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.

[1]  Ying-Hwa Kuo,et al.  Incremental Analysis Updates Initialization Technique Applied to 10-km MM5 and MM5 3DVAR , 2006 .

[2]  N. B. Ingleby,et al.  The Met. Office global three‐dimensional variational data assimilation scheme , 2000 .

[3]  Lawrence L. Takacs,et al.  Data Assimilation Using Incremental Analysis Updates , 1996 .

[4]  Peter Lynch,et al.  Initialization of the HIRLAM Model Using a Digital Filter , 1992 .

[5]  L. Oman,et al.  Large‐Scale Atmospheric Transport in GEOS Replay Simulations , 2017 .

[6]  Bin Zhao,et al.  The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). , 2017, Journal of climate.

[7]  Jean-Michel Brankart,et al.  Incremental Analysis Update Implementation into a Sequential Ocean Data Assimilation System , 2006 .

[8]  David L. T. Anderson,et al.  The ECMWF Ocean Analysis System: ORA-S3 , 2008 .

[9]  A. M. Clayton,et al.  On the Relationship between Incremental Analysis Updating and Incremental Digital Filtering , 2004 .

[10]  Olivier Pannekoucke,et al.  On the Merits of Using a 3D-FGAT Assimilation Scheme with an Outer Loop for Atmospheric Situations Governed by Transport , 2010 .

[11]  Neill E. Bowler,et al.  Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for Global NWP , 2015 .

[12]  Lili Lei,et al.  A Four-Dimensional Incremental Analysis Update for the Ensemble Kalman Filter , 2016 .

[13]  J. Carton,et al.  A Reanalysis of Ocean Climate Using Simple Ocean Data Assimilation (SODA) , 2008 .

[14]  Stephen G. Penny,et al.  The Hybrid Local Ensemble Transform Kalman Filter , 2014 .

[15]  J. Derber,et al.  Introduction of the GSI into the NCEP Global Data Assimilation System , 2009 .

[16]  Amos S. Lawless,et al.  A note on the analysis error associated with 3D‐FGAT , 2010 .

[17]  Thomas M. Hamill,et al.  Ensemble Data Assimilation with the NCEP Global Forecast System , 2008 .

[18]  Richard B. Rood,et al.  An assimilated dataset for Earth science applications , 1993 .

[19]  Mark Buehner,et al.  Implementation of Deterministic Weather Forecasting Systems Based on Ensemble–Variational Data Assimilation at Environment Canada. Part I: The Global System , 2015 .