.68 0.45 1.2 3.8 −0.33 0.18 0.48 2.9 −0.22 0.68 0.45 1.4 3.8 −0.33 0.2 0.48 2.9 −0.23 0.68 0.45 1.6 3.8 −0.33 0.2 0.48 2.9 −0.23 0.68 0.45 1.8 3.8 −0.33 0.2 0.50 2.9 −0.23 0.68 0.50 2.0 3.8 −0.33 0.2 0.52 2.9 −0.23 0.68 0.51

VZJ | Advancing Critical Zone Science p. 6 of 14 Fig. 4. Comparison between measured and simulated values of soil temperature when (a) the groundwater table depth (GTD) was 0.5 m on 1 Jan. 2006 in the fine sand, (b) the GTD was 1.0 m on 1 Jan. 2006 in the fine sand, (c) the GTD was 1.5 m on 1 Mar. 2006 in the sandy loam, and (d) the GTD was 2.0 m on 1 Mar. 2006 in the sandy loam.

ˆ ° where Yi is the measured value, Yi is the simulated value, and n is and 0.101 to 2.139 C, respectively, and the RMSE values of the the number of samples. soil water content were 0.004 to 0.081 m3 m−3 and 0.003 to The RMSE results calculated according to Eq. [8] are shown 0.078 m3 m−3, respectively. The RMSE value of the soil tempera- in Table 4. It can be seen that the RMSE values of the soil tem- ture and soil water content near the phreatic water table was small, perature in the sandy loam and fine sand were 0.104 to 1.909°C which indicates that the simulated values were in good agreement

Fig. 5. Comparison between measured and simulated values of soil moisture content (a) in the fine sand with a groundwater table depth (GTD) of 0.5 m on 1 Jan. 2006, (b) in the fine sand with a GTD of 1.0 m on 1 Jan. 2006, (c) in the sandy loam with a GTD of 1.5 m on 1 Mar. 2006, and (d) in the sandy loam with a GTD of 2.0 m on 1 Mar. 2006.

VZJ | Advancing Critical Zone Science p. 7 of 14 with the measured values, while the RMSE values of the tem- Freezing–Thawing Processes perature and moisture content of the surface soil was large. The Simulation Results RMSE values of net radiation in the sandy loam and fine sand The freezing and thawing process is not only related to the −2 were 26.6 and 29.5 W m , respectively, and these errors were surface vegetation, cover conditions, and meteorological factors but within the specified range compared with other studies (Li et al., were also related to the GTD. In shallow groundwater areas, the 2012; Flerchinger et al., 2003, 2006). Thus, the model parameters soil freezing and thawing process is determined by the exchange were reasonable and reliable. The calibrated SHAW model can be of matter and energy between the soil and the atmosphere and used to simulate the soil water and heat migration under different also by the interaction of soil moisture and soil temperature under GTDs during the freeze–thaw periods. different GTD conditions. Based on the calibrated SHAW model, the freezing and thawing process of the sandy loam and fine sand under different GTDs during the freeze–thaw period from November 2005 to Table 4. Root mean square error of soil temperature and soil moisture March 2006 was simulated. The results are shown in Fig. 6. content during the freeze–thaw period from November 2005 to March 2006. As shown in Fig. 6, the surface soil was frozen on 14 November under different GTDs during the freeze–thaw period, but the Soil temperature Soil water content Groundwater Simulated maximum frost depth was different. The maximum frost depth table depth soil depth Sandy loam Fine sand Sandy loam Fine sand occurred when the GTD was 1.0 m, and the maximum frost depth 3 −3 m m ———— °C ———— ——— m m ——— decreased with the increase of GTD in the sandy loam when 0.5 0 1.874 1.996 0.032 0.045 the GTD was >1.5 m. When the GTD was 1.5 and 2.0 m, the 0.1 1.523 1.599 0.042 0.055 maximum frost depth of the fine sand decreased by 35.7 and 41.8% 0.2 1.036 1.167 0.020 0.021 respectively, compared with the maximum frozen depth when the 0.4 0.512 0.501 0.011 0.006 GTD was 1.0 m. 0.5 0.201 0.225 0.005 0.004 When the GTD was 0.5 m, the maximum frost depth of the 1.0 0 1.904 2.052 0.052 0.062 sandy loam was 49.2 cm on 30 Dec. 2005, while the frost depth of 0.1 1.886 1.926 0.066 0.069 the fine sand was 49.5 cm and reached the maximum frozen depth of 49.8 cm on 19 Jan. 2006, but the complete thawing time of the 0.2 1.542 1.436 0.078 0.062 fine sand was 2 d earlier than that of the sandy loam. 0.4 1.225 1.287 0.069 0.051 When the GTD was 1.0 m, the maximum frozen depth of the 0.6 0.911 0.864 0.065 0.044 sandy loam and fine sand was 97.6 and 98.9 cm on 1 Feb. 2006, 0.8 0.562 0.514 0.021 0.019 which was maximum value for four different GTDs, and the soil 1.0 0.152 0.131 0.007 0.006 was completely thawed on 28 Mar. 2006. 1.5 0 1.889 2.103 0.055 0.058 When the GTD was 1.5 m, there were obvious differences 0.1 1.853 1.932 0.076 0.075 in the soil freezing and thawing process between the sandy loam 0.2 1.526 1.557 0.069 0.071 and fine sand. The sandy loam reached a maximum frost depth 0.4 1.257 1.302 0.071 0.064 of 62.9 cm on 13 Feb. 2006; the thawing process was slow, and 0.6 1.039 0.998 0.061 0.049 the soil was completely thawed on 26 Mar. 2006. The maximum 0.8 0.855 0.803 0.023 0.025 frost depth of the fine sand was 12.7 cm shallower than that of the 1.0 0.520 0.456 0.016 0.019 sandy loam, and it occurred about 18 d earlier; the thawing process 1.2 0.256 0.211 0.010 0.014 was significantly shortened, and the soil was completely thawed on 1.5 0.139 0.123 0.006 0.004 5 Mar. 2006 because the GTD was relatively deeper and the soil 2.0 0 1.909 2.139 0.065 0.061 water content was smaller (Miao et al., 2017). 0.1 1.877 2.014 0.081 0.078 When the GTD was 2.0 m, the sandy loam reached the maxi- mum frost depth of 56.8 cm on 10 Feb. 2006, and the thawing 0.2 1.601 1.785 0.080 0.075 process was still relatively slow. The sandy loam completely thawed 0.4 1.306 1.366 0.075 0.069 on 21 Mar. 2006, which was 5 d earlier than when the GTD was 0.6 1.117 1.214 0.067 0.055 1.5 m. The maximum frost depth of the fine sand occurred earlier, 0.8 0.882 0.895 0.035 0.039 and it was 5.3 cm shallower than that of the sandy loam. The fine 1.0 0.611 0.601 0.023 0.020 sand was completely thawed in early March and the sandy loam 1.2 0.443 0.412 0.011 0.012 in late March. 1.4 0.301 0.321 0.008 0.006 The maximum soil frost depth under different GTDs was 1.6 0.206 0.195 0.007 0.006 sensitive to changes in external meteorological factors. The lowest 1.8 0.126 0.119 0.009 0.007 temperature from November 2006 to March 2007 was −8.2°C, 2.0 0.104 0.101 0.004 0.003 and the daily average temperature was −1.47°C, which were 3.8 and

VZJ | Advancing Critical Zone Science p. 8 of 14 Fig. 6. Soil freezing and thawing process under different groundwater table depths (GTDs) from November 2005 to March 2006: (a) GTD of 0.5 m; (b) GTD of 1.0 m; (c) GTD of 1.5 m; and (d) GTD of 2.0 m.

0.65°C higher than from November 2005 to March 2006. Based was simulated. The results showed that the maximum frost depth on the calibrated SHAW model, the soil freezing and thawing pro- during the freeze–thaw period from 2006 to 2007 was slightly less cess during the freeze–thaw period from November 2006 to 2007 than that from 2005 to 2006 when the GTD was 0.5 and 1.0 m,

VZJ | Advancing Critical Zone Science p. 9 of 14 and it was less sensitive to changes in the outside air temperature. temperature of the soil, some liquid water changes phase into However, the maximum frost depth during the freeze–thaw period ice and the soil water potential decreases. The soil water poten- from 2006 to 2007 was significantly less than that from 2005 to tial gradient results in the transfer of water from high soil water 2006 when the GTD was 1.5 and 2.0 m, which indicates that the potential (unfrozen zone) to low soil water potential (frozen maximum soil frost depth was more sensitive to changes in the air zone). Therefore, under the effect of the soil water potential temperature when the GTD was >1.5 m. The simulation results of gradient during the freezing period, phreatic water migrates the maximum frost depth are shown in Table 5. from the unfrozen zone to the frozen interface and freezes. The As shown in Table 5, almost the whole soil profile was frozen ice crystals in the upper frozen zone increase continuously, the when the GTD was <1.0 m. Under the influence of the negative pores between soil particles are filled, the thermal conductiv- temperature gradient, the freezing front was stable near the phre- ity of soil increases rapidly, and the negative temperature will atic water table, and the negative temperature was transmitted to diffuse rapidly from top to bottom. When the frozen layer devel- the phreatic water through the critical zone between the frozen ops downward, if the GTD is shallower, the phreatic water can front and the phreatic water table. When this equilibrium was migrate into the soil profile quickly under the action of the soil broken, that was the temperature gradient between the freezing water potential gradient, resulting in an increase in the soil water front and the phreatic water table appeared upward, then the freez- content. With an increase of the GTD, the distance from the ing front began to move upward, and the soil thawing from bottom frozen front to the groundwater table increases, the gradient of to top. With the increase of the GTD, the maximum frost depth soil water potential decreases, the influence of soil freezing on was close to that of the field soil in the experimental station, and phreatic inflow becomes weaker, and the variation of the soil the duration was shortened. profile water content decreases. The soil profile water content at the GTDs of 0.5 and 1.0 m varied drastically. The total phre- Mechanism Analysis atic evaporation reached a maximum when the GTD was 1.0 The soil water content and the temperature were different m (Miao et al., 2017). The phreatic water recharged the soil under different GTDs (Miao et al., 2017), so the soil freeze–thaw water, making the soil water content relatively higher (Chen et characteristic was different from the field soil at the experimen- al., 2018). Therefore, the soil temperature dropped more quickly tal station. The freezing and thawing of the soil was essentially a and the freezing rate was faster under the same temperature gra- comprehensive result of the amount of heat and moisture in the dient. Thus, the frost depth was greater when the GTD was 1.0 soil. When the temperature dropped to the freezing point of the m. When the GTD was >1.5 m, the transformation from phreatic soil, the frozen soil was formed. The soil freezing and thawing rate to soil water was less than with a GTD at 1.0 m (Chen et al., was related to the thermal conductivity of the soil profile. The soil 2018), the soil profile water content was lower, and the thermal obtains heat through heat conduction and the amount of the heat conductivity of the soil decreased compared with that at 1.0 m, flux per unit area and per unit time is expressed by so the maximum frost depth decreased compared with that at the 1.0-m depth. ¶T Jk=- [9] The effect of soil texture on the soil profile water content Ts¶ Z under different GTDs is obvious. When the GTD is small (0.5 where ks is thermal conductivity and ¶T/¶Z is the temperature and 1.0 m), the soil profile water content is relatively high. The gradient of the soil profile. soil water content was up to 52% at the depth of 25 to 35 cm in Under the same temperature gradient, the thermal con- the unsaturated zone when the GTD was 0.5 m, and it was up to ductivity directly affects the amount of heat flux. The thermal 51% at the depth of 50 cm in the unsaturated zone when the GTD conductivity of water is 28 times that of air. If the soil water was 1.0 m (Miao et al., 2017); the soil pores were almost filled by content increases, then some pores are filled by water and the water. However, the fine sand has a large pore diameter and the soil thermal conductivity ks becomes larger. During the freez- soil profile water content was lower than that of the sandy loam, so ing period, the soil temperature decreases with the decrease in the soil water was more easily frozen and the maximum frost depth air temperature. When the temperature drops to the freezing of the fine sand was slightly larger than that of the sandy loam under the same external negative temperature environment. When the GTD was 1.5 and 2.0 m, the GTD was relatively deep, and Table 5. Maximum soil frost depth under groundwater table depths from 0.5 to 2.0 m. the capillary rise height determined the soil profile water content. Because of the higher water content of the soil profile, the thermal Soil frost depth Freeze–thaw conductivity ks of the sandy loam was larger, so the maximum frost period Soil texture 0.5m 1.0m 1.5m 2.0m depth was deeper than that of the fine sand. 2005–2006 sandy loam 49.2 97.6 62.9 56.8 During the thawing period, the soil water content was higher fine sand 49.7 98.9 50.2 51.5 and the thermal conductivity was larger, but an increase in the soil 2006–2007 sandy loam 49.2 97.0 41.3 41.0 temperature needed to absorb more heat, so the thawing rate was fine sand 49.6 98.8 39.7 40.1 relatively slow.

VZJ | Advancing Critical Zone Science p. 10 of 14 Relationship between Frost Depth and however, was just the opposite. The ANST was maximum when Accumulated Negative Soil Surface Temperature the GTD was 2.0 m, and it was minimum when the GTD was 0.5 Although the soil freezing depth was relatively sensitive to the m. The results showed that the soil frost depth was linear with the air temperature, the decisive factor of soil frost depth was the ANST. square root of the ANST under different GTDs: Because the soil temperature at the surface gradually decreased with 0.5 Hfn=+ AT B [10] a decrease in the air temperature and the soil profile formed a nega- tive temperature gradient from top to bottom, the soil temperature where Hf is the soil frost depth (cm), Tn is the absolute value of was gradually reduced from top to bottom influenced by the tem- the ANST (°C d), A and B are empirical coefficients, and A is the perature gradient. When the soil temperature at a certain depth freezing rate of the soil under a given ANST. dropped to the freezing temperature, the soil began to freeze. Thus, The fitting curves between the soil frost depth and the ANST the depth of the soil freezing layer was closely related to the ANST. is shown in Fig. 8. The regression coefficient of the relationship While in the shallow groundwater area, the ANST had special char- between the frost depth and the ANST under different GTDs is acteristics with the change of GTD. The ANST of the sandy loam shown in Table 6. From the results of regression analysis, it can be and fine sand measured during the two freeze–thaw periods (from seen that there is a significant correlation between the soil frost depth 2005–2006 and 2006–2007) is shown in Fig. 7. under different GTDs and the ANST, with the sandy loam with its It can be seen that the ANST under different GTDs was smaller particle size having a better regression effect. The regression not simply increasing with the increase in the GTD. During the coefficient A increased with the increase of GTD, which indicates freezing period, groundwater continuously evaporated into the soil that the soil freezing rate increased with the increase of GTD under profile (Miao et al., 2017), and the phase change of liquid water the same ANST. When the ANST was zero, the regression coef- in the soil profile affected the soil temperature, so the ANST was ficient B was equal to the soil frost depth, which indicates that B influenced by the phreatic evaporation. reflects the soil frost depth when the ANST is zero. The regression The ANST of the sandy loam with a GTD of 0.5 m was coefficient B of the sandy loam increased with the increase of GTD, higher than that with a GTD of 1.0 m, and that with a GTD at while B was negative when the GTD was >1.5 m in the fine sand, 1.5 m was higher than that with a GTD at 2.0 m. The fine sand, which indicates that there was no freezing when the ANST was zero.

Fig. 7. Accumulated negative soil surface temperature (ANST) during freeze–thaw periods in the (a) sandy loam and (b) fine sand.

VZJ | Advancing Critical Zone Science p. 11 of 14 Fig. 8. Fitting curves between the soil frost depth and the accumulated negative soil surface temperature (ANST) during the test periods when (a) the groundwater table depth (GTD) was 0.5 m, (b) the GTD was 1.0 m, (c) the GTD was 1.5 m, and (d) the GTD was 2.0 m.

VZJ | Advancing Critical Zone Science p. 12 of 14 thaw periods. Water 10:376. doi:10.3390/w10040376 Table 6. Fitting coefficients between the frost depth and the accumu- lated negative soil surface temperature. Chen, J.F., X.Q. Zheng, Y.B. Zhang, Z.D. Qin, and M. Sun. 2015. Simula- tion of soil moisture evaporation under different groundwater Sandy loam Fine sand level depths during seasonal freeze–thaw period. (In Chinese, Groundwater with English abstract.) Trans. Chin. Soc. Agric. Mach. 46:131–140. table depth A B R2 A B R2 doi:10.6041/j.issn.1000-1298.2015.05.019 m Chen, X., and Q. Hu. 2004. Groundwater influences on soil moisture and surface evaporation. J. Hydrol. 297:285–300. 0.5 3.957 −2.718 0.84 3.718 −0.837 0.85 doi:10.1016/j.jhydrol.2004.04.019 1.0 4.019 −1.655 0.83 4.613 −10.561 0.91 Corrao, M.V., T.E. Link, R. Heinse, and J.U.H. Eitel. 2017. 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Lett. 6:044024. doi:10.1088/1748-9326/6/4/044024 sandy loam, and it occurred about 18 d earlier than for the sandy Frauenfeld, O.W., T. Zhang, R.G. Barry, and D. Gilichinsky. 2004. Interdecadal changes in seasonal freeze and thaw depths in Russia. J. Geophys. Res. loam. When the GTD was >1.5 m, the maximum frost depth was 109:D05101. doi:10.1029/2003JD004245 more sensitive to changes in the air temperature. Fu, W., M.B. Huang, J. Gallichand, and M.A. Shao. 2016. Optimization of plant The decisive factor of soil frost depth was the ANST. The coverage in relation to water balance in the Loess Plateau of China. Geo- derma 173–174:134–144. doi:10.1016/j.geoderma.2011.12.016 frost depth of the soil profile was linear with the square root of the Gao, T.G., T.J. Zhang, X.D. Wan, S.C. Kang, M. Sillanpää, Y.M. Zheng, and L. ANST under different GTDs. There was a significant correlation Cao. 2016. 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Yang, and H.J. Wang. 2011a. Characteristics of land surface hand, this research is of great importance for the rational develop- heat and water exchange under different soil freeze/thaw conditions ment of soil water and heat resources and efficient utilization of over the central Tibetan Plateau. Hydrol. Processes 25:2531–2541. freeze–thaw soil resources in cold regions. doi:10.1002/hyp.8025 Guo, D.L., M.X. Yang, and H.J. Wang. 2011b. Sensible and latent heat flux response to diurnal variation in soil surface temperature and moisture Acknowledgments under different freeze/thaw soil conditions in the seasonal frozen soil This research was supported by the National Natural Youth Science Foundation of China region of the central Tibetan Plateau. Environ. Earth Sci. 63:97–107. (Grant no. 41502243), the National Natural Science Foundation of China (Grant no. doi:10.1007/s12665-010-0672-6 41572239), and the Natural Science Youth Foundation of Shanxi Province, China (Grant no. 2015021169). 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