Regionalised time series models for water table depths

Research output: Thesisexternal PhD, WU


<font size="3"><p>Index words: groundwater head, time series analysis, physical interpretation, resampling, stochastic simulation, accuracy, quantified uncertainty</p><p>Because of its shallow depths, the water table is of significant importance for agriculture and nature conservation in the Netherlands. Water management therefore requires accurate information on the spatial and temporal variations of the water table depth. This information is preferably expressed in terms of probabilities, in order to enable risk assessment. Furthermore, to support strategic decisions in water policy, the information on the water table dynamics should reflect the prevailing climatic conditions (say, the average weather over a 30-year period). Since the number of observation wells and the lengths of the time series are limited for regional studies, spatio-temporal prediction methods should be able to incorporate additional measurements and additional information related to the water table depth.</p><p>Stochastic methods are devised for estimating fluctuation characteristics representing the prevailing climatic and hydrologic conditions. These methods are based on various models for the dynamic relationship between precipitation surplus and water table depth: a physical descriptive, one-dimensional model, SWATRE, supplemented with a univariate time series model for the noise (SWATRE+ARMA), linear transfer function-noise models (TFN), dynamic regression models (DR) or autoregressive exogenous variable models (ARX), and nonlinear threshold autoregressive models (TARSO). These models are applied to extrapolate observed time series of water table depths, by using observed input series on the precipitation surplus having a length of 30 years. Uncertainty is accounted for by generating a large number of realisations using the stochastic model component. The models perform only slightly differently in simulating water table depths, despite their clearly different theoretical starting points. It is shown that a first-order ARX model can easily be expressed in terms of a water balance for a soil column. Moreover, the physically based ARX model can be applied in predicting the effects of human interventions in the hydrological regime on the water table dynamics.</p><p>The ARX model is regionalised to a RARX model, by making its parameters dependent of the spatial co-ordinates. Because of their physical basis, the RARX model parameters can be guessed from auxiliary information such as a digital elevation model (DEM), digital topographic maps and digitally stored soil profile descriptions. Next, the guessed RARX parameters are used to transform a precipitation surplus series into a series of water table depths. Predictions obtained by this 'direct' method are compared with observed water table depths. The observed errors are used to correct the final predictions for systematic errors, and to perform stochastic simulations ('indirect' method). The RARX model is incorporated into a space-time Kalman filter algorithm, which enables predictions conditional to observed water table depths. A cross-validation experiment shows that Kalman filter approaches predict the temporal variation of the water table depths relatively precise, whereas the 'indirect' method yields relatively accurate estimates of expected water table depths, since systematic errors are small. The uncertainty about the temporal variation of the water table depth is underestimated by all methods evaluated. Given the sampling design, the accuracy of the uncertainty about the mean water table depth could not be assessed. Besides efforts to reduce uncertainty, it would be interesting to optimise sampling designs in order to obtain accurate estimates of uncertainty.</p><p> </p></font><FONT FACE="Courier New" SIZE=2><p> </p></font>
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Wageningen University
  • Troch, P.A., Promotor, External person
  • Bierkens, M.F.P., Promotor
Award date3 Oct 2001
Place of PublicationS.l.
Print ISBNs9789058084781
Publication statusPublished - 2001


  • water table
  • groundwater level
  • measurement
  • time series
  • statistical analysis
  • stochastic models
  • simulation models
  • accuracy
  • digital elevation model


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