Non-linearity and error in modelling soil processes

Error in models and their inputs can be propagated to outputs. This is important for modelling soil processes because soil properties used as parameters commonly contain error in the statistical sense, that is, variation. Model error can be assessed by validation procedures, but tests are needed for the propagation of (statistical) error from input to output. Input error interacts with non-linearity in the model such that it contributes to the mean of the output as well as its error. This can lead to seriously incorrect results if input error is ignored when a non-linear model is used, as is demonstrated for the Arrhenius equation. Tests for non-linearity and error propagation are suggested. The simplest test for non-linearity is a graph of the output against the input. This can be supplemented if necessary by testing whether the mean of the output changes as the standard deviation of the input increases. The tests for error propagation examine whether error is suppressed or exaggerated as it is propagated through the model and whether changes in the error in one input influence the propagation of another. Applying these tests to a leaching model with rate and capacity parameters showed differences between the parameters, which emphasized that statements about non-linearity must be for specific inputs and outputs. In particular, simulations of mean annual concentrations of solute in drainage and concentrations on individual days differed greatly in the amount of non-linearity revealed and in the way error was propagated. This result is interpreted in terms of decoherence.