Publication Details |
Category | Text Publication |
Reference Category | Journals |
DOI | 10.5194/hessd-12-2155-2015 |
Title (Primary) | Inverse modelling of in situ soil water dynamics: accounting for heteroscedastic, autocorrelated, and non-Gaussian distributed residuals |
Author | Scharnagl, B.; Iden, S.C.; Durner, W.; Vereecken, H.; Herbst, M. |
Source Titel | Hydrology and Earth System Sciences Discussions |
Year | 2015 |
Department | BOPHY |
Volume | 12 |
Issue | 2 |
Page From | 2155 |
Page To | 2199 |
Language | englisch |
UFZ wide themes | RU1 |
Abstract | Inverse modelling of in situ soil water dynamics is a powerful tool to test
process understanding and determine soil hydraulic properties at the scale of
interest. The observations of soil water state variables are typically
evaluated using the ordinary least squares approach. However, the underlying
assumptions of this classical statistical approach of independent,
homoscedastic, and Gaussian distributed residuals are rarely tested in
practice. In this case study, we estimated the soil hydraulic properties of a
homogeneous, bare soil profile from field observations of soil water
contents. We used a formal Bayesian approach to estimate the posterior
distribution of the parameters in the van Genuchten–Mualem (VGM) model of
the soil hydraulic properties. Three likelihood models that differ with
respect to assumptions about the statistical features of the time series of
residuals were used. Our results show that the assumptions of the ordinary
least squares did not hold, because the residuals were strongly
autocorrelated, heteroscedastic and non-Gaussian distributed. From
a statistical point of view, the parameter estimates obtained with this
classical statistical approach are therefore invalid. Since a test of the
classic first-order autoregressive (AR(1)) model led to strongly biased model
predictions, we introduced an modified AR(1) model which eliminates this
critical deficit of the classic AR(1) scheme. The resulting improved
likelihood model, which additionally accounts for heteroscedasticity and
nonnormality, lead to a correct statistical characterization of the residuals
and thus outperformed the other two likelihood models. We consider the
corresponding parameter estimates as statistically correct and showed that
they differ systematically from those obtained under ordinary least squares
assumptions. Moreover, the uncertainty in the parameter estimates was
increased by accounting for autocorrelation in the observations. Our results
suggest that formal Bayesian inference using a likelihood model that
correctly formalizes the statistical properties of the residuals may also
prove useful in other inverse modelling applications in soil hydrology. |
Persistent UFZ Identifier | https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=16062 |
Scharnagl, B., Iden, S.C., Durner, W., Vereecken, H., Herbst, M. (2015): Inverse modelling of in situ soil water dynamics: accounting for heteroscedastic, autocorrelated, and non-Gaussian distributed residuals Hydrol. Earth Syst. Sci. Discuss. 12 (2), 2155 - 2199 10.5194/hessd-12-2155-2015 |