Diagnosis of systematic analysis increments by using normal modes

This paper applies the normal-mode functions for the three-dimensional diagnosis of systematic analysis increments in the operational systems of ECMWF and NCEP, in the NCEP/NCAR reanalyses and in the ensemble data assimilation system DART/CAM which is developed at NCAR. Non-zero systematic increments are interpreted as the analysis system bias. The main region of tropospheric biases in all systems is the Tropics; most of the large-scale tropical bias resides in the unbalanced (inertio-gravity) motion with the eastward-propagating component being dominant in some datasets. The magnitudes of tropospheric wind-field biases in July 2007 were in the range between 1 ms?? and 2 ms??, illustrating the importance of diagnosing analysis systems in the Tropics where magnitudes of the large-scale variability are of the same order. The systematic increments integrated over the whole models' atmosphere appear predominantly balanced; this balance is associated with biases in the zonally averaged balanced state and, in case of ECMWF and NCEP, with the biases at the model top levels. Spectra of analysis increments averaged over one month show that, on average, 20% to 45% of total energy in increment fields belongs to the inertio-gravity motions.