Model errors and the chaotic nature of atmospheric motions are the two factors limiting the predictability of deterministic forecasts. Ensemble analysis and forecast systems provide estimates of the analysis and forecast uncertainties. In this seminar it will be presented how the normal mode expansion is used to quantify these uncertainties in terms of balanced and unbalanced motions and various scales. The three-dimensional modes used are orthogonal which permits the representation of the wind and mass fields simultaneously and allows energy quantification as a function of a zonal wave number, a meridional mode and a vertical eigenstructure.
Ensembles of analyses and forecasts are results of the Data Assimilation Research Testbed system (DART) and CAM 3.1 T85 model. The 80-member ensemble was run for July 2007 using conventional observations and wind motion vectors. The selection of normal modes is tuned so that the expansion explains over 90% of the flow variance in the free atmosphere. This allows reliable quantification of the percentage of total energy contained in various motions. Of particular interest are large-scale divergent motions, and especially equatorial waves. For a particular ensemble member temporal evolution of the expansion coefficients is obtained for prior and posterior fields. Their difference provides information about the scales and modes which are affected by observations in the assimilation. For a particular time event, information about the ensemble spread is an estimate of the uncertainty in the modal space. Results for the DART/CAM ensemble mean are compared with the NCEP reanalysis and ECMWF operational analysis datasets for the same period.