scholarly journals The Application of Spectral Representations in Coordinates of Complex Frequency for Digital Filter Analysis and Synthesis

10.5772/15241 ◽  
2011 ◽  
Author(s):  
Alexey Mokeev
Keyword(s):  
Digital Filter ◽  
Complex Frequency ◽  
Analysis And Synthesis ◽  
Spectral Representations ◽  
Filter Analysis

scholarly journals The Stability of Incremental Analysis Update

2018 ◽  
Vol 146 (10) ◽  
pp. 3259-3275 ◽  
Author(s):  
Lawrence L. Takacs ◽  
Max J. Suárez ◽  
Ricardo Todling
Keyword(s):  
Digital Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Stability Diagram ◽  
Recent Attempt ◽  
Complex Frequency ◽  
Incremental Analysis ◽  
Wide Range ◽  
The Stability ◽  
Background Fields

Abstract 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 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 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 4D incremental analysis update (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.

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