Steady-state SPAC approach

The compensatory uptake is calculated in the same way as for the simple response approach. But the uptake with any compensation is given as:

             (3.37)

where ψ(z) is the actual water potential in a soil layer z, ψ_min is a parameter that represents the lowest possible water potential of the plant (maximal suction), H_p is the height of the plant, r_p,i is the plant resistance, r_s,i is the soil rhizospere resistance, r_i(∆z) is the relative root density distribution (from eq (3.9)), E_tp^* is the potential transpiration with eventual reduction due to interception evaporation and n_r is the deepest soil horizon with roots present. See viewing function Soil moisture response, steady-state SPAC approach. The resistance of the plant is given as:

   (3.38)

where r_xylem and r_r is are parameters for resistivity in the xylem and the roots, L_r is the root length, and r_i(∆z) is the relative root density distribution. The response functions for osmotic pressure, f(π (z)), temperature, f(T(z)), and oxygen supply at high soil water content, f(θ(z)), are described in the former section. See viewing function Plant resistance function.

The soil rhizospere resistance is described as:

                                                  (3.39)

where k_w is the unsaturated hydraulic conductivity of the soil layers and f_∆l is a characteristic length that depends on the root geometry and many related factor in a complicated way. The characteristic length is estimated from a simple function that accounts for the root density as:

                                  (3.40)

where rδ(z) is the root density in cm/cm³ estimated from the root length, L_r. Three empirical parameters: ∆_lmin, ∆_lmax and p_δ  are used to estimate the numerical value of this characteristic length. See viewing functions Plant and Soil Resistances and Soil rhizosphere distance.

Salt stress is considered quite differently and is more developed in the steady-state SPAC approach compared to the former one. There are different ways to simulate osmotic effects of salinity on water uptake, and these options resemble the options for the pressure head response approach. By switching Salt Influence the choice between different approaches is made. Firstly, salt influence can be added to the pressure head (“Added to pressure head”). In that case the osmotic pressure, π(z), is added to the soil water potential, ψ(z), in eq.(3.37). Secondly the salt response function, f(π (z)), (eq. (3.35)) can be an “added multiplicative response”. This means that the function is multiplied by the actual water uptake calculated in eq. (3.37), here called E_ta, to separate it from the final water uptake after reduction due to salinity, E_ta^*:

                                                      (3.41)

Should the response instead be an added minimum response, the actual water uptake calculated in eq (3.37)  (again labelled E_ta) is substituted with the potential water uptake times the salt response function, f(π (z)), if the latter is smaller than the other:

                                  (3.42)

In the steady-state SPAC approach there is yet another way of accounting for soil salinity, and that is by affecting the plant resistance (see switch “PlantResistance”). Plant resistance, r_p,i, is calculated by eq. (3.38). In this equation there is one term in which the salt response function, f(π (z)), is included. This term is normally put to unity if salt effects are ignored, but by switching “Plant Resistance” to “Salt effect by osmotic pressure” the salt response function, f(π (z)), is calculated as described in eq. (3.35).