106 Geir Evensen
6.4 An example of the analysis scheme
An example is now presented which iIIustrates the analysis step in the EnKF.
Further, as a validation of the derivation performed in the previous section the
results are also compared with the standard Kalman filter analysis.
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KF variance ..... _.
EnKF variance "".
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Fig. 6_1 Comparing results from the KF and the EnKF analysis schemes. On top the true
reference state, the first-guess, and the analyzed estimate. The lower plot shows the
corresponding error variance estimates.
For the experiment a l-dimensional periodic domain in x, with XE [0,50], is
used. We assume a characteristic length scale for the function \jI(x) as 1 = 5. The
interval is discretized into 1008 grid points which means there are a total of about
50 grid points for each characteristic length.
Using the methodology outlined in the Appendix of Evensen (1994b) we can
draw smooth pseudo random functions from a distribution with zero mean, unit
variance and a specified covariance given by