Mathematical and Computer Modelling 58 (2013) 725–730

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Mathematical and Computer Modelling

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Computer forecasting of the soil water infiltration parameters inseasonal freezing and thawing periods✩

Guisheng Fan ∗, Yonghong Han, Danni MaCollege of Water Resources Science and Engineering of Taiyuan University of Technology, Taiyuan Shanxi province, 030024, China

a r t i c l e i n f o

Article history:Received 30 September 2011Accepted 25 October 2011

Keywords:Freezing and thawing soilsParameters of infiltration modelForecasting modelsSoil transmission functionIrrigation

a b s t r a c t

Based on the tests of field soil water infiltration under three kinds of soil texture in threefreezing and thawing periods, with the help of the method of mathematical statistics, aforecasting model of soil infiltration parameter in seasonal freezing and thawing periodshas been established. The result indicates that it is feasible to forecast the soil waterinfiltration parameters in seasonal freezing and thawing periods through soil transmissionfunction; when content of soil physical sticky granule, soil dry density, soil moisturecontent and soil temperature are chosen for input variables of the model, a satisfactoryforecasting accuracy can be obtained; compared with the Product model, the multivariatelinear forecasting model has higher precision. The establishment of the forecasting modelhas scientific meaning for enriching freeze–thaw soil physical theory, and is of practicalsignificance for determining the reasonable irrigation technical parameters in theseseasonal freezing and thawing districts within the winter and early spring seasons.

Published by Elsevier Ltd

1. Introduction

The winter–spring irrigation in many districts in North China has been carried under the condition of seasonal freezingand thawing soils. In winter, the soil temperature within the scope of certain depth below the surface in these areas isbelow 0 °C, which makes part of soil moisture frozen, and compared with the no-frozen soil, the original ratio of the solid,liquid, gas phase of the soil layers changes. Therefore, comparedwith the no-frozen soil, frozen soils have has some inherentcharacteristics; the change of the infiltration characteristics is one of these features. In the past several decades, at homeand abroad, most research on soil moisture infiltration during freezing and thawing periods have been focused on the waterloss and soil erosion caused by snow melting [1–3], the soil swelling from soil frozen-in and the change of moisture andsalinity [4], the influence factors andmechanism of moisture infiltration into freezing and thawing soils [5–9] and so on, butfew of the researches have involved in the soil infiltration model parameters and the forecasting of the model parametersduring freezing and thawing periods in frozen areas. The forefather’s research result shows that the change processes of themoisture infiltration velocity or accumulation with the time can be represented by some experience infiltration models[5–9], in which the most extensive application is Kostiakov–Lewis’s three parameter model H = Ktα + f0t . Howeverup till the present moment, the parameters of all kinds of experience models are only obtained through the infiltrationexperiment method. The infiltration tests are time-consuming, strenuous and difficult to acquire data during freezing andthawing periods. If we can forecast these parameters of k, α and f0 in the Kostiakov–Lewis infiltration model through someregular soil physical parameters observed, namely the forecasting of soil moisture infiltration process is realized, then theproblemwill be solved, which is the soil infiltration model parameters deeded in the determining of the farmland irrigation

✩ Nation Natural Science Foundation project: No. 40671081; Shanxi Province Science and Technology Development project: No. 20100311124.∗ Corresponding author. Tel.: +86 351 6111102, +86 135 03511295; fax: +86 351 6111395.

E-mail addresses: fanguis5507@263.net, fyttxl@163.com (G. Fan).

0895-7177/$ – see front matter. Published by Elsevier Ltddoi:10.1016/j.mcm.2011.10.031

726 G. Fan et al. / Mathematical and Computer Modelling 58 (2013) 725–730

technical parameter. In this paper, based on the tests of field soil water infiltration under three kinds of soil texture at Fenheriver irrigation area in Shanxi Province in three freezing and thawing periods, with the help of the method of mathematicalstatistics, we tried to establish the relationship between soil convention physical parameters and soil moisture infiltrationmodel parameters during freezing and thawing periods, to solve the problem that is soil moisture infiltration parametersin the implementing of saving-water irrigation during freezing and thawing periods, and to supply technology supportfor determining irrigation technical parameters for saving-water irrigation within the winter–spring irrigation in seasonalfreezing and thawing soils.

2. Materials and methods

2.1. The weather condition in the experiment area

The field tests of moisture infiltration into freezing and thawing soils were conducted at three places (Center irrigationexperiment station of Shanxi Province, Ninggu experiment station at Fendong substation irrigation area of Fenhe irrigationarea and Changshou experiment station at north of Fenhe three-dam irrigation substation area) during three freezing andthawing year periods. These three experiment areas are all located in Fenhe irrigation area in Shanxi province. The climateof these experiment areas is a typical continental half-arid monsoon climate, with the 130–135 kJ/cm2 total sun ratio of allyear, the 9.5 °C annual average temperature, the 39.4 °C extreme highest temperature and the −28.0 °C extreme lowesttemperature. The time when the soil of experiment areas begins to freeze is during early November and the time when thesoil thaws is duringMarch of the next year. The coldestmonth is Januarywith−6.5 °C average temperature, the soil deepestfrozen depth is 95 cm. The air temperature and the soil temperature of eachmonth at the 5 cm depth under the surface earthduring the experiment period are listed in Table 1.

2.2. Experiment equipments

The main equipment used in the soil moisture infiltration tests during freezing and thawing periods is a double-ringinfiltration instrument. The diameter of the inner inside ring is 26.3 cm and the diameter of the outside ring is 60 cm. Thisequipment can realize the autowater supply of the inside ring and the auto control of the infiltrationwater head. Consideringthe difficulty in embedding infiltration rings into soils and the freezing of the water supply in Marriott Water Supply Bucketduring winter, the decreasing metering precision of inner ring water supply, before the land surface earth was frozen, wehad processed more than 30 infiltration experiment equipments of the same size, and embedded them into the experimentland, andmetered the infiltration amount of the inner ring with graduated cylinders. The united inbuilt-ring depth into soilsis 20 cm (reaching the bottom of plow). Furthermore we manufacture a control device of water level to ensure the balancebetween the water levels in the inside and outside rings. The water used in the infiltration experiment is well water, thechange of water temperature is 4–9 °C.

2.3. The condition of tested soils

The three experiment stations located in the Fenhe irrigation district in Shanxi province, and at the bottom of TaiyuanBasin, belong to alluvial flatland deposited geomorphology, with a flat terrain. The parent material of the tested soils ismainly constituted of the Fenhe River alluvial and proluvial deposits, and the soil type is moisture soils and meadow soils.The burial depth of ground water table is between 1.0 and 3.0 m. The thickness of the plowed soil layer is between 19 and22 cmand for the reason of the long-termplowing the plowpan is obvious. TheNorth of China belongs to seasonal frozen soilarea, where the farming soils are usually in such three statuses as dead fallowing, not-dead fallowing and growing wintercrops during freezing and thawing periods in winter and spring, so in this experiment we choose those three lands as typicalsoil condition to reflect the different soil textures. During the freezing and thawing periods for three years, there were eightplowing conditions to be conducted in order to carry out the infiltration experiment. The eight soil conditions are listed inTable 2.

3. Establishing of the forecasting models

3.1. The structure of model

At first, the Product model and the multivariate linear forecasting model were adopted as the forecasting model. Thenby considering the model forecasting precision, one between the two models, which has higher precision, is chosen as theforecasting model.(1) The multivariate linear model.

Y = β0 + β1x1 + β2x2 + β3x3 + · · · + βnxn (1)

where Y—some forecasted parameter of infiltration model; βi—regression coefficient of model; xi—influence elementparameter of number i; n—the amount of variables.

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Table 1Air and soil temperature of each month during test (°C).

The periods of experiment Month November December January February March

1995/11–1996/3 The month average air temperature 2.9 −3.4 −5.7 −3.4 3.5The month average soil temperature at 5 cm 9.5 −3.2 −4.9 −2.8 2.8

1998/11–1999/3 The month average air temperature 6.1 −1.3 −3.4 0.8 6.8The month average soil temperature at 5 cm −4.5 −8.6 −10.9 −7.7 −1.1

1999/11–2000/3 The month average air temperature 4.3 −2.3 −7.1 −1.3 7.3The month average soil temperature at 5 cm −2.3 −8.9 −12.6 −8.0 −1.4

Table 2Soil conditions at eight kinds of plowing status.

Site Content of physical clay (%) Plowing status Dry density (g cm−3) Volumetric water content0–5 cm 5–20 cm

Center station 55.7Fall plowing land 1.06 1.08 5.3–19.8Winter wheat land 1.07 1.18 6.0–20.2Not-farming land 1.36 1.20 6.9–25.3

Ninggu station 45.3 Fall plowing land 1.09 1.08 12.8–20.9Not-farming land 1.21 1.23 17.3–25.2

North Changshou station 50.98Fall plowing land 1.10 1.13 21.1–10.4Winter wheat land 1.15 1.21 22.8–18.5Not-farming land 1.23 1.32 10.8–8.7

(2) The Product model.

Y = α0pα11 pα2

2 pα33 · · · pαn

n (2)

where αi—regression coefficient of model; pi—influence element parameter of number i.

3.2. The choice of model variables

Two types of variables will be used in the model, one is forecasting variable, and another is self-variable.(1) Forecasting variableThe forecasting variable is infiltration coefficient k, infiltration exponent α and relative stable infiltration ratio f0 in the

three parameter infiltration model H = Ktα + f0.(2) Self-variablesUnder the non-frozen soil condition, themain elements that influence the soil infiltration characteristics are soil texture,

structure and the moisture content. Under the frozen soil condition, in addition to the above factors there are some otherinfluence elements, which are the soil temperature, the irrigationwater temperature, the thickness, quantity and position ofthe frozen layers and so on [5]. If all the influence elements are considered as the input variables of the forecasting model, itwill be difficult to determine and apply the parameters ofmodel. For this reason, whenwe choose themodel input variables,we just consider some main variables, and the other secondary influence elements are contained in the parameter of β0.According to the analysis of experimental results, under the frozen soil condition, the main influence elements of the soilinfiltration characteristics are soil texture, soil structure, moisture content and the soil temperature. Each influence elementis listed as follows.

① Soil texture. Soil texture influences soil infiltration characteristics through the effecting on soil water potential andhydraulic transmissibility. The quantity indicator of soil texture is generally marked by the distribution of soil granule. Inthe forecasting model, the ratio that the soil weight of less than some grain diameter in the total soil weight is selectedas reflection index of soil texture. The analysis results of the relation between the infiltration model parameters of threekinds of soils and the physical clay content and the clay content indicates that the relation between the soil infiltrationmodel parameters and the physical clay content is more closer than that of the clay content, so the physical clay contentwas chosen as the index to reflect the influence of the soil texture on soil infiltration characteristics.

② Soil structure. The soil structure reflects soil density and hardened degree. In thismodel, the influence of soil structure onsoil infiltration characteristics is reflected through the soil dry density. Moisture infiltration into soils is a process wherethe moisture enters soil via surface ground, so the land surface as the upper boundary of soil moisture infiltration playsa control role to the ability of soil moisture infiltration in most cases. Therefore the average soil density from the landsurface to 10 cm depth was chosen as the input variable reflecting soil structure influence in the forecasting model.

③ Soilmoisture content.Moisture content of soil is one of themain influence elements on soilmoisture infiltration capacity.Under the non-frozen condition of soils, the moisture content of soil influences mainly soil moisture infiltration capacitythrough its influence on water potential gradient. Under the frozen condition of soils, because the soil moisture contentis the material foundation of soil phase changing generated from the negative soil temperature, the water content has

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bigger influence on the ability of soilmoisture infiltration. The land surface is control interface of soilmoisture infiltration,and the moisture infiltration depth is small under frozen soil condition, so the moisture content from the land surface to10 cm depth is chosen as the index reflecting the soil moisture influence in the forecasting model.

④ Soil temperature. Under frozen soil condition, the soil temperature becomes a main element that influences the soilmoisture infiltration characteristics. The analyzed result of the infiltration tests that there has a better correlationbetween the parameters of the soil moisture infiltration model and the soil temperature at 5 cm depth. Therefore, inthe forecasting model, the soil temperature at 5 cm depth is taken for the variable reflecting the temperature influenceon the ability of soil moisture infiltration. To be satisfied with the demand of the nonzero and nonnegative variablein model parameter evaluating and hypothesis testing, the soil temperature is expressed in the absolute value of thenegative temperature.

⑤ Other elements. The thickness of soil frozen crust, the buried depth of groundwater table, the irrigation watertemperature etc. also have influence on the frozen soil infiltration characteristics. Nevertheless, there is better relevancebetween the thickness of soil frozen crust and the absolute value of the soil negative temperature, so the influence ofthe thickness of frozen crust on the frozen soil infiltration characteristics is included in the influence of soil negativetemperature on the infiltration ability. Therefore the thickness of the frozen crust is not considered as an independentvariable in the model. The temperature of irrigation water has some influence on the ability of soil infiltration also.The infiltration water temperature in the experiment is considered to be an independent variable in the model design.Nevertheless, the inspected result of the significance for the input variables, indicated that compared with other inputvariables the influence of water temperature variable is not significant; thus in the sequential model establishing thewater temperature is not considered as an independent variable.

In conclusion, the main independent variables in this forecasting model are soil texture, soil structure, soil moisturecontent and soil temperature. Owing to the complex nature of the problem, the influence of other variables is syntheticallyconsidered in the model constant coefficient item. Need to say: there are different input elements for different forecastedoutput parameters; thus the T testing method of statistics is used to select the input variables during the subsequentestablishment of forecasting model.

3.3. The establishment of a forecasting model

3.3.1. Forecasting model under the given soil texture conditionUnder the given soil texture condition, there are mainly three influence elements on the forecasted parameters. In order

to inspect the significance of irrigation water temperature to the forecasted parameters, two input variable combinationsare designed as follows: ① three input variables combination, including the soil density, water content and soil negativetemperature absolute value; ② four input variables combination, including the soil density, water content and soil negativetemperature absolute value and the temperature of infiltration water.

Taking the tested data at Ninggu experiment station in Pingyao county for the data sample, through calculating withhelp of the statistics method and computer, the regression coefficients of the two chosenmodels forecasting thosemoistureinfiltration model parameters (k, a and f0) of freezing and thawing soils, the significant testing value F of the regressionmodels and the significant testing value Ti of each input variables in the two input variable combinations are based on,according to twokinds ofmodel structure and input variable combination are listed in Tables 3 and4. The level of significancetest of the regression and the input variables are designated as 5%, and the calculated relevant Fα (n,m − n − 1) andTα/2 (m − n − 1) are listed in Table 3.

From Tables 3 and 4, we know the following.

(1) For the forecasting of the parameters α and f0 in infiltration mode, no matter what model structure and variablecombinations are used, all the values of F are greater than the F0.05, which indicates that the regression is significant.However for the parameter K , the value of F is less than F0.05, which indicates that the regression is not significant.

(2) For the input variable of infiltration water temperature, the values of T4 are less than Tα/2 in most cases, which indicatethat its influence on forecasted parameters is non-significant. However for the other variables beyond the variable ofinfiltration water temperature, there are only special variable having non-significant influence in the regression modelof parameter α and f0. Totally, they have significant influence on the forecasted variable.

(3) Totally, the three variables combination has higher significance in regression and variable influence than four variablescombination.

(4) There is non-significant difference betweenmultivariate linear regressionmodels and Product model in the significanceof regression and variable influence. For the regression of the parameter α, the multivariate linear regression model isbetter than Product model, but for the regression of the parameter f0 the latter is better than the former. However fromthe forecasted intervals of these two kinds of models in the continued Table 3, under a given confidence probability, thelatter has far longer forecasted interval than the former.

Based on the comprehensive analysis of the calculated and inspected results, it can be considered that for the infiltrationindexα and the stable infiltration rate f0 in the soil infiltrationmodel, it is available to use the given forecastingmodels for theforecasting. Compared with four variable combination, the three variable combination has higher regression significance;

G. Fan et al. / Mathematical and Computer Modelling 58 (2013) 725–730 729

Table 3The parameter estimation and survey of the infiltration parameter forecasting model.

Forecasted parameters Model QT Qsurplus Qregression F F0.05 T1 T2 T3 T4 T0.025 DOF

α

I 0.24 0.07 0.17 6.06 2.45 −6.45 −5.25 −0.52 2.54 1.96 67II 13.14 4.88 8.26 5.17 2.45 −4.55 −4.62 −1.72 1.73 1.96 68III 0.24 0.08 0.16 6.56 2.68 −6.14 −5.37 −4.59 1.96 68IV 13.14 5.11 8.03 5.79 2.68 −4.6 −4.40 −3.91 1.96 68

k

I 18.35 16.23 2.12 1.57 2.45 −2.51 −0.15 0.93 1.59 1.96 80II 9.10 8.33 0.77 1.32 2.45 −2.04 0.74 0.23 1.14 1.96 81III 19.35 16.77 1.58 1.55 2.68 −2.65 −0.04 −0.51 1.96 81IV 9.10 8.47 0.63 1.38 2.68 −2.22 0.92 −0.84 1.96 81

f0

I 0.07 0.05 0.02 2.77 2.45 −3.35 −1.87 −0.33 −1.5 1.96 78II 118.3 36.41 81.9 6.41 2.45 −2.75 −5.19 −2.50 4.24 1.96 78III 0.07 0.05 0.02 3.05 2.68 −3.48 −1.80 −2.22 1.96 78IV 118.3 45.38 72.93 6.30 2.68 −3.12 −4.09 −6.35 1.96 78

Forecasting parameters Model β0 β1 β2 β3 β4 Forecasting value Forecasting interval Sample’s length

α

I 0.6727 −0.3844 −0.0025 −0.0009 0.0048 0.199 −0.721 1.119 67II 1.5866 −2.7029 −0.6348 −0.02921 0.1509 0.184 −2.971 3.339 68III 0.7395 −0.3812 −0.0027 −0.0046 0.189 0.071 0.307 68IV 1.9959 −2.7667 −0.6064 −0.0493 0.181 −2.782 3.144 68

k

I 3.6771 −1.8842 −0.0010 0.0181 0.0307 1.767 0.677 2.857 80II 1.3297 −1.3218 0.0798 0.0038 0.0997 1.649 −1.107 4.405 81III 4.2142 −2.0002 −0.0003 −0.0062 1.686 0.704 2.668 81IV 1.5642 −1.4265 0.0983 −00098 1.625 −1.099 4.349 81

f0

I 0.2261 −0.1581 −0.0006 −0.0004 0.0017 0.037 −0.027 0.101 78II 1.1835 −4.3678 −1.6888 −0.0938 0.8431 0.027 −15.143 15.197 78III 0.2558 −0.1646 −0.0006 −0.0016 0.032 −0.036 0.1 78IV 3.8809 −5.4279 −1.4564 −0.1988 0.023 −16.347 16.393 78

Annotation: I—four kinds of variable multivariate linear model; II—four kinds of variable product model; III—three kinds of variable multivariate linearmodel; IV—three kinds of variable product model.

Table 4Parameter estimation and survey of the infiltration parameter forecasting model.

Forecasting item QT Qsurplus Qregression F F0.05 T1 T2 T3 T4 T0.025 Free degree

α 0.29 0.13 0.17 5.06 2.45 −6.94 4.58 −2.30 −7.53 1.96 83k 13.55 9.48 1.07 2.89 2.45 0.01 −3.16 −2.35 −0.66 1.96 83f0 0.02 0.01 0.01 5.14 2.45 −6.27 −3.70 −3.44 −7.71 1.96 82

Forecasting item β0 β1 β2 β3 β4 Forecasting value Forecasting interval Sample length

α 0.8059 −0.8319 −0.1442 −0.0005 −0.0132 0.194 0.107 0.281 83k 3.0961 0.0096 −0.9673 −0.0097 −0.0102 2.094 1.301 2.887 83f0 0.1699 −0.1913 −0.0324 −0.0004 −0.0034 0.029 0.008 0.05 82

the multivariate linear regression model is of better effect than the Product model. Consequently, the multivariate linearregressionmodel with three input variable combination can be adopted to forecast the parameters of soil infiltrationmodel.

3.3.2. The forecasting model of various texture soilsIf the multivariate linear regression model of three variable combination (soil density, water content and the absolute

value of soil negative temperature) is applied to frozen soil infiltration model parameter forecasting with various texturesoils, another input variable (the content of soil physical clay) will be added, then the three variable combination becomes afour variables combination. The estimated value of regression coefficient, the testing value F of regression significance, thetesting value T of regression variable, and forecasting intervals are listed in Table 4 and continued in Table 4.

The calculated and inspected results in Table 4 showed that for the multivariate linear model, the regression significanceof all the infiltration model parameters are significant, and the regression significance of the large sample is better than thesmall one.

4. Forecasting examples

Two groups of the testing datum were randomly drawn from the testing datum, the first group data (A) was obtainedat Ninggu test station of Pingyao during the later stage of soil steady frozen phase, the other group data (B) was obtainedat the Center experiment station during the later stage of thawing phase, the soil physical parameters are listed in Table 5.

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Table 5Soil physical parameters of the example.

Group Physical clay content (%) Soil density (g/cm3) Soil water content (wt%) The absolute value of negative temperature (°C)

A 0.51 1.322 21.73 3.4B 0.56 1.0 4.1 0.01

Table 6Forecasted result of infiltration model parameters.

Group Method α k (cm/min) f0 (cm/min) H90 (cm) Infiltration model

A Actual measurement 0.1934 1.5177 0.0215 4.98 H = 1.5177 × t0.1934 + 0.0215 × f0Forecasting 0.1350 1.5770 0.0100 3.80 H = 1.5770 × t0.1350 + 0.0100 × f0

B Actual measurement 0.2487 2.3499 0.0047 7.560 H = 2.3499 × t0.2478 + 0.0047 × f0Forecasting 0.1940 2.0940 0.0290 7.623 H = 2.0940 × t0.1940 + 0.0290 × f0

With the help of the established forecasting model, the soil infiltration model parameters forecasted, and the forecastedparameters and the soil moisture infiltration models are listed in continued Table 6.

5. Conclusions

(1) It is available to forecast the soil infiltration ability through the multivariate linear regression model.(2) The inspected result of the significance for the regression model and the significance of the input variables to the

forecasted variables indicates that the forecasted result of the multivariate linear regression model is better than theProduct model; among all the factors which reflect the physical and chemical characteristics of the frozen soil, thephysical clay content (less than 0.02 mm), the dry density, the four factors of the moisture content and the absolutevalue of negative temperature of soils have significant influence on soilmoisture infiltrationmodel parameters,while thetemperature of the infiltration water has non-significant influence on the ability of soil infiltration. These four variablesabove can be used as input variables of the forecasting model of the infiltration model parameters.

(3) It is available to use themultivariate linear regressionmodel to forecast the infiltrationmodel parameters σ and relativestable infiltration rate f0; the significance of forecasting parameter k is worse than σ and f0.

References

[1] D.L. Kane, J. Stein, Water movement into seasonally frozen soils, Water Resources Research 19 (6) (1983) 1547–1557.[2] J.L. Pikul, J.F. Zuzel, D.E. Wilkins, Water infiltration into frozen soil: field measurements and simulation, in: Proceedings of the National Symposium,

December 16–17, Chicago, Illinois, USA.[3] J.L. Pikul, J.F. Zuzel, D.E. Wilkins, Infiltration into frozen soil as affected by ripping, Transactions of the ASAE 35 (1) (1992) 83–89.[4] Xingfa Huang, QianWang, Dechao Zeng, Experimental study on thermalmotion regular of soil water during freezing period, Transactions of the Chinese

Society of Agricultural Engineering 9 (3) (1993) 28–32.[5] Fan Guisheng, Jia Hongj, Li Hanyan, Experimental study on main factors influencing water infiltration features of freezing and thawing soils,

Transactions of the Chinese Society of Agricultural Engineering 15 (4) (1999) 88–94.[6] Fan Guisheng, Xiuqing Zheng, Pan Guangzai, Experimental study on the influence of the buried depth of groundwater level on the infiltration

characteristics of freeze–thaw soils, Shui Li Xue Bao 29 (3) (1999) 21–26 (in Chinese with English abstract).[7] Zheng Xiuqing, Chen Junfeng, Xing Shuyan, et al., Soil temperature variation in plough layer and soil freeze–thaw characteristics during seasonal

freezing and thawing period, Journal of Irrigation and Drainage (2009) 6 (in Chinese with English abstract).[8] Zheng Xiuqing, Guishng Fan, Influence of moisture content on infiltration characteristics in seasonal frozen and thawed soils, Transactions of the

Chinese Society of Agricultural Engineering 16 (6) (2000) 52–55 (in Chinese with English abstract).[9] Chen Junfeng, Zheng Xiuqing, Xing Shuyan, et al., Influence of plastic film mulching on infiltration into seasonal freezing-thawing soil, Transactions of

the Chinese Society of Agricultural Engineering 22 (7) (2006) 18–21 (in Chinese with English abstract).