The Stability of Incremental Analysis Update.

A recent attempt to downscale the 50 km MERRA-2 analyses to 7 km revealed an instability associated with the Incremental Analysis Update (IAU) procedure that has thus far gone unnoticed. A theoretical study based on a simple damped harmonic oscillator with complex frequency provides the framework to diagnose the problem and suggests means to avoid it. Three possible approaches to avoid the instability are to: (i) choose an "ideal" ratio of the lengths of the Predictor and Corrector steps of IAU based on a theoretical stability diagram; (ii) time average the background fields used to construct the IAU tendencies with given frequency; or (iii) apply a digital filter modulation to the IAU tendencies. All these are shown to control the instability for a wide range of resolutions when doing up- or down-scaling, experiments with the NASA/GMAO atmospheric general circulation model. Furthermore, it is found that combining IAU with the ensemble re-centering step typical of hybrid ensemble-variational approaches, also results in an instability based on the same mechanisms in the members of the ensemble. An example of such occurrence arises in an experiment performed with the GMAO 12.8 km hybrid 4D-EnVar system. Modulation of the ensemble IAU tendencies with a digital filter is shown to avoid the instability. In addition, the stability of certain 4DIAU implementations is analyzed and a suggestion is made to improve its results, though a complete study of this subject is postponed to a follow up work.

Maintaining Atmospheric Mass and Water Balance in Reanalyses.

This study describes the modifications made to the Goddard Earth Observing System (GEOS) Atmospheric Data Assimilation System (ADAS) to conserve atmospheric dry-air mass and to guarantee that the net source of water from precipitation and surface evaporation equals the change in total atmospheric water. The modifications involve changes to both the atmospheric model and the analysis procedure. In the model, sources and sinks of water are included in the continuity equation; in the analysis, constraints are imposed to penalize (and thus minimize) analysis increments of dry-air mass. Finally, changes are also required to the Incremental Analysis Update (IAU) procedure. The effects of these modifications are separately evaluated in free-running and assimilation experiments. Results are also presented from a multiyear reanalysis (Version 2 of the Modern Era Retrospective-Analysis for Research and Applications: MERRA-2) that uses the modified system.