It is assumed that soil, crops, mulch and atmospheric conditions are uniform, that is, the average situation of the field is studied.

1. Soil structure

It is found that sandy loam is the main soil above 70cm, silty sand is the main soil below 70cm, and the soil depth is 120cm. In this way, the soil layer structure is generalized as a two-layer structure, and the soil in each layer is homogeneous, ignoring the spatial variability.

2. Unsaturated soil flow state

During the whole test period, the buried depth of groundwater level is relatively large (4 ~ 5m), and the calculation area is unsaturated zone. It is assumed that unsaturated soil water belongs to one-dimensional flow and only moves in the vertical direction, ignoring the lateral water exchange, and the water moves vertically through the interface, where θ is discontinuous and H is continuous. Regardless of solute potential and temperature potential. Unsaturated flow in which water movement satisfies Richards' (193 1) Darcy's law;

Numerical simulation of soil water and salt transport

or

Numerical simulation of soil water and salt transport

Where: water cycle; K(θ) is the permeability coefficient; ψ ψ is the gradient of water potential. The water potential gradient is further expressed as:

Numerical simulation of soil water and salt transport

Where: gradφ is the gradient vector of water potential; , and are unit vectors along the positive direction of the coordinate axis (x, y, z).

For vertical one-dimensional flow, the above water potential gradient can be simplified as:

Numerical simulation of soil water and salt transport

3. Boundary conditions

Sui Hongjian et al. (1992) regarded wheat straw as a porous medium according to the definition of Jacob Bell (translated by Li Jingsheng et al., 1983) in porous medium fluid dynamics, and adopted the basic theory and method of porous medium to solve the problem of its influence on water vapor transmission. Compared with the soil layer, because the covering layer is thin, the gap is large and the liquid water content in the field is very small, it is simplified as a barrier layer with certain resistance to water vapor, and the resistance of water vapor passing through the covering layer is considered in the calculation of evaporation intensity.

Under the condition of (1) evaporation; The upper boundary condition (at the interface between soil and mulch) is expressed as:

Numerical simulation of soil water and salt transport

Where: e is evaporation intensity (mm/d).

Similar to soil, wheat straw mulch is a porous medium. Therefore, Hillel( 1976) algorithm and aerodynamic drag method are used to calculate evaporation intensity. When calculating evaporation resistance, the influence of mulch on water vapor migration is considered, and it is assumed that the water vapor flux is a certain value in the vertical direction of the whole mulch, which is equal to the evaporation rate on the surface of mulch (Figure 1.4.65438

Figure 1.4. 1 superimposed resistance diagram

Numerical simulation of soil water and salt transport

Among them, rm is the evaporation resistance (s/m) of the covering layer, which is a function of the thickness and density of the covering layer and is related to the type and arrangement of the covering material; Rcm is aerodynamic drag (s/m); Hs and Ha are the absolute air humidity (kg/m3) at ground level and reference height respectively; Rs is the evaporation resistance (s/m) of the surface.

(2) Under the condition of rainfall, the overburden has a great influence on soil moisture infiltration. Because the soil under the mulch is not directly hit by raindrops, its surface soil density is low, which can increase the infiltration speed of rainwater. In the case of porous material covering, because the covering layer is thin and the pores are larger than the soil layer, the impermeability of the covering layer can be ignored.

For the actual rain pattern, when the rainfall intensity R is less than the soil infiltration rate I (the amount of water infiltrated into the soil through the unit surface area in unit time, in mm/d), the actual infiltration rate is the rainfall intensity, that is, I = r；; When the rainfall intensity is greater than the soil infiltration rate, the surface begins to accumulate water, and the upper limit condition is that the surface is always saturated. Here, assuming that all the residual water flows away, the upper boundary condition (at the interface between soil and mulch) is expressed as:

Numerical simulation of soil water and salt transport

Where θ0(t) is the surface water content; θs is the saturated water content of soil; R is the actual rainfall intensity (mm/d); Tp critical time.

Under the condition of evaporation, because of the complexity of water vapor transmission in the overburden, the parameters rm, Rcm and rs in the model are difficult to determine from the general observation data, and it is still difficult to apply. Therefore, the covering layer is simplified as a resistance layer that can block the migration of water vapor, and its resistance to evaporation is considered when calculating the evaporation intensity. According to two main factors affecting evaporation intensity, one is external evaporation, that is, meteorological conditions; The second is the water transport capacity of soil from the lower soil, which decreases with the decrease of water content. Under the condition of wheat straw mulching, the evaporation intensity E can be calculated by regression analysis according to the actual observation data, and the empirical formula of E-θ under the condition of wheat straw mulching can be found out to calculate E(E includes the resistance of mulching layer), and the upper boundary condition is the second boundary condition.

As 1993 Yongle Store is a dry year, the rainfall is relatively small, and there is no surface water and surface runoff. It is assumed that the rainfall intensity does not exceed the infiltration capacity of soil, which is similar to evaporation and belongs to the second boundary. When the upper boundary is irrigated, it is treated as the first boundary according to the actual situation of the ground, but when the irrigation process is over, the upper boundary is transformed into the second boundary. In this experiment, there is no irrigation, so the surface is treated as the second kind of boundary in the calculation.

(2) Mathematical model

1. Basic equation

See figure 1.4.2 for the calculated area covered by crops. Ignoring the influence of soil temperature distribution and change on soil moisture movement, the basic equation of vertical one-dimensional soil moisture movement is different in the root layer soil area and the soil area below the root layer.

In the root zone:

Numerical simulation of soil water and salt transport

Where θ is the soil volume water content (cm3/cm3); Z ordinate (cm) (downward from the ground), t time (d); D(θ) diffusivity (cm2/d); K(θ) hydraulic conductivity (cm/d); S is the root water absorption rate (cm3/cm3 d =1/d).

Below the root zone:

Numerical simulation of soil water and salt transport

Figure 1.4.2 Calculated area with crop cover

Where: depth of lr root layer (cm); L Calculate the depth of the area (cm).

2. Definite solution conditions

(1) initial condition: the initial water content is known, i.e.

θ(z，t)=θ0(z)t=0 ( 1.4. 10)

(2) Boundary conditions

Upper boundary condition: if the water supply intensity r does not exceed the soil infiltration capacity when the surface is in infiltration state, or the evaporation intensity is E when it is in evaporation state, the upper boundary condition is expressed as:

In the infiltration process,-D (θ)+K (θ) = Rz = 0 (1.4.11).

During evaporation,-d (θ)+k (θ) = ez = 0 (1.4.12).

Lower limit condition: during the test, the buried depth of groundwater level is relatively large, with the measured groundwater level of 5m on September 25th, 1993, and it was generally around 4m at the end of June last year. According to the θ data measured at the bottom point of neutron gauge (130cm) and the H data measured at the bottom point of negative pressure gauge (120cm), the θ and H values have not changed much during the whole test, so the lower boundary is taken as the first boundary:

θ(z，t)=θ(l，t)z=l ( 1.4. 13)

3. Mathematical model (definite solution problem)

To sum up, when crops grow, the mathematical model θ equation of vertical one-dimensional soil moisture movement is described by the following definite solution problem.

Numerical simulation of soil water and salt transport

θ(z，t)=θ0(z)0≤z≤l t = 0( 1.4 . 14)

-D(θ) +K(θ)=R(t) (or -E(t))z=0, and t≥0.

θ(z，t)=θ(l，t)z=l，t≥0

Where θ is the soil water content (cm3/cm3); Z is the ordinate (cm), which is positive downward from the ground; T is time (h); D(θ) is the diffusivity (cm2/h); K(θ) is hydraulic conductivity (cm/h); E(θ) is the evaporation intensity of topsoil (cm/h); R is rainfall intensity (cm/hour); L is the total thickness of soil layer (cm); Lr is the depth of root layer (cm), which varies with the growth stage of crops; S(z, t) is the source and sink term, which represents the water absorption rate of crop roots, that is, the water absorbed by roots from unit volume of soil in unit time (cm3/cm3/h= 1/h).

If the H equation is used, the definite solution problem can be expressed as:

Numerical simulation of soil water and salt transport

Where: h(hH2O) is the negative pressure head (cm); C(h) is water content (1/cm); Other symbols are the same as above.

The equations in equations (1.4. 14) and (1.4. 15) are partial differential equations of unsaturated soil water movement, because water content C(θ), diffusion D(θ) and permeability coefficient K(θ) are matrix potential h or water content. Except for a few problems, it is generally difficult to find analytical solutions, and a large number of problems must be solved by numerical methods.