Publication Date:
2012-04-04
Description:
Dynamic data for parameter estimation in groundwater hydrology are often strongly sensitive to averages of porosity and permeability over extended regions, but only weakly sensitive to the properties of individual gridblocks. Consequently, updates of gridblock parameters from the ensemble Kalman filter (EnKF) will be subject to substantial error due to spurious correlations when the size of the ensemble is small. It has been shown that adaptive localization methods can reduce the magnitude of spurious correlations and regularize updates from the EnKF. In this paper we show that when data are sensitive to an average of parameters over extended regions, adaptive localization methods may eliminate true, but weak, correlations. For this type of data, there appears to be a relationship between the spatial scale of the model variables and the sensitivity of observations to the variables. By introducing a multiscale expansion with adaptive localization, we are able to increase the sensitivity to variables corresponding to large spatial scales and more accurately compute their magnitudes, while eliminating updates to variables corresponding to small spatial scales with weak correlations. Three examples with distinct features are used to compare the new method of combining adaptive localization with wavelet parameterization to the case of no localization and adaptive localization with standard gridblock parameterization. We show that the Kalman gain estimated using the wavelet parameterization with adaptive localization is less biased and has smaller root-mean-square error for the problems in which spatial averaging is important and the Kalman gain has large-scale features.
Print ISSN:
0043-1397
Electronic ISSN:
1944-7973
Topics:
Architecture, Civil Engineering, Surveying
,
Geography
Permalink
