Mathematical Modelling of Soil Hydraulic Properties and Numerical Analyses of Moisture Dynamic


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Mathematical Modelling of Soil Hydraulic Properties and Numerical Analyses of Moisture Dynamic

Alhan Sariyev ¹, Veysel Polat ², Metin Müjdeci ¹, Melahat Yusufova ³, Erhan Akça ¹

¹ University of Çukurova, Faculty of Agriculture, Department of Soil Science, Adana/Turkey
² University of Çukurova, Vocational School of Adana, Adana/Turkey
³ University of Çukurova, Computer Sciences Research and Application Center, Adana/Turkey

Abstract

For determination of the state of soil water, which is a function of time and depth in soil system, water flux in soil should be modelled. Therefore, designating a suitable model yielding the interactions between soil moisture content (W), water potential (P) and hydraulic conductivity (K) is the prerequisite. Some samples collected from the some physical and chemical properties. Hydraulic conductivity and soil moisture characteristics of the studied soil were determined by utilizing SIMONA (SIMONA, is basic model describing physical and bio physical processes in agro ecosystem) software most suitable model known at present (Poluektov, 1991). For the solution of soil moisture dynamic equation finite differences method was used (Implicate). The soil water dynamics values obtained from the model and laboratory measurements were also correlated in the studies.

Introduction

Soil is a very complex system due to the numerous individual and mutual factors effecting irrigation, soil amelioration, illuvation, evapotranspiration and on circulation of pollutant materials applied to soil, soil thus determination of quantity and direction of water flow is very important (Rollston et al, 1976), for sustainable land management.Plant development models are being widely used in recent years. Approaches for developing models may be different, however, the basic principle of models is generally based on block system. In all plant development models, soil water flow block is always used (Veries and Laar, 1982; Bonderenko et al., 1982, Anlauf, 2001). Thus, one of the important dynamic block is soil flux, and for modelling of time and depth dependant process, two basic soil hydro physical properties, namely soil moisture dynamic and hydraulic conductivity should be well defined for accurate determination.

Theory
Definition of Soil Water Model: Soil suction curve and hydraulic conductivity should be determined initially for utilizing the model. Any changes of moisture content of certain layers at certain periods are determined by calculating water input and output of the layer. Energy and mass transfer in soils are expressed by diffusion processes, thus diffusion formulas used in mathematics and physics are used for determination of these transfer. Also, for adjusting heat flux, observation of soil moisture content, soil hydraulic conductivity and differential moisture content capacity are in accordance with above mentioned diffusion processes. Any change of soil moisture content (Dw) at Dt = tk+1-tk time increment is equal to water input and output of a layer, and expressed as below;

Water flux level in soil is calculated according to Darcy law.

where, V is water flux in soil. Change in moisture content at (tk + 1-tk) time is hj ; F is the thickness of the layer, area;

(Vj + 1-Vj): change of flux in the layer when flux is measured in layers j-1, j and j+1 according Darcy law in equation (3) then equation below is attained

where, hj : constant. When, Kj + 1 = Kj = Kj - 1 = K, is accepted as constant and (Vj ve Vj+1) flux, mentioned above is taken as:

Then the final equation is :

If equation is simplified in expression as: (h=hı=h2…….=hj)

For Wj layer the final equation is

The value of P is (cm and therefore Wj(tk +1) is dimensionless. Moreover, the conditions of upper and lower limits (at surface v=0) can be expressed as follows at selected NR depth, X=XR

Evaporated water and precipitation levels are expressed as Es and R, respectively in the formula. Water moisture curve and hydraulic conductivity in the formula are expressed as:

Soil water potential and moisture contents are expressed as Pd and Wd respectively. In the equation, A and m are semiamprical coefficients. Soil evaporation, which is an effective factor on soil water flux, model is:

where, pa : density of air (gcm-3), Ds : molecular moisture conductivity (cms-1) between soil and atmosphere, to wind velocity, qs(0) and qa are the soil surface and atmosphere's absolute moisture contents respectively (g H2Og-1 air). Generally absolute moisture content is a function of temperature (T) according to Magnus law (Poluektov, 1991)

Initial condition of model is:

Mathematical model of soil water flux should be analytical in relation to depth at some periods of other blocks.

Materials and Methods

The physical and chemical properties of disturbed and undisturbed soil samples collected from the Experimental Farm of Soil Science Department, University of Çukurova were determined according to the following methods. Texture Bouyoucos (1951), Bulk density on undisturbed soil samples collected by 100 cc cylinders (Blake&Hartge1986), Hydraulic conductivity (Klute&Dirksen,1986), pF curve at plate apparatus (Klute,1986), Salinity (U.S. Salinity Laboratory Staff, 1954), pH (Schlichting and Blume, 1966) (Tabel 1).

Results and Discussion

Soil water flux model, defined by equations 1-14, was used for simulating soil moisture contents of each 10 cm layers of 100 cm soil profiles, which is related to time, by utilising visual programming for Delphi 3.0 (Computer Program Language) software (Sarıyev and Polat, 1999).

By using the data in table 1 and 2, the equation 12 and 13 were used with the application of pF model bank in the simulation model. Equations (12-13) used in the model Pd =-5 cm, Wd=0.48 cm3cm-3, A=24, Kf = 0.87 cmh-1, m=2.1, ra=1.2*10 -3 gcm-3, Ds=1 cms-1 values are used for identification. Besides, for the certain block the initial moisture contents of the input parameters below are used.

Output parameters of the model are as follows:

For testing the soil moisture dynamic in accordance with the results from the simulation model, field measurements at one-week intervals, at same time, the volumetric soil contents were measured from 3 parallels of each sample (moisture dynamics of the model are observed according to initial field value). Results obtained both from field and the model is interpreted in Figure 1, 2, 3.

Conclusions

For the solution of soil moisture dynamic final differences method were used and stability state was observed in the solution. Results of investigated revealed that the model and field measurements are generally in accordance. Further studies conducted by the authors aim to integrate a model developed in this study into Energy-Mass Transfer and Plant Development Models in relation with other blocks, i.e the soil on movement Blocks and Plant Development Blocks. Two approach proposed in the study could be used for practical studies of bare soils water dynamic. Water budget was simplified on soil surface (runoff, deep infiltration, plant uptake were not included). This model could be used in arid and semi arid regions particularly fallowed land where no runoff occurs.

References

. Anlauf, R. 2001. Theory and Practice of Simulation Models for Processes in the Soil. University of Applied Sciences-FH Osnabrueck Faculty of Agricultural Sciences, Osnabrueck, Germany.
. Blake, G.R.,& Hartge, K.H.,1986. Bulk Density In: Methods of Soil Analysis, Part 1, Physical and Mineralogical Methods. (Ed: A. Klute) Agr. Monogr. 9. ASA and SSSA, Madison WI.p.363-375.
. Bondarenko, N.F., Jukovskı, E.E., Muskın, I.G., Nerpın, S.V., & Poluektov, R.A., 1982. Simulation of Agroecosystem Productivity. Gidrometeoziad, Leningrad. 262 p.
. Bouyoucos, G.J., 1951. Hydrometer Method Improved For Marking Particle Size Analysis of Soils. Agronomy J. 54, pp: 464-465.
. Klute, A., 1986. Water Retention: Laboratory Methods. In: Methods of Soil Analysis, Part 1, Physical and Mineralogical Methods. (Ed: A. Klute)Agr. Monogr. ). ASA and SSSA Madison WI. p. 635-662.
. Klute, A., & Dirksen, C.,1986. Hydraulic Conductivity and Diffusivity: Laboratory Methods. In: Methods of Soil Analysis, Part1, Physical and Mineralogical Methods. (Ed: A. Klute) Agr. Monogr. 9.ASA and SSSA, Madison WI p. 687-734.
. Poluektov, R.A., 1991. Simulation of Agroecosystem Dynamics. Gidrometoizadat, St-Petersburg, Rusia. 312p.
. Rollston, D.E., Sing, S., & Dakshınamurtı, C., 1976. Evaluation of The Field For Measuring of The Predicting Soil Water Properties J. Indiana. Soil Sci. 124, 2, pp.101-103.
. Sarıyev, A.,& Polat, V.,1999. Mathematical Modelling and Calculation of Energy and Mass Transfer in Soil-Plant-Atmosphere continuity. TBUS-3. Symposium of Computer Application in Agronomy. Computer Center of the Çukurova University, Adana-Turkey. p.14.
. Schlichting, E., & Blume, E., 1966. Bodenkundliches Practikum. Verlag Paul Parey. Hamburg and Berlin.
. U.S., Salinity Laboratory Staff, 1954. Diagnosis and Improvement of Soil Saline and Alkaline Soils. Agricultural Handbook No:60.
. Veries, F.W.T., & Van Laar, H.H.,1982. Simulation of Plant growth and crop production. Wageningen. 320 p.

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