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## Data Assimilation (data + assimilation)
Kinds of Data Assimilation
Terms modified by Data Assimilation
## Selected Abstracts## Data assimilation of high-density observations. THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005I: Impact on initial conditions for the MAP/SOP IOP2bAbstract 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] ## Data assimilation and inverse problem for fluid traffic flow models and algorithms INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2008P. JaissonAbstract This article deals with traffic data assimilation and algorithms that are able to predict the traffic flow on a road section. The traffic flow is modellized by the Aw,Rascle hyperbolic system. We have to minimize a functional whose optimization variables are initial condition. We use the Roe method to compute the solution to the traffic flow modelling system. Then we compute the gradient of the functional by an adjoint method. This gradient will be used to optimize the functional. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Data assimilation with regularized nonlinear instabilities THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 648 2010Henry D. I. AbarbanelAbstract In variational formulations of data assimilation, the estimation of parameters or initial state values by a search for a minimum of a cost function can be hindered by the numerous local minima in the dependence of the cost function on those quantities. We argue that this is a result of instability on the synchronization manifold where the observations are required to match the model outputs in the situation where the data and the model are chaotic. The solution to this impediment to estimation is given as controls moving the positive conditional Lyapunov exponents on the synchronization manifold to negative values and adding to the cost function a penalty that drives those controls to zero as a result of the optimization process implementing the assimilation. This is seen as the solution to the proper size of ,nudging' terms: they are zero once the estimation has been completed, leaving only the physics of the problem to govern forecasts after the assimilation window. We show how this procedure, called Dynamical State and Parameter Estimation (DSPE), works in the case of the Lorenz96 model with nine dynamical variables. Using DSPE, we are able to accurately estimate the fixed parameter of this model and all of the state variables, observed and unobserved, over an assimilation time interval [0, T]. Using the state variables at T and the estimated fixed parameter, we are able to accurately forecast the state of the model for t > T to those times where the chaotic behaviour of the system interferes with forecast accuracy. Copyright © 2010 Royal Meteorological Society [source] ## Flash flood forecasting: What are the limits of predictability? THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 622 2007C. G. CollierAbstract Flash floods may occur suddenly and be accompanied by other hazards such as landslides, mud flows, damage to infrastructure and even death. In the UK such events are comparatively rare occurring on average only once or twice per year. Warning systems must depend upon the accurate real-time provision of rainfall information, high-resolution numerical weather forecasts and the operation of hydrological model systems in addition to forecast delivery procedures not discussed in this paper. In this paper we review how flash floods are forecast considering the limitations and uncertainty involved in both the meteorological and hydrological aspects of forecasting systems. Data assimilation and the use of ensembles are both key elements across disciplines. Assessing the susceptibility of river catchments to extreme flooding is considered, and statistical methods of estimating the likelihood of extreme rainfall and floods within a changing climate are examined. Ways of constraining flash flood forecasts are noted as one way to improve forecast performance in the future. Copyright © 2007 Royal Meteorological Society [source] ## Data assimilation of high-density observations. THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005I: Impact on initial conditions for the MAP/SOP IOP2bAbstract 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] ## Data assimilation of high-density observations. THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005II: Impact on the forecast of the precipitation for the MAP/SOP IOP2bAbstract The impact of the data assimilation of high-density (space and time) data on the precipitation forecast is evaluated by improving the initial conditions of a mesoscale model. The high-frequency data allow for improving the three-hourly initial and boundary conditions as well. The data assimilation is performed using initial objective analysis (Cressman and multiquadric schemes) and 3D-Var. The MM5 (version 3) mesoscale model from Penn State University/National Center for Atmospheric Research is used to evaluate the impact of the improved initial and boundary conditions on the model simulations. The comparison of model results with observations shows: (i) the forecast of the precipitation at high resolution produces better results than those without data assimilation only if three-hourly data are assimilated by multiquadric; (ii) the mean error of the model rainfall largely decreases only if 3D-Var is used, but no comparable improvement in the spatial distribution of the precipitation is found; (iii) the improvement for the rainfall is not as good as it is for the initial conditions for all experiments. Moreover, the observations ingested by objective analysis modify both the amount and the timing of the precipitation on the Po valley. On the other hand, 3D-Var modifies only the amount of the precipitation, but both techniques barely recover large-model failure. Copyright © 2005 Royal Meteorological Society [source] ## Data assimilation and inverse problem for fluid traffic flow models and algorithms INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2008P. JaissonAbstract This article deals with traffic data assimilation and algorithms that are able to predict the traffic flow on a road section. The traffic flow is modellized by the Aw,Rascle hyperbolic system. We have to minimize a functional whose optimization variables are initial condition. We use the Roe method to compute the solution to the traffic flow modelling system. Then we compute the gradient of the functional by an adjoint method. This gradient will be used to optimize the functional. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## The variational Kalman filter and an efficient implementation using limited memory BFGS INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010H. AuvinenAbstract In the field of state space estimation and data assimilation, the Kalman filter (KF) and the extended Kalman filter (EKF) are among the most reliable methods used. However, KF and EKF require the storage of, and operations with, matrices of size n×n, where n is the size of the state space. Furthermore, both methods include inversion operations for m×m matrices, where m is the size of the observation space. Thus, KF methods become impractical as the dimension of the system increases. In this paper, we introduce a variational Kalman filter (VKF) method to provide a low storage, and computationally efficient, approximation of the KF and EKF methods. Furthermore, we introduce a variational Kalman smoother (VKS) method to approximate the fixed-lag Kalman smoother (FLKS) method. Instead of using the KF formulae, we solve the underlying maximum a posteriori optimization problem using the limited memory Broyden,Fletcher,Goldfarb,Shanno (LBFGS) method. Moreover, the LBFGS optimization method is used to obtain a low storage approximation of state estimate covariances and prediction error covariances. A detailed description of the VKF and VKS methods with LBFGS is given. The methodology is tested on linear and nonlinear test examples. The simulated results of the VKF method are presented and compared with KF and EKF, respectively. The convergence of BFGS/LBFGS methods is tested and demonstrated numerically. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Comparison of sequential data assimilation methods for the Kuramoto,Sivashinsky equation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010M. JardakAbstract The Kuramoto,Sivashinsky equation plays an important role as a low-dimensional prototype for complicated fluid dynamics systems having been studied due to its chaotic pattern forming behavior. Up to now, efforts to carry out data assimilation with this 1-D model were restricted to variational adjoint methods domain and only Chorin and Krause (Proc. Natl. Acad. Sci. 2004; 101(42):15013,15017) tested it using a sequential Bayesian filter approach. In this work we compare three sequential data assimilation methods namely the Kalman filter approach, the sequential Monte Carlo particle filter approach and the maximum likelihood ensemble filter methods. This comparison is to the best of our knowledge novel. We compare in detail their relative performance for both linear and nonlinear observation operators. The results of these sequential data assimilation tests are discussed and conclusions are drawn as to the suitability of these data assimilation methods in the presence of linear and nonlinear observation operators. Copyright © 2009 John Wiley & Sons, Ltd. [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 2008I. HoteitAbstract 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] ## Assessing the spatial and temporal variation in the skill of precipitation forecasts from an NWP model METEOROLOGICAL APPLICATIONS, Issue 1 2008Nigel RobertsAbstract It is becoming increasingly important to be able to verify the spatial accuracy of precipitation forecasts, especially with the advent of high-resolution numerical weather prediction (NWP) models. In this article, the fractions skill score (FSS) approach has been used to perform a scale-selective evaluation of precipitation forecasts during 2003 from the Met Office mesoscale model (12 km grid length). The investigation shows how skill varies with spatial scale, the scales over which the data assimilation (DA) adds most skill, and how the loss of that skill is dependent on both the spatial scale and the rainfall coverage being examined. Although these results come from a specific model, they demonstrate how this verification approach can provide a quantitative assessment of the spatial behaviour of new finer-resolution models and DA techniques. Copyright © 2008 Royal Meteorological Society [source] ## Unbiased ensemble square root filters PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007S. L. DanceEnsemble square root filters are a method of data assimilation, where model forecasts are combined with observations to produce an improved state estimate, or analysis. There are a number of different algorithms in the literature and it is not clear which of these is the best for any given application. This work shows that in some implementations there can be a systematic bias in the analysis ensemble mean and consequently an accompanying shortfall in the spread of the analysis ensemble as expressed by the ensemble covariance matrix. We have established a set of necessary and sufficient conditions for the scheme to be unbiased. While these conditions are not a cure-all and cannot deal with independent sources of bias such as model and observation errors, they should be useful to designers of ensemble square root filters in the future. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [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 2010Reima EresmaaAbstract 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] ## Data assimilation with regularized nonlinear instabilities THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 648 2010Henry D. I. AbarbanelAbstract In variational formulations of data assimilation, the estimation of parameters or initial state values by a search for a minimum of a cost function can be hindered by the numerous local minima in the dependence of the cost function on those quantities. We argue that this is a result of instability on the synchronization manifold where the observations are required to match the model outputs in the situation where the data and the model are chaotic. The solution to this impediment to estimation is given as controls moving the positive conditional Lyapunov exponents on the synchronization manifold to negative values and adding to the cost function a penalty that drives those controls to zero as a result of the optimization process implementing the assimilation. This is seen as the solution to the proper size of ,nudging' terms: they are zero once the estimation has been completed, leaving only the physics of the problem to govern forecasts after the assimilation window. We show how this procedure, called Dynamical State and Parameter Estimation (DSPE), works in the case of the Lorenz96 model with nine dynamical variables. Using DSPE, we are able to accurately estimate the fixed parameter of this model and all of the state variables, observed and unobserved, over an assimilation time interval [0, T]. Using the state variables at T and the estimated fixed parameter, we are able to accurately forecast the state of the model for t > T to those times where the chaotic behaviour of the system interferes with forecast accuracy. Copyright © 2010 Royal Meteorological Society [source] ## Ensemble data assimilation with the CNMCA regional forecasting system THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 646 2010Massimo BonavitaAbstract The Ensemble Kalman Filter (EnKF) is likely to become a viable alternative to variational methods for the next generation of meteorological and oceanographic data assimilation systems. In this work we present results from real-data assimilation experiments using the CNMCA regional numerical weather prediction (NWP) forecasting system and compare them to the currently operational variational-based analysis. The set of observations used is the same as the one ingested in the operational data stream, with the exception of satellite radiances and scatterometer winds. Results show that the EnKF-based assimilation cycle is capable of producing analyses and forecasts of consistently superior skill in the root mean square error metric than CNMCA operational 3D-Var. One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. To combat this problem a number of different parametrizations of the model error unaccounted for in the assimilation cycle have been proposed. In the CNMCA system a combination of adaptive multiplicative and additive background covariance inflations has been found to give adequate results and to be capable of avoiding filter divergence in extended assimilation trials. The additive component of the covariance inflation has been implemented through the use of scaled forecast differences. Following suggestions that ensemble square-root filters can violate the gaussianity assumption when used with nonlinear prognostic models, the statistical distribution of the forecast and analysis ensembles has been studied. No sign of the ensemble collapsing onto one or a few model states has been found, and the forecast and analysis ensembles appear to stay remarkably close to the assumed probability distribution functions. Copyright © 2010 Royal Meteorological Society [source] ## Assimilation of SEVIRI infrared radiances with HIRLAM 4D-Var THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 645 2009M. StengelAbstract 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] ## Simultaneous state estimation and attenuation correction for thunderstorms with radar data using an ensemble Kalman filter: tests with simulated data THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 643 2009Ming XueAbstract A new approach to dealing with attenuated radar reflectivity data in the data assimilation process is proposed and tested with simulated data using the ensemble square-root Kalman filter. This approach differs from the traditional method where attenuation is corrected in observation space first before observations are assimilated into numerical models. We build attenuation correction into the data assimilation system by calculating the expected attenuation within the forward observation operators using the estimated atmospheric state. Such a procedure does not require prior assumption about the types of hydrometeor species along the radar beams, and allows us to take advantage of knowledge about the hydrometeors obtained through data assimilation and state estimation. Being based on optimal estimation theory, error and uncertainty information on the observations and prior estimate can be effectively utilized, and additional observed parameters, such as those from polarimetric radar, can potentially be incorporated into the system. Tests with simulated reflectivity data of an X-band 3 cm wavelength radar for a supercell storm show that the attenuation correction procedure is very effective,the analyses obtained using attenuated data are almost as good as those obtained using unattenuated data. The procedure is also robust in the presence of moderate dropsize-distribution-related observation operator error and when systematic radar calibration error exists. The analysis errors are very large if no attenuation correction is applied. The effect of attenuation and its correction when radial velocity data are also assimilated is discussed as well. In general, attenuation correction is equally important when quality radial velocity data are also assimilated. 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 2008I: Characteristics, measurements of forecast error covariancesAbstract 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 2008II: Modelling the forecast error covariance statisticsAbstract 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] ## 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] ## Jacobian mapping between vertical coordinate systems in data assimilation THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 627 2007Y. J. RochonAbstract 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] ## Three-dimensional variational assimilation of Special Sensor Microwave/Imager data into a mesoscale weather-prediction model: A case study THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 626 2007C. FaccaniAbstract Assimilation of data from the Special Sensor Microwave/Imager (SSM/I) is performed in order to improve the forecast of a heavy-precipitation case (IOP2b, 20,21 September 1999) of the Mesoscale Alpine Programme 1999. The three-dimensional variational data assimilation technique of the MM5 model is used. Either brightness temperatures or precipitable water and surface wind speed are assimilated. The sensitivity of the model to SSM/I data is also tested by selectively excluding SSM/I frequencies and changing the size of the thinning box. All the experiments are performed using the European Center for Medium range Weather Forecasting (ECMWF) analysis on pressure level. The new initial conditions show considerable underestimation of the surface wind component V, and, even more, of the surface water vapour mixing ratio. This last error is partially corrected by assimilation of precipitable water alone, although these data produce a large increase in the mean error of the other surface variables (U, V and T). However, the forecast with this new set of initial conditions shows a good agreement (high correlation coefficient) with the rain gauge observations for the 1 h accumulated precipitation 3 h after the initial time. With a doubled box size, there is low sensitivity to the density of the observations used. In this case, the effect of the SSM/I data is slight, and the rainfall pattern produced is comparable to that obtained without any data assimilation. The model performance is also degraded if the 22 GHz brightness temperatures are removed from the assimilated measurements: the correlation coefficient for the precipitation is lower than in the case where all the frequencies are assimilated, and it decreases over time. In general, the use of precipitable water and surface wind speed affects the early stages (3 h) of the rainfall forecast, reducing the model spin-up. Brightness temperatures affect the forecast at a longer range (10 h). Copyright © 2007 Royal Meteorological Society [source] ## High-resolution reconstruction of a tracer dispersion event: application to ETEX THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 625 2007Marc BocquetAbstract In a previous two-part paper, new methods for reconstructing the source of an atmospheric tracer at regional scale were developed. Specifically, the ,maximum entropy on the mean' (MEM) method was extended to large (though linear) data assimilation problems. Tests using twin experiments and a limited subset of the data from the European Tracer Experiment (ETEX) were performed. Although temporal reconstruction knowing the location of the source was satisfying, a full three-dimensional reconstruction with real data was still out of reach. In this paper, using the MEM method and some of its refinements, a reconstruction using all ETEX-I measurements at a resolution of 1.125 × 1.125 × 1 h is shown to be possible. This allows for a reconstruction of the full dispersion event. The MEM retrieval of the tracer plume using what is believed to be a good prior is then compared to retrievals using other priors, including Gaussian priors. Eventually, a reconstruction using all data sequentially in time (rather than all together) is obtained. This helps define what a maximum-entropy filter applied to sequential data assimilation of a linear tracer should be able to do, with a view to an efficient emergency response in case of an accidental release of pollutant. Copyright © 2007 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] ## Accounting for an imperfect model in 4D-Var THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006Yannick Tr'emoletAbstract 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 2006S. J. FletcherAbstract 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] ## Diagnosis and tuning of observational error in a quasi-operational data assimilation setting THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 615 2006Bernard ChapnikAbstract Desroziers and Ivanov proposed a method to tune error variances used for data assimilation. The implementation of this algorithm implies the computation of the trace of certain matrices which are not explicitly known. A method proposed by Girard, allowing an approximate estimation of the traces without explicit knowledge of the matrices, was then used. This paper proposes a new implementation of the Desroziers and Ivanov algorithm, including a new computation scheme for the required traces. This method is compared to Girard's in two aspects: its use in the implementation of the tuning algorithm, and the computation of a quantification of the observation impacts on the analysis known as Degrees of Freedom for Signal. Those results are illustrated by studies utilizing the French data assimilation/numerical weather-prediction system ARPEGE. The impact of a first quasi-operational tuning of variances on forecasts is shown and discussed. 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 2005M. FisherAbstract 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] ## Adaptive thinning of atmospheric observations in data assimilation with vector quantization and filtering methods THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005T. OchottaAbstract In data assimilation for numerical weather prediction, measurements of various observation systems are combined with background data to define initial states for the forecasts. Current and future observation systems, in particular satellite instruments, produce large numbers of measurements with high spatial and temporal density. Such datasets significantly increase the computational costs of the assimilation and, moreover, can violate the assumption of spatially independent observation errors. To ameliorate these problems, we propose two greedy thinning algorithms, which reduce the number of assimilated observations while retaining the essential information content of the data. In the first method, the number of points in the output set is increased iteratively. We use a clustering method with a distance metric that combines spatial distance with difference in observation values. In a second scheme, we iteratively estimate the redundancy of the current observation set and remove the most redundant data points. We evaluate the proposed methods with respect to a geometric error measure and compare them with a uniform sampling scheme. We obtain good representations of the original data with thinnings retaining only a small portion of observations. We also evaluate our thinnings of ATOVS satellite data using the assimilation system of the Deutscher Wetterdienst. Impact of the thinning on the analysed fields and on the subsequent forecasts is discussed. Copyright © 2005 Royal Meteorological Society [source] ## Convective-scale assimilation of radar data: progress and challenges THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005Juanzhen SunAbstract Active research has been carried out in recent years to assimilate high-resolution observations into numerical models to improve precipitation forecasting. Considerable progress has been made although great scientific and technological challenges still exist. This paper reviews techniques used in convective-scale data assimilation research. Experiences in the assimilation of radar observations into high-resolution numerical models are presented. A number of future challenges in convective-scale data assimilation are discussed. Copyright © 2005 Royal Meteorological Society [source] |