Similarity of soil freezing characteristic and soil water characteristic: Application in saline frozen soil hydraulic properties prediction

Journal Pre-proof Similarity of soil freezing characteristic and soil water characteristic: Application in saline frozen soil hydraulic properties prediction

Xiao Tan, Mousong Wu, Jiesheng Huang, Jingwei Wu, Jingjing Chen PII:

S0165-232X(17)30602-X

DOI:

https://doi.org/10.1016/j.coldregions.2019.102876

Reference:

COLTEC 102876

To appear in:

Cold Regions Science and Technology

Received date:

16 December 2017

Revised date:

28 December 2018

Accepted date:

4 September 2019

Please cite this article as: X. Tan, M. Wu, J. Huang, et al., Similarity of soil freezing characteristic and soil water characteristic: Application in saline frozen soil hydraulic properties prediction, Cold Regions Science and Technology(2018), https://doi.org/ 10.1016/j.coldregions.2019.102876

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© 2018 Published by Elsevier.

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Similarity of Soil Freezing Characteristic and Soil Water Characteristic: Application in Saline Frozen Soil Hydraulic Properties Prediction Xiao Tan1,2a, Mousong Wua1,3 , Jiesheng Huang1 , Jingwei Wu1 , Jingjing Chen4 1 State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, Hubei, China

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2 State Key Laboratory of Hydraulics and Mountain River Engineering, College of

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Water Resource & Hydropower, Sichuan University, Chengdu 610065, Sichuan, China

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3 International Institute for Earth System Science (ESSI), Nanjing University, China

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4 Zhijiang College, Zhejiang University of Technology, Shaoxing 312000, Zhejiang,

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Abstract

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China

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Accurate prediction of hydraulic properties in frozen soils is of importance for the role of frozen soil water dynamics in cold region water cycles. Furthermore, the existence of solute is known to complicate the water, heat and solute transport in frozen soils. To predict hydraulic properties in saline frozen soils more accurately, experiments on soil water characteristic curves (SWCCs) and soil freezing characteristic curves (SFCCs) were conducted under five solute types combined with five solute content levels. Results showed that, under low salinity conditions (e.g., no Corresponding author. E-mail: [email protected] a These two authors contribute equally to this work .

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higher than 1.0% g/g dry soil), the conversion of SFCCs to SWCCs (or SWCCs to SFCCs) was possible by using generalized Clausius-Clapeyron equation (GCCE). The combination of these two curves could predict more reliable hydraulic parameters for the compensation in experimental data ranges. Comparison of the combining method with other direct or indirect experimental results indicated that accurate and integral

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l - h relationships could result in accurate estimation in hydraulic parameters in

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frozen saline soils. This study has proposed an improved method for predicting

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hydraulic parameters in saline frozen soils, and more validation work with

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experiments under various soil and solute conditions is needed before incorporating it

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into frozen soil properties predicting frameworks.

Keywords: soil water characteristic, soil freezing characteristic, hydraulic parameters,

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Introduction

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saline frozen soils, combining prediction method

Soil freezing and thawing is important in understanding the influences of climate changes on water resources management in cold regions. Freezing and thawing of soils could result in a number of problems in agricultural activities and engineering, e.g., frost heave due to ice formation (Konrad and Morgenstern, 1980), water and solutes transport and redistributions due to temperature and potential (Baker and Spaans, 1997), as well as soil erosion and water quality degradation (Singh et al., 2009; Shanley and Chalmers, 1999) due to snow/ice melting- induced runoff. The detection of liquid water under various freezing temperatures is necessary

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for obtaining soil freezing characteristics. Time Domain Reflectometry (TDR) as a rapid and effective method, is applied widely for in situ measurement of liquid water content continuously at multi-depth (Topp et al., 1980; Patterson and Smith, 1980). The TDR method was available for lower potential range due to the drastic phase transition when soil temperature is below freezing point, thus it is usually difficult to

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detect accurate liquid water content when soil temperature is just below freezing point,

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though nearly half of the total water content becomes ice at this stage (Kozlowski,

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2003a). It has been hypothesized that the soil freezing characteristic and soil water

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characteristic contain the similar information for the drying and wetting phenomena

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that are similar to freezing and thawing phenomena (Schofield, 1935; Williams, 1964; Miller, 1966; Spaans and Baker, 1996). And the feasibility of estimating the soil water

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characteristic through the soil freezing characteristic has been investigated under

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laboratory (Koopmans and Miller, 1966; Bittelli et al., 2003; Azmatch et al., 2012)

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and field conditions (Spaans and Baker, 1996; Flerchinger et al., 2006; Kelleners and Norton, 2012). And the Clausius-Clapeyron equation makes it possible to relate the soil freezing characteristic and soil water characteristic by conversion of temperature to matric potential (Everett, 1959; Koopmans and Miller, 1966; Black and Tice, 1989; Lebeau and Konrad, 2012). However, the studies are mainly on no n-saline soils, the effects of solutes on soil freezing characteristic and soil water characteristic and their conversion have been studied by few. Azmatch et al. (2012) found that solutes in frozen soils cause deviations when converting soil water characteristic to soil freezing characteristic, as also pointed out by Cary et al. (1979), solutes change osmotic

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potential in freezing front and block migration of water. Also, due to the complexity of frozen soils, the hydraulic conductivity determination is a challenge for characterizing water and solutes flow in frozen soils, since it is a function of temperature and water content, as well as solute characteristics. Direct measurement of hydraulic conductivity of partially frozen soils was conducted

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by Burt and Williams (1976) and Horiguchi and Miller (1983) under temperatures

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around freezing point of soils, and the results indicated that the direct measurements

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of hydraulic conductivity for partially frozen soils was at the developing stage and

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required extremely precise and stable control of temperature and long equilibrium

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periods. The difficulties faced in making direct measurement limit the credibility of the direct measurement methods. Therefore, indirect measurement of the hydraulic

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conductivity of partially frozen soils has become the general approach. Likewise,

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indirect measurement methods are generally based on the similarity between the

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drying and wetting phenomena in unfrozen soils and the freezing and thawing phenomena in frozen soils (e.g., Spaans and Baker, 1996). This assumption has been used by many researchers such as Williams (1964), Koopmans and Miller (1966), Black and Tice (1989), and Spaans and Baker (1996). Hence, the soil water characteristic of the soil together with the hydraulic conductivity estimation methods from the soil water characteristic is used to obtain the hydraulic conductivity of partially frozen soils. Meanwhile, some authors suggested applying an impedance factor to calculate hydraulic conductivities of frozen soils (Jame and Norum, 1980) for they thought the

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hydraulic conductivity obtained

from soil water characteristic lead to an

overestimation (Harlan, 1973; Jame and Norum, 1980; Taylor and Luthin, 1978), though it was suggested that there is no need to apply an impedance factors (e.g., Newman and Wilson, 1997) and the impedance factor method has no physical sense (Berg, 1983; Lundin, 1990; Black and Hardenberg, 1991). As a result, a frozen soil

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hydraulic conductivity model was built by Watanabe and Flury (2008) through

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introducing the capillary bundle model to frozen soils water flow. They also verified it

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with experimental results and provided a new perspective theoretically for dealing

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with water flow in frozen soils (Watanabe et al., 2012).

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In Inner Mongolia, China, the soil surface is suffering from salinity due to high evaporation rate during crop growing season. Although the leaching practice is

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conducted every year after harvest in autumn, poor drainage systems result in large

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amount of salt in shallow groundwater. Freezing and thawing of soil in the winter will

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cause water and salt to move toward the surface, leading to secondary accumulation of salt on surface. Even though the movement of water in frozen agricultural field was studied by many (Flerchinger and Saxton, 1989b; Flerchinger and Saxton, 1989a; Iwata et al., 2008; Iwata et al., 2010; Iwata et al., 2011; Iwata et al., 2013), relationships between water, heat and solute during soil freezing and thawing are still sparse. The knowledge of water, heat and solute transport in frozen saline soils is important in solving the secondary accumulation of salt in this region, and the proper estimation of hydraulic parameters for saline frozen soils is also of high significance when characterizing water and solute flow in frozen soils.

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Due to the limitations discussed above of using the soil water characteristic or soil freezing characteristic solely to estimate the water retention and hydraulic conductivity of saline, frozen soils, this study focuses on (1) the properties of soil water characteristic curves (SWCCs) and soil freezing characteristic curves (SFCCs) under different solute conditions; (2) similarities between soil water characteristic and

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soil freezing characteristic; and (3) the availability of combining soil water

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characteristic with soil freezing characteristic curves for predicting hydraulic

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properties in saline frozen soils.

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Material and Methods Study Site Description

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Soil samples were dug from an agricultural field (20 ha) in Yonglian

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Experimental Site (40o 15’N, 108o 37’E), locating in Wuyuan County, Inner-Mongolia,

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China. Soil was sampled from depths of 0- to 140-cm in a plot of the field with low salinity (solute content below 0.20% g/g dry soil). Soil in this study was from the same plot as described in Wu et al. (2015), and was classified as silt loam according to percentages of clay (15.1%), silt (73.1%), and sand (11.8%) in upper 140 cm depth. The field is used to plant sunflower from May to October every year, then irrigated with about 20 cm deep water to leach salt at the end of October or the beginning of November. Soil samples were then transported to Wuhan University for experiments. Experiments were conducted in the laboratory of Wuhan University. Soil was air-dried and washed by using deionized water to salt mass content of 0.10% (g/g dry soil) or

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less, then passed 2-mm sieve. Soil samples passed the sieve were then put into plastic bags and stored in a 5 o C incubator for experiments.

Soil Freezing Characteristic Tests To detect liquid water content in frozen soil, the adapted TDR (patent No.

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CN203572781U) was used in this study. The TDR was adapted from the commercial

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one (CS605, Campbell Co. Ltd.) by adding a fourth probe painted with 1- mm

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ethoxyline to the 3-probe TDR to eliminate the influences of solute, which was a little

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different from that in Wu et al. (2015) for incorporating heat pulse probe into this

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patent. The calibration for the adapted TDR was conducted to obtain the relationship between liquid water content and soil dielectric permittivity with the same method as

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Wu et al. (2015). Firstly, the standard soil freezing characteristic curve was obtained

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by testing freezing temperature ( TP and TL ) of soil sample with initial water content

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around plastic limit  P (10% vol.) and liquid limit  L (40% vol.) with the calibration apparatus, and using a power function ( u

a T

b

) to fit the parameters b

( b   ln L  ln P  /  ln TP  ln TL  ) and a ( a  LTL b ). Then, the adapted TDR was used to test the soil freezing characteristic curve for the same soil sample in a 10×10×20 cm3 acrylic soil column by freezing at various soil temperatures, and calibrated against the standard curve obtained before. Calibration results showed good correlation (R2 =0.9998), indicating that the adapted TDR could be used in determining unfrozen water content in frozen saline soil. In this study, as demonstrated by Wu et al. (2015), five types of solute (NaCl,

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KCl, CaCl2 , MgSO 4 , and MgCl2 ) combining five solute content levels (0.10%, 0.30%, 0.50%, 0.70%, and 1.00% g/g dry soil) were tested in determining soil freezing characteristic curve (SFCC), with the same initial volumetric water content of 30.0% (cm3 /cm3 ), with one replicate for each treatment. Solute was mixed with deionized water to obtain the set water and salinity level for each treatment. Additional, one

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freezing experiment with original soil sample (without adding solutes) was conducted

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with one replicate, to serve as CK treatment in this experiment.

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Soil sample was packed into a 10×10×20 cm3 acrylic soil column, with bulk

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density of 1.50 g/cm3 . Soil column was compacted by each 5-cm depth to get uniform

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bulk density. The packed height of soil sample was 20 cm. TDR probes and temperature sensors were inserted to the middle of soil column and test after packing.

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Freezing tests were conducted in a freezing cell as described by Wu et al. (2015),

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which could control temperature with accuracy of 0.5 o C. Unfrozen water content and

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temperature were collected with data- loggers with 4- h intervals, and temperature of freezing cell was adjusted stepped from 0 to -25 oC with interval of 1 o C from 0 to -5 o

C and interval of 5 o C from -5 to -25 o C.

Soil Water Characteristic Tests Treatments of soil water characteristic curve (SWCC) experiments with different solute types and solute content levels were the same with SFCC experiments, with five solute types combining five solute content levels, as well as one control without solute addition (CK), and each treatment with one replicate. High-speed centrifuge

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machine (H-1400PF, Kokusan Co. Ltd.) was used to determine SWCC. The speed of centrifuge is related to water potential by a pre-calibrated relationship, and water content was determined by gravimetric method. Water content under different potential was obtained by adjusting the speed of centrifuge. The relationships between speed ( n ) and water potential (  ) could be described as below, with consideration of shrinkage in soil sample during experiment:

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  -1.398  10-5 n 2 r -( l 1  l 2 ) 3r  l 1  l 2 

[1]

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where  is water potential, cm; n is rotational speed, r/min; r is rotational radius,

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( r =8.35 cm in this study); l 1 is the distance between axis and top of centrifugal box,

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3.50 cm; and l 2 is the compression height of soil sample, cm. To depict the characteristics of SWCC, the V-G model was introduced to fit the

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experimental data (Mualem, 1976).

 s  r  h0 m r  1   h n  l ( h )       h0  s

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[2]

K ( h )  K s Sel 1  (1  Se1/m )m 

where

2

m  1  1/ n, n  1

Se ( h ) 

 ( h )  r  s  r

[3]

[4] [5]

where l ( h ) is liquid water content, cm3 /cm3 ;  r is residual water content, cm3 /cm3 ;  s is saturated water content, cm3 /cm3 ;  is inverse of the air-entry value (or

bubbling pressure), 1/cm; n is pore-size distribution index; m

is empirica l

parameter; h is water potential, cm; K ( h ) is hydraulic conductivity, cm/d; K s is

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saturated hydraulic conductivity, cm/d; l is pore-connectivity parameter, assumed to be 0.5 as an average for many soils; Se ( h ) is effective saturation. For the unfrozen soil without semipermeable membrane, the total water potential (matric potential, osmotic potential, pressure potential and gravimetric potential) equals to matric potential, but the osmotic potential can not be neglected because of

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the freezing point depression caused by dissolved solutes in frozen soil. Thus, before

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combining the SFCCs with SWCCs, the osmotic potential should be subtracted from

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total water potential which was converted from temperature using generalized

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Clausius-Clapeyron equation (GCCE) for SFCCs. Osmotic potential was calculated as below (Fuchs et al., 1978):

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  cRTK / g

[6]

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where c is solute concentration in soil solution (mol/kg);

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is gravitational acceleration

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(m/s2 ).

g

is gas constant ( R

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=8.31 J/(mol K)); TK is temperature in Kelvin; and

R

SWCC under Different Solute Conditions Fig. 1 shows the SWCC of different solute content levels and solute types. The matric potentials ranged from about 100 cm to 10000 cm and water content (θl) decreased from 0.45 cm3 /cm3 to around 0.10 cm3 /cm3 . Solutes in soils made the SWCC different in comparison with the SWCC of soil without solute (CK). In the V-G model,  is related to the air-entry potential ( ha ), which is the

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matric potential where air first enters (  first decreases). Lower  value means the air-entry region is broad, and more water exists in soil. While n affects the steepness of SWCC, and larger n will result in a steeper SWCC.  r as the lowest water content when soil is subject to a very large suction, is related to soil particle surface tension, and seen as a constant for a specific soil, however, it is difficult to obtain and

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often treated as a fitting parameter in V-G model. Parameter  decreased with solute

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content (Fig. 2(a)) and it decreased more rapidly when solute content was smaller

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than 0.30%. And more water content was measured in high solute content soil than

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low solute content one when set to the same potential h . Similarly, the other two parameters n and  r also changed with solute content (Fig. 2(a) and (b)), and n

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decreased with solute content while  r increased with solute content, resulting in a

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higher water exist in high solute content soil. The changes in the two parameters also

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presented more obviously when solute content was lower than 0.30%.

SFCC under Different Solute Conditions SFCCs of different solute types and solute content levels are depicted in Fig. 3. SFCCs changed with solute types and solute content, and liquid water content in soil decreased differently under different freezing temperature conditions. Solute in soil increased liquid water content in comparison with soil absent from solute (CK). It could be detected from Fig. 3 that liquid water content decreased rapidly when soil temperature changed from 0 to -5 o C. Liquid water content decreased from 0.30 cm3 /cm3 to about 0.05 cm3 /cm3 with rates of 0.01 to 0.03 cm3 /cm3 /o C for this

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decreasing rates of liquid water content also changed with solute types, and freezing

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process in soil samples with solutes of NaCl and MgCl2 seemed to be easier, with

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average rates of 0.02 cm3 /cm3 /o C, respectively, when soil was freezing under

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temperature of 0 to -5 o C. While the latter period (-5 to -25 oC) of freezing seemed to

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be less different for various solute types.

The SFCC was often described with a power function as below: b

[7]

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l  a T

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are fitted parameters.

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where  l is liquid water content, cm3 /cm3 ; T is soil temperature, o C; a and b

Based on Eq. [7], the best fitting parameters of a and b were obtained with R2 ranging from 0.77 to 0.99. The changes of two fitted parameters with solute content as well as solute types are shown in Table 1. Generally, parameters a and

b decreased with increasing solute content, and solute type could also influence the fitted values of parameters strongly. Parameter a in Eq. [7] controls the vertical translation of SFCC in Cartesian coordinates, and parameter b determines the rotation of SFCC. Standard deviation in fitted a calculated from various solute content levels ranged from 0.02 to 0.05 for five different types of solute, with highest

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value for MgSO 4 treatment. While for parameter b , standard deviation had a range of 0.02 to 0.07 for all five solute types, and highest values were detected for NaCl and MgSO 4 solute treatments. Mean values for these two parameters indicated that NaCl treatment showed obvious differences from other treatments for in this treatment, a had the lowest mean value of 0.19, while b had the highest mean value of 0.23.

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and means values of b ranged from 0.17 to 0.18.

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While for the other solute treatments, mean values of a ranged from 0.28 to 0.30,

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Discussion

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Comparison of SFCC with SWCC for Saline Soils

The SFCC could be compared with SWCC by using generalized form of the

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generalized Clausius-Clapeyron equation (Eq. [8]) to correlate water potential to soil

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temperature, assuming the ice pressure to be atmospheric (Fuchs et al., 1978).

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  h  

Lf  T    g  TK 

[8]

where  , h , and  are total, matric and osmotic potential, respectively, m; L f is latent heat of freezing water, J/kg; g is acceleration due to gravity, m/s2 ; T is freezing temperature of bulk water in degree Celsius, o C; and TK is soil temperature in Kelvin, K. The results for SFCC and SWCC under l  h relationship are shown in Fig. 4. SFCC matched SWCC well when plotted in the same coordinate, using Eq. [8], despite the SWCC was mainly obtained in low suction range ( h  104 cm) while SFCC was mainly in high suction range ( h  104 cm). SFCC could supplement the

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shortage of centrifuge method in determining SWCC for the limited potential range it could obtain. This made the l  h relationships more integral, and it would reduce errors in estimating hydraulic parameters due to limited experimental data in comparison with using SFCC or SWCC solely. The results were a little different from those of Azmatch et al. (2012), who

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concluded that the use of SFCC with salinity (5 g/L) to compare with SWCC would

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lead to wrong results. The experiments of Azmatch et al. (2012) were conducted

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under pressure of 50kPa, and the solute concentration was larger than that in this study.

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In this study, solute content was not very high (≤1%), thus the effects of solutes on

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SFCC were not as obvious as pointed out by them (Azmatch et al., 2012). Hence, it is suggested that the GCCE could still be used under low salinity.

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In Table 2, the V-G model fitting parameters  and n as well as the

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determination coefficients, R2 are presented. The inverse of air-entry potential,  ,

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increased when adding experimental data to SFCC for fitting V-G model, indicating a more narrow region of air-entry. This was because the SFCC data was mainly obtained at lower matric potentials and the curves changed more gradual for strong adsorptive effects of soil particle. This would lead to an inaccurate estimation of  for it is mainly determined by results of matric potentials between -10 to -100 cm. Meanwhile, the parameter n , as an index of curve steepness, tended to decrease, indicating the curves were more gradual. This was obvious for the extension of experimental data to low suction region, supplementing the experimental data more integral, and more close to the V-G model curve. In general, the combination of

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SWCC and SFCC achieved a better approach for estimation of SWCC parameters of soils, the R2 improved significantly for the combining method. To investigate the accuracy on r determination using different experimental data, the estimated r based on SWCC and combination of SWCC and SFCC was compared in Fig. 5. The simply using of SWCC data generally caused an overestimation of residual water content ( r ) in most cases. r derived only from

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SWCC was generally between 0.05 and 0.15 cm3 /cm3 , which presented to be higher

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than prediction, for the silt loam has low residual water content due to lower specific

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area. By combining SWCC and SFCC, the estimated r obviously decreased to

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below 0.10 cm3 /cm3 , and for most cases when solute content was not very high, r was estimated to be zero.

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The parameters estimated here were similar to Kelleners and Norton (2012), who

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observed the best fit of 0.74≤R2 ≤0.93 when determined V-G model parameters from

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SFCC data. In our study, the R2 ranged from 0.72 to 0.98 for SFCC derived SWCC and 0.90 to 0.99 for combination of SFCC and SWCC method. The low quality of the fitted curves using the sensor data, as they speculated, was also due to the relatively small range in the liquid water content. And the higher initial water content values and more severe soil water freezing were suggested to improve the quality of fitted curves. In this study, the experimental data was obtained from two parallel experiments for each treatment, thus the fitted curves were better than those of Kelleners and Norton (2012). Thus, we suggest that, to obtain an accurate and integral  l - h relationship for modeling water transport in frozen and unfrozen soil, the comb ination of SWCC

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and SFCC data could be used.

Frozen Soil Hydraulic Properties Determination Based on SWCC and SFCC Data The fitted parameters for V-G model were obtained based on combination of SWCC and SFCC results for each solute type and solute content and resulted in

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K ( h )-|T |, K ( h )-|h | relationships based on Eq. [3-5], as shown in Fig. 6. Hydraulic

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conductivities decreased with soil temperatures and the deviations for different solute

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content levels and solute types were obvious in Fig. 6. Hydraulic conductivities of

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soils were reduced by 36% to 77% for different solute treatments of soils when soil

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temperatures decreased from 0.0001 to 0.01 o C. Comparing to the CK, the hydraulic conductivity of soils with solute increased for 3 out of 5 solutes, but the relationship

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between hydraulic conductivity and solute content was not obvious. The results

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indicated that solute would suspend the freezing process of soils due to the freezing

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point depression effects and solute characteristics in soil solution.. The results also indicated that frozen soil hydraulic conductivities were much lower than unfrozen soils, and the existence of ice in frozen soils had great effects on water and solute transport, as concluded by many (Burt and Williams, 1976; Horiguchi and Miller, 1983; Jury and Horton, 2004). In Fig. 7, soil water retention and hydraulic conductivity results obtained by different methods are depicted. Results of combination of SWCC and SFCC method were compared with that of capillary bundle model (Watanabe and Flury, 2008) and impedance factor method (Hansson et al., 2004), as well as experimental data

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(Horiguchi and Miller, 1983; Watanabe and Flury, 2008; Watanabe et al., 2012). And the capillary bundle model and impedance factor method were described in appendix. Combination of SWCC and SFCC method could well predict liquid water content changes with matric potentials and freezing temperatures, as shown in Fig. 7(a). The curve could fit experimental data at both high potentials (or low

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temperatures) and low potentials (or high temperatures) well for silt loam or even

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loam from different methods. This was mainly attributed to the integral range of

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potential by the combination of SWCC and SFCC method, which made the

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parameters for V-G model more reliable. However, for Silt loam 2 by Watanabe and Flury (2008), the water retention data were higher than other for whole matric

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potentials range, due to the low bulk density of silt loam (1.13 g/cm3 ), and soil was

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under disturbed condition, which made it higher saturated water content (0.57

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cm3 /cm3 ) and larger air-entry value (  value of only 0.0016 cm-1 ). The capillary

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bundle model could also illustrate the water retention characteristics well at high suction range, but it tended to underestimate liquid water content when soil was at low suction conditions (e.g. h ≤100 cm). The capillary bundle model neglected the soil microstructure effects on water holding or ice formation when assuming the soil pores to be a bundle of capillary tubes, this would lead to underestimation of liquid water in soil when soil was beginning to freeze for the microstructures had more complex adsorption than capillary tubes. Therefore, the use of capillary bundle model for frozen soil water prediction should be cautious about the underestimation under high temperature ranges.

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Frozen soil hydraulic conductivities calculated by different methods as well the experimental data were compared in Fig. 7(b). Experimental data were measured by Horiguchi and Miller (1983) on Chena silt, Calgary loam, and Illite under 0 to -0.35 o

C. The comparison of hydraulic conductivities calculated by capillary bundle model

and measured through experiment showed that the capillary bundle model could work well for estimating frozen soil hydraulic conductivity on Chena silt, Calgary loam,

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and Illite. However, limited by the narrow temperature range (0 to -0.35 o C) in

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Horiguchi and Miller`s experiment (1983), and applicability of the capillary bundle

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model in wider temperature range needs to be further investigated by experiment.

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By comparing hydraulic conductivity results of Inner Mongolia silt loam calculated by Eq. [A1], Eq. [A3] as well as the combination of SWCC and SFCC

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method, it could be seen that frozen soil hydraulic conductivity decreased rapidly

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when soil temperature was within 0 to -1 o C. And the hydraulic conductivity

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calculated by Eq. [A3] by using an impedance factor to modify hydraulic conductivity of unfrozen soils seemed to be useful for it described the drastic decrease of hydraulic conductivity when soil temperature was lower than freezing point. However, the decrease of frozen soil hydraulic conductivity was too rapid at lower temperatures (e.g., -1 o C), which has been detected by Zhao et al. (2012), who used a multistep outflow method to determine hydraulic conductivity of frozen soils by using antifreeze solution as liquid. And their results showed that when soil matric potential was lower than -100 cm (corresponding to -0.8

o

C for soil temperature), the

impedance method tended to underestimate hydraulic conductivity. This might be due

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to the soil pores complexity and there might be macropores for preferential flow and or pores blocked by ice, these factors were not taken into consideration by Eq. [A3]. That is why it was criticized by many researchers (Newman and Wilson, 1997) the use of impedance factor being meaningless for it was lacking in physical significance, and they also believed the accuracy of using detailed soil water characteristic curves for

f

predicting hydraulic parameters in both frozen and unfrozen soils.

oo

Thus, combination of SWCC and SFCC method was suggested to use for

pr

predicting frozen soil hydraulic conductivity, though seemed to overestimate

e-

hydraulic conductivity of frozen soils in comparison with the other two methods. As

Pr

the method considered the soil water retention and soil freezing info rmation by using GCCE to plot these two kinds of curves in the same figure, and it seemed to be more

al

theoretically reliable when the method was applied to numerical models for

rn

simulating water, heat and solute flow considering both frozen and unfrozen

Jo u

conditions. Further work is needed to test the combining method with directly measured experimental data from frozen soils with different textures as well as different solute conditions, by using the method suggested by previous studies (e.g., Burt and Williams, 1976; Horiguchi and Miller, 1983; McCauley et al., 2002; Zhao et al., 2012), before it was incorporated into numerical models for frozen soil simulation.

Conclusions In this study, we applied two approaches to obtain SWCCs and SFCCs under

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various solute conditions, and then compared the similarity between the two curves and assessed the applicability through combining them to predict hydraulic parameters in frozen saline soil. Solute contents and types showed significant influences on SWCCs and SFCCs, due to the special properties of different solutes and the changes of saline soil osmotic potential. Two groups of curves connected well

f

under MgSO 4 and MgCl2 conditions based on the generalized Clausius-Clapeyron

oo

equation; for NaCl, the water contents of SFCCs were a little greater than that of

pr

SWCCs at the connecting point; for KCl and CaCl2 , the two groups of curves agreed

e-

well at the connecting point while the water contents of SFCCs showed unusually

Pr

high within the suction range of 104 ~105 cm. Comparisons of V-G model parameters estimated by SFCC solely with combination of SWCC and SFCC indicated that the

al

combining method could result in more reliable parameters due to wider data range.

rn

Also, the availability of this combining method in predicting hydraulic parameters for

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frozen soils was discussed by comparing this method with other experimental data and indirect prediction models. The combining method could predict hydraulic parameters for a wider suction range, but it could slightly overestimate the hydraulic conductivity at low suction head comparing to the capillary bundle model and impedance factor method. We strongly suggest more detailed tests about the influence of soil texture and bulk density on hydraulic properties of frozen soil. Besides, hydraulic conductivities under wider freezing temperature range and more saline conditions would be of high interest for testing this combining method before applied to numerical models.

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Acknowledgements This research was funded by the National Key Research and Development Program of China (Grant Nos. 2016YFA0600204 ， 2017YFC0403304), Major Program of National Natural Science Foundation of China (Grant Nos. 51790532,

f

51790533), National Natural Science Foundation of China (Grant Nos. 51379151)

oo

and Open Foundation of State Key Laboratory of Water Resources and Hydropower

pr

Engineering Science (No. 2017NSG02). In addition, we would like to thank Ai`ping

e-

Chen from the Yichang Experimental Site for supplying sample soil from the study

and processing data in laboratory.

al

Appendix

Pr

site and Mr. Dacheng Li and Mr. Weixing Quan for helping analyze the soil samples

rn

For capillary bundle model, frozen soil hydraulic conductivity and unfrozen

al., 2012):

Jo u

water content could be determined as follow (Watanabe and Flury, 2008; Watanabe et

 g Kf  w 8

2  R J2  riJ2    4 4  n J R J  riJ    ln  riJ / R J   J 1   M

[A1]

where K f is hydraulic conductivity of frozen soils, m/s; 

is tortuosity, 

=0.00059; w is density of water, kg/m3 ; g is acceleration due to gravity, g =9.81 m/s2 ;



is

constant,

3.14;



is

dynamic

viscosity

of

water,

  9.62  107 exp  2046/T  , Pa·s; n J is the number of capillaries per unit area 1/m2 ; R J

is radius of J th capillary, m; riJ is radius of ice column in J th capillary, m; J is the index for capillary size class; and M is the number of capillary size classes (here,

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M =70 was used).

The determination of R J , riJ and the ice column formation conditions were described in detail by Watanabe and Flury (2008). l  

M

 n R

J  k 1

J

2 J

 riJ2 

[A2]

where  l is unfrozen water content in frozen soils, cm3 /cm3 ; k is an index for each  decrease, k =0, 1, 2 ….

oo

f

For impedance factor method, hydraulic conductivity of frozen soils K f could

pr

be calculated by (Hansson et al., 2004):

e-

K f  10i /(t r ) K u

[A3]

where K u is hydraulic conductivity for unfrozen soils, derived from Eq. [3-5], m/s;

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 is impedance factor, 6.5 for silt loam (Zhao et al., 2012);  i is ice content, m /m ; 3

3

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References

rn

al

 t is total water content of soils, m3 /m3 ; and  r is residual water content, m3 /m3 .

Azmatch, T.F., Sego, D.C., Arenson, L.U. and Biggar, K.W., 2012. Using soil freezing characteristic curve to estimate the hydraulic conductivity function of partially frozen soils. Cold Regions Science and Technology, 83-84, 103-109. Baker, J.M. and Spaans, E.J.A., 1997. Mechanics of meltwater movement above and within frozen soil. In: Hanover, N.H. (Ed.), International Symposium on Physics, Chemistry, and Ecology of Seasonally Frozen Soils. U.S. Army Cold Reg. Res. and Eng. Lab., Fairbanks, Alaska, pp. 31-36. Berg, R.L., 1983. Status of numerical models of heat and mass transfer in frost-susceptible soils. Proceedings of the Fourth International Conference on Permafrost, Fairbanks, Alaska, pp. 67-71. Bittelli, M., Flury, M. and Campbell, G.S., 2003. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res., 39 (2), 1041. Black, P.B. and Tice, A.R., 1989. Comparison of soil freezing curve and soil-water curve for Windsor sandy loam. Water Resour. Res., 25, 2205-2210. Black, P.B. and Hardenberg, M.J., 1991. Historical perspectives in frost heave

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research, the early works of S. Taber and G. Beskow. CRREL Special report. Burt, T.P. and Williams, P.J., 1976. Measurement of hydraulic conductivity of froze n soils. Canadian Geotechnical Journal, 11, 647-650. Cary, J.W., Papendick, R.I. and Campbell, G.S., 1979. Water and salt movement in unsaturated frozen soil: Principles and field observations. Soil Sci. Soc. Am. J., 43, 3-8. Everett, D.H., 1959. An introduction to the study of chemical thermodynamics. Longmans Green and Co., New York. Flerchinger, G. and Saxton, K., 1989a. Simultaneous heat and water model of a freezing snow-residue-soil system II. Field verification. Trans. ASAE, 32 (2), 573-578. Flerchinger, G. and Saxton, K., 1989b. Simultaneous heat and water model of a freezing snow-residue-soil system I. Theory and development. Trans. ASAE, 32 (2), 565-571. Flerchinger, G.N., Seyfried, M.S. and Hardegree, S.P., 2006. Using soil freezing characteristics to model multi-season soil water dynamics. Vadose Zone Journal, 8, 1143-1153. Fuchs, M., Campbell, G. and Papendick, R., 1978. An analysis of sensible and latent heat flow in a partially frozen unsaturated soil. Soil Science Society of America Journal, 42 (3), 379-385. Hansson, K., Simunek, J., Mizoguchi, M. and Genuchten, M.T.v., 2004. Water flow and heat transport in frozen soil: Numerical solution and freeze-thaw applications. Vadose Zone Journal, 3, 693-704. Harlan, R.L., 1973. Analysis of coupled heat- fluid transport in partially frozen soil. Water Resour. Res., 9, 1314-1323. Horiguchi, K. and Miller, R.D., 1983. Hydraulic conductivity function of frozen materials. Proc. 4th Int. Conf. Permafrost. National Academy Press, Washington, D.C., pp. 504-508. Iwata, Y., Hayashi, M. and Hirota, T., 2008. Comparison of Snowmelt Infiltration under Different Soil-Freezing Conditions Influenced by Snow Cover. Vadose Zone Journal, 7 (1), 79. 10.2136/vzj2007.0089 Iwata, Y., Hayashi, M., Suzuki, S., Hirota, T. and Hasegawa, S., 2010. Effects of snow cover on soil freezing, water movement, and snowmelt infiltration: A paired plot experiment. Water Resources Research, 46 (9), 1-11. 10.1029/2009wr008070 Iwata, Y., Nemoto, M., Hasegawa, S., Yanai, Y., Kuwao, K. and Hirota, T., 2011. Influence of rain, air temperature, and snow cover on subsequent spring-snowmelt infiltration into thin frozen soil layer in northern Japan. Journal of Hydrology, 401 (3-4), 165-176. 10.1016/j.jhydrol.2011.02.019 Iwata, Y., Yazaki, T., Suzuki, S. and Hirota, T., 2013. Water and nitrate movements in an agricultural field with different soil frost depths: field experiments and numerical simulation. Annals of Glaciology, 54 (62), 157-165. 10.3189/2013AoG62A204 Jame, Y.W. and Norum, D.L., 1980. Heat and mass transfer in freezing unsaturated porous media. Water Resour. Res., 16, 811-819. Jury, W.A. and Horton, R., 2004. Soil Physics. John Wiley, Hoboken, N.J.

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Kelleners, T.J. and Norton, J.B., 2012. Determining water retention in seasonally frozen soils using Hydra impedance sensors. Soil Sci. Soc. Am. J., 76, 36-50. Konrad, J.M. and Morgenstern, N.R., 1980. Heat and mass transfer in freezing unsaturated porous media. Canadian Geotechnical Journal, 17, 473-486. Koopmans, R.W.R. and Miller, R.D., 1966. Soil freezing and soil water characteristic curves. Soil Science Society of America Journal, 30 (6), 680-685. Kozlowski, T., 2003a. A comprehensive method of determining the soil unfrozen water curves: 1. Application of the term of convolution. Cold Regions Science and Technology, 36, 71-79. Lebeau, M. and Konrad, J., 2012. An extension of the capillary and thin film flow model for predicting the hydraulic conductivity of air- free frozen porous media. Water Resour. Res., 48, W07523. Lundin, L.C., 1990. Hydraulic properties in an operational model of frozen soil. Journal of Hydrology, 118, 289-310. McCauley, C.A., White, D.M., Lilly, M.R. and Nyman, D.M., 2002. A comparison of hydraulic conductivities, permeabilities and infiltration rates in frozen and unfrozen soils. Cold Regions Science and Technology, 34, 117-125. Miller, R.D., 1966. Phase equilibra and soil freezing. In: I.N., L. (Ed.), Int. Conf. Proc. Permafrost. Natl. Research Council, Wahsington, D.C., pp. 193-197. Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res., 12 (3), 513-522. Newman, G.P. and Wilson, G.W., 1997. Heat and mass transfer in unsaturated soils during freezing. Canadian Geotechnical Journal, 34, 63-70. Patterson, D.E. and Smith, M.W., 1980. The use of time domain reflectometery for the measurement of unfrozen water content in frozen soils. Cold Regions Science and Technology, 3, 205-210. Schofield, R.K., 1935. The pF of water in the soil. In: Crowther, E.M. (Ed.), Trans. Int. Congr. Soil Sci. Thomas Murby & Co., London, Oxford, UK, pp. 37-48. Shanley, J.B. and Chalmers, A., 1999. The effect of frozen soil on snowmelt runoff at Sleepers River, Vermont. Hydrological Processes, 13 (12‐ 13), 1843-1857. Singh, K.P., Basant, A., Malik, A. and Jain, G., 2009. Artificial neural network modeling of the river water quality—a case study. Ecological Modelling, 220 (6), 888-895. Spaans, E.J.A. and Baker, J.M., 1996. The soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic. Soil Science Society of America Journal, 60, 205-210. Taylor, G.S. and Luthin, J.N., 1978. A model for coupled heat and moisture transfer during soil freezing. Canadian Geotechnical Journal, 15, 548-555. Topp, G.C., Davis, J.L. and Annan, A.P., 1980. Electromagnetic determination of soil water content: Measurement in coaxial transmission lines. Water Resour. Res., 16, 574-582. Watanabe, K. and Flury, M., 2008. Capillary bundle model of hydraulic conductivity for frozen soil. Water Resources Research, 44, 1-9. Watanabe, K., Kito, T., Dun, S.H., Wu, J.Q., Greer, R.C. and Flury, M., 2013. Water

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infiltration into a frozen soils with simultaneous melting of the frozen layer. Vadose Zone Journal, 12(1). 10.2136/vzj2011.0188 Williams, P.J., 1964. Unfrozen water content of frozen soils and soil moisture suction. Géotechnique, 14 (3), 231-246. Wu, M., Tan, X., Huang, J., Wu, J. and Jansson, P.-E., 2015. Solute and water effects on soil freezing characteristics based on laboratory experiments. Cold Regions Science and Technology, 115, 22-29. Zhao, Y., Nishimura, T., Hill, R. and Miyazaki, T., 2012. Determining hydraulic conductivity for air- filled porosity in an unsaturated frozen soil by the multistep outflow method. Vadose Zone Journal, 12 (1). 10.2136/vzj2012.0061

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Tables Table 1. Statistical analysis for fitted parameters of SFCC under various solute conditions. Solute content (g g -1 dry soil)

Statistical results

a

Solute type

Mean

Standard

value

deviation

0.15

0.19

0.03

0.25

0.26

0.28

0.02

0.29

0.25

0.27

0.28

0.02

0.28

0.30

0.24

0.27

0.30

0.05

0.27

0.30

0.25

0.30

0.28

0.02

0.30%

0.50%

0.70%

1.00%

NaCl

0.24

0.20

0.16

0.18

KCl

0.29

0.31

0.27

CaCl2

0.28

0.32

MgSO4

0.38

MgCl2

0.29

0.22

0.30

KCl

0.22

0.22

0.16

CaCl2

0.20

0.24

0.20

MgSO4

0.31

0.14

0.20

MgCl2

0.19

0.17

0.18

0.16

0.15

0.23

0.07

0.15

0.14

0.18

0.03

0.12

0.14

0.18

0.04

0.12

0.14

0.18

0.07

0.13

0.17

0.17

0.02

e-

0.33

al

Pr

NaCl

pr

b

oo

f

0.10%

rn

Table 2. V-G model parameters estimated by SFCC and the combination of SWCC and SFCC.

Solute content

NaCl

Jo u

Solute type

SFCC

SWCC

+SFCC

KCl

SFCC

SWCC +SFCC

CaCl2 SWCC

SFCC

+SFCC

MgSO4 SFCC

SWCC +SFCC

MgCl2 SFCC

SWCC +SFCC

 1/cm

CK

0.0095

0.0183 0.0089 0.0200

0.0096 0.0184 0.0089 0.0200

0.0633 0.0298

0.10%

0.0020

0.0045 0.0011 0.0050

0.0010 0.0036 0.0017 0.0047

0.0130 0.0121

0.30%

0.0017

0.0083 0.0042 0.0118

0.0122 0.0135 0.0037 0.0051

0.0272 0.0164

0.50%

0.0037

0.0104 0.0043 0.0109

0.0046 0.0136 0.0046 0.0093

0.0162 0.0084

0.70%

0.0038

0.0068 0.0101 0.0217

0.0095 0.0201 0.0122 0.0165

0.0311 0.0208

1.00%

0.0093

0.0135 0.0201 0.0590

0.0192 0.0170 0.0051 0.0073

0.0143 0.0109

n CK

1.3102

1.2880 1.3078 1.2803

1.3092 1.2874 1.3078 1.2803

1.2214 1.2522

0.10%

1.2464

1.2117 1.2953 1.2183

1.3072 1.2405 1.2568 1.2079

1.1680 1.1718

0.30%

1.2471

1.1899 1.2120 1.1794

1.1891 1.1908 1.2176 1.2047

1.1770 1.1957

0.50%

1.2165

1.1860 1.2209 1.1906

1.2020 1.1756 1.2105 1.1894

1.1848 1.2103

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1.2439

1.2218 1.1898 1.1740

1.2027 1.1850 1.1926 1.1883

1.1744 1.1867

1.00%

1.1964

1.1862 1.1429 1.1265

1.1714 1.1816 1.2128 1.2015

1.1988 1.2100

R

2

0.9486

0.9800 0.9475 0.9758

0.9472 0.9797 0.9475 0.9758

0.9777 0.9644

0.10%

0.9192

0.9679 0.7650 0.8977

0.7218 0.9050 0.9308 0.9732

0.9571 0.9737

0.30%

0.8650

0.9393 0.8977 0.9626

0.8933 0.9577 0.9326 0.9660

0.9639 0.9710

0.50%

0.8332

0.9318 0.9340 0.9772

0.8596 0.9402 0.9211 0.9625

0.9764 0.9786

0.70%

0.9627

0.9841 0.8849 0.9605

0.9055 0.9579 0.9199 0.9672

0.9753 0.9782

1.00%

0.8837

0.9681 0.7988 0.9151

0.8396 0.9489 0.9252 0.9768

0.9803 0.9923

Jo u

rn

al

Pr

e-

pr

oo

f

CK

oo

f

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Jo u

rn

al

Pr

e-

pr

Fig. 1. SWCCs of soils with different solute types and solute content levels.

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Jo u

rn

al

Pr

e-

pr

oo

f

Fig. 2. Plot of mean fitting V-G model parameters for SWCCs.

oo

f

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Jo u

rn

al

Pr

e-

pr

Fig. 3. SFCCs of soils with different solute types and solute content levels.

oo

f

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Fig. 4. Combination of SWCCs and SFCCs of soils with different solute types and

Jo u

rn

al

Pr

e-

pr

solute content levels.

e-

pr

oo

f

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Pr

Fig. 5. Comparison of θr estimated from SWCCs data and combination data of

Jo u

rn

al

SWCCs and SFCCs.

pr

oo

f

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e-

Fig. 6. Hydraulic conductivities of soils with different solute conditions calculated

Jo u

rn

al

Pr

from combination data of SWCCs and SFCCs.

f

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oo

Fig. 7. Comparison of (a) water retention curves and (b) hydraulic conductivities

pr

calculated by different methods (conventional methods: hanging water method,

e-

-160
Pr

Symbols in (a) were measured values for silt loam, loam (Watanabe et al., 2013), silt loam 1 and silt loam 2 (Watanabe and Flury, 2008) by different methods. Red solid

al

line in (a) denoted silt loam data of soil from Inner Mongolia calculated by capillary

rn

bundle model, and blue solid line represented soil water retention by combination of

Jo u

SWCC and SFCC method. Hydraulic conductivities of Chena, Calgary, and Illite (open symbols) in (b) were results measured by Horiguchi and Miller (1983). Green solid line, green dot line and purple dash line in (b) were results calculated by capillary bundle model for Chena, Calgary and Illite soil respectively. Red solid line in (b) was the result of combination of SWCC and SFCC method for silt loam in Inner Mongolia; pink dash line denoted capillary bundle model (Eq.[A1]) results for silt loam in Inner Mongolia; blue dot line in (b) represented hydraulic conductivity calculated by impedance factor method (Eq.[A3]).

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The effects of solute type and content on SWCC and SFCC were investigated through experiments The hydraulic properties of saline frozen soil were predicted by the

rn

al

Pr

e-

pr

oo

f

combination of SWCC and SFCC

Jo u

