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.