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Stability issues

Par ECOLA Dernière modification 12/04/2012 10:50

The resolution of the data assimilation linear system has shown sensitivity to numerical issues related to the conditionning of the system covariance matrix, in relation to the decorrelation function shape and length scale.

 

The following figures illustrates system matrix eigen values for different decorrelation length scales of a linear function shape.

 

The following figures illustrates system matrix eigen values for different decorrelation shapes with the same decorrelation length scale (4000km).

 

 

The following figures illustrates system matrix eigen values for different decorrelation shapes with the same decorrelation length scale (8000km).

 

 

 

Data assimilation system matrix are displayed below when a linear decorrelation is applied on the representer matrix (left) or not (right). The decorrelation length scale is 4000km.

 

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