The Stability of Incremental Analysis Update

AbstractA 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 downscaling, experiments with the NASA GMAO atmospheric general circulation model. Furthermore, it is found that combining IAU with the ensemble recentering step typical of hybrid ensemble–variational approach...