Loading the field values of a variable into a vector T which dimension varies with the spatial extension of the field (e.g. model level or volume field), the field RMSE and PCC are respectively defined by,

RMSE º   æ Ö (Tf- ^ T   )T (Tf- ^ T   )   = ||Tf- ^ T   ||2 ,     (1)

PCC = (Tf-Tb)T ( ^ T   -Tb) ||Tf-Tb||2  || ^ T   -Tb||2      (2)

where T (hat) denotes the true ocean, T^f its forecast, T^b a background field vector (e.g. large-scale field, climatological field), and || ·||₂ the vector l₂ norm.

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File translated from T_EX by T_TH, version 2.51.
On 13 Jun 2001, 22:37.