The modeling of the essential hydrostatic soil characteristic, the water retention curve, appears to have reached its ultimate form. The power function proposed by Van Genuchten in 1980 and its twin sister, the exponential function proposed by Groenevelt and Grant in 2004, produce virtually identical fitting curves. The GG function is more elegant than the VG function and is easier to differentiate and integrate. Otherwise, it appears that the power of mathematics to produce one single equation for the fitting of both, the convex and the concave part of the WRC, has been fully exploited.

In contrast, the modeling of the essential hydrodynamic soil characteristic, the unsaturated hydraulic conductivity curve, is in embarrassingly poor shape. The modeling by the Van Genuchten-Mualem method, leading to incomplete beta functions, often requires unrealistic assumptions and sometimes produces unacceptable predictions. The results obtained by the Groenevelt-Grant-Burdine method, leading to incomplete gamma functions, accepting bi-modality as a physical reality, produces excellent predictions. But then, there is the elusive character of the tortuosity. In contrast to the Mualem approach, where the formulation of the tortuosity term is established by pre-curve-fitting, the Burdine approach is based on physical gut-feeling. There, the formulation of the tortuosity term by the relative water content to the power two, is a clever choice, but is otherwise a testimonium paupertatis. This essential hydrodynamic parameter, requires in- depth analysis. For this, the easy access to incomplete gamma functions will be exploited.