Estimation of saturated hydraulic conductivity with pedotransfer functions: A review

Saturated hydraulic conductivity (K_s) is a singular parameter in earth system science. K_s not only governs the rate of flow of water under a hydraulic gradient as specified by the Darcy equation for saturated conditions, but also acts as a scaling factor in many unsaturated flow and transport applications that involve pore-size distribution models. Without knowledge of saturated hydraulic conductivity, it would be difficult to accurately describe the transport of water and dissolved or suspended constituents in soils and sediments, or calculate groundwater transport and recharge, and quantify the exchange between soils and the atmosphere. While the determination of K_s is not especially difficult, it is expensive and (in many cases) infeasible to carry out field or lab experiments for large-scale applications. Pedotransfer functions (PTFs) are a class of largely data-driven empirical models that aim to estimate K_s (and often other hydraulic quantities such as water retention characteristics) from easily available data. In this review, we first briefly discuss the history of the development of the concept of saturated hydraulic conductivity and its relation to the Kozeny-Carman (KC) equation. The KC equation serves as a central point in this review because it determines which soil variables affect saturated flow at the pore-scale, a domain which now can also be visited by computational fluid dynamics models. The KC equation also provides us with a structure in which we can classify the large number of PTFs that have been developed for estimating K_s. Datasets and statistical techniques available for PTF development are discussed, and we also describe common metrics used to assess the accuracy and reliability of PTF estimates. The mutual agreement of two main classes (i.e., an effective porosity KC-based and soil texture-based) of PTFs is analyzed using a number of global maps of predicted K_s. Finally, we discuss challenges and perspectives that might lead to PTFs with improved estimates of K_s. In particular, we suggest establishing and utilizing large and completely independent databases to assess the accuracy and reliability of PTFs for global use, while also drawing in information from pedological and remote sensing sources.