Chapter 3
Accuracy and uncertainty in PTF predictions

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This chapter discusses optimization, accuracy, and uncertainty in pedotransfer functions (PTFs). Optimization criteria are the objective functions used to calibrate empirical parameters in PTFs. Accuracy criteria relate to the statistical methods used to test the performance of indirect methods, preferably using data distinct from those used for calibration. Uncertainty estimates provide information about the probability distribution of estimated hydraulic quantities. Thus, a PTF can make accurate estimates (i.e., it produces the correct values on average), but it may not be reliable sometimes; for example, real-world variability is larger than estimated with the PTF. Alternatively, a PTF can be deemed inaccurate when it produces estimates that, on average, differ systematically from observations.

Section snippets

Optimization criteria

All indirect methods, whether physically based or empirical, contain parameters that must be optimized using databases containing both independent data (predictors) and dependent data (hydraulic properties or parameters in hydraulic functions). Virtually all indirect methods are optimized by least-squares methods, and define the objective function asSSQ=N(ς−ς(b)′)2where N is the number of data points and b is a parameter vector containing the empirical PTF coefficients. For point-based methods

Criteria for evaluating the accuracy of PTFS

The accuracy of PTFs is commonly tested using independent data sets. That is, the real value of a PTF can only be evaluated using data that were not used for the calibration of the PTF in question. When a PTF is developed for a particular data set, this PTF should perform well on that data set. However, success on other data sets is not guaranteed as illustrated by Schaap and Leij (1998) who showed that the performance of a PTF depends on the data set used for calibration and the one used for

Evaluating the uncertainty of PTF predictions

PTFs generally provide estimates of hydraulic properties with only a modest level of accuracy. Overconfidence in PTF estimates should be avoided because the random or systematic errors made by PTFs may for example lead to inaccurate estimates of contaminant transport through soils and sediments. In some cases it would be worthwhile to use a probabilistic approach that associates an uncertainty to a PTF estimate, such as a confidence interval. Three general approaches are possible.

The first

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