Abstract
We start in Sect. 4.1 with the specific storage coefficient and the specific yield, which occur in terms with a time derivative. Next, we deal with flow caused by time-dependent driving mechanisms like recharge and varying pumping well rates. In such cases, we can determine a series of time-dependent parameter estimates, from which the mean value and the standard deviation (the spread of the observation noise) can be determined. According to Bayesian theory on conditional probabilities, the uncertainty in a parameter’s mean value will decrease below the spread with increasing length of the time series. Section 4.2 presents the relevant Kalman filter equations, while Sect. 4.3 presents a comprehensive in-depth explanation. This section also presents calibration by the ensemble Kalman filter (EnKF) with hints how the double constraint methodology (DCM) could be applied to mitigate some disadvantages of the EnKF.
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Zijl, W., De Smedt, F., El-Rawy, M., Batelaan, O. (2018). Time Dependency. In: The Double Constraint Inversion Methodology. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-71342-7_4
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