Estimation of coefficients

The figure below (Figure 2.5) shows how experimental data of water retention can be used when estimating coefficients in the Brooks & Corey equation. The procedure used is based on least square fitting where three coefficients are estimated by allowing the residual water content to vary in a range until the best linear fit will be obtained, see figure below. All data points are given equal weights but the user can select a suitable restricted range to improve the fitting.

Figure 2.5. Log S_e as a function of log ψ. The air entry pressure (ψ_a) is given at S_e=1.0. Pore size distribution index (λ) is the slope of the line

The coefficients in the Brooks & Corey equation can also be estimated by using the pedofunctions as proposed by Rawl and Brankensiek (1980). The θ_r, λ and ψ_a can be estimated by using the amount of sand, clay and silt as input. Saturated hydraulic conductivity is also estimated from the texture and in addition the saturation value.

The van Genuchten coefficients are not estimated directly but can easily be assigned from the Brooks & Corey coefficients:

                                                                    (2.34)

and

                                                                 (2.35)

and finally

                                                               (2.36)