The unsaturated hydraulic conductivity function K(9), or K(h), is somewhat difficult to determine accurately, insofar as it cannot be measured directly and, in any case, it varies over many orders of magnitude not only among different soils, but also for the same soil as water content ranges from saturation to very dry conditions. Even though, at present, no proven specific measuring devices are commonly available to determine the hydraulic conductivity function, the numerous proposed methods usually involve measurements of water content and pressure potential for which widespread and well-known commercial devices do exist.
One of the more common and better-known methods for determining K(9), or K (h), is the instantaneous profile method . Although the related procedure is quite tedious, one of the main advantages of this method is that it can be applied with minor changes under both laboratory and in situ conditions. The crust method often is used as a field method [23, 24]. For information on operational aspects, applicability, and limitations of these or other methods, the reader is referred to the specific papers cited.
However, evaluating the dependence of the hydraulic conductivity K on water content 9 by direct methods is time-consuming, requires trained operators, and is therefore very costly. Several attempts have been made to derive models for the function K(9) from knowledge of the soil water-retention characteristic 9 (h), which is easy to determine and reflects well the pore-size geometry, which in turn strongly affects the unsaturated hydraulic properties. A hydraulic conductivity model that is used frequently by hydrolo-gists and soil scientists was developed by van Genuchten, combining the relation (5.104), subject to the constraint m = 1 — 1/n, with Mualem's statistical model [25, 26]. According to this model, unsaturated hydraulic conductivity is related to volumetric water content by the following expression:
where Se and m already have been defined under "Description of Soil Water-Retention Curve," X is a dimensionless empirical parameter on average equal to 0.5, and K0 is the hydraulic conductivity when 9 = 90. The advantages of using this relation are that it is a closed-form equation, has a relatively simple mathematical form, and depends mainly on the parameters describing the water retention function. To obtain the hydraulic conductivity curve for a certain soil under study, at least one value of K should be measured at a fixed value of 9 .It is customary that the prediction be matched to saturation conditions, such that 90 = 9s and K0 = Ks. However, this criterion is not very effective, mainly because hydraulic conductivity at saturation may be ill-defined since it is strongly affected by macroporosity, especially in the case of structured soils. It thus has been suggested that the K (9) curve be matched at a point K0 measured under unsaturated conditions (90 < 9s) .
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