## 2 Materials and Methods
### Available Data
#### 2.2.2 Data Processing  
Soil texture was provided by the percentage values of sand, silt, and clay, with the values summing to 100%, forming a ternary simplex. Texture can be provided from a particle size distribution curve (PSD) or from values for sand, silt, and clay. Where the texture ternary simplex values did not sum to 100%, all three values were scaled to force the sum to that value, provided the original sum was within the range [95%, 100%]. Where both PSD and discrete values for the sand, silt, and clay were available, the PSD values were used by preference. PSD values were available for most of the sample soil profiles in the NSDR. Sand, silt, and clay estimates were available in the NSDR for most samples from appropriate values of the particle size distribution. For a small number of samples where this was not the case, texture was estimated using a monotonically constrained B-Spline  
Figure 1: Distribution of points across New Zealand in the assembled NSDR dataset. One point is missing from this map since there were no spatial coordinates available. curve [16] to the cumulative PSD data parameterized by the log transform of the particle size and using the logit-transformed cumulative PSD as the response; we also added continuity constraints for the PSD at values of 0.0 and 1.0 for nominal particle size values of \(10^{-3}\) and \(10^{4}\)\(\upmu\)m for stability. The definitions of'sand','silt', and 'clay' vary by country, typically affecting the border between silt and sand (see Table 3). Where the Australian, European, or North American texture system is needed for a PTF and when the PSD is available, sand, silt, and clay estimates were generated so that the data can be used in PTFs for TAW using the relevant definition. In this paper, the texture definitions implicitly refer to the New Zealand system, but for PTFs developed elsewhere, we assumed that the appropriate texture definition had been used. In addition to texture values provided in the ternary simplex, texture is also defined as a categorical variable (e.g., sandy, loamy, clayy, see Table 1) from the parsed functional horizon string. This categorical descriptor is defined by ranges of texture values [11], so might be expected to have low influence in the regression model. The texture ternary simplex has an inherent structural correlation, since changing any one value changes the other two, regardless of any functional correlation between them. The ternary simplex values were transformed to a two-component Cartesian system denoted \(\omega_{1}\) and \(\omega_{2}\) such that: \(\omega_{1}=2\rho_{\text{SAND}}-\rho_{\text{SILT}}-\rho_{\text{CLAY}}\) and \(\omega_{2}=\rho_{\text{SILT}}-\rho_{\text{CLAY}}\) (where \(\rho_{\text{SAND}}\), \(\rho_{\text{SILT}}\), and \(\rho_{\text{CLAY}}\) are the fractions of soil in sand, silt, and clay, respectively. [19]), and these Cartesian components were used as predictors in the regression. Several NZSC soil orders were split. This splitting was based on the NZSC soil group where groups differentiated soils of different bulk densities, which is an important influence in predicting the water response. Brown soils were split into Allophanic and non-Allophanic Browns, Gley soils into Immature and Mature Gleys, and Pallic soils into Immature and Mature Pallic. Other data pruning and processing steps include:  
1. The total porosity (TP) was calculated from fine-earth bulk density (BD) and particle density (PD) if TP was missing, using the functional relationship \(\text{TP}=1-\text{BD}/\text{PD}\). 2. Water content values outside the range [0, 1] (0% to 100%) were dropped. 3. Water content values for a sample were only retained where the soil water values from tensions of 0 to \(-\)1500 kPa were non-increasing. However, TP is measured using a different method from other tensions, and sometimes the TP response is less than the response measured at \(-\)5 kPa by a very small amount (typically 0.5%).