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Variational Data Assimilation (variational + data_assimilation)

Distribution by Scientific Domains

Earth and Environmental Science	88%

Selected Abstracts

Data assimilation of high-density observations.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005
I: Impact on initial conditions for the MAP/SOP IOP2b
Abstract An attempt is made to evaluate the impact of the data assimilation of high-frequency data on the initial conditions. The data assimilation of all the data available on the Mesoscale Alpine Program archive for a test case is performed using the objective analysis and the Variational Data Assimilation (Var) techniques. The objective analysis is performed using two different schemes: Cressman and multiquadric; 3D-Var is used for the variational analysis. The European Centre for Medium-Range Weather Forecasts analyses are used as first guess, and they are blended together with the observations to generate an improved set of mesoscale initial and boundary conditions for the Intensive Observing Period 2b (17,21 September 1999). A few experiments are performed using the initialization procedure of MM5, the mesoscale model from Penn State University/National Center for Atmospheric Research. The comparison between improved initial conditions and observations shows: (i) the assimilation of the surface and upper-air data has a large positive impact on the initial conditions depending on the technique used for the objective analysis; (ii) a large decrease of the error for the meridional component of the wind V at the initial time is found, if assimilation of three-hourly data is performed by objective analysis; (iii) a comparable improvement of the initial conditions with respect to the objective analysis is found if 3D-Var is used, but a large error is obtained for the V component of the wind. Copyright © 2005 Royal Meteorological Society [source]

An observing-system experiment with ground-based GPS zenith total delay data using HIRLAM 3D-Var in the absence of satellite data

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 650 2010
Reima Eresmaa
Abstract Ground-based receiver networks of the Global Positioning System (GPS) provide observations of atmospheric water vapour with a high temporal and horizontal resolution. Variational data assimilation allows researchers to make use of zenith total delay (ZTD) observations, which comprise the atmospheric effects on microwave signal propagation. An observing-system experiment (OSE) is performed to demonstrate the impact of GPS ZTD observations on the output of the High Resolution Limited Area Model (HIRLAM). The GPS ZTD observations for the OSE are provided by the EUMETNET GPS Water Vapour Programme, and they are assimilated using three-dimensional variational data assimilation (3D-Var). The OSE covers a five-week period during the late summer of 2008. In parallel with GPS ZTD data assimilation in the regular mode, the impact of a static bias-correction algorithm for the GPS ZTD data is also assessed. Assimilation of GPS ZTD data, without bias correction of any kind, results in a systematic increase in the forecast water-vapour content, temperature and tropospheric relative topography. A slightly positive impact is shown in terms of decreased forecast-error standard deviation of lower and middle tropospheric humidity and lower tropospheric geopotential height. Moreover, verification of categorical forecasts of 12 h accumulated precipitation shows a positive impact. The application of the static bias-correction scheme is positively verified in the case of the mean forecast error of lower tropospheric humidity and when relatively high precipitation accumulations are considered. Copyright © 2010 Royal Meteorological Society [source]

A reduced-order simulated annealing approach for four-dimensional variational data assimilation in meteorology and oceanography

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
I. Hoteit
Abstract Four-dimensional variational data assimilation in meteorology and oceanography suffers from the presence of local minima in the cost function. These local minima arise when the system under study is strongly nonlinear. The number of local minima further dramatically increases with the length of the assimilation period and often renders the solution to the problem intractable. Global optimization methods are therefore needed to resolve this problem. However, the huge computational burden makes the application of these sophisticated techniques unfeasible for large variational data assimilation systems. In this study, a Simulated Annealing (SA) algorithm, complemented with an order-reduction of the control vector, is used to tackle this problem. SA is a very powerful tool of combinatorial minimization in the presence of several local minima at the cost of increasing the execution time. Order-reduction is then used to reduce the dimension of the search space in order to speed up the convergence rate of the SA algorithm. This is achieved through a proper orthogonal decomposition. The new approach was implemented with a realistic eddy-permitting configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) of the tropical Pacific Ocean. Numerical results indicate that the reduced-order SA approach was able to efficiently reduce the cost function with a reasonable number of function evaluations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

An observing-system experiment with ground-based GPS zenith total delay data using HIRLAM 3D-Var in the absence of satellite data

Assimilation of SEVIRI infrared radiances with HIRLAM 4D-Var

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 645 2009
M. Stengel
Abstract Four-dimensional variational data assimilation (4D-Var) systems are ideally suited to obtain the best possible initial model state by utilizing information about the dynamical evolution of the atmospheric state from observations, such as satellite measurements, distributed over a certain period of time. In recent years, 4D-Var systems have been developed for several global and limited-area models. At the same time, spatially and temporally highly resolved satellite observations, as for example performed by the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) on board the Meteosat Second Generation satellites, have become available. Here we demonstrate the benefit of a regional NWP model's analyses and forecasts gained by the assimilation of those radiances. The 4D-Var system of the HIgh Resolution Limited Area Model (HIRLAM) has been adjusted to utilize three of SEVIRI's infrared channels (located around 6.2 µm, 7.3 µm, and 13.4 µm, respectively) under clear-sky and low-level cloud conditions. Extended assimilation and forecast experiments show that the main direct impact of assimilated SEVIRI radiances on the atmospheric analysis were additional tropospheric humidity and wind increments. Forecast verification reveals a positive impact for almost all upper-air variables throughout the troposphere. Largest improvements are found for humidity and geopotential height in the middle troposphere. The observations in regions of low-level clouds provide especially beneficial information to the NWP system, which highlights the importance of satellite observations in cloudy areas for further improvements in the accuracy of weather forecasts. Copyright © 2009 Royal Meteorological Society [source]

A review of forecast error covariance statistics in atmospheric variational data assimilation.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 637 2008
I: Characteristics, measurements of forecast error covariances
Abstract This article reviews the characteristics of forecast error statistics in meteorological data assimilation from the substantial literature on this subject. It is shown how forecast error statistics appear in the data assimilation problem through the background error covariance matrix, B. The mathematical and physical properties of the covariances are surveyed in relation to a number of leading systems that are in use for operational weather forecasting. Different studies emphasize different aspects of B, and the known ways that B can impact the assimilation are brought together. Treating B practically in data assimilation is problematic. One such problem is in the numerical measurement of B, and five calibration methods are reviewed, including analysis of innovations, analysis of forecast differences and ensemble methods. Another problem is the prohibitive size of B. This needs special treatment in data assimilation, and is covered in a companion article (Part II). Examples are drawn from the literature that show the univariate and multivariate structure of the B -matrix, in terms of variances and correlations, which are interpreted in terms of the properties of the atmosphere. The need for an accurate quantification of forecast error statistics is emphasized. Copyright © 2008 Royal Meteorological Society [source]

A review of forecast error covariance statistics in atmospheric variational data assimilation.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 637 2008
II: Modelling the forecast error covariance statistics
Abstract This article reviews a range of leading methods to model the background error covariance matrix (the B -matrix) in modern variational data assimilation systems. Owing partly to its very large rank, the B -matrix is impossible to use in an explicit fashion in an operational setting and so methods have been sought to model its important properties in a practical way. Because the B -matrix is such an important component of a data assimilation system, a large effort has been made in recent years to improve its formulation. Operational variational assimilation systems use a form of control variable transform to model B. This transform relates variables that exist in the assimilation's ,control space' to variables in the forecast model's physical space. The mathematical basis on which the control variable transform allows the B-matrix to be modelled is reviewed from first principles, and examples of existing transforms are brought together from the literature. The method allows a large rank matrix to be represented by a relatively small number of parameters, and it is shown how information that is not provided explicitly is filled in. Methods use dynamical properties of the atmosphere (e.g. balance relationships) and make assumptions about the way that background errors are spatially correlated (e.g. homogeneity and isotropy in the horizontal). It is also common to assume that the B -matrix is static. The way that these, and other, assumptions are built into systems is shown. The article gives an example of how a current method performs. An important part of this article is a discussion of some new ideas that have been proposed to improve the method. Examples include how a more appropriate use of balance relations can be made, how errors in the moist variables can be treated and how assumptions of homogeneity/isotropy and the otherwise static property of the B -matrix can be relaxed. Key developments in the application of dynamics, wavelets, recursive filters and flow-dependent methods are reviewed. The article ends with a round up of the methods and a discussion of future challenges that the field will need to address. Copyright © 2008 Royal Meteorological Society [source]

Jacobian mapping between vertical coordinate systems in data assimilation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 627 2007
Y. J. Rochon
Abstract Radiances measured by remote-sensing instruments are now the largest component of the atmospheric observation network. The assimilation of radiances from nadir sounders involves fast radiative transfer (RT) models which project profiles provided by forecast models onto the observation space for direct comparison with the measurements. One of the features typically characterizing fast RT models is the use of a fixed vertical coordinate. If the vertical coordinate of the RT model is not identical to that used by the forecast model, an interpolation of forecast profiles to the RT model coordinate is necessary. In variational data assimilation, the mapping of the Jacobians (derivatives of the RT model output with respect to its inputs) from the RT model coordinate to the forecast model coordinate is also required. This mapping of Jacobians is accomplished through the adjoint of the forecast profile interpolator. As shown, the nearest-neighbour log-linear interpolator commonly used operationally can lead to incorrect mapping of Jacobians and, consequently, to incorrect assimilation. This incorrect mapping occurs as a result of leaving out intermediate levels in the interpolation. This problem has been previously masked in part through the smoothing effect of forecast-error vertical correlations on the analysis increments. To solve this problem, two simple versions of an interpolator relying on piecewise log-linear weighted averaging over the layers are investigated. Both markedly improve Jacobian mappings in the assimilation of observations, with one being slightly favoured over the other. This interpolator is being incorporated into the RTTOV model used by several operational weather forecasting centres. Copyright © 2007 Crown in the right of Canada. Published by John Wiley & Sons, Ltd. [source]

Accounting for an imperfect model in 4D-Var

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006
Yannick Tr'emolet
Abstract In most operational implementations of four-dimensional variational data assimilation (4D-Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D-Var. We present three approaches for the formulation of weak-constraint 4D-Var: estimating explicitly a model-error forcing term, estimating a representation of model bias or, estimating a four-dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D-Var are discussed. We show that 4D-Var with an additional model-error representation as part of the control variable is essentially an initial-value problem and that its characteristics are very similar to that of strong constraint 4D-Var. Taking the four-dimensional state as the control variable, however, leads to very different properties. In that case, weak-constraint 4D-Var can be interpreted as a coupling between successive strong-constraint assimilation cycles. A possible extension towards long-window 4D-Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society [source]

A data assimilation method for log-normally distributed observational errors

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006
S. J. Fletcher
Abstract In this paper we change the standard assumption made in the Bayesian framework of variational data assimilation to allow for observational errors that are log-normally distributed. We address the question of which statistic best describes the distribution for the univariate and multivariate cases to justify our choice of the mode. From this choice we derive the associated cost function, Jacobian and Hessian with a normal background. We also find the solution to the Jacobian equal to zero in both model and observational space. Given the Hessian that we derive, we define a preconditioner to aid in the minimization of the cost function. We extend this to define a general form for the preconditioner, given a certain type of cost function. Copyright © 2006 Royal Meteorological Society [source]

On the equivalence between Kalman smoothing and weak-constraint four-dimensional variational data assimilation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005
M. Fisher
Abstract The fixed-interval Kalman smoother produces optimal estimates of the state of a system over a time interval, given observations over the interval, together with a prior estimate of the state and its error covariance at the beginning of the interval. At the end of the interval, the Kalman smoother estimate is identical to that produced by a Kalman filter, given the same observations and the same initial state and covariance matrix. For an imperfect model, the model error term in the covariance evolution equation acts to reduce the dependence of the estimate on observations and prior states that are well separated in time. In particular, if the assimilation interval is sufficiently long, the estimate at the end of the interval is effectively independent of the state and covariance matrix specified at the beginning of the interval. In this case, the Kalman smoother provides estimates at the end of the interval that are identical to those of a Kalman filter that has been running indefinitely. For a linear model, weak-constraint four-dimensional variational data assimilation (4D-Var) is equivalent to a fixed-interval Kalman smoother. It follows that, if the assimilation interval is made sufficiently long, the 4D-Var analysis at the end of the assimilation interval will be identical to that produced by a Kalman filter that has been running indefinitely. The equivalence between weak-constraint 4D-Var and a long-running Kalman filter is demonstrated for a simple analogue of the numerical weather-prediction (NWP) problem. For this nonlinear system, 4D-Var analysis with a 10-day assimilation window produces analyses of the same quality as those of an extended Kalman filter. It is demonstrated that the current ECMWF operational 4D-Var system retains a memory of earlier observations and prior states over a period of between four and ten days, suggesting that weak-constraint 4D-Var with an analysis interval in the range of four to ten days may provide a viable algorithm with which to implement an unapproximated Kalman filter. Whereas assimilation intervals of this length are unlikely to be computationally feasible for operational NWP in the near future, the ability to run an unapproximated Kalman filter should prove invaluable for assessing the performance of cheaper, but suboptimal, alternatives. Copyright © 2005 Royal Meteorological Society [source]

Gravity wave drag estimation from global analyses using variational data assimilation principles.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005
I: Theory, implementation
Abstract A novel technique to estimate gravity wave drag from global-scale analyses is presented. It is based on the principles of four-dimensional variational data assimilation, using a dynamical model of the middle atmosphere and its adjoint. The global analyses are treated as observations. A cost function that measures the mismatch between the model state and observations is defined. The control variables are the components of the three-dimensional gravity wave drag field, so that minimization of the cost function gives the optimal gravity wave drag field. The minimization is performed using a conjugate gradient method, with the adjoint model used to calculate the gradient of the cost function. In this work, we present the theory behind the new technique and evaluate extensively the ability of the technique to estimate the gravity wave drag using so-called twin experiments, in which the ,observations' are given by the evolution of the dynamical model with a prescribed gravity wave drag. The results show that the technique can estimate accurately the prescribed gravity wave drag. When the cost function is suitably defined, there is good convergence of the minimization scheme under realistic atmospheric conditions. We also show that the cost function gradient is well approximated taking into account only adiabatic processes. We note some limitations of the technique for estimating gravity wave drag in tropical regions if satellite temperature measurements are the only observational information available. Copyright © 2005 Royal Meteorological Society. [source]

A convection scheme for data assimilation: Description and initial tests

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 606 2005
Philippe Lopez
Abstract A new simplified parametrization of subgrid-scale convective processes has been developed and tested in the framework of the ECMWF Integrated Forecasting System for the purpose of variational data assimilation, singular vector calculations and adjoint sensitivity experiments. Its formulation is based on the full nonlinear convection scheme used in ECMWF forecasts, but a set of simplifications has been applied to substantially improve its linear behaviour. These include the specification of a single closure assumption based on convective available potential energy, the uncoupling of the equations for the convective mass flux and updraught characteristics and a unified formulation of the entrainment and detrainment rates. Simplified representations of downdraughts and momentum transport are also included in the new scheme. Despite these simplifications, the forecasting ability of the new convective parametrization is shown to remain satisfactory even in seasonal integrations. A detailed study of its Jacobians and the validity of the linear hypothesis is presented. The new scheme is also tested in combination with the new simplified parametrization of large-scale clouds and precipitation recently developed at ECMWF. In contrast with the simplified convective parametrization currently used in ECMWF's operational 4D-Var, its tangent-linear and adjoint versions account for perturbations of all convective quantities including convective mass flux, updraught characteristics and precipitation fluxes. Therefore the new scheme is expected to be beneficial when combined with radiative calculations that are directly affected by condensation and precipitation. Examples are presented of applications of the new moist physics in 1D-Var retrievals using microwave brightness temperature measurements and in adjoint sensitivity experiments. Copyright © 2005 Royal Meteorological Society. [source]

A singular vector perspective of 4D-Var: Filtering and interpolation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005
Christine Johnson
Abstract Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society [source]

A hybrid multivariate Normal and lognormal distribution for data assimilation

ATMOSPHERIC SCIENCE LETTERS, Issue 2 2006
Steven J. Fletcher
Abstract In this article, we define and prove a distribution, which is a combination of a multivariate Normal and lognormal distribution. From this distribution, we apply a Bayesian probability framework to derive a non-linear cost function similar to the one that is in current variational data assimilation (DA) applications. Copyright © 2006 Royal Meteorological Society [source]