## 2 Materials and Methods
### Model Assessment  
Goodness-of-fit (GOF) measures provide a way of comparing models by aggregating results over all training or validation samples of data. They are useful as a general method of comparison between pairwise samples of data where observed data are reliable but only crudely differentiate between models and cannot describe the detailed differences at different response values. In this comparison, we used mean error (ME, range unbounded), mean absolute error (MAE, range [0, \(\infty\)]), root-mean-square error (RMSE, range [0, \(\infty\)]), Nash-Sutcliffe efficiency (NSE, range [\(-\infty\), 1] [23]), coefficient of determination (R2, range [0, 1]), and the index of agreement (d, range [0, 1], [24]), defined as follows:  
\[\text{ME}=\frac{\sum_{i=1}^{N}y_{m,i}-y_{o,i}}{N}\]  
\[\text{MAE}=\frac{\sum_{i=1}^{N}\  
water response between two different tension values. In New Zealand, total available water content is defined as the difference in response between \(-10\) and \(-1500\) kPa, but there are other definitions of this property in the literature, adapting to local circumstances, and for specific purposes. Since most PTFs have been designed with sets of explanatory variables that happen to be available, and because the definition of derived properties varies, it is relatively rare for PTFs to be straightforwardly compared. Added to this complexity are the differences in the definition of the size of silt and sand (Table 3), which is frequently an influential explanatory variable in soil water PTFs ([PERSON], 2018). The requirement was to compare the PTF generated in this paper with one or more PTFs in the literature where the explanatory variables from S-map could be used and where the various explanatory variables had the same definition as used in S-map. PTFs used for the comparison had to be computable from published equations or available via software packages. We excluded PTFs that used components of the soil-water response (e.g., wilting point, total porosity) as explanatory parameters (and that are sometimes found in the literature) since they are highly influential predictors of the response. In these PTFs, the total porosity (TP) or wilting point (WP) was a required parameter, which means that predictions for 0 and \(-1500\) kPa are perfect or nearly perfect (depending on the nature of the model). Given the above restrictions, very few PTFs were available for direct comparison with the PTF developed in this paper. One suitable set of PTFs, however, was the European hydraulic pedotransferer functions (EUPTF2, ([PERSON], 2018)). These are an update of previously published European PTFs ([PERSON], 2018), EUPTF v1.4.0, which provides prediction uncertainty. EUPTF2 was derived for point predictions of soil water content at saturation (0 kPa), field capacity (at both 10 and 33 kPa), wilting point (1500 kPa), plant available water, and saturated hydraulic conductivity, as well as the van Genuchten model parameters of the moisture retention and hydraulic conductivity curve ([PERSON], 2018). The models can use a selection of inputs, with a minimum of soil depth, sand, silt, and clay content. Additional information such as soil organic carbon content, bulk density, calcium carbonate content, pH, and cation exchange capacity can also be included, although these are not viable as explanatory parameters for S-map. A complication when using S-map information in the EUPTF2 model is that texture is defined using different classifications for sand, silt, and clay compared to those used in New Zealand (Table 3), so texture cannot be used without some kind of transformation of standard S-map texture values from New Zealand to those compatible with EUPTF2. For the purposes of comparison with the PTF developed in this paper, sample data from the particle size distribution were used to generate estimates of sand, silt, and clay content using the USDA/FAO (Table 3) with a monotonically constrained B-Spline curve ([PERSON], 2018), as outlined in Section 2.2.2, along with the sample depth.