# Hydrological Pedotransfer Functions for New Zealand Soils

### Overview

A soil hydrological pedotransfer function is a statistical regression model that estimates key properties of a specified soil from some measured properties of that soil. The soil properties that are estimated can include, for example, total available water or wilting point. The measured soil properties include attributes such as the soil type, texture or other readily-measured properties. A key requirement for the specification of soil hydrological pedotransfer function is the estimation of the uncertainty of the predicted soil property, typically by stating confidence limits.

### Detailed description

These hydrological pedotransfer functions estimate the volumetric soil water content (cm3/cm3) for pre-defined tensions (0, 5, 10, 20, 40, 100, and 1500 kPa), given the range of available information within S-map for the soil, as well as the estimated texture (percentage of sand, silt, and clay). From these basic regression functions, estimates can also be obtained for the total available water, bulk density, macroporosity, wilting point, and field capacity.

The regression functions also yield the estimated uncertainty of the soil water content and derived properties (e.g. total available water), by specifying the 95% confidence interval of the predictions. This is the range of values that one can be certain contains the true mean of the soil property with a 0.95 probability.

In addition, the regression functions are constructed so that the estimated soil properties are physically reasonable; that is, the properties conform to constraints that we would expect in practice. For example, the estimated volumetric soil water content is constrained to be in the range 0–100 %, as are derived physical properties such as the total available water. This also applies to the measures of uncertainty, so that the upper- and lower-confidence 95% confidence limits also lie within the 0–100 % range.

### Definition of the pedotransfer functions

The pedotransfer functions use the functional horizon description available within S-map. This description provides the explanatory variables of topsoil (True or False), ped size (e.g. earthy, fine, or coarse), and tephra (e.g. acidic, basic). In addition to these variables, the NZSC soil order is required, as well as the sand, silt, and clay percentages, and the rock class of fines for the soil. Organic soils are specifically excluded from consideration.

The pedotransfer functions are constrained so that the volumetric soil water content lies in the range 0–100 %. The water content is also constrained so that the estimated value for a specified tension is strictly less than zero as the tension increases. In addition to these structural constraints, the estimates for water content are constructed so that the correlation between estimates at different potentials matches the measured correlation from all the available data.

### Derived properties

While the pedotransfer functions provide estimates of the volumetric soil water content for pre-defined tensions, many users are more interested in estimated values of derived properties, such as the total available water. These properties and their uncertainty are calculated from the predicted soil water content at different tensions, while accounting for the correlation between them.

### Limitations

The uncertainty, or accuracy, of the volumetric soil water content and derived properties depends on the number of samples available in each of the different explanatory factors. Estimates for Brown soils, for instance, are

consistently accurate as a result of the large number of samples, while soils derived from limestone are relatively inaccurate. The uncertainty also depends strongly on whether the specific soil under consideration has sand, silt, and clay values that are covered by the range of samples used to fit the pedotransfer functions. The pedotransfer function estimates of soil hydrological properties are not given in S-map for those soils where the uncertainty is considered to be too high (when the 95% confidence interval is large relative to the predicted value).

### Examples

Figure 1 compares the predicted and measured volumetric soil water content for two different tension values.

Figure 2 shows a ternary plot of sand, silt, and clay showing the restriction in the range of possible soil textures that can be adequately covered by the available soil data.