Effects of systematic errors in observations on model prediction uncertainty.

Observations of soil states obtained from in-situ or remote sensors have various sources of errors. A crude way to represent these errors is to assume that part of the error is purely random whereas another part persists and does not change over time. Since the persistent part does not cancel out when more data become available over time whereas the random part does, the partitioning of the error into a persistent and random part is important to assess the uncertainty of model parameters and model predictions that are derived from these observations. Two approaches can be followed to represent these systematic errors in model parameter estimation. The first approach represents the systematic error as an additional parameter representing the bias that is estimated using additional unbiased observations, which we assumed to have only random errors. A second approach represents the systematic error as a covariance in the error-covariance matrix. The uncertainty of the model predictions in the first approach consists of a term that represents the uncertainty of the bias estimation, which is independent of the magnitude of the bias and depends only on the uncertainty of the unbiased additional observations. When additional unbiased measurements are included in the second approach, which represents bias as error covariance, smaller model prediction uncertainty is obtained than using the first approach. This is especially the case when the covariance representing the bias is smaller than the variance of the average error of the random observations. Including prior knowledge about the bias in the error covariance, reduces the model parameter and prediction uncertainty.