Elsevier

Journal of Hydrology

Volume 575, August 2019, Pages 1011-1030
Journal of Hydrology

Research papers
Estimation of saturated hydraulic conductivity with pedotransfer functions: A review

https://doi.org/10.1016/j.jhydrol.2019.05.058Get rights and content

Highlights

  • Predictors to estimate Ks are analyzed from mechanistic and empirical viewpoints.

  • The estimations of Ks are presented from pore scale to global scale.

  • Challenges still exist for Ks estimation, and we provide some perspectives.

Abstract

Saturated hydraulic conductivity (Ks) is a singular parameter in earth system science. Ks 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 Ks 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 Ks (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 Ks. 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 Ks. Finally, we discuss challenges and perspectives that might lead to PTFs with improved estimates of Ks. 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.

Introduction

Soil plays a fundamental role in the Earth’s terrestrial biosphere by controlling the transfer of mass and energy between land surface and atmosphere (Amundson et al., 2015, Bittelli et al., 2015). Near-surface soil is especially important because it regulates the local water balance through infiltration, evapotranspiration, surface runoff, groundwater recharge and hence has a substantial effect on regional and global land surface water and energy balances (Montzka et al., 2017, Vereecken et al., 2016, Verhoef and Egea, 2014). For example, nearly 60% of the terrestrial precipitation is returned to the atmosphere through the soil-plant-atmosphere continuum (Katul et al., 2012, Oki and Kanae, 2006), while around half of the global biomass production and related carbon cycle depend on soil processes (Cleveland et al., 2013). Accurate characterization and prediction of these soil processes usually require an accurate parameterization of soil hydraulic properties (i.e., the soil water retention curve, the unsaturated hydraulic conductivity curve, and saturated hydraulic conductivity). In many cases, however, direct measurement of soil hydraulic properties is time-consuming and labor intensive, and especially impractical for large-scale applications (Dai et al., 2013, Vereecken et al., 2010). As an alternative, soil scientists have developed pedotransfer functions (PTFs) to estimate soil hydraulic properties from commonly available soil information such as soil texture and bulk density.

In the past few decades, numerous PTFs have been developed for a variety of purposes and objectives, ranging from theoretical studies to small plot-scale empirical relations to considerable efforts that meet the needs of regional and global-scale weather and climate modeling. Thorough reviews of the work in this field have previously been given by Wösten et al., 2001, Pachepsky and Rawls, 2004, Vereecken et al., 2010, and Van Looy et al. (2017). Wösten et al. (2001) reviewed PTFs to estimate soil hydraulic parameters, including soil water retention and hydraulic conductivity characteristics. Vereecken et al. (2010) specifically reviewed PTFs to estimate van Genuchten-Mualem (Mualem, 1976, van Genuchten, 1980) soil hydraulic properties. Van Looy et al. (2017) reviewed PTFs in different disciplines of the earth system science, including PTFs for water, solute, heat, and biogeochemical soil processes.

Previous reviews did not focus primarily on the soil saturated hydraulic conductivity (Ks), which is a simple, yet critical, soil property. Saturated hydraulic conductivity is needed to calculate flow rates in saturated soils using Darcy’s equation. However, Ks is also important in the Richards equation for unsaturated flow where it is needed to scale relative hydraulic conductivity predicted by the pore-scale models of Burdine, 1953, Mualem, 1976, and Alexander and Skaggs (1987) into unsaturated hydraulic conductivity. In a broader sense, our ability to estimate (un)saturated flow is crucial to many Earth Systems Science applications, including oil and gas recovery from geological reservoirs, the protection of natural groundwater resources, the remediation of polluted soil and groundwater, and the long-term stewardship of waste disposal sites.

The main thrust of this paper is to review the state-of-the-art PTFs for estimating saturated hydraulic conductivity in soil science and hydrology. In order to provide a comprehensive overview, we will first provide a brief historical context of saturated hydraulic conductivity. This overview starts with the empirical Darcy equation for saturated flow and proceeds to the physically-based Kozeny-Carman equation (see Kozeny, 1927, Carman, 1956, Carman, 1937). The Kozeny-Carman (KC) equation subsequently provides us with a convenient framework to briefly discuss computational fluid dynamics (CFD) methods, which are able to simulate saturated flow networks at the pore-scale. The flow fields computed with CFD allow us to compute saturated hydraulic conductivity (and other quantities) in a mechanistic way from observed or specified pore-structure. The KC equation, as well as CFD methods, subsequently provide us with insight which soil variables should affect saturated hydraulic conductivity, which we will use as a guide to group the many existing empirical PTFs according to their predictors. We will subsequently discuss datasets and statistical techniques available for PTF development and evaluate a number of PTFs comprehensively. Accuracy and reliability of PTFs are analyzed based on commonly used criteria. Key challenges for the development and using PTFs are finally identified by evaluating a selection of widely-used PTFs on a global data set.

It is noted that throughout most of the review, we will use the term “saturated hydraulic conductivity” which is abbreviated by Ks with units of length over time. However, it should be pointed out that other disciplines such as civil engineering designates this quantity as permeability (Sanchez-Vila et al., 2006), whereas soil sciences, geology, and petroleum engineering use permeability to indicate the (more fundamental) concept of intrinsic permeability k, which is related to Ks as follows:Ks=kρg/μwhere ρ, g, and μ are fluid density, acceleration of gravity, and dynamic viscosity, respectively. This expression indicates that Ks depends on both fluid properties (the density and dynamic viscosity) and the intrinsic, fluid-independent, permeability of the porous medium. The units of intrinsic permeability are squared length units, with one “darcy” unit being equivalent to a permeability of 9.869233 × 10−13 m2 and defined in terms of standard atmospheric pressure and unit viscosity and flow rate.

Section snippets

A brief history of saturated hydraulic conductivity and estimation from PTFs

The concept of saturated hydraulic conductivity originated in the middle of the 19′th century with Henry Darcy (1856). As an inspector for roads and bridges in the French city of Dijon, he wrote a publication that mainly dealt with the distribution of water through the city’s aqueducts. However, in his Appendix D, Darcy (1856) also reported on a series of experiments on the flow of water through sand “filters” (Fig. 1). Darcy stated that the flow (“ecoulement” in French) is proportional to the

Predictors of saturated hydraulic conductivity

The Kozeny-Carman expression for permeability (Equation (6)) indicates that soil saturated hydraulic conductivity, Ks, depends on particle size (i.e., soil constituents) and soil porosity (i.e., soil voids), hydraulic radius, and a pore shape factor. In Section 3.1, we use computational fluid dynamics simulations on artificially generated medium to show how these factors affect the permeability from a mechanistic viewpoint. However, while insightful, the pore-scale imaging process and the

Calibration and evaluation data

PTF development typically aims to estimate difficult-to-measure soil properties by establishing relations between accessible input data and estimands. In order to achieve this, the PTF developer must have access to data sets that contain both observed hydraulic data as well as the predictors. The requirements that these data sets need to meet depends on the objectives being pursued. If the aim is merely to identify which variables affect Ks (e.g., in our numerical example in Section 3.1),

A comparison of global estimates of saturated hydraulic conductivity

It is currently difficult to objectively evaluate how reliable Ks estimates by PTFs are at a global scale because global-scale data currently are lacking. While large databases with substantial global coverage such as NCSS and WoSIS contain observed retention data, they lack observed Ks values. No definitive statements can be made which PTF (or combination of PTFs) provides the best estimates at a global scale. However, the relative agreement among PTFs for estimating Ks can be tested by

Challenges and perspectives for PTFs to estimate saturated hydraulic conductivity

In this review, we have introduced the history, predictors, and statistical techniques for PTF development of saturated hydraulic conductivity, and summarized the accuracy and reliability of existing PTFs. Some issues and areas that might improve the PTF development have been highlighted. Here we summarize the challenges and perspectives for further improving PTFs to estimate saturated hydraulic conductivity.

Conclusions

Saturated hydraulic conductivity (Ks) is crucial to many Earth systems science applications. Obtaining this soil property heavily depends on soil pedotransfer functions (PTFs) by utilizing easily measurable basic soil properties. In this review, we have given an overview of the historical background of deriving and utilizing saturated hydraulic conductivity. By using computational fluid dynamics model based on synthetic data, we showed how permeability (extendable to saturated hydraulic

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Acknowledgments

Yonggen Zhang thanks the National Natural Science Foundation of China (grant 41807181); Marcel G. Schaap was supported by the USDA National Institute of Food and Agriculture under Multistate Research Project W3188, entitled “Soil, Water, and Environmental Physics Across Scales”.

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