Global Journal of Science Frontier Research, D: Agriculture and Veterinary, Volume 23 Issue 1

Where t, z: time and depth respectively (t, l), SSI: dimensionless soil stress index, c(h): soil water holding capacity ( l -1 ), K: unsaturated hydraulic conductivity (l/t). β: soil hydraulic capacitance. Ψ: soil potential. S(z,t)= SSI . β = PSI. S max Tc (z,t)= SSI . β = PSI. Tp (4) Where S, Smax: actual and potential water uptake, respectively, Tp: actual and potential transpiration, respectively. The factors affecting the soil hydraulic capacitance are TP, PSI and SSI. The term β allows us to study, analyze and compare different groups of soil types, plant species, varieties and atmospheric conditions. This comparison may be either inter, intra or in combination between them. Such a comparison allows us to select from the latter groups the types of components which cause the maximum crop yield with minimum agricultural precise inputs in order to choose the good from the best. There are three special cases from the soil hydraulic capacitance: as follows:  Tc (z,t)= β = Tp , SSI=PSI=1 This means that soil moisture reservoir of the continuum hydraulic capacitance is able to meet the required potential transpiration and there is no stress and the uptake is uncompensated.  SSI> PSI, Tp> β This means that the soil moisture reservoir of the continuum hydraulic capacitance is unable to meet all the needs of the plant hydraulic machinery system. Plant roots respond to this moisture deficit by compensatory root growth for compensating water uptake from another layer which has a higher soil moisture reservoir of the continuum hydraulic capacitance (Hegazy, 2022). This type of compensation is called partially compensated water uptake.  SSI < PSI, Tp < β β = ( , ) − − − − – ( ) − − (3)  Equation (3) is the stress form of Richard's equation (Hegazy, 2022b) β this means that the soil moisture reservoir of the continuum’s hydraulic capacitance is unable to meet all the needs of the plant hydraulic machinery system and there is another soil reservoir that can recover the moisture deficit actually by compensated root growth for compensated water uptake. This type of compensation is called fully compensated water uptake. 1 Year 2023 33 © 2023 Global Journals Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( )D The Modified Richard’s Equation for Assessing the Impact of Drought and Salinity in Arid and Semi-Arid Zones. Part Two: A Soil Hydraulic Capacitance