Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks

Weaver, Anthony; Vialard, Jérôme; Anderson, David L. T.

doi:10.1175/1520-0493(2003)131<1360:tafvaw>2.0.co;2

Cited by 191 publications

(181 citation statements)

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“…Compared with economic 3D-Var analysis (Derber and Rosati, 1989;Zhu et al, 2006), the 4D-Var data assimilation method is more dynamically and mathematically consistent (e.g., Dommenget and Stammer, 2004;Sugiura et al, 2008). For instance, Weaver et al (2003) assimilated in situ temperature data into an OGCM by the 3D-Var and 4D-Var methods, and demonstrated that 4D-Var is more effective than 3D-Var in producing a consistent ocean state between model solutions and observations. Additionally, the 4D-Var method has been applied to ENSO prediction using various models and has achieved some success (Kleeman et al, 1995;Galanti et al, 2003;Dommenget and Stammer, 2004).…”

Section: Introductionmentioning

confidence: 99%

Testing a four-dimensional variational data assimilation method using an improved intermediate coupled model for ENSO analysis and prediction

Gao

2016

Adv. Atmos. Sci.

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A four-dimensional variational (4D-Var) data assimilation method is implemented in an improved intermediate coupled model (ICM) of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The "observation" of the SST anomaly, which is sampled from a "truth" model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.

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Section: Introductionmentioning

confidence: 99%

Testing a four-dimensional variational data assimilation method using an improved intermediate coupled model for ENSO analysis and prediction

Gao

2016

Adv. Atmos. Sci.

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“…The data assimilation method is a variant of the multivariate incremental 3D-Var FGAT (First-Guess at Appropriate Time) method described in Weaver et al (2003Weaver et al ( , 2005 and Ricci et al (2005). A short description is given below to highlight those features of the method that are important in this study.…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…The correlation functions implied by the diffusion model are approximately Gaussian. The parameters of the 3D diffusion model are the same as those used for the univariate T correlations in Weaver et al (2003), except for the vertical correlation scales which have been slightly reduced here (they are proportional to the local vertical grid depths). Identical correlation parameters are used for T and S U .…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…using w b instead of w b (t i ) in Equation (2)). Here, following Weaver et al (2003) and Ricci et al (2005), we take, as in 4D-Var, w b to be the background state at the start of the window (w b ≡ w b (t 0 )). This choice was made mainly for simplifying the technical implementation of 3D-Var in our system, which also supports 4D-Var.…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…Weaver et al (2003) illustrate how this simple variance parametrization can capture some of the dynamical effects implicit in 4D-Var. A similar parametrization is used in the operational ocean data assimilation systems at the National Centers for Environmental Prediction (NCEP; Behringer et al, 1998) and ECMWF ).…”

Section: Parametrized Error Variance Matrix: D (1) ( W)mentioning

confidence: 99%

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Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

Daget

Weaver

Balmaseda

2009

Quart J Royal Meteoro Soc

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This paper studies the sensitivity of global ocean analyses to two flow-dependent formulations of the background-error standard deviations (σ b ) for temperature and salinity in a three-dimensional variational data assimilation (3D-Var) system. The first formulation is based on an empirical parameterization of σ b in terms of the vertical gradients of the background temperature and salinity fields, while the second formulation involves a more sophisticated approach that derives σ b from the spread of an ensemble of background states. The ensembles are created by explicitly perturbing both the surface fluxes (wind stress, fresh water and heat) used to force the model and the observations (temperature and salinity profiles) used in the assimilation process. The two formulations are compared in two cycled 3D-Var experiments for the period 1993-2000. In both experiments, the observation-error standard deviations (σ o ) are geographically dependent and estimated from a model-data comparison prior to assimilation. An additional 3D-Var experiment that employs the parametrized σ b but a simpler σ o formulation, and a control experiment involving no data assimilation, were also conducted and used for comparison.All 3D-Var experiments produce a significant reduction in the mean and standard deviation of the temperature and salinity innovations compared to those of the control experiment. The largest differences between the two σ b formulations occur in the upper 150 m, where the parametrized σ b are notably larger than the ensemble σ b . In this region, the innovation statistics are slightly better for the parametrized σ b . Statistical consistency checks indicate that both schemes underestimate σ b , the underestimation being stronger with the ensemble formulation. The error growth between cycles, however, is much reduced with the ensemble σ b , suggesting that the analyses produced with the ensemble σ b are in better balance than those produced with the parametrized σ b . This claim is supported by independent data comparisons involving model fields not directly constrained by the assimilated temperature and salinity profiles. In particular, sea-surface height (SSH) anomalies in the northwest Atlantic and zonal velocities in the equatorial Pacific are clearly better with the ensemble σ b than with the parametrized σ b . Results also show that while some aspects of those variables are improved with data assimilation (SSH anomalies and currents in the central and eastern Pacific), other aspects are degraded (SSH anomalies in the northwest Atlantic, currents in the western Pacific). Areas for improving the ensemble method and for making better use of the ensemble information are discussed.

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A 3‐D variational assimilation scheme in coupled transport‐biogeochemical models: Forecast of Mediterranean biogeochemical properties

et al. 2014

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[1] Increasing attention is dedicated to the implementation of suitable marine forecast systems for the estimate of the state of the ocean. Within the framework of the European MyOcean infrastructure, the pre-existing short-term Mediterranean Sea biogeochemistry operational forecast system has been upgraded by assimilating remotely sensed ocean color data in the coupled transport-biogeochemical model OPATM-BFM using a 3-D variational data assimilation (3D-VAR) procedure. In the present work, the 3D-VAR scheme is used to correct the four phytoplankton functional groups included in the OPATM-BFM in the period July 2007 to September 2008. The 3D-VAR scheme decomposes the error covariance matrix using a sequence of different operators that account separately for vertical covariance, horizontal covariance, and covariance among biogeochemical variables. The assimilation solution is found in a reduced dimensional space, and the innovation for the biogeochemical variables is obtained by the sequential application of the covariance operators. Results show a general improvement in the forecast skill, providing a correction of the basin-scale bias of surface chlorophyll concentration and of the local-scale spatial and temporal dynamics of typical bloom events. Further, analysis of the assimilation skill provides insights into the functioning of the model. The computational costs of the assimilation scheme adopted are low compared to other assimilation techniques, and its modular structure facilitates further developments. The 3D-VAR scheme results especially suitable for implementation within a biogeochemistry operational forecast system.

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Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks

Cited by 191 publications

References 53 publications

Testing a four-dimensional variational data assimilation method using an improved intermediate coupled model for ENSO analysis and prediction

Testing a four-dimensional variational data assimilation method using an improved intermediate coupled model for ENSO analysis and prediction

Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

A 3‐D variational assimilation scheme in coupled transport‐biogeochemical models: Forecast of Mediterranean biogeochemical properties

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