1. Introduction
Irrigation scheduling is one of the most important factors for healthy breeding of crops. Quantification of water consumption is necessary for both adequate crop breeding and improved irrigation efficiency. Mechanism of water consumption and soil water movement is affected by crop roots because the soil structure and physical properties are changed by crop root physiological activities, including growth or water extraction. To quantify the water consumption in crop fields, the crop root effects on soil physical properties should be clarified.
Various researches have been conducted to clarify the biochemical and physical effects of soil on crop root growth. Drew (1975) [1] studied the adequate external concentrations of nitrogen and phosphorus required by root growth. Effects of various chemical materials of soil on crop root growth have been clarified [2-9]. Iijima et al. (1991) [10] determined the effects of soil compaction on the development of root system components of rice and maize. A combined root growth and water extraction model was introduced by Bengough (1997) [11]. Crop root cellular response to soil physical stress was evaluated by Bengough et al. (2006) [12]. Effects of the soil water content and bulk density on crop root development processes were investigated by Becel et al. (2012) [13].
Although the effects of soil biochemical and physical conditions on crop root growth have been extensively studied, the effects of the crop root on the physical properties and water consumption of soil have not been clarified.
Studies have been conducted to clarify soil water movement and quantify water consumption in the crop fields [14,15]. However, the crop root effect on the physical properties of soil was not considered in these studies, as a method to evaluate soil water movement considering the effect of the crop root on the soil physic properties has not been established.
The objective of this study is to clarify the effects of the crop root on soil water retentivity and soil water movement. A numerical model was introduced to simulate the soil water and heat transfer considering the crop root effect on soil water retentivity. Cultivation experiments were conducted to clarify the relationship between soil water retentivity and crop root content and to verify the accuracy of the numerical model.
2. Methodology
2.1. Governing Equations of Soil Water and Heat Transfer
To estimate the soil water transport considering the crop root effect on soil water retentivity and hydraulic conductivity, a numerical model was introduced. The governing equation describing soil water and heat transfers can be described as follows:
(1)
(2)
where Cv is the volumetric heat capacity (J∙m−3∙˚C−1), Dθ is the isothermal water diffusivity (m2∙s−1), Dθv is the isothermal vapor diffusivity (m2∙s−1), DT is the thermal water diffusivity (m2∙s−1∙˚C−1), K is the hydraulic conductivity (m∙s−1), L is the latent heat of water vaporization (J∙kg−1), S is the sink(m3∙m−3∙s−1),T is the soil temperature (˚C), t is the time(s), λ is the thermal conductivity (W∙m−1∙˚C−1), ρl is the water density (kg∙m−3), and θ is the volumetric soil water content (m3∙m−3).
2.2. Boundary Conditions
The energy budget on the soil surface at the crop field can be described as follows:
(3)
where Rn is the net radiation (W×m−2), E is the latent heat flux (W×m−2), H is the sensible heat flux (W×m−2), and G is the ground heat flux (W×m−2).
The net radiation Rn can be estimated using the following equation considering the shortwave and longwave radiation balance.
(4)
where Rs is the shortwave radiation on the soil surface (W×m−2), Lc is the longwave radiation from the crop body (W×m−2), Lsky is the longwave radiation from the sky (W×m−2), and Lsoil is the longwave radiation from the soil surface (W×m−2).
The sensible heat flux and the latent heat flux on the soil surface can be estimated as follows
(5)
(6)
where Ts is the soil surface temperature (˚C), cp is the specific heat of the air (J∙kg−1∙˚C−1), ea is the air vapor pressure (hPa), es is the vapor pressure on the soil surface (hPa), ra is the diffusion resistance (s∙m−1), α is the albedo, γ is the psychrometer constant (hPa∙˚C−1), and ρa is the air density (kg∙m−3).
The diffusion resistance can be calculated using the following equation (Chamberlain, 1968):
(7)
where Dv is the molecular diffusion coefficient (m2∙s−1), u* is the friction velocity (m∙s−1), z is the height of the measurement of the wind velocity (m), z0 is the roughness length (m), ξ is the effective soil surface roughness (m), and ν is the kinematic viscosity of air (m2∙s−1). The constants a, b, and c are reported as 0.52, 0.45, and 0.8, respectively, by Chamberlain (1968) [16].
Using energy balance estimated by Equations (3)-(7), boundary conditions on the soil surface can be described as follows:
(8)
(9)
2.3. Model Structure
Figure 1 shows the numerical model describing water and heat transfers in the soil. To solve the two-dimensional transfers of water and heat, the finite-differential method was used. As the bottom boundary condition, the soil water potential was set as constant. The matric potential and hydraulic conductivity were set considering the root content for an interior node. The sink was set using the transpiration rate.
3. Cultivation Experiments
A cultivation experiment was conducted to evaluate the
Figure 1. Schematic view of the numerical model describing the water and heat transfers in soil.
effect of the crop root on soil water retentivity. The soil containing the crop root was sampled. Soil moisture characteristic curves were estimated, and the volumetric root contents of soil samples were measured to clarify the relationship between the soil water retentivity and root contents.
To verify the numerical model accuracy, an observation using acrylic slit pot was also conduced. Figure 2 shows the condition of the experiment. Broccoli was planted in the acrylic slit pot, at a size of 0.5 m × 0.6 m × 0.1 m. The ballasts were paved at the bottom of the acrylic slit pot, and the weathered granite soil was filled at a depth of 0.48 m. The volumetric water content and soil temperature were measured by soil moisture sensors (SM200, Delta-T) and thermo-couples at the depths shown in Figure 3. The solar radiations on the soil surface were measured by pyranometers (LI-200, LI-COR) to calculate the net radiation by Equation (4). In addition, the air temperature and humidity were measured to estimate the sensible and latent heat fluxes by Equations (5) and (6). The crop root content in 5 cm × 5 cm soil portion was measured by imaging analysis using the cross-sectional photograph taken from the front side of the acrylic slit pot.
4. Results and Discussion
4.1. Relationship between Soil Water Retentivity and Root Content
Figure 4 shows the relationship between the soil water retention curves and the crop root content in the soil sample. This figure indicates that the soil water retentive-