Impacts of localisation in the EnKF and EnOI: experiments with a small model |
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Authors: | Peter R Oke Pavel Sakov Stuart P Corney |
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Institution: | (1) CSIRO Marine and Atmospheric Research and Wealth from Oceans Flagship Program, Hobart, Tasmania, Australia |
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Abstract: | The performance of an inexpensive, ensemble-based optimal interpolation (EnOI) scheme that uses a stationary ensemble of model
anomalies to approximate forecast error covariances, is compared with that of an ensemble Kalman filter (EnKF). The model
to which the methods are applied is a pair of “perfect”, one-dimensional, linear advection equations for two related variables.
While EnOI is sub-optimal, it can give results that are comparable to those of the EnKF. The computational cost of EnOI is
typically about times less than that of EnKF, where is the ensemble size. We suggest that EnOI may provide a practical and cost-effective alternative to the EnKF for some applications
where computational cost is a limiting factor. We demonstrate that when the ensemble size is smaller than the dimension of
the model’s sub-space, both the EnKF and EnOI may require localisation around each observation to eliminate effects of sampling
error and to increase the effective number of independent ensemble members used to construct an analysis. However, localisation
can degrade an analysis if the length-scales of the localising function are too short. We demonstrate that, as the length-scale
of the localising function is decreased, localisation can significantly compromise the model’s dynamical balances. We also
find that localisation artificially amplifies high frequencies for applications of the EnKF. Based on our experiments, for
applications where localisation is necessary, the length-scales of the localisation should be larger than the decorrelation
length-scales of the variables being updated. |
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Keywords: | Data assimilation Ensemble Kalman filter |
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