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Coupled water and heat flow in a grass field with aggregated Andisol during soil-freezing periods
Cold Regions Science and Technology 62 (2010) 98–106
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Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / c o l d r e g i o n s
Coupled water and heat flow in a grass field with aggregated Andisol during soil-freezing periods Ieyasu Tokumoto a, Kosuke Noborio b,⁎, Kiyoshi Koga c a b c
Department of Soil and Crop Sciences, Texas A&M University, College Station, TX, USA School of Agriculture, Meiji University, Kawasaki, Kanagawa 214-8571, Japan Faculty of Agriculture, Iwate University, Japan
a r t i c l e
i n f o
Article history: Received 4 September 2009 Accepted 18 March 2010 Keywords: Water flow The generalized Clausius–Clapeyron equation Soil-freezing-curve Aggregated Andisol Heat flow
a b s t r a c t During soil-freezing periods, coupled water and heat flow is important for predicting frost depth and unsaturated water flow between frozen and unfrozen soil. We investigated water and heat flow in Andisol with aggregated soil structure at a grass field during soil-freezing periods. The water retention curve (WRC) had a stepwise shape, in which water content, θ, decreased drastically at air entry value, h = −0.3 m, and matric potential, h = −10 m. The profiles of θ and temperature, T, in an Andisol were measured using thermally-insulated tensiometers and thermo-time domain reflectometry (thermo-TDR) probes in the northeastern part of Japan. As the surface soil froze, soil water moved upward because of the matric potential gradients. Although unfrozen water content, θ, in water-saturated frozen soil may be described using the generalized Clausius–Clapeyron theory, the theory cannot express θ in unsaturated frozen soil. When soil started to freeze in unsaturated conditions at a field, the matric potential may be a significant factor to determine the temperature for freezing point depression of soil water. We proposed a modified theory to relate T to θ for both unsaturated and saturated conditions. The modified model for the aggregated soil showed good agreement between the calculated and the experimental θ–T relationship. Sensible heat flux decreased due to small temperature gradients in the transition layer between frozen and unfrozen layers. However, when the freezing front advanced further below the soil surface, latent heat of freezing appeared to be larger than the sensible heat because the phase of soil water changed to ice. The heat transport in the transition layer should be taken into account for better prediction of soil-freezing in Andisol. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Coupled water and heat flow is important for predicting frost depth and unsaturated water flow between frozen and unfrozen soils. Recent fieldwork has reported a significant role of water flow in a volcanic ash soil, Andisol, during soil-freezing periods (Iwata and Hirota, 2005b). In the soil-freezing process, heat flow is also important for interpreting soil water flow between frozen and unfrozen soil layers. However, coupled water and heat flow in unsaturated soil during freezing is poorly understood. Studies on water flow in frozen soil have relied on the frost heave theory developed from laboratory experiments. Taber (1930) showed frost heave could take place in benzene-saturated soil under sub-zero temperature. Corte (1962) demonstrated experimentally that soil particles in distilled water were expelled from ice that formed. He speculated that an unfrozen water film existed between soil particles and surrounding ice, which helped the soil particles migrate. He also
⁎ Corresponding author. Tel.: + 81 44 934 7156; fax: + 81 44 934 7902. E-mail address: [email protected] (K. Noborio). 0165-232X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2010.03.005
suggested that water moved from unfrozen to frozen soil through the unfrozen water film. In some laboratory experiments, water movement toward the freezing front and accumulation at the freezing front was investigated (Dirksen and Miller, 1964; Hoekstra, 1966). Dirksen and Miller (1964) observed rapid increases in water content in a frozen soil layer that could not be explained by thermal vapor diffusion from an unfrozen soil layer. Therefore, the existence of unfrozen water is vital to frost heaving in frozen soil. To measure unfrozen water content in a frozen soil, several methods have been applied: X-ray diffraction (Anderson and Hoekstra, 1965), γ-ray attenuation (Hoekstra, 1966) and time domain reflectometry (TDR) (Seyfried and Murdock, 1996). Anderson and Hoekstra (1965) found from X-ray diffraction that the unfrozen film was located immediately adjacent to the interlamellar soil surface, and that the thickness of the unfrozen film in montmorillonite, with specific surface area of 800 m2 g− 1, was calculated to be on the order of 0.5 to 1 nm. This observation agreed with the thermodynamic theory. Fletcher (1961) indicated from a thermodynamic analysis that the thickness of a liquid film is on the order of 10 nm, decreases as temperature decreases, and vanishes below about −30 °C. Low et al. (1968) also obtained a relationship between freezing water
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depression and unfrozen water content in partially frozen clay. Time domain reflectometry (TDR) offers a unique technique to measure continuously unfrozen water content in frozen soil, and TDR measurements have shown water movement into seasonally frozen soil (Kane and Stein, 1983; Stein and Kane, 1983; Hayhoe and Bailey, 1985). Water flow between frozen and unfrozen soils is complicated because the phase of water changes in unfrozen and frozen soils, and heat transport takes place at the same time. Little research on thermal properties in frozen soil has been conducted in the field. Therefore, understanding of water flow in frozen soil is needed to investigate mass and energy transport in a cold region. The TDR probes combined with dual probe heat-pulse probes technique has been developed and can be used to simultaneously measure liquid water content (θ ), heat capacity (ρc), and thermal conductivity (λ) (Noborio et al., 1996). Ren et al. (2003) showed that the θ, ρc, and λ measured with a thermo-TDR probe agreed well with results from theoretical models and gravimetric measurements. Iwata and Hirota (2005a) developed a tensiometer for monitoring soil matric potential, h, in a freezing environment. Matric potential in frozen soil is expressed as a function of temperature below 0 °C using the generalized Clausius–Clapeyron equation (Mizoguchi, 1993) as ΔhL = 125:4ΔTf
ð1Þ Fig. 1. Schematic of a thermo-time domain reflectmetory (TDR) probe.
In general, Topp's Eq. (3) is applicable to many different types of soils. However, it is not suitable for organic soils (Topp et al., 1980), and volcanic ash soils (Miyamoto and Chikushi, 2000). For volcanic ash soils, a calibration must be performed prior to TDR measurements (Miyamoto et al., 2001). Noborio et al. (2005) described an ε–θ relationship for Andisol by multiplying Topp's relationship by 1.35. The relationship was confirmed and validated through measurement and estimation of volumetric water contents that were within a reasonable agreement range between 0.5 and 0.75 m3 m− 3. A thermo-TDR probe also measures temporal changes in soil thermal properties by applying an electric current to the heater. Thermal diffusivity, κ, is estimated as (Bristow et al., 1994):
2. Materials and methods κ=
2.1. Thermo-TDR probes A thermo-time domain reflectometry (thermo-TDR) probe is a unified three-electrode TDR probe and a dual pulse heat probe. We constructed the thermo-TDR probes in our laboratory using three hypodermic needles that were 1.2×10− 3 m in diameter and 4.0×10− 2 m long, placed 7.5×10− 3 m apart (Fig. 1). The center needle enclosed a line heater, and the others enclosed thermocouple junctions at the midpoint of the length. Each hypodermic needle was filled with thermal-conductive silicon. A 75 Ω coaxial cable was connected to the end of the needles, and the needles were fixed on a plastic plate using epoxy glue. Dielectric constant, ε, is determined with TDR by measuring the propagation time of electromagnetic waves along the thermo-TDR probe (Topp et al., 1980) as:
r2 1 1 − 4 tm −t0 tm
ln
tm tm −t0
ð4Þ
where tm is the time (s) at which the maximal temperature occurred, t0 is a heat-pulse duration (s), and r is the radial distance (m) between the heater and the thermocouple. Using κ in Eq. (4), volumetric heat capacity, ρc, and thermal conductivity, λ, may be respectively calculated as: ρc =
" !# ! 2 2 q −r −r Ei −Ei 4πκΔTm 4κðtm −t0 Þ 4κtm
ð5Þ
and λ = κρc
2
ε = ðct = 2LÞ
=
where ΔhL is the liquid pressure in frozen soil (m H2O), and ΔTf is the temperature difference in frozen soil below 0 °C. Eq. (1) is a theoretical equation to define equilibrium between unfrozen water and ice in frozen soil based on chemical thermodynamics. The main objective of this research was to investigate water flow in frozen Andisol and to verify the generalized Clausius–Clapeyron equation for estimation of unfrozen water content. Eq. (1) was evaluated by comparing it with the measured relationship between θ and Tf in frozen soil. Heat flux was also estimated in the soil. Temporal changes in h, θ, ρc, and λ under the field conditions during soilfreezing periods were investigated for better understanding of coupled water and heat flow in the frozen soil.
ð6Þ
ð2Þ
where c is the velocity of light in a vacuum (3 × 108 m s− 1), t is the travel time of the signal along the probe length (s), and L is the length of the TDR probe (m). Dielectric constant of water, air, and soil particles is 80 at 20 °C, 1, and 2–11, respectively (Noborio, 2001). The apparent dielectric constant of soil depends on the volumetric water content, θ. The most popular relationship between ε and θ derived by Topp et al. (1980) is expressed as: 2
3
ε = 3:03 + 9:3θ + 146θ −76:7θ
ð3Þ
where ΔTm is the maximal temperature change (°C), q is the amount of heat input per unit of time per unit length of a probe (W m− 1), and −Ei(-x) is an exponential integral. An amount of heat, q = 51.5 (W m− 1), was applied to the line heater by applying a constant voltage pulse for 13 s. Temperature changes in the thermocouple and the applied voltage were recorded using a data-logger, CR23X (Campbell Scientific Inc., Logan, UT). Using these data, the values of ΔTm and tm were determined, and ρc and λ were calculated using Eqs. (4)–(6). In this study, ΔTm and tm were approximately 0.6 °C and 120 s, respectively. An apparent distance r
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was determined in an agar solution (1 kg m− 3) at 20 °C before use according to the procedure described by Campbell et al. (1991). 2.2. Thermally-insulated tensiometer Iwata and Hirota (2005a) developed a tensiometer for measuring matric potential under soil-freezing and snow accumulation conditions. On the basis of their design, we built thermally-insulated tensiometers (Fig. 2). A 100 cm3 water reservoir to refill de-aired water was placed in an insulated box that was kept approximately at 2 °C by a heat source under the sub-zero condition. Near the soil surface, tubing between the water reservoir and a porous cup (I.D. is 1.3 × 10− 2 m, saturated hydraulic conductivity is 1.2 × 10− 7 m s− 1) was insulated using glass wool. A voltage output pressure transducer, whose calibration was determined in an ambient temperature of 2 °C, was used to measure the suction of the tensiometer. It was angled about 20° to prevent discontinuous water flow due to air bubbles that normally occurred in the tubing when the soil was dry. The porous cups of the tensiometers were installed at 0.075, 0.15, 0.30 and 0.45 m deep. Matric potential data from the pressure transducer was recorded using a data-logger CR10X (Campbell Scientific Inc., Logan, UT). 2.3. Field site The study was conducted in a grass field located in the northeastern part of Japan (39°48′N, 141°05′E). The field had a southeastern-facing maximal slope of 6% and was vegetated with reed canary grass. A flat site, covered with a 0.3–0.4 m thick layer of volcanic ash soil, Andisol, was selected for experiments. The predominant soil texture was sandy loam. Observation periods were from December 2005 to January 2006. An iron plate (0.01 m thick, 0.3 m long, and 0.3 m wide) covered with a plastic sheet was used to prevent snow accumulation at the soil surface and produce the freezing condition in the field (Fig. 3). Thermo-TDR probes were installed at 0.025, 0.075, 0.15, and 0.30 m deep, and insulated tensiometers were installed at 0.075, 0.15, 0.30, and 0.45 m deep under the plate. Type T (copper-constantan) thermocouples that were inserted in the Thermo-TDR probes were also installed vertically at 0, 0.005, 0.015, 0.025, 0.030, 0.068, 0.083, 0.143, 0.158, 0.292, and 0.308 m deep. In order to improve accuracy of the thermocouple thermometers, the outputs were modified using
0 °C liquid water in ice–water equilibrium. The distance between the thermo-TDR probe and the tensiometer at each depth was about 0.1 m. The thermo-TDR probes were connected to a cable tester (1502C, Tektronix Inc., Beaverton, OR) through a multiplexer to measure dielectric constant in soil. First, the dielectric constant was measured with the TDR followed by the thermal properties of the soil. The dielectric constant was estimated by a computer with WinTDR software (Or et al., 2004). Soil surface temperature, air temperature and the depth of snow accumulation were also measured during soilfreezing periods. The data were continuously collected every 30 min using the data-loggers. 3. Results 3.1. Bulk density and hydraulic conductivity Fig. 4 shows the profile of the average of soil bulk density and hydraulic conductivity in each observed point (N = 5). Andisol has low bulk density, ρb, except for the soil surface within about 0.10 m deep due to compaction by a tractor. The average ρb between 0.15 and 0.30 m deep was 0.63 Mg m− 3. However, the hydraulic conductivity of the surface soil layer was higher than that of the bottom soil layer. This may be caused by high grass root density near the surface. 3.2. Water retention curves for aggregated Andisol Measured water retention curves (WRCs) for undisturbed soil collected at depths of 0.075, 0.15, and 0.30 m are shown in Fig. 5. They were measured by the hanging water method (Nakano et al., 1995) for the matric potential range (h), between 0 and −1.20 m. For −101 b h b −1.2 m the centrifuge method (Yawata, 1975) was applied. The WRCs were measured in the range of h from 0 to −1.20 m using saturated soil samples, and then they were continuously measured using the same samples in the lower h range (less than −1.20 m). The centrifuge method can be used to measure the moisture equivalent of soils (Kutilek and Nielsen, 1994), so it was assumed that measured error due to the different methods between the hanging water method and the centrifuge method could be neglected. The average of the three depths saturated volumetric water content, θs, was 0.72 m3 m−3. Water content was relatively constant until h reached −0.30 m, and then decreased in a stepwise function
Fig. 2. Schematic of a thermally-insulated tensiometer.
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Fig. 3. Schematic figure of the soil-freezing experiment.
(Fig. 5). Although the WRCs for depths of 0.075, 0.15, and 0.30 m differed at h N −10 m, the curves converged near h b −10 m. Tokumoto et al. (2005) showed that a WRC for disturbed Andisol had a stepwise shape as well. Water content decreased from 0.75 to 0.5 m3 m−3 as matric potential decreased from −0.15 to −0.50 m. Although θ decreased gradually from h = −0.50 to −30 m, θ decreased drastically at lower than −30 m. This is caused by aggregated soil structures, and the intra-aggregate pores were estimated as 50% volume of porosity. Miyamoto et al. (2003) demonstrated that stepwise shapes for Andisols disappeared after the soil was crushed. They revealed that the stepwise shape is caused by an aggregated soil structure. Since our result of undisturbed Andisol (Fig. 5) is similar to these results, the undisturbed Andisol can have a unique dual porosity structure such as the disturbed Andisol. However, the stepwise shaped WRC cannot be expressed by a WRC model for non-aggregated soils, which is reported by van Genuchten (1980). Therefore, we used bimodal-type model to express WRC for the aggregated soil. The bimodal retention function was expressed as (Durner, 1994): h i k n −mi θ = ðθs −θr Þ ∑ wi ð1 + jαi hj i Þ + θr i=1
ð7Þ
where θs is saturated water content, θr is residual water content, k is the number of “subsystems” that form the total pore-size distribution, and wi is a weighting factor for the sub-curves, subject to 0 b wi b 1 and
Fig. 4. Profiles of bulk density and saturated hydraulic conductivity in a grass field.
Σwi = 1. As for the bimodal curve, the parameters of the sub-curves (αi, ni, and mi) are subject to the conditions αi N 0, mi N 0, ni N 1. The subscript i is the bimodal porosity number. In the case of WRCs for the aggregated soil, the i is less than 2. The measured data were fitted to a bimodal model using a root mean square error (RMSE), and the optimized parameters are shown in Table 1. The measured and estimated WRCs were in good agreement (r2 = 0.999) (Fig. 5). 3.3. Freezing soil experiment in the field 3.3.1. Liquid water content profile during frozen process Fig. 6 shows temporal changes in soil temperature at depths of 0, 0.005, 0.015, and 0.030 m beneath the iron plate. Soil surface temperature fluctuated due to the daily variation of air temperature. However, the other soil temperatures decreased over time. After the soil-freezing experiment, we found a frozen soil layer near the plate (Fig. 7). Soil surface was completely frozen down to a couple of centimeters. Fig. 8 shows the profile of soil temperature (T), h, and θ. The profile of T, between 0 and 0.030 m, was plotted in Fig. 8a to focus on the frozen soil depth during the experimental period. It was obvious that the soil had frozen between depths of 0 and 0.015 m by January 3rd, 2006.
Fig. 5. Water retention curves for aggregate soil at depths of 0.075, 0.015, and 0.030 m. Fitted curves are expressed by Eq. (6), which is bimodal retention function model reported by Durner (1994).
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Table 1 Estimated parameters of the bimodal retention functional model for Eq. (7). Depth (m)
θs
θr
α1
n1
α2
n2
w2
0.075 0.015 0.03
0.707 0.705 0.732
0.030 0.030 0.030
0.028 0.033 0.022
3.716 2.386 3.717
0.0014 0.0005 0.0014
1.168 1.227 1.178
0.967 0.902 0.950
Fig. 8b shows the initial h at 0.075 m deep was −0.26 m, which was approximately equal to the air entry value, so the soil seemed to be in a saturated condition of the unfrozen soil. However, h decreased gradually down to a depth of 0.45 m as the soil froze. On January 3 rd, h at 0.075 m deep was −1.2 m and h near frozen soil became smaller than h at deeper soil depth. In fact, maximum soil surface temperature had been less than −0.5 °C (Fig. 6), and seemed to keep soil surface frozen. Thus, the matric potential gradients in unfrozen soil suggest that water flowed from a deeper portion toward frozen soil. Volumetric water content at the observed depth below the frozen soil layer also decreased during the experimental period (Fig. 8c). In particular, θ at 0.025 m deep decreased more than at other depths measured, supporting the idea that freezing of soil resulted in large matric potential gradients in frozen soil. We didn't monitor ice content in frozen soil, but the decline in θ at 0.025 m deep was 0.08 (m3 m− 3). This θ could have been shifted into the frozen soil layer for the observed period. For the verification of WRC for the Andisol shown in Fig. 5, measured θ were compared with calculated θ on the basis of observed WRC. As a
result, measured θ agreed well with calculated θ. For instance, the calculated θ at 0.075 m deep on December 29th was 0.687 (m3 m− 3), and the difference between calculated and observed θ was 0.043 (m3 m− 3). The value was enough smaller to the available water content (θs–θr) shown in Table 1, so this result concludes that water migration in the freezing Andisol can be estimated using Durner Model. 3.3.2. Heat flux profile during the freezing process Fig. 9 shows the profiles of λ, T, and heat flux. The thermal conductivity for Andisol was approximately 0.6 W m− 1 K− 1, (half that of sand, and close to the value for liquid water (Fig. 9a)). Soil temperatures below a depth of 0.15 m were relatively constant at 2 °C,
Fig. 6. Profiles of soil surface temperature during soil-freezing periods.
Fig. 7. Photo of frozen soil layer near soil surface after the soil-freezing experiment.
Fig. 8. Profiles of (a) soil temperature, (b) matric potential, (c) volumetric water content during soil-freezing periods in 2006.
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soil. However, determining latent heat flux of frozen soil water in the unsaturated condition may be difficult because soil water might not be frozen at 0 °C in terms of h. Discussion of latent heat flux is described in Section 4.2 after the relationship between h and T is indicated. In this section, attention was paid mainly to the influence of sensible heat flux in unfrozen soil, and it is expressed as: Jh = −λ
dT dz
ð8Þ
where T is the temperature (K) and z is the depth (m). Therefore, Jh can be calculated with measured λ multiplied by observed temperature gradient. With respect to the direction of Jh, upward flux was negative. Fig. 8c shows that heat flux, Jh, increased from the depth of 0.30 m to 0.15 m and then stayed constant between depths of 0.15 m and 0.075 m, after which, it decreased from depths of 0.075 to 0.025 m. Although we were not able to measure Jh on the soil surface covered by the iron plate, negative air temperature enabled the iron plate to work as a soil cooling system. Namely, Jh on the soil surface was expected to be smallest Jh because of heat loss from soil surface to the atmosphere. In fact, soil surface above 0.025 m deep was frozen, so this contradiction can be explained by heat transport of latent heat as well as sensible heat. In the narrow soil temperature range from 0 to −0.1 °C, however, the influence of the heat transport might not reveal. Therefore, the latent heat effect is discussed based on the generalized Clausius–Clapeyron equation in the discussion section. 4. Discussion 4.1. Unfrozen water content in unsaturated frozen soil Unfrozen water is important in dealing with mass transfer in frozen soil, so the experiment was carried out continuously to measure θ at negative soil temperatures till January 8th. To observe θ in frozen soil, a thermo-TDR probe at 0.025 m deep was used. With respect to estimating θ in frozen soil, we applied Soil-Freezing-Curves (SFC) that are similar to a water retention curve (WRC) through a scaling relationship between ice pressure (which in turn was seen as a function of temperature alone by using Eq. (1)) and capillary pressure (Koopmans and Miller, 1966). Our field measurements of bulk electrical conductivity (EC) were approximately 4 mS m−1 during the soil-freezing periods, so it was assumed that the osmotic potential was negligible. Furthermore, it was also assumed that ΔT in Eq. (1) was related to θ in frozen soil using the WRC for Andisol. By substituting Eq. (1) into Eq. (7), we obtained a new relationship between ΔTf and θ. h k −mi i n + θr θ = ðθs −θr Þ ∑ wi ð1 + jαi ⋅125:4Tf j i Þ i=1
Fig. 9. Profiles of (a) thermal conductivity, (b) soil temperature, (c) heat flux during soil-freezing periods in 2006.
and the temperature gradient between depths of 0.025 and 0.015 m was large because of frozen soil near the soil surface (Fig. 9b). Moreover, the temperature gradient in frozen soil was larger between the depths of 0.025 and 0.005 m and increased toward the soil surface. Soil heat flux, Jh in a frozen and unfrozen soil is defined as summation of sensible heat flux and latent heat flux. In particular, the energy for latent heat can be caused by the effects of vapor and frozen water in soil. However, the energy for latent heat of vapor wouldn't be introduced at such high water content shown in Fig. 8c because water content increases as the energy near the water content decreases. To calculate latent heat flux of frozen soil water, it is significant to understand how much an amount of unfrozen water changes to ice in
ð9Þ
where Tf is an absolute value of soil temperature below 0 °C. Both measured and estimated θ are plotted as a function of temperature in Fig. 10. The temperature of 0.0001 °C in Fig. 10 was apparently determined as 0 °C to show stepwise shape of the WRC for Andisol shown in Fig. 5. The measured θ at 0 °C was approximately 0.48 m3 m− 3 and decreased gradually with decreasing soil temperature. In particular, the measured data were collected in the soil-freezing condition without soil-thawing cycles because Spaans and Baker (1996) showed hysteresis curves due to soil-freezing–thawing cycles. Eq. (9) overestimated measured θ by about 0.22 m3 m− 3 at ΔT = 0 °C. However, the difference between estimated and measured θ became smaller as T decreased. The generalized Clausius–Clapeyron theory was based on the idea of standard state of water–ice equilibrium, which represented a saturated condition in frozen soil. If ice pressure equals the atmospheric pressure in an unsaturated condition, Eq. (1) must be
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Taking this into account requires observations of the forming of the ice lens in aggregated Andisol during the soil-freezing processes. It should be noted that unfrozen water flow occurs toward the soil surface even after soil freezes. Additionally, this experiment was an in situ observation of directionally freezing Andisol, so the slight decrease of measured θ in Fig. 10 might be caused by the soil water movement to the upper frozen soil layer. For instance, water flux was calculated based upon hydraulic conductivity, K(h), and matric potential gradient by Eq. (1) when observed soil temperature at 0.15 and 0.35 m deep was −0.35 °C and −0.15 °C, respectively. If the matric potential corresponding to the average temperature of −0.25 °C was used to estimate K(h) for the unfrozen soil, it might be 6.46 × 10−6 m d−1. As a result, the water flux may be 0.01 m d−1. This value seemed to be acceptable to explain the change in θ of about 0.01 m3 m−3. However, K(h) for the soil would need to be assessed by K(h) for the frozen soil in order to cause such a water movement within a couple of days, because Taylor and Luthin (1978) demonstrated that K(h) in frozen soil was 1/100–1/1000 times as small as that in unfrozen soil.
Fig. 10. Unfrozen water content as a function of frozen soil temperatures.
derived thermodynamically (Mizoguchi, 1993). We assumed to expand upon this idea to SFC for unsaturated conditions in terms of ice distributions in frozen soil. As Tf decreases, ice particles in frozen soil may be formed at locations where matric pressure, hL, expressed by Eq. (1) reaches a certain value. Apparently ice distributions in frozen soil might be similar to air distributions in unfrozen soil, if liquid water content can be converted to ice content or air content as a function of matric potential. Namely, matric potential describes the effect of unsaturated condition on how freezing point of soil changes during soil-freezing processes. Using this analogy, freezing point may be predictable on the basis of initial water content at a field, and Eq. (9) can show θ theoretically at Tf, which is lower than the freezing point. Thus, a modification to Eq. (9) is proposed which involves modifying the temperature (or Clausius–Clapeyron differential temperature) by the subtracting an empirically fitted constant. h k ni −mi i + θr θ = ðθs −θr Þ ∑ wi ð1 + jαi ⋅125:4ðTf −T0 Þj Þ i=1
ð10Þ
where T0 is soil temperature corresponding to water content at ΔT = 0 °C under unsaturated conditions. The physical meaning of T0 is freezing point depression of soil water caused by matric potential at ΔT = 0 °C. The parameter T0 was obtained as 0.594 °C by optimizing data with root mean square error. Eq. (10) is also shown in Fig. 9 and it agreed well with measured data (r2 = 0.943). In other words, the data indicated that SFC can be applied for unsaturated soils as well as saturated soils in the freezing process. Although Fig. 10 showed that unfrozen water content was expressed well as a function of soil temperature in spite of the unsaturated condition, unfrozen water content, θ, decreased gradually with decreasing soil temperature to approximately −0.1 °C. Unfortunately, there might be no effective range in measured liquid water content from which to evaluate the approach because the change in θ is about 0.01 m3 m− 3 well within measurement error. However, similar findings were reported by Kozlowski (2003). This differs from the theoretical idea that θ remains constant until soil temperature reaches the freezing point depression that corresponds to hL at T = 0 °C. Basically, SFC would agree well with WRC when (i) ice was assumed at atmospheric pressure, (ii) water content was expressed gravimetrically, and (iii) water–ice interfacial forces were neglected (Spaans and Baker, 1996). As shown above, it is tempting to consider that the distribution of ice is similar to that of air. However, as the liquid water changes to ice, the volume must be increased by the expansion. Expansion might cause increases of ice volume and, consequently, a decrease in apparent unfrozen water content in the soil. In our observation, it was not possible to measure directly the volume change accompanying decreasing unfrozen water content.
4.2. Heat transport between a frozen layer and unfrozen layer through frozen fringe As air temperature decreased, latent heat of freezing soil water is caused by phase transition from liquid water to ice in addition to sensible heat. Total soil heat flux, Jt, in a frozen and unfrozen soil is defined as (Mizoguchi, 1990): Jt = −λ
dT dθ + rhoi Lw i dz dt
ð11Þ
where rhoi is the ice density (0.99984 × 103 kg m− 3), Lw is the latent heat of freezing (approximately 3.34 × 105 J kg− 1), and dθi/dt is the temporal change of ice content (m3 m− 3). Terms on the right-hand side represent, respectively, soil heat flow due to conduction, and transport of latent heat due to the water–ice phase transition. In contrast to Stephan model (Yong and Warkentin, 1975), which expressed latent heat by soil-freezing rate, Eq. (11) can take unfrozen water content into account. The temporal change of ice content is a function of temperature, which is expressed by Eq. (10). However, it is difficult to know how long it takes to change liquid water into ice completely when temperature drops below a freezing point depression. In the field condition, we consider that soil-freezing rate might be an indicator for the quantitative analysis of ice content. Using the chain rule, we modified Eq. (11) into: Jt = −λ
dT dθ dz + rhoi Lw i dz dz dt
ð12Þ
where dθi/dz is the gradient of unfrozen water content and dz/dt is the soil-freezing rate (m s− 1). In Eq. (12), dθi/dz is the temporal change in volumetric water content below 0 °C, which was measured with a thermo-TDR probe at a depth of 0.025 m. Mizoguchi (1990) showed temperature gradients were constant in the soil-freezing process due to a constant freezing rate. If the analogy is applied hypothetically to our observation, dz/dt can be estimated by temporal changes in temperature profiles in frozen soil, as shown in Fig. 11. Using the temperature gradient in Fig. 11, soil temperature, Ta, at the average of the depths, z0, is estimated. After the freezing depth advances from soil surface, soil depth, za, at Ta for measured time interval is calculated. The difference of the soil depths, z0 − za, can be assumed as a freezing soil depth for the measured interval. During our experiment period, the estimated dz/dt was 3.26 × 10− 8 (m s− 1). For example, if θi of 0.01 (m3 m− 3) was frozen at a depth of 0.025 m, latent heat flux of freezing soil water would be 0.11 (W m− 2) equaling sensible heat flux at a depth of 0.075 m. As a result, Jt at a depth of 0.025 m was expected to increase gradually with the advance
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Fig. 11. Illustration of determining the freezing soil rate during the freezing soil periods.
of the freezing front from the soil surface. In the unsaturated Andisol, however, soil temperature at 0.025 m deep was not below −0.594 °C, so that we were not able to calculate latent heat flux of freezing soil water for the experimental period. Regarding decline in sensible heat flux at the soil depth between frozen and unfrozen soil layers, we considered three constituents: a frozen soil, a frozen fringe, and an unfrozen soil. The frozen fringe is a thin transitional zone between the freezing front and the growing surface of an ice layer, and its temperature would be kept approximately at 0 °C in saturated soil. According to observed temperature for a few days of the soil-freezing experiment, we found low temperature gradient zone was located between observed depths of 0.015 m and 0.030 m (Fig. 9b). The temperature at the depths had been kept approximately at 0 °C, although temperature for frozen fringe of the Andisol may be −0.594 °C theoretically. The gradient caused lower heat flux at a depth of 0.025 m than that at the other observed depths (Fig. 9c). The unfrozen soil below the freezing front must be unsaturated due to water movement from the unfrozen soil toward the frozen soil (Fig. 8c). The decrease of soil water might retard the advance of the penetration of the freezing front because thermal conductivity decreases with decreasing θ in the unfrozen soil. As a result, the importance of the location between the frozen and the unfrozen layers must be especially emphasized in order to predict the profile of water contents. Takeda and Nakano (1990) showed that maximum thickness of frozen fringe in saturated soils was 3 mm by visible observations controlling frozen and unfrozen soil temperature. However, the thickness of frozen fringe might depend on both λ and the initial water content in soil at the field. Andisols can retain a large amount of water in its intra-aggregate pores. Since water has a large specific heat, Andisols might be able to have a thicker frozen fringe than other colloidal soils such as sand and silt. The thermal conductivity of ice is about 2 W m− 1 K− 1 at 0 °C and increases with decreasing temperature (Kinoshita, 1982). Therefore, Jt in frozen soil might be three times as large as heat flux in unfrozen soil. Ignoring frozen fringe will result in overestimation of soil frozen depth. It is also important to determine its depth and thickness for a good estimate of a frozen layer depth.
5. Conclusions Coupled water and heat flow were investigated with thermallyinsulated tensiometers and thermo-TDR probes in Andisol at a grass field during soil-freezing periods. Andisol with aggregated soil structure retained water content of 0.5 m3 m− 3 in intra-aggregated pore when the soil froze. In this paper, we discussed that water and
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heat transport toward the shallow frozen layer, which was approximately 0.025 m thick. Matric potential gradients showed water flow from unfrozen to frozen soil layers, and unfrozen water content was estimated in frozen soil by a modified generalized Clausius–Clapeyron theory in order to quantify how much amounts of water shifted toward the frozen soil. The original theory is applicable only under a saturated condition in freezing soil at 0 °C. However, unfrozen soil at a depth of few mm below frozen soil seems to be unsaturated condition because of smaller matric potential in frozen soil. Indeed, the original theory overestimated experimental unsaturated water content. Therefore, the generalized Clausius–Clapeyron theory was modified and made applicable for both unsaturated and saturated conditions in the frozen soil. An excellent relationship was obtained between unfrozen water content and frozen soil temperature (−0.594 °C for the Andisol). A transition region between frozen and unfrozen soil was crucial to predict the profile of heat flow accurately. The transition layer had the effect of decreasing sensible heat flux because of latent heat of freezing between water and ice. However, total heat flux including both of sensible and latent heat would be greater toward frozen soil surface, influencing heat loss to the atmosphere. Theoretically, transition region may be found at freezing point depression of soil water to play the most important role, determining soil-freezingcurve for the Andisol. Accordingly for good estimation of heat transport in a frozen soil, the importance of the transition layer must be emphasized.
Acknowledgements This research was supported in part by the Grant-in-Aid for Scientific Research (B) (15380160) from Japan Society for the Promotion of Science (JSPS), and a grant for Iwate University in the 21st Century Center of Excellence Program (K-03) from the Ministry of Education, Science, Sports and Culture of Japan. We are grateful to Mr. Muneaki Yokota for maintaining the grass field and supporting our research. We thank Mr. Yukiyoshi Iwata and Dr. Tomoyoshi Hirota, National Agricultural Research Center for the Hokkaido Region, for valuable advices on the technique for a thermallyinsulated tensiometer. We also thank Dr. Masaru Mizoguchi, University of Tokyo, and Dr. James L. Heilman, Texas A&M University, for their constructive comments regarding heat transport in frozen soil.
References Anderson, D.M., Hoekstra, P., 1965. Crystallization of clay-adsorbed water. Science 149, 318–319. Bristow, K.L., Kluitenberg, G.J., Horton, R., 1994. Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J. 58, 1288–1294. Campbell, G.C., Calissendorff, C., Williams, J.H., 1991. Probe for measuring soil specific heat using a heat-pulse method. Soil Sci. Soc. Am. J. 55, 291–293. Corte, A.E., 1962. Vertical migration of particle in front of a moving freezing front. J. Geophys. Res. 67, 1085–1090. Dirksen, C., Miller, R.D., 1964. Closed-system freezing of unsaturated soil. Soil Sci. Soc. Am. Proc. 30, 168–172. Durner, W., 1994. Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour. Res. 30, 211–223. Fletcher, N.H., 1961. Surface structure of water and ice. Phil. Mag. 7, 255–269. Hayhoe, H.N., Bailey, W.G., 1985. Monitoring changes in total and unfrozen water content in seasonally frozen soil using time domain reflectometry and neutron moderation techniques. Water Resour. Res. 21, 1077–1084. Hoekstra, P., 1966. Moisture movement in soil under temperature gradient with the cold-side temperature below freezing. Water Resour. Res. 2, 241–250. Iwata, Y., Hirota, T., 2005a. Development of tensiometer for monitoring soil–water dynamics in a freezing and snow covered environment. J. Agri. Meteorol. 60, 1065–1068. Iwata, Y., Hirota, T., 2005b. Monitoring over-winter soil–water dynamics in a freezing and snow-covered environment using a thermally insulated tensiometer. Hydrol. Process. 19, 3013–3019. Kane, D.L., Stein, J., 1983. Water movement into seasonally frozen soils. Water Resour. Res. 19, 1547–1557.
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Kinoshita, S., 1982. Thermal property. In: Ogata, N. (Ed.), Physics of Frozen Soil. Morikita Press, Japan, pp. 76–78 (in Japanese). Koopmans, R.W.R., Miller, R.D., 1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. J. 30, 680–685. Kozlowski, T., 2003. A comprehensive method of determining the soil unfrozen water curves. 2. Stages of the phase change process in frozen soil–water system. Cold Reg. Sci. Technol. 36, 81–92. Kutilek, M., Nielsen, D.R., 1994. Soil Hydrology. Catena Verlag, Germany, p. 223. Low, P.F., Anderson, D.M., Hoekstra, P., 1968. Some thermodynamic relationship for soils at or below the freezing point. 1. Freezing point depression and heat capacity. Water Resour. Res. 4, 379–394. Miyamoto, T., Chikushi, J., 2000. Relation between soil water content apparent dielectric constant evaluated by dielectric mixing models. Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 206, 57–62 (in Japanese, with English abstr.). Miyamoto, T., Kobayashi, R., Annaka, T., Chikushi, J., 2001. Applicability of multiple length TDR probes to measure water distributions in an Andisol under different tillage systems in Japan. Soil Till. Res. 60, 91–99. Miyamoto, T., Annaka, T., Chikushi, J., 2003. Soil aggregate structure effects on dielectric permittivity of an Andisol measured by time domain reflectometry. Vadose Zone J. 2, 90–97. Mizoguchi, M., 1990. Water, heat and salt transport in freezing soils. Ph.D. Thesis (in Japanese, with English abstr.), Univ. of Tokyo, Japan. Mizoguchi, M., 1993. A driving force of matric potential in frozen soil. Bull. Fac. Bioresour. Mie Univ., Japan 10, 175–182. Nakano, M., Miyazaki, T., Shiozawa, S., Nishimura, T., 1995. Physical and Environmental Analysis of Soils. Univ. of Tokyo Press, Japan, pp. 74–76 (in Japanese). Noborio, K., 2001. Measurements of soil water content and electrical conductivity time domain reflectometry: a review. Comput. Electron. Agric. 31, 213–237. Noborio, K., Mclnnes, K.J., Heilman, J.L., 1996. Measurements of soil water content, heat capacity, and thermal conductivity with a single TDR probe. Soil Sci. 161, 22–28.
Noborio, K., Satta, N., Koga, K., Baba, H., Mukaida, Y., 2005. Measurements of water and nitrate contents in unsaturated soil using time domain reflectometry. J. Environ. Syst. Eng. 783, 33–38 (in Japanese, with English abstr.). Or, D., Jones, S.B., VanShaar, J.R., Haphries, S. and Koberstein, L., 2004. WinTDR soil analysis software —users-guide. (http://soilphysics.usu.edu/wintdr/documentation. htm#ManualFall2004). Ren, T., Ochsner, T.E., Horton, R., 2003. Development of thermo-time domain reflectometry for vadose zone measurements. Vadose Zone J. 2, 544–551. Seyfried, M.S., Murdock, M.D., 1996. Calibration of time domain reflectometry for measurement of liquid water in frozen soils. Soil Sci. 161, 87–98. Spaans, E.J.A., Baker, J.M., 1996. The soil freezing characteristic: its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J. 60, 13–19. Stein, J., Kane, D.L., 1983. Monitoring the unfrozen water content of soil and snow using time domain reflectometry. Water Resour. Res. 19, 1573–1584. Taber, S., 1930. The mechanics of frost heaving. J. Geol. 38, 303–317. Takeda, K., Nakano, Y., 1990. Quasi-steady problems in freezing soils, II. Experiments on the steady growth of an ice layer. Cold Reg. Sci. Technol. 18, 225–247. Taylor, G.S., Luthin, J.N., 1978. A model for couple of heat and moisture transfer during soil freezing. Can. Geotech. J. 15, 548–555. Tokumoto, I., Toride, N., Inoue, M., 2005. Hydrodynamic dispersion for an Andisol with aggregated soil structure. J. Japan Soc. Hydrol. Water Resour. 18, 401–410 (in Japanese, with English abstr.). Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurement in coaxial transmission lines. Water Resour. Res. 16, 574–582. van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. Yawata, T., 1975. Soil Physics. Univ. of Tokyo Press, Japan, pp. 61–62 (in Japanese). Yong, R.N., Warkentin, B.P., 1975. Soil Properties and Behavior. Elservier Scientific publishing co, Amsterdam. NL, pp. 391–393.
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Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / c o l d r e g i o n s
Coupled water and heat flow in a grass field with aggregated Andisol during soil-freezing periods Ieyasu Tokumoto a, Kosuke Noborio b,⁎, Kiyoshi Koga c a b c
Department of Soil and Crop Sciences, Texas A&M University, College Station, TX, USA School of Agriculture, Meiji University, Kawasaki, Kanagawa 214-8571, Japan Faculty of Agriculture, Iwate University, Japan
a r t i c l e
i n f o
Article history: Received 4 September 2009 Accepted 18 March 2010 Keywords: Water flow The generalized Clausius–Clapeyron equation Soil-freezing-curve Aggregated Andisol Heat flow
a b s t r a c t During soil-freezing periods, coupled water and heat flow is important for predicting frost depth and unsaturated water flow between frozen and unfrozen soil. We investigated water and heat flow in Andisol with aggregated soil structure at a grass field during soil-freezing periods. The water retention curve (WRC) had a stepwise shape, in which water content, θ, decreased drastically at air entry value, h = −0.3 m, and matric potential, h = −10 m. The profiles of θ and temperature, T, in an Andisol were measured using thermally-insulated tensiometers and thermo-time domain reflectometry (thermo-TDR) probes in the northeastern part of Japan. As the surface soil froze, soil water moved upward because of the matric potential gradients. Although unfrozen water content, θ, in water-saturated frozen soil may be described using the generalized Clausius–Clapeyron theory, the theory cannot express θ in unsaturated frozen soil. When soil started to freeze in unsaturated conditions at a field, the matric potential may be a significant factor to determine the temperature for freezing point depression of soil water. We proposed a modified theory to relate T to θ for both unsaturated and saturated conditions. The modified model for the aggregated soil showed good agreement between the calculated and the experimental θ–T relationship. Sensible heat flux decreased due to small temperature gradients in the transition layer between frozen and unfrozen layers. However, when the freezing front advanced further below the soil surface, latent heat of freezing appeared to be larger than the sensible heat because the phase of soil water changed to ice. The heat transport in the transition layer should be taken into account for better prediction of soil-freezing in Andisol. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Coupled water and heat flow is important for predicting frost depth and unsaturated water flow between frozen and unfrozen soils. Recent fieldwork has reported a significant role of water flow in a volcanic ash soil, Andisol, during soil-freezing periods (Iwata and Hirota, 2005b). In the soil-freezing process, heat flow is also important for interpreting soil water flow between frozen and unfrozen soil layers. However, coupled water and heat flow in unsaturated soil during freezing is poorly understood. Studies on water flow in frozen soil have relied on the frost heave theory developed from laboratory experiments. Taber (1930) showed frost heave could take place in benzene-saturated soil under sub-zero temperature. Corte (1962) demonstrated experimentally that soil particles in distilled water were expelled from ice that formed. He speculated that an unfrozen water film existed between soil particles and surrounding ice, which helped the soil particles migrate. He also
⁎ Corresponding author. Tel.: + 81 44 934 7156; fax: + 81 44 934 7902. E-mail address: [email protected] (K. Noborio). 0165-232X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2010.03.005
suggested that water moved from unfrozen to frozen soil through the unfrozen water film. In some laboratory experiments, water movement toward the freezing front and accumulation at the freezing front was investigated (Dirksen and Miller, 1964; Hoekstra, 1966). Dirksen and Miller (1964) observed rapid increases in water content in a frozen soil layer that could not be explained by thermal vapor diffusion from an unfrozen soil layer. Therefore, the existence of unfrozen water is vital to frost heaving in frozen soil. To measure unfrozen water content in a frozen soil, several methods have been applied: X-ray diffraction (Anderson and Hoekstra, 1965), γ-ray attenuation (Hoekstra, 1966) and time domain reflectometry (TDR) (Seyfried and Murdock, 1996). Anderson and Hoekstra (1965) found from X-ray diffraction that the unfrozen film was located immediately adjacent to the interlamellar soil surface, and that the thickness of the unfrozen film in montmorillonite, with specific surface area of 800 m2 g− 1, was calculated to be on the order of 0.5 to 1 nm. This observation agreed with the thermodynamic theory. Fletcher (1961) indicated from a thermodynamic analysis that the thickness of a liquid film is on the order of 10 nm, decreases as temperature decreases, and vanishes below about −30 °C. Low et al. (1968) also obtained a relationship between freezing water
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depression and unfrozen water content in partially frozen clay. Time domain reflectometry (TDR) offers a unique technique to measure continuously unfrozen water content in frozen soil, and TDR measurements have shown water movement into seasonally frozen soil (Kane and Stein, 1983; Stein and Kane, 1983; Hayhoe and Bailey, 1985). Water flow between frozen and unfrozen soils is complicated because the phase of water changes in unfrozen and frozen soils, and heat transport takes place at the same time. Little research on thermal properties in frozen soil has been conducted in the field. Therefore, understanding of water flow in frozen soil is needed to investigate mass and energy transport in a cold region. The TDR probes combined with dual probe heat-pulse probes technique has been developed and can be used to simultaneously measure liquid water content (θ ), heat capacity (ρc), and thermal conductivity (λ) (Noborio et al., 1996). Ren et al. (2003) showed that the θ, ρc, and λ measured with a thermo-TDR probe agreed well with results from theoretical models and gravimetric measurements. Iwata and Hirota (2005a) developed a tensiometer for monitoring soil matric potential, h, in a freezing environment. Matric potential in frozen soil is expressed as a function of temperature below 0 °C using the generalized Clausius–Clapeyron equation (Mizoguchi, 1993) as ΔhL = 125:4ΔTf
ð1Þ Fig. 1. Schematic of a thermo-time domain reflectmetory (TDR) probe.
In general, Topp's Eq. (3) is applicable to many different types of soils. However, it is not suitable for organic soils (Topp et al., 1980), and volcanic ash soils (Miyamoto and Chikushi, 2000). For volcanic ash soils, a calibration must be performed prior to TDR measurements (Miyamoto et al., 2001). Noborio et al. (2005) described an ε–θ relationship for Andisol by multiplying Topp's relationship by 1.35. The relationship was confirmed and validated through measurement and estimation of volumetric water contents that were within a reasonable agreement range between 0.5 and 0.75 m3 m− 3. A thermo-TDR probe also measures temporal changes in soil thermal properties by applying an electric current to the heater. Thermal diffusivity, κ, is estimated as (Bristow et al., 1994):
2. Materials and methods κ=
2.1. Thermo-TDR probes A thermo-time domain reflectometry (thermo-TDR) probe is a unified three-electrode TDR probe and a dual pulse heat probe. We constructed the thermo-TDR probes in our laboratory using three hypodermic needles that were 1.2×10− 3 m in diameter and 4.0×10− 2 m long, placed 7.5×10− 3 m apart (Fig. 1). The center needle enclosed a line heater, and the others enclosed thermocouple junctions at the midpoint of the length. Each hypodermic needle was filled with thermal-conductive silicon. A 75 Ω coaxial cable was connected to the end of the needles, and the needles were fixed on a plastic plate using epoxy glue. Dielectric constant, ε, is determined with TDR by measuring the propagation time of electromagnetic waves along the thermo-TDR probe (Topp et al., 1980) as:
r2 1 1 − 4 tm −t0 tm
ln
tm tm −t0
ð4Þ
where tm is the time (s) at which the maximal temperature occurred, t0 is a heat-pulse duration (s), and r is the radial distance (m) between the heater and the thermocouple. Using κ in Eq. (4), volumetric heat capacity, ρc, and thermal conductivity, λ, may be respectively calculated as: ρc =
" !# ! 2 2 q −r −r Ei −Ei 4πκΔTm 4κðtm −t0 Þ 4κtm
ð5Þ
and λ = κρc
2
ε = ðct = 2LÞ
=
where ΔhL is the liquid pressure in frozen soil (m H2O), and ΔTf is the temperature difference in frozen soil below 0 °C. Eq. (1) is a theoretical equation to define equilibrium between unfrozen water and ice in frozen soil based on chemical thermodynamics. The main objective of this research was to investigate water flow in frozen Andisol and to verify the generalized Clausius–Clapeyron equation for estimation of unfrozen water content. Eq. (1) was evaluated by comparing it with the measured relationship between θ and Tf in frozen soil. Heat flux was also estimated in the soil. Temporal changes in h, θ, ρc, and λ under the field conditions during soilfreezing periods were investigated for better understanding of coupled water and heat flow in the frozen soil.
ð6Þ
ð2Þ
where c is the velocity of light in a vacuum (3 × 108 m s− 1), t is the travel time of the signal along the probe length (s), and L is the length of the TDR probe (m). Dielectric constant of water, air, and soil particles is 80 at 20 °C, 1, and 2–11, respectively (Noborio, 2001). The apparent dielectric constant of soil depends on the volumetric water content, θ. The most popular relationship between ε and θ derived by Topp et al. (1980) is expressed as: 2
3
ε = 3:03 + 9:3θ + 146θ −76:7θ
ð3Þ
where ΔTm is the maximal temperature change (°C), q is the amount of heat input per unit of time per unit length of a probe (W m− 1), and −Ei(-x) is an exponential integral. An amount of heat, q = 51.5 (W m− 1), was applied to the line heater by applying a constant voltage pulse for 13 s. Temperature changes in the thermocouple and the applied voltage were recorded using a data-logger, CR23X (Campbell Scientific Inc., Logan, UT). Using these data, the values of ΔTm and tm were determined, and ρc and λ were calculated using Eqs. (4)–(6). In this study, ΔTm and tm were approximately 0.6 °C and 120 s, respectively. An apparent distance r
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was determined in an agar solution (1 kg m− 3) at 20 °C before use according to the procedure described by Campbell et al. (1991). 2.2. Thermally-insulated tensiometer Iwata and Hirota (2005a) developed a tensiometer for measuring matric potential under soil-freezing and snow accumulation conditions. On the basis of their design, we built thermally-insulated tensiometers (Fig. 2). A 100 cm3 water reservoir to refill de-aired water was placed in an insulated box that was kept approximately at 2 °C by a heat source under the sub-zero condition. Near the soil surface, tubing between the water reservoir and a porous cup (I.D. is 1.3 × 10− 2 m, saturated hydraulic conductivity is 1.2 × 10− 7 m s− 1) was insulated using glass wool. A voltage output pressure transducer, whose calibration was determined in an ambient temperature of 2 °C, was used to measure the suction of the tensiometer. It was angled about 20° to prevent discontinuous water flow due to air bubbles that normally occurred in the tubing when the soil was dry. The porous cups of the tensiometers were installed at 0.075, 0.15, 0.30 and 0.45 m deep. Matric potential data from the pressure transducer was recorded using a data-logger CR10X (Campbell Scientific Inc., Logan, UT). 2.3. Field site The study was conducted in a grass field located in the northeastern part of Japan (39°48′N, 141°05′E). The field had a southeastern-facing maximal slope of 6% and was vegetated with reed canary grass. A flat site, covered with a 0.3–0.4 m thick layer of volcanic ash soil, Andisol, was selected for experiments. The predominant soil texture was sandy loam. Observation periods were from December 2005 to January 2006. An iron plate (0.01 m thick, 0.3 m long, and 0.3 m wide) covered with a plastic sheet was used to prevent snow accumulation at the soil surface and produce the freezing condition in the field (Fig. 3). Thermo-TDR probes were installed at 0.025, 0.075, 0.15, and 0.30 m deep, and insulated tensiometers were installed at 0.075, 0.15, 0.30, and 0.45 m deep under the plate. Type T (copper-constantan) thermocouples that were inserted in the Thermo-TDR probes were also installed vertically at 0, 0.005, 0.015, 0.025, 0.030, 0.068, 0.083, 0.143, 0.158, 0.292, and 0.308 m deep. In order to improve accuracy of the thermocouple thermometers, the outputs were modified using
0 °C liquid water in ice–water equilibrium. The distance between the thermo-TDR probe and the tensiometer at each depth was about 0.1 m. The thermo-TDR probes were connected to a cable tester (1502C, Tektronix Inc., Beaverton, OR) through a multiplexer to measure dielectric constant in soil. First, the dielectric constant was measured with the TDR followed by the thermal properties of the soil. The dielectric constant was estimated by a computer with WinTDR software (Or et al., 2004). Soil surface temperature, air temperature and the depth of snow accumulation were also measured during soilfreezing periods. The data were continuously collected every 30 min using the data-loggers. 3. Results 3.1. Bulk density and hydraulic conductivity Fig. 4 shows the profile of the average of soil bulk density and hydraulic conductivity in each observed point (N = 5). Andisol has low bulk density, ρb, except for the soil surface within about 0.10 m deep due to compaction by a tractor. The average ρb between 0.15 and 0.30 m deep was 0.63 Mg m− 3. However, the hydraulic conductivity of the surface soil layer was higher than that of the bottom soil layer. This may be caused by high grass root density near the surface. 3.2. Water retention curves for aggregated Andisol Measured water retention curves (WRCs) for undisturbed soil collected at depths of 0.075, 0.15, and 0.30 m are shown in Fig. 5. They were measured by the hanging water method (Nakano et al., 1995) for the matric potential range (h), between 0 and −1.20 m. For −101 b h b −1.2 m the centrifuge method (Yawata, 1975) was applied. The WRCs were measured in the range of h from 0 to −1.20 m using saturated soil samples, and then they were continuously measured using the same samples in the lower h range (less than −1.20 m). The centrifuge method can be used to measure the moisture equivalent of soils (Kutilek and Nielsen, 1994), so it was assumed that measured error due to the different methods between the hanging water method and the centrifuge method could be neglected. The average of the three depths saturated volumetric water content, θs, was 0.72 m3 m−3. Water content was relatively constant until h reached −0.30 m, and then decreased in a stepwise function
Fig. 2. Schematic of a thermally-insulated tensiometer.
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Fig. 3. Schematic figure of the soil-freezing experiment.
(Fig. 5). Although the WRCs for depths of 0.075, 0.15, and 0.30 m differed at h N −10 m, the curves converged near h b −10 m. Tokumoto et al. (2005) showed that a WRC for disturbed Andisol had a stepwise shape as well. Water content decreased from 0.75 to 0.5 m3 m−3 as matric potential decreased from −0.15 to −0.50 m. Although θ decreased gradually from h = −0.50 to −30 m, θ decreased drastically at lower than −30 m. This is caused by aggregated soil structures, and the intra-aggregate pores were estimated as 50% volume of porosity. Miyamoto et al. (2003) demonstrated that stepwise shapes for Andisols disappeared after the soil was crushed. They revealed that the stepwise shape is caused by an aggregated soil structure. Since our result of undisturbed Andisol (Fig. 5) is similar to these results, the undisturbed Andisol can have a unique dual porosity structure such as the disturbed Andisol. However, the stepwise shaped WRC cannot be expressed by a WRC model for non-aggregated soils, which is reported by van Genuchten (1980). Therefore, we used bimodal-type model to express WRC for the aggregated soil. The bimodal retention function was expressed as (Durner, 1994): h i k n −mi θ = ðθs −θr Þ ∑ wi ð1 + jαi hj i Þ + θr i=1
ð7Þ
where θs is saturated water content, θr is residual water content, k is the number of “subsystems” that form the total pore-size distribution, and wi is a weighting factor for the sub-curves, subject to 0 b wi b 1 and
Fig. 4. Profiles of bulk density and saturated hydraulic conductivity in a grass field.
Σwi = 1. As for the bimodal curve, the parameters of the sub-curves (αi, ni, and mi) are subject to the conditions αi N 0, mi N 0, ni N 1. The subscript i is the bimodal porosity number. In the case of WRCs for the aggregated soil, the i is less than 2. The measured data were fitted to a bimodal model using a root mean square error (RMSE), and the optimized parameters are shown in Table 1. The measured and estimated WRCs were in good agreement (r2 = 0.999) (Fig. 5). 3.3. Freezing soil experiment in the field 3.3.1. Liquid water content profile during frozen process Fig. 6 shows temporal changes in soil temperature at depths of 0, 0.005, 0.015, and 0.030 m beneath the iron plate. Soil surface temperature fluctuated due to the daily variation of air temperature. However, the other soil temperatures decreased over time. After the soil-freezing experiment, we found a frozen soil layer near the plate (Fig. 7). Soil surface was completely frozen down to a couple of centimeters. Fig. 8 shows the profile of soil temperature (T), h, and θ. The profile of T, between 0 and 0.030 m, was plotted in Fig. 8a to focus on the frozen soil depth during the experimental period. It was obvious that the soil had frozen between depths of 0 and 0.015 m by January 3rd, 2006.
Fig. 5. Water retention curves for aggregate soil at depths of 0.075, 0.015, and 0.030 m. Fitted curves are expressed by Eq. (6), which is bimodal retention function model reported by Durner (1994).
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Table 1 Estimated parameters of the bimodal retention functional model for Eq. (7). Depth (m)
θs
θr
α1
n1
α2
n2
w2
0.075 0.015 0.03
0.707 0.705 0.732
0.030 0.030 0.030
0.028 0.033 0.022
3.716 2.386 3.717
0.0014 0.0005 0.0014
1.168 1.227 1.178
0.967 0.902 0.950
Fig. 8b shows the initial h at 0.075 m deep was −0.26 m, which was approximately equal to the air entry value, so the soil seemed to be in a saturated condition of the unfrozen soil. However, h decreased gradually down to a depth of 0.45 m as the soil froze. On January 3 rd, h at 0.075 m deep was −1.2 m and h near frozen soil became smaller than h at deeper soil depth. In fact, maximum soil surface temperature had been less than −0.5 °C (Fig. 6), and seemed to keep soil surface frozen. Thus, the matric potential gradients in unfrozen soil suggest that water flowed from a deeper portion toward frozen soil. Volumetric water content at the observed depth below the frozen soil layer also decreased during the experimental period (Fig. 8c). In particular, θ at 0.025 m deep decreased more than at other depths measured, supporting the idea that freezing of soil resulted in large matric potential gradients in frozen soil. We didn't monitor ice content in frozen soil, but the decline in θ at 0.025 m deep was 0.08 (m3 m− 3). This θ could have been shifted into the frozen soil layer for the observed period. For the verification of WRC for the Andisol shown in Fig. 5, measured θ were compared with calculated θ on the basis of observed WRC. As a
result, measured θ agreed well with calculated θ. For instance, the calculated θ at 0.075 m deep on December 29th was 0.687 (m3 m− 3), and the difference between calculated and observed θ was 0.043 (m3 m− 3). The value was enough smaller to the available water content (θs–θr) shown in Table 1, so this result concludes that water migration in the freezing Andisol can be estimated using Durner Model. 3.3.2. Heat flux profile during the freezing process Fig. 9 shows the profiles of λ, T, and heat flux. The thermal conductivity for Andisol was approximately 0.6 W m− 1 K− 1, (half that of sand, and close to the value for liquid water (Fig. 9a)). Soil temperatures below a depth of 0.15 m were relatively constant at 2 °C,
Fig. 6. Profiles of soil surface temperature during soil-freezing periods.
Fig. 7. Photo of frozen soil layer near soil surface after the soil-freezing experiment.
Fig. 8. Profiles of (a) soil temperature, (b) matric potential, (c) volumetric water content during soil-freezing periods in 2006.
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soil. However, determining latent heat flux of frozen soil water in the unsaturated condition may be difficult because soil water might not be frozen at 0 °C in terms of h. Discussion of latent heat flux is described in Section 4.2 after the relationship between h and T is indicated. In this section, attention was paid mainly to the influence of sensible heat flux in unfrozen soil, and it is expressed as: Jh = −λ
dT dz
ð8Þ
where T is the temperature (K) and z is the depth (m). Therefore, Jh can be calculated with measured λ multiplied by observed temperature gradient. With respect to the direction of Jh, upward flux was negative. Fig. 8c shows that heat flux, Jh, increased from the depth of 0.30 m to 0.15 m and then stayed constant between depths of 0.15 m and 0.075 m, after which, it decreased from depths of 0.075 to 0.025 m. Although we were not able to measure Jh on the soil surface covered by the iron plate, negative air temperature enabled the iron plate to work as a soil cooling system. Namely, Jh on the soil surface was expected to be smallest Jh because of heat loss from soil surface to the atmosphere. In fact, soil surface above 0.025 m deep was frozen, so this contradiction can be explained by heat transport of latent heat as well as sensible heat. In the narrow soil temperature range from 0 to −0.1 °C, however, the influence of the heat transport might not reveal. Therefore, the latent heat effect is discussed based on the generalized Clausius–Clapeyron equation in the discussion section. 4. Discussion 4.1. Unfrozen water content in unsaturated frozen soil Unfrozen water is important in dealing with mass transfer in frozen soil, so the experiment was carried out continuously to measure θ at negative soil temperatures till January 8th. To observe θ in frozen soil, a thermo-TDR probe at 0.025 m deep was used. With respect to estimating θ in frozen soil, we applied Soil-Freezing-Curves (SFC) that are similar to a water retention curve (WRC) through a scaling relationship between ice pressure (which in turn was seen as a function of temperature alone by using Eq. (1)) and capillary pressure (Koopmans and Miller, 1966). Our field measurements of bulk electrical conductivity (EC) were approximately 4 mS m−1 during the soil-freezing periods, so it was assumed that the osmotic potential was negligible. Furthermore, it was also assumed that ΔT in Eq. (1) was related to θ in frozen soil using the WRC for Andisol. By substituting Eq. (1) into Eq. (7), we obtained a new relationship between ΔTf and θ. h k −mi i n + θr θ = ðθs −θr Þ ∑ wi ð1 + jαi ⋅125:4Tf j i Þ i=1
Fig. 9. Profiles of (a) thermal conductivity, (b) soil temperature, (c) heat flux during soil-freezing periods in 2006.
and the temperature gradient between depths of 0.025 and 0.015 m was large because of frozen soil near the soil surface (Fig. 9b). Moreover, the temperature gradient in frozen soil was larger between the depths of 0.025 and 0.005 m and increased toward the soil surface. Soil heat flux, Jh in a frozen and unfrozen soil is defined as summation of sensible heat flux and latent heat flux. In particular, the energy for latent heat can be caused by the effects of vapor and frozen water in soil. However, the energy for latent heat of vapor wouldn't be introduced at such high water content shown in Fig. 8c because water content increases as the energy near the water content decreases. To calculate latent heat flux of frozen soil water, it is significant to understand how much an amount of unfrozen water changes to ice in
ð9Þ
where Tf is an absolute value of soil temperature below 0 °C. Both measured and estimated θ are plotted as a function of temperature in Fig. 10. The temperature of 0.0001 °C in Fig. 10 was apparently determined as 0 °C to show stepwise shape of the WRC for Andisol shown in Fig. 5. The measured θ at 0 °C was approximately 0.48 m3 m− 3 and decreased gradually with decreasing soil temperature. In particular, the measured data were collected in the soil-freezing condition without soil-thawing cycles because Spaans and Baker (1996) showed hysteresis curves due to soil-freezing–thawing cycles. Eq. (9) overestimated measured θ by about 0.22 m3 m− 3 at ΔT = 0 °C. However, the difference between estimated and measured θ became smaller as T decreased. The generalized Clausius–Clapeyron theory was based on the idea of standard state of water–ice equilibrium, which represented a saturated condition in frozen soil. If ice pressure equals the atmospheric pressure in an unsaturated condition, Eq. (1) must be
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Taking this into account requires observations of the forming of the ice lens in aggregated Andisol during the soil-freezing processes. It should be noted that unfrozen water flow occurs toward the soil surface even after soil freezes. Additionally, this experiment was an in situ observation of directionally freezing Andisol, so the slight decrease of measured θ in Fig. 10 might be caused by the soil water movement to the upper frozen soil layer. For instance, water flux was calculated based upon hydraulic conductivity, K(h), and matric potential gradient by Eq. (1) when observed soil temperature at 0.15 and 0.35 m deep was −0.35 °C and −0.15 °C, respectively. If the matric potential corresponding to the average temperature of −0.25 °C was used to estimate K(h) for the unfrozen soil, it might be 6.46 × 10−6 m d−1. As a result, the water flux may be 0.01 m d−1. This value seemed to be acceptable to explain the change in θ of about 0.01 m3 m−3. However, K(h) for the soil would need to be assessed by K(h) for the frozen soil in order to cause such a water movement within a couple of days, because Taylor and Luthin (1978) demonstrated that K(h) in frozen soil was 1/100–1/1000 times as small as that in unfrozen soil.
Fig. 10. Unfrozen water content as a function of frozen soil temperatures.
derived thermodynamically (Mizoguchi, 1993). We assumed to expand upon this idea to SFC for unsaturated conditions in terms of ice distributions in frozen soil. As Tf decreases, ice particles in frozen soil may be formed at locations where matric pressure, hL, expressed by Eq. (1) reaches a certain value. Apparently ice distributions in frozen soil might be similar to air distributions in unfrozen soil, if liquid water content can be converted to ice content or air content as a function of matric potential. Namely, matric potential describes the effect of unsaturated condition on how freezing point of soil changes during soil-freezing processes. Using this analogy, freezing point may be predictable on the basis of initial water content at a field, and Eq. (9) can show θ theoretically at Tf, which is lower than the freezing point. Thus, a modification to Eq. (9) is proposed which involves modifying the temperature (or Clausius–Clapeyron differential temperature) by the subtracting an empirically fitted constant. h k ni −mi i + θr θ = ðθs −θr Þ ∑ wi ð1 + jαi ⋅125:4ðTf −T0 Þj Þ i=1
ð10Þ
where T0 is soil temperature corresponding to water content at ΔT = 0 °C under unsaturated conditions. The physical meaning of T0 is freezing point depression of soil water caused by matric potential at ΔT = 0 °C. The parameter T0 was obtained as 0.594 °C by optimizing data with root mean square error. Eq. (10) is also shown in Fig. 9 and it agreed well with measured data (r2 = 0.943). In other words, the data indicated that SFC can be applied for unsaturated soils as well as saturated soils in the freezing process. Although Fig. 10 showed that unfrozen water content was expressed well as a function of soil temperature in spite of the unsaturated condition, unfrozen water content, θ, decreased gradually with decreasing soil temperature to approximately −0.1 °C. Unfortunately, there might be no effective range in measured liquid water content from which to evaluate the approach because the change in θ is about 0.01 m3 m− 3 well within measurement error. However, similar findings were reported by Kozlowski (2003). This differs from the theoretical idea that θ remains constant until soil temperature reaches the freezing point depression that corresponds to hL at T = 0 °C. Basically, SFC would agree well with WRC when (i) ice was assumed at atmospheric pressure, (ii) water content was expressed gravimetrically, and (iii) water–ice interfacial forces were neglected (Spaans and Baker, 1996). As shown above, it is tempting to consider that the distribution of ice is similar to that of air. However, as the liquid water changes to ice, the volume must be increased by the expansion. Expansion might cause increases of ice volume and, consequently, a decrease in apparent unfrozen water content in the soil. In our observation, it was not possible to measure directly the volume change accompanying decreasing unfrozen water content.
4.2. Heat transport between a frozen layer and unfrozen layer through frozen fringe As air temperature decreased, latent heat of freezing soil water is caused by phase transition from liquid water to ice in addition to sensible heat. Total soil heat flux, Jt, in a frozen and unfrozen soil is defined as (Mizoguchi, 1990): Jt = −λ
dT dθ + rhoi Lw i dz dt
ð11Þ
where rhoi is the ice density (0.99984 × 103 kg m− 3), Lw is the latent heat of freezing (approximately 3.34 × 105 J kg− 1), and dθi/dt is the temporal change of ice content (m3 m− 3). Terms on the right-hand side represent, respectively, soil heat flow due to conduction, and transport of latent heat due to the water–ice phase transition. In contrast to Stephan model (Yong and Warkentin, 1975), which expressed latent heat by soil-freezing rate, Eq. (11) can take unfrozen water content into account. The temporal change of ice content is a function of temperature, which is expressed by Eq. (10). However, it is difficult to know how long it takes to change liquid water into ice completely when temperature drops below a freezing point depression. In the field condition, we consider that soil-freezing rate might be an indicator for the quantitative analysis of ice content. Using the chain rule, we modified Eq. (11) into: Jt = −λ
dT dθ dz + rhoi Lw i dz dz dt
ð12Þ
where dθi/dz is the gradient of unfrozen water content and dz/dt is the soil-freezing rate (m s− 1). In Eq. (12), dθi/dz is the temporal change in volumetric water content below 0 °C, which was measured with a thermo-TDR probe at a depth of 0.025 m. Mizoguchi (1990) showed temperature gradients were constant in the soil-freezing process due to a constant freezing rate. If the analogy is applied hypothetically to our observation, dz/dt can be estimated by temporal changes in temperature profiles in frozen soil, as shown in Fig. 11. Using the temperature gradient in Fig. 11, soil temperature, Ta, at the average of the depths, z0, is estimated. After the freezing depth advances from soil surface, soil depth, za, at Ta for measured time interval is calculated. The difference of the soil depths, z0 − za, can be assumed as a freezing soil depth for the measured interval. During our experiment period, the estimated dz/dt was 3.26 × 10− 8 (m s− 1). For example, if θi of 0.01 (m3 m− 3) was frozen at a depth of 0.025 m, latent heat flux of freezing soil water would be 0.11 (W m− 2) equaling sensible heat flux at a depth of 0.075 m. As a result, Jt at a depth of 0.025 m was expected to increase gradually with the advance
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Fig. 11. Illustration of determining the freezing soil rate during the freezing soil periods.
of the freezing front from the soil surface. In the unsaturated Andisol, however, soil temperature at 0.025 m deep was not below −0.594 °C, so that we were not able to calculate latent heat flux of freezing soil water for the experimental period. Regarding decline in sensible heat flux at the soil depth between frozen and unfrozen soil layers, we considered three constituents: a frozen soil, a frozen fringe, and an unfrozen soil. The frozen fringe is a thin transitional zone between the freezing front and the growing surface of an ice layer, and its temperature would be kept approximately at 0 °C in saturated soil. According to observed temperature for a few days of the soil-freezing experiment, we found low temperature gradient zone was located between observed depths of 0.015 m and 0.030 m (Fig. 9b). The temperature at the depths had been kept approximately at 0 °C, although temperature for frozen fringe of the Andisol may be −0.594 °C theoretically. The gradient caused lower heat flux at a depth of 0.025 m than that at the other observed depths (Fig. 9c). The unfrozen soil below the freezing front must be unsaturated due to water movement from the unfrozen soil toward the frozen soil (Fig. 8c). The decrease of soil water might retard the advance of the penetration of the freezing front because thermal conductivity decreases with decreasing θ in the unfrozen soil. As a result, the importance of the location between the frozen and the unfrozen layers must be especially emphasized in order to predict the profile of water contents. Takeda and Nakano (1990) showed that maximum thickness of frozen fringe in saturated soils was 3 mm by visible observations controlling frozen and unfrozen soil temperature. However, the thickness of frozen fringe might depend on both λ and the initial water content in soil at the field. Andisols can retain a large amount of water in its intra-aggregate pores. Since water has a large specific heat, Andisols might be able to have a thicker frozen fringe than other colloidal soils such as sand and silt. The thermal conductivity of ice is about 2 W m− 1 K− 1 at 0 °C and increases with decreasing temperature (Kinoshita, 1982). Therefore, Jt in frozen soil might be three times as large as heat flux in unfrozen soil. Ignoring frozen fringe will result in overestimation of soil frozen depth. It is also important to determine its depth and thickness for a good estimate of a frozen layer depth.
5. Conclusions Coupled water and heat flow were investigated with thermallyinsulated tensiometers and thermo-TDR probes in Andisol at a grass field during soil-freezing periods. Andisol with aggregated soil structure retained water content of 0.5 m3 m− 3 in intra-aggregated pore when the soil froze. In this paper, we discussed that water and
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heat transport toward the shallow frozen layer, which was approximately 0.025 m thick. Matric potential gradients showed water flow from unfrozen to frozen soil layers, and unfrozen water content was estimated in frozen soil by a modified generalized Clausius–Clapeyron theory in order to quantify how much amounts of water shifted toward the frozen soil. The original theory is applicable only under a saturated condition in freezing soil at 0 °C. However, unfrozen soil at a depth of few mm below frozen soil seems to be unsaturated condition because of smaller matric potential in frozen soil. Indeed, the original theory overestimated experimental unsaturated water content. Therefore, the generalized Clausius–Clapeyron theory was modified and made applicable for both unsaturated and saturated conditions in the frozen soil. An excellent relationship was obtained between unfrozen water content and frozen soil temperature (−0.594 °C for the Andisol). A transition region between frozen and unfrozen soil was crucial to predict the profile of heat flow accurately. The transition layer had the effect of decreasing sensible heat flux because of latent heat of freezing between water and ice. However, total heat flux including both of sensible and latent heat would be greater toward frozen soil surface, influencing heat loss to the atmosphere. Theoretically, transition region may be found at freezing point depression of soil water to play the most important role, determining soil-freezingcurve for the Andisol. Accordingly for good estimation of heat transport in a frozen soil, the importance of the transition layer must be emphasized.
Acknowledgements This research was supported in part by the Grant-in-Aid for Scientific Research (B) (15380160) from Japan Society for the Promotion of Science (JSPS), and a grant for Iwate University in the 21st Century Center of Excellence Program (K-03) from the Ministry of Education, Science, Sports and Culture of Japan. We are grateful to Mr. Muneaki Yokota for maintaining the grass field and supporting our research. We thank Mr. Yukiyoshi Iwata and Dr. Tomoyoshi Hirota, National Agricultural Research Center for the Hokkaido Region, for valuable advices on the technique for a thermallyinsulated tensiometer. We also thank Dr. Masaru Mizoguchi, University of Tokyo, and Dr. James L. Heilman, Texas A&M University, for their constructive comments regarding heat transport in frozen soil.
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