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## Data Assimilation Scheme (data + assimilation_scheme)
## Selected Abstracts## Model error and sequential data assimilation: A deterministic formulation THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008A. CarrassiAbstract Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first-order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short-time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white-noise assumption. The universal short-time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society [source] ## Three-dimensional spatial interpolation of surface meteorological observations from high-resolution local networks METEOROLOGICAL APPLICATIONS, Issue 3 2008Francesco UboldiAbstract An objective analysis technique is applied to a local, high-resolution meteorological observation network in the presence of complex topography. The choice of optimal interpolation (OI) makes it possible to implement a standard spatial interpolation algorithm efficiently. At the same time OI constitutes a basis to develop, in perspective, a full multivariate data assimilation scheme. In the absence of a background model field, a simple and effective de-trending procedure is implemented. Three-dimensional correlation functions are used to account for the orographic distribution of observing stations. Minimum-scale correlation parameters are estimated by means of the integral data influence (IDI) field. Hourly analysis fields of temperature and relative humidity are routinely produced at the Regional Weather Service of Lombardia. The analysis maps show significant informational content even in the presence of strong gradients and infrequent meteorological situations. Quantitative evaluation of the analysis fields is performed by systematically computing their cross validation (CV) scores and by estimating the analysis bias. Further developments concern the implementation of an automatic quality control procedure and the improvement of error covariance estimation. Copyright © 2008 Royal Meteorological Society [source] ## Can 4D-Var use dynamical information from targeted observations of a baroclinic structure? THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 651 2010E. A. IrvineAbstract Targeted observations are generally taken in regions of high baroclinicity, but often show little impact. One plausible explanation is that important dynamical information, such as upshear tilt, is not extracted from the targeted observations by the data assimilation scheme and used to correct initial condition error. This is investigated by generating pseudo targeted observations which contain a singular vector (SV) structure that is not present in the background field or routine observations, i.e. assuming that the background has an initial condition error with tilted growing structure. Experiments were performed for a single case-study with varying numbers of pseudo targeted observations. These were assimilated by the Met Office four-dimensional variational (4D-Var) data assimilation scheme, which uses a 6 h window for observations and background-error covariances calculated using the National Meteorological Centre (NMC) method. The forecasts were run using the operational Met Office Unified Model on a 24 km grid. The results presented clearly demonstrate that a 6 h window 4D-Var system is capable of extracting baroclinic information from a limited set of observations and using it to correct initial condition error. To capture the SV structure well (projection of 0.72 in total energy), 50 sondes over an area of 1×106 km2 were required. When the SV was represented by only eight sondes along an example targeting flight track covering a smaller area, the projection onto the SV structure was lower; the resulting forecast perturbations showed an SV structure with increased tilt and reduced initial energy. The total energy contained in the perturbations decreased as the SV structure was less well described by the set of observations (i.e. as fewer pseudo observations were assimilated). The assimilated perturbation had lower energy than the SV unless the pseudo observations were assimilated with the dropsonde observation errors halved from operational values. Copyright © 2010 Royal Meteorological Society [source] ## The characteristics of Hessian singular vectors using an advanced data assimilation scheme THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 642 2009A. R. LawrenceAbstract Initial condition uncertainty is a significant source of forecast error in numerical weather prediction. Singular vectors of the tangent linear propagator can identify directions in phase-space where initial errors are likely to make the largest contribution to forecast-error variance. The physical characteristics of these singular vectors depend on the choice of initial-time metric used to represent analysis-error covariances: the total-energy norm serves as a proxy to the analysis-error covariance matrix, whereas the Hessian of the cost function of a 4D-Var assimilation scheme represents a more sophisticated estimate of the analysis-error covariances, consistent with observation and background-error covariances used in the 4D-Var scheme. This study examines and compares the structure of singular vectors computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System using these two types of initial metrics. Unlike earlier studies that use background errors derived from lagged forecast differences (the NMC method), the background-error covariance matrix in the Hessian metric is based on statistics from an ensemble of 4D-Vars using perturbed observations, which produces tighter correlations of background-error statistics than in previous formulations. In light of these new background-error statistics, this article re-examines the properties of Hessian singular vectors (and their relationship to total-energy singular vectors) using cases from different periods between 2003 and 2005. Energy profiles and wavenumber spectra reveal that the total-energy singular vectors are similar to Hessian singular vectors that use all observation types in the operational 4D-Var assimilation. This is in contrast to the structure of Hessian singular vectors without observations. Increasing the observation density tends to reduce the spatial scale of the Hessian singular vectors. Copyright © 2009 Royal Meteorological Society [source] ## Use of potential vorticity for incremental data assimilation THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621C 2006M. WlasakAbstract Decomposing the mass and wind fields in a data assimilation scheme into balanced and unbalanced flow is part of the process of defining a covariance model. It is not uncommon to assume that the dynamic balanced part of the flow is approximated solely by the rotational part of the wind, which is obtained from a Helmholtz decomposition of the horizontal momentum (with an associated balanced pressure being diagnostically inferred from a balance equation, for example). The unbalanced flow is then represented by the divergence and the residual unbalanced pressure. The assumption that the rotational part of the momentum is a good approximation to the total balanced flow is only valid in certain regimes. We propose a new approach that incorporates flow regime dependence, where we assume that the balanced part of the flow is approximated instead by a linearized potential vorticity increment. We show the benefit of such a formulation in the context of shallow-water equations defined on a hemisphere. Copyright © 2006 Royal Meteorological Society [source] |