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| Titel |
Coupling Ensemble Kalman filter and groundwater flow moment equations for real time data assimilation |
| VerfasserIn |
Marco Panzeri, Monica Riva, Alberto Guadagnini, Shlomo P. Neuman |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250074129
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| Zusammenfassung |
| We consider data assimilation through ensemble Kalman filter (EnKF) in the context of
groundwater flow through complex geologic media. EnKF enables one to efficiently
assimilate diverse data types to characterize earth system models. The approach allows
real-time Bayesian updating of system states and parameters as new data are collected.
Modeling hydraulic conductivity as a correlated random field conditioned on measured
conductivity and/or hydraulic head values renders the corresponding (conditional)
groundwater flow equations stochastic. Solving these equations and coupling them with
EnKF is typically performed within a numerical Monte Carlo (MC) simulation framework.
We circumvent the need for MC through a direct solution of approximate nonlocal
(integrodifferential) moment equations (MEs) that govern the space-time evolution of
conditional ensemble means (statistical expectations) and covariances of hydraulic heads and
fluxes. Embedding the solution of MEs in EnKF provides sequential updates of
conductivity and head estimates throughout the space-time domain of interest. This
is well suited for cases where real-time measurements can be used immediately
to obtain a constantly up-to-date estimate of the aquifer parameters and avoids
the need of assimilating all the available data in batch, where the process has to
be repeated for all (previous and recent) data when new measurements become
available. The methodology is illustrated through a hypothetical two-dimensional
example in which a well pumps water from a randomly heterogeneous aquifer of finite
extent. We analyze different scenarios, investigating the impact on the parameters
estimates of (a) the number of head measurements assimilated, (b) the error variance
associated with log conductivity measurements and (c) the initial hydraulic head field.
We demonstrate the computational feasibility and accuracy of our methodology
and show that hydraulic conductivity estimates are more sensitive to early than
to later head values and improve with increasing assimilation frequency at early
time. Increasing the variance of log hydraulic conductivity measurement errors by
one order of magnitude brought about only a minor deterioration in the quality of
corresponding parameter estimates. We test the influence of variogram model and
parameters adopted to obtain the initial distributions of log hydraulic conductivity (Y )
mean and covariance on the resulting estimates of (a) hydraulic conductivity and (b)
head. Our results show that assuming initial variogram sill and integral scale values
different from the true ones has (in general) no adverse effect on the final estimate of
Y . In contrast, adopting an incorrect variogram model caused the quality of the
parameter estimates to deteriorate during the assimilation of head measurements. |
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