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The Infrared Atmospheric Sounding Interferometer (IASI) provides 8461 channels in the infrared spectrum. In current numerical weather prediction (NWP) models, it is not feasible to assimilate all channels and it is known that the information content between adjacent channels is redundant. This issue has been addressed in NWP centres by employing a channel selection strategy. The goal of this article is to add new channels to the existing IASI operational channel selection, aimed at improving the data assimilation in cloudy conditions and the simultaneous retrieval of cloud microphysical variables, specifically liquid and ice water contents. Cloudy profiles from the French convective-scale model Applications of Research to Operations at MEsoscale (AROME) are used in the study to focus on the retrieval of cloud variables over the Mediterranean region. Three channel selection methodologies were evaluated in this study: a statistical approach based on the degrees of freedom of the signal (DFS), a physical method based on the channel spectral sensitivity to the cloud variables and a random selection. To validate the new selections, an idealized framework is used with observing system simulation experiments (OSSE) in the context of one-dimensional variational retrievals. The current operational IASI selection has already been shown to provide good retrievals of cloud variables. However, all the different channel selections improve the results with small differences in the 1D-Var retrievals. Based on the physical and DFS methods, the final sets of 134 channels sensitive to cloud variables are proposed for future investigation in operational implementation. Additional tests on temperature and water-vapour retrieval results, air-mass dependence and cloud microphysical parametrization have also been conducted.

This article focuses on the simulation and the assimilation of satellite infrared observations in convective-scale numerical weather prediction (NWP) systems. A radiative transfer model that includes profiles for liquid-water content, ice-water content and cloud fraction was used to simulate cloud-affected radiances as background equivalents. This approach avoids the use of cloud parameters (cloud-top pressure and effective cloud fraction) deduced from a CO2 slicing algorithm and the modelling of clouds by single-layer clouds. The advanced radiative transfer model was evaluated using infrared observations measured by the Infrared Atmospheric Sounding Interferometer (IASI). The observation-screening procedure that was developed to improve the selection of usable cloudy scenes led to a good agreement between observations and background equivalents. For that purpose, a radiance analysis of collocated Advanced Very High Resolution Radiometer (AVHRR) pixels inside each IASI field of view was used. The goal of this preliminary work is to assess the feasibility of adding the cloud variables (liquid and ice-water contents) to the state vector of the assimilation system. The approach is illustrated with one-dimensional variational (1D-Var) retrievals. The physical consistency of the 1D-Var adjustments is verified with real observations. Then observing-system simulation experiments (OSSE) are used to validate the 1D-Var retrievals.

This article compares different methods of deriving cloud properties in the footprint of the Infrared Atmospheric Sounding Interferometer (IASI), onboard the European MetOp satellite. Cloud properties produced by ten operational schemes are assessed and an intercomparison of the products for a 12 h global acquisition is presented. Clouds cover a large part of the Earth, contaminating most of the radiance data. The estimation of cloud top height and effective amount within the sounder footprint is an important step towards the direct assimilation of cloud-affected radiances. This study first examines the capability of all the schemes to detect and characterize the clouds for all complex situations and provides some indications of confidence in the data. Then the dataset is restricted to thick overcast single layers and the comparison shows a significant agreement between all the schemes. The impact of the retrieved cloud properties on the residuals between calculated cloudy radiances and observations is estimated in the long-wave part of the spectrum. Copyright © 2011 Royal Meteorological Society, Crown in the right of Canada, and British Crown copyright, the Met Office

Since July 2008, Infrared Atmospheric Sounder Interferometer (IASI) radiances have been assimilated in the French global model Action de Recherche Petite Echelle Grande Echelle (ARPEGE) and since April 2010 at high density in the French convective-scale model Applications of Research to Operations at MEsoscale (AROME). The impact of the assimilation of clear IASI data on forecast skill is found to be positive for both models. As many observed scenes are cloudy, several ways to characterize the clouds within the observed spectra are investigated. Firstly, a simple approach that enables the determination of both the cloud-top pressure and the effective cloud amount of an equivalent single-layer cloud is followed using a CO2-slicing method. The first assimilation trials in overcast conditions lead to a small positive impact on forecast skill. Another approach would be to take advantage of the fact that cloud water variables are described at high resolution in the convective-scale model AROME. Model cloud fields have to be used in conjunction with a cloudy radiative transfer model. The first simulations using this technique are performed and compared against observations. Copyright © 2011 Royal Meteorological Society

International audience; Real-time surface and upper-air observations are crucial to the analysis and forecasting of the West African monsoon (WAM). This paper will focus on the African Monsoon--Multidisciplinary Analyses (AMMA)-driven reactivation and modernisation of the radiosonde network over West Africa, its potential long-term impact on upper-air operations in the region, the influence of the additional data in WAM analyses and forecasting, and the AMMA-related development and usage of the West African Analysis/Forecasting (WASA/F) forecast method.

In the context of its responsibilities as a Regional Specialised Meteorological Centre (RSMC) for the Southwest Indian Ocean, Meteo-France operates a tropical cyclone warning centre which sends advisories to all the concerned countries in the area. In assistance to the forecasters and as part of the operational suite for the short-range forecasts, a limited-area model (ALADIN Reunion) is run with four daily analyses. Assimilated observations include conventional observations – radiosondes, buoys, surface stations, aircraft reports, upper-wind reports – and satellite observations. The latter include QuikSCAT surface winds, atmospheric motion vectors from geostationary satellites, and radiances from polar-orbiting satellites. Assimilation of satellite radiance data is done in clear-sky conditions, and thus cannot be used in the vicinity of tropical cyclones. Two new sources of pseudo-observations are investigated that can bring new information content to those regions: Total Column Water Vapour (TCWV) pseudo-observations deduced from cloudy/rainy SSM/I data, as well as a 3D wind bogus. The TCWV algorithm is obtained from SSM/I brightness temperatures through a simple statistical regression from the 1D-Var analyses of the European Centre for Medium-Range Weather Forecasts, which are derived from complex inversion methods using moist physics and radiative transfer models. The 3D wind bogus is derived from structural information contained in the tropical cyclone advisories issued by the RSMC and contains a low-level vortex composed of two concentric rings of eight winds each, at each of the surface, 850, 700 and 500 hPa levels. Forecast scores and fit of the model to the observations are improved and indicate a positive impact of those new datasets. Structural validation is investigated through the comparison of model and TMI ‘observed’ rain rates: it is found that assimilating and cycling cloudy/rainy TCWV helps achieve more realistic cyclonic features. Copyright © 2008 Royal Meteorological Society

For its short-range forecasts over Western Europe, Meteo-France runs the limited-area model ALADIN operationally with four daily analyses obtained with a 3D-Var data assimilation system. This system includes, among other observation types, radiances from AMSU-A, AMSU-B, HIRS and SEVIRI radiometers. SEVIRI is on board the geostationary platform Meteosat-8 and provides continuous observations in space and in time over the region of interest at several wavelengths, while the others, which are on board polar-orbiting satellites, have poorer temporal and horizontal resolutions but a better spectral resolution than SEVIRI. Observing System Experiments (OSEs) have been performed with the operational 3D-Var to assess the impact of such satellite data on analyses and on forecasts. DFS (Degrees of Freedom for Signal) have been computed and have shown the complementarity between WV channels from the different radiometers. In the operational version of the 3D-Var, DFS values show that analyses are strongly controlled by SEVIRI data in the mid to high troposphere. This is consistent with the large number of assimilated SEVIRI radiances. HIRS and AMSU-B WV data would provide more information if SEVIRI data were not assimilated and if ATOVS data were used with a higher density. However, using ATOVS data with a higher horizontal resolution makes the analyses more dependent on these data, and it does not appear to be beneficial in this particular context, probably because of a non-optimal bias correction. In that case however, the individual impact of each pixel decreases because of the horizontal correlation lengths of the structure functions. Forecast scores and predicted precipitation patterns display the positive impact of SEVIRI data.

SUMMARY AMSU-A and -B measurements are stillnot extensively used over land surfaces for atmospheric applications. Recent studies have shown that it should now be possible to take advantage of the information content of these instruments provided land emissivity and skin temperature estimates are improved. This paper reports on comparisons between three land-surface schemes using the Meteo-France four-dimensional variational (4D-Var) assimilation system. Firstly, a monthly mean estimated land emissivity atlas using AMSU data is used. A second land-surface scheme based on direct emissivity calculations is developed to obtain dynamically emissivity values. The third approach is based on the first one with the addition of a dynamic skin temperature estimation based on one AMSU-A or AMSU-B window channel. The land-surface schemes described above have been implemented within the 4D-Var system and their results have been compared with those of the operational surface scheme (which uses emissivity models). All land schemes have been evaluated by examining the performances of the observation operator for sounding channels prior to the assimilation. With dynamically varying emissivities and/or skin temperatures or with averaged emissivities, the simulations are clearly improved compared with the operational model and many more data pass the quality-control check.

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

An experiment took place during autumn 2003 with the aim of testing the feasibility of an operational targeting of observations over the North Atlantic Ocean in the context of the international programme THORPEX. The purpose of this paper is to evaluate the impact of these additional observations in the French operational model ARPEGE during the last three weeks of the campaign. Results are shown for large regions over and around the North Atlantic Ocean and for specific verification areas. Over Europe, the addition of observations is slightly beneficial for the forecast, mostly in the low troposphere over wide areas and above 100 hPa. However, the impact of extra data is more significant but also more mixed for the dedicated verification areas: they are case, forecast-range and level dependent. In addition, the information content is studied with the Degrees of Freedom for Signal (DFS) for the evaluation of the observation impact on the analysis of one case of December 2003. Firstly, the variations of the DFS have been illustrated in a simplified data assimilation system. It has been found for that case that satellite data have the most important global contribution to the overall analysis, especially the humidity sensitive infrared radiances. For the conventional data, the wind measurements of the aircraft and from the geostationary satellites are the most informative. For the targeted area, the data from aircraft and the dropsondes have the largest DFS. It has been noted that the DFS of the dropsondes located in the sensitivity maximum is larger than the other one even if there is no link between the DFS and the forecast. However, the impact of the dropsondes grows with respect to the forecast range and leads to an improvement of the forecast for this case. Copyright © 2006 Royal Meteorological Society

Recent data assimilation developments which have taken place at numerical weather-prediction centres are briefly discussed, from the perspectives of both the importance of data and algorithmic developments. The increase in quality and quantity of satellite data is seen to play a major role in the improvement of forecast performance, particularly in the southern hemisphere. Further optimization of the use of observations is possible through the proper evaluation of data impact and the optimization of the amount of data to be assimilated. The generalized advent of four-dimensional variational assimilation is presented, and trends in the specification of error statistics are described. Finally, a more interactive forecasting system including an adaptive component is a new challenge to bring additional improvement to the forecasting of high-impact weather. Copyright © 2005 Royal Meteorological Society

The assimilation of the Atmospheric InfraRed Sounder (AIRS) data is expected to improve the quality of NWP products. Currently, operational use of such data is limited to the cloud-free pixels or to the channels far above the clouds for cloudy pixels. This paper focuses on the validation of various cloud-detection schemes applied to AIRS data. The clouds are detected and characterized, in cloud-top and cover, by using the NESDIS, ECMWF, CO2-slicing and MLEV schemes. These four different AIRS cloud descriptions are evaluated by independent information retrieved with the Meteo-France cloud mask applied to MODIS data and taken as our reference. The validation for a ten-day period over the North-east Atlantic is presented. The use of satellite cloudy radiances is a great challenge for numerical weather prediction. Work is in progress to assimilate such data by using enhanced observation operators dealing with clouds. In this work, we try to contribute to this effort by investigating the linearity assumption of an observation operator, with a simple diagnostic cloud scheme, for different cloud types. Copyright © 2005 Royal Meteorological Society

The method for tuning observational or background error statistics is presented and some of its properties are exposed using theoretical considerations and experiments carried out in a simplified framework. In particular, the method is shown to be equivalent to a maximum-likelihood evaluation and its efficiency is seen to depend on the number of observations. The results of several experiments carried out with the variational assimilation system of the French numerical weather-prediction system ARPEGE, both with simulated and actual datasets involving satellite radiances, are also presented. The temporal stability of the results and their consistency with the known quality of the measurements are shown. Copyright © 2004 Royal Meteorological Society

The cloudiness in simulated Infrared Atmospheric Sounding Interferometer (IASI) pixels deduced from the Advanced Very-High-Resolution Radiometer (AVHRR) satellite imager is studied specifically in meteorologically sensitive areas during the Fronts and Atlantic Storm-Track Experiment. It is found that few clear AVHRR observations are located in the IASI pixels in these regions, which are covered by high-level and low-level clouds. The IASI channel selection is then studied in the context of the sensitive areas for the pixels with low-level clouds. The Entropy Reduction (ER) method, which was previously studied in a general context, is compared with two other channel selection methods using selection criteria based on adjoint sensitivity: the sensitivity to observations and the so-called Kalman-filter sensitivity. It is found that, even though the ‘sensitive’ methods give slightly better results than the ER one, the latter performs quite robustly and at a lower computational cost. The robustness to the specification of the background-error covariance matrix is then studied. It is shown that channel selection based on the ER method is particularly robust to the specification of the background-error covariance matrix, but the analysis step itself requires an accurate determination of the background-error covariance matrix. In addition it is shown that an independently computed constant channel set gives comparable results to the optimal channel set. Copyright © 2004 Royal Meteorological Society.

The skill of numerical weather prediction depends to a large extent upon the quantity of globally available observations. Only a fraction of the available observations (especially high-density observations) is used in current operational assimilation systems. In this paper, the potential of high-density observations is studied in a practical four-dimensional variational assimilation context. Two individual meteorological situations are used to examine the impact of different observation densities on the analysis and the forecast. A series of observing-system simulation experiments are performed. Both direct observations (temperature and surface pressure) and indirect observations (radiance) are simulated, with uncorrelated or correlated errors. In general, it is verified that a small reduction (increase) of the initial error in a sensitive area can produce a considerable improvement (degradation) of the targeted forecast. In particular, the results show that increasing the observation density for the uncorrelated-error case can generally improve the analysis and the forecast. However, for correlated observation errors and the use of a diagonal observation-error covariance matrix in the assimilation, an increase in the observation number such that the error correlation between two adjacent observations becomes greater than a threshold value (around 0.2) degrades the analysis and the forecast. Posterior diagnostics of the sub-optimality of the assimilation scheme for correlated observation errors are analysed. Finally, it is shown that a risk of using high-density observations and poor vertical resolution is that deficiencies in the background-error statistics can lead to unrealistic analysis increments at some levels where no observations are present, and so produce a degradation of the analysis at these levels. Copyright © 2003 Royal Meteorological Society

In this paper, the optimal configurations of model resolution, observation resolution and observation density are investigated in a simple one-dimensional framework. In this context, the representativeness error is formalized and estimated before being used in the analysis-error formulation. Some optimal and suboptimal assimilation-schemes, differing from different approximations of observation-error covariance and observation operator, are compared. The optimal observation-extent is determined as a function of model resolution. Increasing the observation density is usually beneficial, except for suboptimal schemes similar to the ones used in operational practice. The impact of thinning the observations with correlated error is also studied from a suboptimal viewpoint. Copyright © 2002 Royal Meteorological Society

International audience; Advanced infrared sounders will provide thousands of radiance data at every observation location. The number of individual pieces of information is not usable in an operational numerical weather-prediction context, and we have investigated the possibilities of choosing an optimal subset of data. These issues have been addressed in the context of optimal linear estimation theory, using simulated Infrared Atmospheric Sounding Interferometer data. Several methods have been tried to select a set of the most useful channels for each individual atmospheric profile. These are two methods based on the data resolution matrix, one method based on the Jacobian matrix, and one iterative method selecting sequentially the channels with largest information content. The Jacobian method and the iterative method were found to be the most suitable for the problem. The iterative method was demonstrated to always produce the best results, but at a larger cost than the Jacobian method. To test the robustness of the iterative method, a variant has been tried. It consists in building a mean channel selection aimed at optimizing the results over the whole database, and then applying to each profile this constant selection. Results show that this constant iterative method is very promising, with results of intermediate quality between the ones obtained for the optimal iterative method and the Jacobian method. The practical advantage of this method for operational purposes is that the same set of channels can be used for various atmospheric profiles.

The use of the Infrared Atmospheric Sounding Interferometer (IASI) to improve short-range forecasts by the analysis of cloud variables is presented. After the retrieval of cloud microphysical variables, a one-dimensional (1D) version of the French convective scale model AROME is used here to discuss the persistence of the cloudy increment in the numerical weather prediction (NWP) model. The analysis of cloud variables is shown to significantly improve the forecasts of cloud variables, temperature and humidity during 3 h. This maintenance of the cloud information in the NWP model is expected to have a high impact on the forecasts of clouds and heavy rainfall events.

The first two papers of this series describe the development of the operational four-dimensional variational assimilation (4D-Var) configuration implemented at the European Centre for Medium-Range Weather Forecasts (ECMWF). The basic features are a 6-hour incremental 4D-Var set-up with two minimization steps, using very simplified physics in the first minimization and a more complete set of linear physics in the second. This paper describes the validation of this configuration. Prior to implementation, 12 weeks of experimentation showed a consistent improvement relative to 3D-Var. After an additional 6 weeks of encouraging parallel operation with the then current operational suite, 4D-Var with physics was introduced in operations at ECMWF in November 1997. The difference in scores is statistically significant, and the fast-growing components of the 4D-Var analysis errors are shown to be smaller than their 3D-Var counterparts. The performance of this new operational assimilation system is studied for the month of January 1998, for which the 4D-Var analyses exhibit more realistic baroclinic waves than the 3D-Var, especially in the Pacific area. A case-study illustrates the improvement one can expect in forecast terms in the mid latitudes. The 4D-Var system improved the forecast skill in the Tropics in general. Observing-system experiments show that the current 4D-Var operational system benefits from the assimilation both of satellite data and conventional observations.

Results of four-dimensional variational assimilations, 4D-Var, in cycling mode, over a few two-week assimilation periods are presented. 4D-Var is implemented in its incremental formulation, with a high-resolution model with the full physical parametrization package to compare the atmospheric states with the observations, and a low-resolution model with simplified physics to minimize the cost-function. The comparison of 4D-Var using several assimilation windows (6, 12 and 24 hours) with 3D-Var (the equivalent of 4D-Var with no time-dimension) over a two-week period shows a clear benefit from using 4D-Var over a 6 or 12—hour window compared to the static 3D-Var scheme. It also exhibits some problems with the forecasts started using 4D-Var over a 24-hour window. The poorer performance of 4D-Var over a relatively long assimilation window can be partly explained by the fact that, in these experiments, the tangent-linear and adjoint models used in the minimization are only approximations of the assimilating model (having lower resolution and crude physics). The error these approximations introduce in the time evolution of a perturbation affects the convergence of the incremental 4D-Var, with larger discontinuities in the values of the cost-function when going from low to high resolution for longer assimilation windows. Additional experiments are performed comparing 4D-Var using a 6-hour window with the 3D-Var system. Two additional 2-week periods show a consistent improvement in extratropical forecast scores with the 4D-Var system. The main 4D-Var improvements occur in areas where the 3D-Var errors were the largest. Local improvement can be as large as 35% for the root-mean-square of the 5-day-forecast error, averaged over a two-week period. A comparison of key analysis errors shows that, indeed, 4D-Var using a 6-hour window is able to reduce substantially the amplitude of its fast-growing error components. The overall fit to observations of analyses and short-range forecasts from 3D-Var and 4D-Var is comparable. In active baroclinic areas, the fit of the background to the data is considerably better for the 4D-Var system, resulting in smaller increments. It appears that in these areas (and in particular over the west Atlantic), 4D-Var is able to better use the information contained in the observations. The ability of 4D-Var to extrapolate some aircraft data in the vertical with a baroclinic tilt is illustrated. Problems exist in the tropics and mountainous areas due partly to a lack of physics in the tangent-linear model. Possible improvements to the system (the introduction of more physics; better behaviour of the incremental approach owing to a line search at high resolution) are also discussed.

Satellite microwave radiometers provide measurements of precipitable water content (PWC) over the oceans, with a horizontal resolution of a few tens of kilometres. These data represent the water vapour content integrated over the atmospheric column. We assess the value of this source of information for numerical weather prediction systems. We used the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System with a four-dimensional variational method to assimilate the Special Sensor Microwave/Imager (SSM/I) PWC data over a 24-hour period. Our experiments use an incremental variational method. Comparison with observations is made using a multi-level global primitive-equation T106 spectral model with physical parametrizations. Minimization is performed using a T63 adiabatic dynamics model which includes only simplified physics (horizontal diffusion, a simple surface drag and a vertical diffusion scheme). Comparing the control and assimilation experiments with aircraft and other data shows that the use of PWC data from SSM/I improves the analysis. We also obtain a slight improvement in short-range forecasts of almost all parameters when SSM/I-PWC data are used in the assimilation.

Structure functions for the 3D-Var assimilation scheme of the European Centre for Medium-Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time. Results compare satisfactorily with those reported in the existing literature. Non-separability of the correlation functions is a pervasive feature. Accounting for non-separability in 3D-Var is necessary to reproduce geostrophic characteristics of the statistics, such as the increase of length-scale with height for the horizontal correlation of the mass variable, sharper vertical correlations for wind than for mass and shorter horizontal length-scales for temperature than for mass. In our non-separable 3D-Var, the vertical correlations vary with total wave-number and the horizontal correlation functions vary with vertical level.

An iteration procedure minimizing the short-range forecast error leads, after some iterations, to so-called key analysis errors. These are estimates of the part of analysis errors that is largely responsible for the short-range forecast errors. The first step of the minimization procedure provides a scaled gradient of the two-day forecast errors for which the ‘energy’ inner-product provides an efficient way of identifying the analysis errors at scales that are relevant for forecast error growth. By using an ‘enstrophy’ like inner-product as an alternative to ‘energy’ the sensitivity gradient obtains an unrealistically large scale. Performing a few more steps in the minimization provides better estimates of the analysis error in the directions spanned by the leading singular vectors of the tangent-linear model. On a case study it is shown that three steps provide key analysis increments which, when added to the analysis, both significantly improve the fit to the available data, and substantially improve the subsequent model integration. It does not appear to be beneficial to do more steps of the minimization because of the uncertainty in the definition of the short-range forecast error, and of approximations in the tangent-linear model. Key analysis errors represent an improved estimate of analysis errors compared to the scaled gradient of day-2 forecast errors. In particular the geographical distribution shows the stability dependence of the scaled gradient. The projection of the gradient on the fastest growing errors limits maximum sensitivity to the major baroclinic zones. The close correspondence of evolved key analysis errors and forecast errors shows that key analysis errors are more realistically projecting on to full analysis errors. The close link between the stability of the flow and the gradient of the forecast errors implies an unreasonably strong seasonal variation of analysis errors estimates. In contrast, key analysis errors are nearly seasonally independent, which means that their detrimental effect on forecast errors in absolute terms in summer and winter is comparable.

In the first of this set of three papers, the formulation of the European Centre for Medium-Range Weather Forecasts (ECMWF) implementation of 3D-Var is described. In the second, the specification of the structure function is presented, and the last is devoted to the results of the extensive numerical experimentation programme which was conducted. The 3D-Var formulation uses a spherical-harmonic expansion, much as the ECMWF optimal interpolation (OI) scheme used an expansion of Bessel functions. This formulation is introduced using a convolution algebra over the sphere expressed directly in spectral space. It is shown that all features of the OI statistical model can be implemented within 3D-Var. Furthermore, a non-separable statistical model is described. In the present formulation, geostrophy is accounted for through a Hough-modes separation of the gravity and Rossby components of the analysis increments. As in OI, the tropical analysis remains essentially non-divergent and with a weak mass-wind coupling. The observations used, as well as their specified statistics of errors, are presented, together with some implementation details. In the light of the results, 3D-Var was implemented operationally at the end of January 1996.

The adjoint method has been used to calculate the sensitivity of short-range forecast errors to the initial conditions. The gradient of the energy of the day 2 forecast error with respect to the initial conditions can be interpreted as a sum of rapidly growing components of the analysis error. An analysis modified by subtracting an appropriately scaled vector, proportional to the gradient, provides initial conditions for a ‘sensitivity integration’ that can be used to diagnose the effect of initial-data errors on forecast errors. Statistics of sensitivity calculations for the month of April 1994 characterize the sensitivity patterns as small-scale, middle or lower tropospheric structures which are tilted in the vertical. The general pattern of these structures is known to be associated with the fastest possible growth of forecast error. When used as initial perturbations, they evolve rapidly into synoptic-scale structures, propagating both downstream and to higher atmospheric levels. On average, the sensitivity integration corrects for about a tenth of the day 2 forecast error, which indicates that indeed not all of the error is in the fastest-amplifying modes. But the fraction of the error corrected at day 2 is important for an improvement in the medium-range, as this fraction continues to grow substantially in the non-linear regime. These results have proved that there is still scope for great improvement in the medium-range forecast, particularly over Europe, by a better description of the initial conditions. The sensitivity experimentation suggests that many cases of major forecast-errors may be explained by defects in the analysis. A small but well-chosen change in the analysis can frequently improve the forecast quality.

The aim of this study is to make a strict comparison between two assimilation algorithms, sequential and four-dimensional variational, on a 24-hour period extracted from a baroclinic instability situation representative of mid-latitude dynamics. In the case of linear dynamics, and under the hypothesis of a perfect model, these two four-dimensional algorithms are known to lead to the same optimal estimate of the atmosphere at the end of the assimilation period, and both methods can be generalized in the nonlinear case. Because the full sequential algorithm is too resource-demanding to be implemented as such, we shall test the four-dimensional variational method (4D-VAR), and a simplified sequential method based on three-dimensional variational analysis (3D-VAR), deliberately not exceeding the range of validity of the tangent-linear model in the experiments. 4D-VAR is then expected to be almost equivalent to the generalization of the sequential Kalman filter in the nonlinear case, i.e. the extended Kalman filter. As for the simplified sequential algorithm, it can be seen as an approximation of this full extended Kalman filter, for which the forecast error matrices are evaluated only approximately before each analysis, instead of being explicitly computed from the complete dynamical equations. In the four-dimensional variational scheme, the consistency of the propagation of information with the dynamics is illustrated in an experiment assimilating some localized AIREP data. The large impact which these additional observations have over a large geographical area appears to be very beneficial for the quality of the analysis. Comparing the results of both methods in various configurations, we found that 4D-VAR systematically behaved substantially better than the simplified sequential algorithm, and had a more accurate analysis at the end of the assimilation period and a much smaller error growth rate in subsequent forecasts. On the one hand, extremely bad specifications of initial forecast errors were found to be detrimental to both algorithms. On the other hand, the four-dimensional variational algorithm proves to be more robust to the way by which gravity-wave control is implemented.

Current operational assimilation methods have revealed deficiencies in cases of strong baroclinic development. Baroclinic conditions are therefore appropriate for evaluating the potential for improvement which could be achieved through the implementation of a fully four-dimensional data assimilation. In this paper the behaviour of a variational scheme is investigated for a typical baroclinic instability problem, where a wave develops and retroacts on to the basic zonal flow