2.2. Pedotransfer Functions
For this study 13 pedotransfer functions (PTFs) were used, whereby eight
predict the hydraulic parameters for the MvG (van Genuchten, 1980) and
five PTFs predict the parameters in the BC (Brooks & Corey, 1964) or
Campbell (Campbell, 1974) functions. Out of these 13 PTFs, four were so
called class-transfer functions, where only the USDA textural
classes will be used as input for the prediction of the hydraulic
parameters. It has to be noted that the PTF of Clapp and Hornberger,
(1978) (from here on Clapp&Hornberger) does not specify hydraulic
parameters for the silt class. All other PTFs use textural information
(gravimetric percentage of sand, silt, and clay) as basic inputs.
Additionally, some PTFs require information about bulk density (BD) such
as the PTFs of Schaap et al. (2001) (here referred to as Rosetta
SSC+BD), Wösten et al. (1999) (here Woesten), Weynants et al. (2009) and
Weihermüller et al. (2017) (here Weynants), and that of Tóth et al.,
(2015) for the topsoil (here ‘Toth continuous’). Others need information
about the organic carbon content (Corg), which are the
Woesten, Weynants, and ‘Toth continuous’ PTFs. Here, it has to be noted
that an updated version of Rosetta (Rosetta3) is also available (Zhang
& Schaap, 2017), which provides more accurate soil hydraulic parameters
compared with the estimation from the original Rosetta model.
Nevertheless, we decided to use the older Rosetta version. as it is
widely in use and also imbedded in some hydrological software such as
HYDRUS (Šimůnek et al., 2008; Šimůnek & van Genuchten, 2008).
Soil organic carbon is used as a predictor for the PTFs as it affects
soil bulk density, hydraulic conductivity, and water retention because
of its effect on soil structure and adsorption properties (van Genuchten
& Pachepsky, 2011).
Total porosity ϕ , as estimated from bulk density (BD), is used
only by Rawls and Brakensiek (1985) (here Rawls MvG), and pH and cation
exchange capacity (CEC) are inputs in ‘Toth continuous’. An overview of
all used PTFs, their abbreviations, and their inputs is provided in Tab.
1. The region from where data were taken to train the PTF are from
either the USA or Europe. Rosetta is the only PTF combining two data
regions, whereas Weynants PTF is based on samples from Belgium only. In
addition, the number of samples used for PTF development greatly
differs, ranging from 5320 for Rawls PTFs to 166 for Weynants. Important
for the PTF development is the data used to generate the PTFs, whereby
either only retention data (θ (h )) or a
combination of retention (θ(h) ) and unsaturated
hydraulic conductivity (K (h )) data was
used. θ (h ) andK (h ) were used in the development of the
PTFs Rosetta, Woesten, Weynants, and Toth, whereby the percentage of
available K (h ) data is typically low
compared to the availability of θ (h ) data,
generally due to the more complex and laborious procedures required to
determine K (h ). Even though in some cases
both types of data (θ (h ) andK (h )) were used in the development of some
PTFs, the data were not jointly inverted to estimate the hydraulic
parameters, meaning that Rosetta, Woesten, and Toth fitted the hydraulic
parameters sorely on the retention curve and used the fitted αand n values of the Mulaem van Genuchten equation to predictK (h ). In contrast, Weynants used joint
inversion of both hydraulic characteristics
(θ (h ) andK (h )) simultaneously to estimate the
parameters including a near saturation hydraulic conductivityKs * at a predefined pressure
head of – 6 cm. All other PTFs either used the closed form expression
of van Genuchten (1980) or Brooks and Corey (1964) to predictK(h) , using the estimated parameters from the
retention data, together with measured Ks values,
to estimate the unsaturated hydraulic conductivity based on either van
Genuchten (1980) or Brooks and Corey (1964).
In this study, we will compare model simulations for 12 soil textural
classes. For the estimation of hydraulic parameters from texture based
continuous PTFs a representative soil texture was used for each soil
class located in the centre of the respective class area in the textural
triangle; bulk density and Corg were set to 1.4 g
cm-3 and 1 %, respectively. The texture of the
corresponding class is depicted in Fig. 1 and the predicted hydraulic
parameters for all applied PTFs are listed in Annex Tab. 1 and Annex
Tab. 2.
In general, it is known that relatively small changes in the shape of
the soil water retention curve near saturation can significantly affect
the results of numerical simulations of water flow for variably
saturated soils, including the performance of the numerical stability
and rate of convergence (Vogel et al., 2001; Schaap & van Genuchten,
2006). To address this problem, especially in fine textured soils, the
estimated air entry value (i.e., the reciprocal of α) from the PTF for
the van Genuchten formulation (Eq. 4) was set to -2 cm as proposed by
Vogel et al. (2001), whenever the originally proposed set of hydraulic
properties from the PTF did not lead to numerical convergence.