A weak‐constraint four‐dimensional variational analysis system in the stratosphere

Lindskog, Magnus; Dee, Dick; Trémolet, Yannick; Andersson, Erik; Radnóti, Gábor; Fisher, Mike

doi:10.1002/qj.392

Cited by 13 publications

(8 citation statements)

References 15 publications

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“…The result that 12 h variances are a few percent more balanced than 3 h variances and that the large-scale balanced variance gained during 9 h forecast is mainly in the balanced and Kelvin modes may be at least partially related to the largescale noise in the input forecast differences. This explanation is supported by the results of Lindskog et al (2009), who found that analysis increments in the stratosphere are noisy. Fisher et al (2009) discuss two possible reasons for the noisy ensemble differences.…”

Section: Discussionsupporting

confidence: 55%

Balance properties of the short‐range forecast errors in the ECMWF 4D‐Var ensemble

Žagar

Isaksen

Tan

et al. 2012

Quart J Royal Meteoro Soc

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In this paper the normal-mode function framework is applied to the representation of time-averaged structure of short-term forecast error variances in the 20-member ensemble based on the 4D-Var assimilation system of ECMWF. The applied methodology provides an attractive way to measure the balance by splitting forecast error variances into parts projecting on the balanced and inertio-gravity (IG) circulations; the approach is particularly suitable for the Tropics, where IG circulation dominates on all scales.A little over 50% of the global forecast error variance at short range is balanced. The component of the variance associated with eastward IG modes dominates over the westward IG modes on all zonal scales but the difference gets larger as the zonal wave number increases. There is a major difference in the vertical variance distribution between the balanced and IG modes. A large part of the balanced variance projects on to the barotropic structure in the troposphere, while the IG variances are found in vertical modes that have equatorially trapped horizontal structures corresponding to equivalent depths between a few tens and few hundred metres. The variance growth between 3 h and 12 h range is substantially different in the balanced, eastward and westward IG modes. The balanced variance growth dominates whereas the variance growth in the westerly IG modes is small. In the eastward IG modes, the variance growth is most significant in the large-scale equatorial Kelvin mode.

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Section: Discussionsupporting

confidence: 55%

Balance properties of the short‐range forecast errors in the ECMWF 4D‐Var ensemble

Žagar

Isaksen

Tan

et al. 2012

Quart J Royal Meteoro Soc

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“…The alternating positive/negative anomalies in the temperature vertical structure in high latitudes, visible particularly in the stratosphere, are similar to deficiencies in analyses and increments reported previously concerning other datasets (Uppala et al, 2005;Tremolet, 2007;Lindskog et al, 2009). By contrast, these authors used time-invariant, regressionbased constraints, which indicates that the issue is generic and not related to flow dependence.…”

Section: Validation Of Solution Proceduresmentioning

confidence: 49%

Variational data‐assimilation experiments using flow‐dependent dynamical constraints

Reszka

Polavarapu

2012

Quart J Royal Meteoro Soc

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Mass-wind and vorticity-divergence balance constraints based on the linearized Charney and quasi-geostrophic omega equations, respectively, are assessed in a developmental version of the global, three-dimensional variational dataassimilation system at Environment Canada. Unlike traditional balance constraints, which are averaged in time, the new constraints are flow-dependent and reflect a more complete set of dynamics. Single observation experiments demonstrate that the new covariance model leads to asymmetrical increments that are qualitatively aligned with the instantaneous background wind field. Data-assimilation experiments using real observations are performed for a period of five weeks during two different seasons, employing the control and experimental constraints. Subsequent forecast verification against radiosondes shows a definite benefit of the new covariances in the Tropics; however, the impact in the Extratropics is neutral or slightly negative. Verifications against analysis show virtually no change in the troposphere; however, a significant improvement is observed in the stratosphere at all lead times. Compared with the Charney mass-wind balance, the contribution of the quasigeostrophic omega constraint is rather minimal, at least in its current adiabatic form. The new balance scheme requires a considerable amount of computational time in the context of our 3D-Var system, although the relative cost in a 4D-Var setting may be far less significant. Moreover, the present experiments are useful in elucidating several important aspects of covariance modelling, particularly the dependence of balance dynamics on spatial scale.

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“…The work of [80] illustrated the implementation of weak-constraint 4D-Var using such a matrix, again in the ECMWF system, to estimate a constant bias error in the stratosphere, where the model is known to have biases. A similar scheme has been introduced into the operational assimilation system of ECMWF [40].…”

Section: Weak Constraint Variational Assimilationmentioning

confidence: 99%

Variational data assimilation for very large environmental problems

Lawless¹

2013

Large Scale Inverse Problems

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Variational data assimilation is commonly used in environmental forecasting to estimate the current state of the system from a model forecast and observational data. The assimilation problem can be written simply in the form of a nonlinear least squares optimization problem. However the practical solution of the problem in large systems requires many careful choices to be made in the implementation. In this article we present the theory of variational data assimilation and then discuss in detail how it is implemented in practice. Current solutions and open questions are discussed.

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A weak‐constraint four‐dimensional variational analysis system in the stratosphere

Cited by 13 publications

References 15 publications

Balance properties of the short‐range forecast errors in the ECMWF 4D‐Var ensemble

Balance properties of the short‐range forecast errors in the ECMWF 4D‐Var ensemble

Variational data‐assimilation experiments using flow‐dependent dynamical constraints

Variational data assimilation for very large environmental problems

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