Application of Normal Mode Functions to DART/CAM Analysis and Forecast Fields

Normal mode functions are eigensolutions of a linearized primitive equation system. A set of normal modes as derived by Akira Kasahara in the early 80s has been applied to the outputs of the DART/CAM ensemble data assimilation system. A special advantage of this set is that 3D modes are orthogonal which permits the representation of the wind and mass fields simultaneously. This allows energy quantification as a function of a zonal wave number, a meridional mode and a vertical eigenstructure as well as balanced and unbalanced motions. Normal mode coefficients are computed for an 80-member ensemble run with CAM 3.1 T85 for July 2007. For a particular ensemble member (and the ensemble mean), temporal evolution of the expansion coefficients is obtained separately for prior and posterior fields. Their difference provides information about the scales and modes which are affected by observations and assimilation modeling. For a particular analysis time, information about the ensemble spread in the wave space is provided. For the departure (with respect to the ensemble mean) fields, variances of errors in the prior and posterior ensembles are estimated.
Analyzing this information provides some understanding about how the assimilation is treating various modes. Of particular interest are divergent tropical motions, known to be poorly analyzed by traditional analysis methods.