Application of Stress Forms of Richard’s Equation in the Irrigation Deficit Scenarios and Dry Agriculture. Soil Stress Index Model (SSIMOD)

Anthropogenic emissions of heat trapping greenhouse gases are causing adverse widespread effects on the Earth’s climate. The shrinkages of glaciers and ice sheets, earlier breakup of river and lake sheets, shifts in geographic distribution of planta and animalia especially mammals, sea rise, saline water intrusion, intense heat waves, droughts, salinity, desertification, etc. are examples. The adverse effects of global climate changes and associated risks depend on mitigated and adapted actions in each proposed managerial scenarios by IPCC to deal with global climatic changes The adverse effects of global climate changes and associated risks depend on mitigated and adapted actions in each proposed managerial scenarios by IPCC to deal with. The agro-ecosystem continuum will receive precedential waves of drought, salinity, heat shocks, and wildlife shifts or migration due to global climatic changes. Some regions will be mammalian uninhabitable due to the same reason [1]. In the incoming section we will focus the macroscopic point of view on a recently achieved model, SSIMOD [2]. Its equations, assumptions, and applications.

The managerial practices of agro-ecosystem continuum under such conditions involve the use of silicate fertilizers for enhancing soil physical properties [3], yield, and plantation. A new form of Richard’s equation is achieved and discussed. The stress form of Richard’s equation is a Soil Stress Index (SSI) based [2]. The Soil Stress Index Model (SSIMOD), the conceptual macroscopic model, expresses the sink/ source terms by the assumption of recharge/ discharge of the soil capacitor in between processes of water uptake and water infiltration respectively [4].

The author found that the term plant water uptake (S) is the product of multiplying the soil stress index (SSI) with a new term called soil water hydraulic capacitance (β). Hence, S= SSI * β. A strong correlation appeared between stress indices of plants and soil. The latter imperical correlation will be opening the gate to a new way of assessing the plant response to environmental abiotic stresses using the stress form of Richard’s equation. As PSI is the dependent variable of the SSI, predictions of PSI under temporal, spatial, and tempo spatial variabilities were achieved and discussed. The control finite volume assumptions were used to achieve the numerical solution of the new stress form equation. Water redistribution and accordingly root distribution (bz) is also a newborn of the stress form. Finally, the gained value (bt), representing the amount of water reached the vadoze root zone depth under abiotic stresses conditions in relation to the optimum wetness, is gained [5].

The recent discovered four terms from the new achieved stress form distinguish the type and amount of plant root water and nutrient uptake from the variably saturated zone. The governing forces are stress, strain, and weathered controlled forces. The author would like to name the latter four discovered terms as the abiotic stressors’ constants (Hegazy constants). Managerial practices under the studied abiotic stressed conditions involve silicon foliar application. By using abiotic stressors’ constants in assessing the impacts of combined drought and salinity on plants’ yield and plantations under silica fertilization, silicon proved that it is the plant first aid for enhancing the agricultural production under unfavorable abiotic stress conditions of global climatic changes [5].

Assume that the immobile moisture content is redundant in water flow researches and the soil moisture at permanent wilting point is redundant in root water uptake. The hydraulic parameter of Van-genuchten n, m, and α could be estimated if SSI is known (reverse solution) or from HYDRUS 1D [6].

Where: Smax, S: Potential yield and actual yield respectively. h*: Total soil potential at field capacity (m).h: Total soil potential at each point (cm H₂O).t, z: Time and depth respectively (Day, cm). μ: Direct proportional coefficient between SSI and α (h, 𝚿) and can be estimated empirically. SSI: Soil stress index. α (h, 𝚿): Plant Stress Index. C: Soil water holding capacity (cm^-1). K(h): Unsaturated soil hydraulic conductivity

Two proposed nominations for the term b(z) in variably saturated conditions. The first, the water redistribution due to the evapotranspiration from the root domain. as root distributions follow water redistributions, the proposed second nomination is the root distribution seeking the optimum wetness because of moisture deficit in the domain (L- 2). z1 water or root depth at h1, z2 water or root depth at h2, Δz= the change in water or root depth during categorizing the energy states of soil water by plant’s root to water. b(t) = k(h)/h*= (L/T)/L3= T-1 L-2. I would like to nominate the term b(t) as the gaining value of moisture per time (t) and root domain (ꭥ) due to the ability of soil to conduct water toward a control volume in the root domain under the driving forces of gravity, hydraulic gradient, or moisture deficits. i.e. if the unsaturated hydraulic conductivity equals 2m/hr., water potential at field capacity equal 2-meter head then it takes one hr. to gain the relative moisture optima due to the ability of soil to conduct water under the latter driving forces. Hence, SSI, β, b(t), and b(z) are new valuable tools for assessing some environmental impacts of global climatic changes on the agro ecosystem continuum under abiotic stressors of drought and salinity.

Equations (1, 2, and 3) will be nominated as the stress forms of Richard’s equation where: C(SSI): water holding capacity(T-1), SSI: Soil stress index, β: Soil water hydraulic capacitance. b(t): b (t) = k(h)/h*= (L/T)/L3= T-1 L-2 . The gaining value of moisture per time (t) and root domain (ꭥ) due to the ability of soil to conduct water toward a control volume in the root domain under the driving forces of gravity, hydraulic gradient, and/or moisture deficits. b(z): b (z) = (dz/h*). The root distribution seeking the optimum wetness because to moisture deficit in the domain (L- 2), z, t: time and depth, respectively (Figure 1).

Figure 1:Conceptual physical nonequilibrium models for water flow and solute transport [6].

The soil stress index model is a macroscopic mathematical conceptual model. SSIMOD could be calculated based on the concepts of total soil water potential. Hence, it may be either additive (ASSIMOD) or multiplicative (MSSIMOD). Under abiotic stressed conditions, SSIMOD assumes that plants follow the bath which save its consumed energy during navigating soil system categorizing the energy states of soil water seeks the most available water to uptake. It assumes that root domain consists of finite discretized control volumes. Increasing the number if iteration makes the numerical solution of the model touch the certainty. In addition, it assumes a dependent root system where the moisture deficit in some parts of root domain is either partially or fully compensated from the yield value of moisture optima in other parts. There are three ways of compensation: The water redistribution(bz) after gaining the moisture, root distribution during categorizing the energy states of soil water to preferably uptake the most available water, and overall total water potential of the dependent root sap system. Stress forms of Richard’s equation were solved numerically using the assumptions of finite volume approximation [5]. SSIMOD allows to study the prediction of values of plant stress index temporally and spatially by using the corresponding values of soil stress index [5]. SSIMOD is based on a hydrodynamic approach. This is because it assumes that water flow’s governed passively by gradients of water potentials between soil, plant xylem, and atmosphere at a rate controlled by the water paths’ hydraulic resistances. Therefore, it requires the input variables of the transpiration rate (Tc), total soil water potentials (πt), and root distribution (bz). Each number of one parent material homogeneously packed finite control volumes froms a layer. The layer is a capacitor recharged by the source and discharged by the sink [4]. Furthermore, SSI MOD is found to have an application in managing the agro-ecosystems recycle the liquid emissions or use the poor water quality in agriculture development [8]. It’s the moisture redistribution (bz) which makes the curvature of SSI becomes gradual and hence saves plants life as long as possible now and then each wetting drying cycle. It’s the gaining factor which determines the moisture’s regimes should be adopted in the deficit irrigation scenarios without causing a reliable reduction in crop yield and plantation properties. Finally, it’s the soil stress index and/or soil water hydraulic capacitance which determine the type and amount of water and nutrients’ uptake in accordance with stress and/or stress, strain, and weathered controlled forces.

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