Comparing Equations Fitted to Water Retention Data from a Manured, Non-Manured, and Eroded Silt Loam.

Water retention (WR) is one of the most important of a soil's hydraulic properties. For ease in modeling, measured WR values are commonly fit to equations proposed by Brooks and Corey (1964), Campbell (1974), and van Genuchten (1980). When the same soil is manured or eroded, which equation fits WR data best? In our study, we first fit these equations to WR measured at eight matric potentials for three treatments (never manured, manured 4 y earlier, or eroded) of a Portneuf silt loam (Durinodic Xeric Haplocalcid). Secondly, we quantified each equation's goodness of fit using the root mean square error, RMSE (m³ m^-3), the ratio of the RMSE to the measured data's standard deviation, RSR (unitless, ranging upward from a best of 0), model efficiency, ME (unitless, ranging from -∞ to 1), and percent bias, PBIAS (%, where values > 0 indicate overestimation and vice versa). The satiated water content was 0.48 m³ m^-3 for the non-manured, 0.51 m³ m^-3 for the manured, and 0.52 m³ m^-3 for the eroded treatment. Campbell's equation is a special case of that of Brooks and Corey (BC) when, as in our study, the residual water content was fitted to its specified lower bound, 0, and will not be discussed. The RMSEs were acceptable, never exceeding 0.02 m³ m^-3 for BC or for van Genuchten (VG), though greatest for the eroded treatment. Model efficiencies were good overall, never less than 0.95. The PBIAS, positive in every case, was 0.11% or less for BC and 0.18% or less for VG. The PBIAS varied most among treatments when data were fitted to the VG equation. Water retention data for the same soil treated differently were modeled well with either the BC or VG equation.