Error Estimates for an Ocean General Circulation Model from Altimeter and Acoustic Tomography Data

Menemenlis, Dimitris; Chechelnitsky, Michael Y.

doi:10.1175/1520-0493(2000)128<0763:eefaog>2.0.co;2

Cited by 19 publications

(8 citation statements)

References 33 publications

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“…The difference between model outputs and observations is used in the covariance matching method (Fu et al, 1993) and its extended version (Menemenlis and Chechelnitsky, 2000), which specifies the covariance matrices for system noise and observation noise simultaneously for linear system and observation equations.…”

Section: Calculation Of Statistics (Sample Covariance)mentioning

confidence: 99%

Covariance regularization in inverse space

Ueno

Tsuchiya

2009

Quart J Royal Meteoro Soc

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ABSTRACT:In data assimilation, covariance matrices are introduced in order to prescribe the weights of the initial state, model dynamics, and observation, and suitable specification of the covariances is known to be essential for obtaining sensible state estimates. The covariance matrices are specified by sample covariances and are converted according to an assumed covariance structure. Modelling of the covariance structure consists of the regularization of a sample covariance and the constraint of a dynamic relationship. Regularization is required for converting the singular sample covariance into a non-singular sample covariance, removing spurious correlation between variables at distant points, and reducing the required number of parameters that specify the covariances. In previous studies, regularization of sample covariances has been carried out in physical (grid) space, spectral space, and wavelet space. We herein propose a method for covariance regularization in inverse space, in which we use the covariance selection model (the Gaussian graphical model). For each variable, we assume neighbouring variables, i.e. a targeted variable is directly related to its neighbours and is conditionally independent of the non-neighbouring variables. Conditional independence is expressed by specifying zero elements in the inverse covariance matrix. The non-zero elements are estimated numerically by the maximum likelihood using Newton's method. Appropriate neighbours can be selected with the AIC or BIC information criteria. We address some techniques for implementation when the covariance matrix has a large dimension. We present an illustrative example using a simple 3 × 3 matrix and an application to a sample covariance obtained from sea-surface height observations.

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Section: Calculation Of Statistics (Sample Covariance)mentioning

confidence: 99%

Covariance regularization in inverse space

Ueno

Tsuchiya

2009

Quart J Royal Meteoro Soc

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“…While all data assimilation applications include some estimate of the observation error, there is a wide range of approaches used (e.g., Oke and Sakov 2008). A statistical method that involves various assumptions originally proposed by Fu et al (1993) has been widely used in ocean data assimilation (Fukumori 2000;Menemenlis and Chechelnitsky 2000;Leeuwenburgh 2007;Daget et al 2009), but some of the assumptions are made purely for practical convenience and are questionable (see, e.g., Menemenlis and Chechelnitsky 2000;Daget et al 2009). As discussed in detail below, we set the observation error estimates by assuming a constant background/observation error (i.e., square root of error variance) ratio of 0.47.…”

Section: Peodasmentioning

confidence: 99%

An Ensemble Ocean Data Assimilation System for Seasonal Prediction

Yin

Alves

Oke

2011

Monthly Weather Review

127

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A new ensemble ocean data assimilation system, developed for the Predictive Ocean Atmosphere Model for Australia (POAMA), is described. The new system is called PEODAS, the POAMA Ensemble Ocean Data Assimilation System. PEODAS is an approximate form of an ensemble Kalman filter system. For a given assimilation cycle, a central forecast is integrated, along with a small ensemble of forecasts that are forced with perturbed surface fluxes. The small ensemble is augmented with multiple small ensembles from previous assimilation cycles, yielding a larger ensemble that consists of perturbed forecasts from the last month. This larger ensemble is used to represent the system's time-dependent background error covariance. At each assimilation cycle, a central analysis is computed utilizing the ensemble-based covariance. Each of the perturbed ensemble members are nudged toward the central analysis to control the ensemble spread and mean. The ensemble-based covariances generated by PEODAS potentially yield dynamically balanced analysis increments. The time dependence of the ensemble-based covariance yields spatial structures that change for different dynamical regimes, for example during El Niñ o and La Niñ a conditions. These differences are explored in terms of the dominant dynamics and the system's errors. The performance of PEODAS during a 27-yr reanalysis is evaluated through a series of comparisons with assimilated and independent observations. When compared to its predecessor, POAMA version 1, and a simulation with no assimilation of subsurface observations, PEODAS demonstrates a quantitative improvement in skill. PEODAS will form the basis of Australia's next operational seasonal prediction system.

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“…The method has been widely used in ocean data assimilation (Fukumori, 2000;Menemenlis and Chechelnitsky, 2000;Leeuwenburgh, 2007). Given a vector w c = (T c , S c ) T of temperature and salinity fields computed from a model integration without data assimilation (the control run in this study), the Fu et al method estimates the observation-error variances from the covariance between co-located observation and observation-minus-control anomalies:…”

Section: Observation-error Variance Matrix: D (Y)mentioning

confidence: 99%

“…It is more difficult, however, to justify ignoring the third term (E[ x t ( c ) T ] ≈ 0), as already pointed out by Menemenlis and Chechelnitsky (2000) who provide evidence in their analysis of TOPEX/Poseidon altimeter data that suggests that this term is not negligible. This third assumption is made purely for practical convenience and should be treated with caution.…”

Section: Appendix Amentioning

confidence: 99%

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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Error Estimates for an Ocean General Circulation Model from Altimeter and Acoustic Tomography Data

Cited by 19 publications

References 33 publications

Covariance regularization in inverse space

Covariance regularization in inverse space

An Ensemble Ocean Data Assimilation System for Seasonal Prediction

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

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