Ensemble Of Data Assimilations Research Articles

Enhancing Extreme Precipitation Predictions With Dynamical Downscaling: A Convection‐Permitting Modeling Study in Texas and Oklahoma

AbstractPrecipitation in the Southern Plains of the United States is relatively well depicted by the Community Earth System Model (CESM). However, despite its ability to capture seasonal mean precipitation anomalies, CESM consistently underestimates extreme pluvial and drought events, rendering it an insufficient tool for extending simulation lead times for exceptional events, such as the abnormally dry May 2011, which helped drive Texas into its worst period of drought in more than a century, and the abnormally wet May 2015, which led to widespread flooding in that state. Ensemble‐based regional climate experiments are completed for the two extreme years using Weather Research and Forecasting model (WRF) and downscaled from CESM. WRF simulations are at convection‐permitting grid resolution for improved physical representation of simulated precipitation over the Southern Great Plains. By integrating convection‐permitting models (CPMs) into each individual member of a CESM ocean data assimilation ensemble, this study demonstrates that high‐resolution dynamical downscaling can improve model skillfulness at capturing these two events and is thus a potentially useful tool for forecasting extremely high and extremely low precipitation events at subseasonal or even seasonal lead times.

Uncertainty growth and forecast reliability during extratropical cyclogenesis

Abstract. In global numerical weather prediction, the strongest contribution to ensemble variance growth over the first few days is at synoptic scales. Hence it is particularly important to ensure that this synoptic-scale variance is reliable. Here we focus on wintertime synoptic-scale growth in the North Atlantic storm track. In the 12 h background forecasts of the Ensemble of Data Assimilations (EDA) from the European Centre for Medium-Range Weather Forecasts (ECMWF), we find that initial variance growth at synoptic scales tends to be organized in particular flow situations, such as during the deepening of cyclones (cyclogenesis). Both baroclinic and diabatic aspects may be involved in the overall growth rate. However, evaluation of reliability through use of an extended error–spread equation indicates that the ECMWF ensemble forecast, which is initialized from the EDA but with additional singular vector perturbations, appears to have too much variance at a lead time of 2 d and that this over-spread is associated with cyclogenesis situations. Comparison of variance growth rates and reliability with other forecast systems within The International Grand Global Ensemble (TIGGE) archive indicates some sensitivity to the model or its initialization. For the ECMWF ensemble forecast, sensitivity experiments suggest that a large part of the total day-2 spread in cyclogenesis cases is associated with the growth of EDA uncertainty, but up to 25 % can be associated with the additional singular vector perturbations to the initial conditions and up to 25 % with the representation of model uncertainty. The sensitivities of spread to resolution, the explicit representation of convection, and the assimilation of local observations are also considered. The study raises the question of whether the EDA now successfully represents initial uncertainty (and the enhanced growth rates associated with cyclogenesis) to the extent that singular vector perturbations could be reduced in magnitude to improve storm track reliability. This would leave a more seamless forecast system, allowing short-range diagnostics to better help improve the model and model-uncertainty representation, which could be beneficial throughout the forecast range.

Simulation of analysis error contributions arising from uncertainties in the parametrisation of deep convection

AbstractIn order to simulate analysis error contributions resulting from observation errors and model errors, a possible methodology is to run a data assimilation ensemble that includes observation perturbations and a multiphysics approach. This method is examined here formally and experimentally, in order to investigate the effects of deep convection parametrisation uncertainties on analysis errors. A linearised expansion of initial condition errors is first employed to decompose them into contributions arising from observation errors and model errors. This is compared formally with a similar expansion for analysis differences resulting from the use of two different model versions, as in a multiphysics approach. Experimental results with the Action de Recherche Petite Echelle Grande Echelle global model are then examined. Observation error contributions are simulated by analysis differences between an unperturbed experiment and another experiment that includes observation perturbations that are drawn from specified observation error covariances. This is compared with analysis differences resulting from the use of two different parametrisation schemes of deep convection. The results indicate that the contribution of convection uncertainties is relatively large in the Tropics, with similar amplitudes to the contribution of observation errors. Simulated model errors are also found to be pronounced in the boundary layer and in convective areas where the analysis constraint by observations is relatively small, due to lower observation density.

Towards Full Flow‐Dependence: New Temporally Varying EDA Quotient Functionality to Estimate Background Errors in CERRA

AbstractA new temporally evolving quotient on the Ensemble of Data Assimilations (EDA) technique for estimating background error covariances has been developed for the Copernicus European Regional Re‐Analysis (CERRA). The B‐matrix is modeled on a bi‐Fourier limited area model. Background errors are assumed isotropic, homogeneous and non‐separable. Linearized geostrophic and hydrostatic balances are incorporated as multivariate relationships, coupling vorticity, and geopotential extended to mass‐wind and specific humidity fields via the f‐plane approximation. The EDA comprises two main pools: seasonal and daily. The seasonal component comprises winter and summer EDA forecast differences at reanalysis resolution (5.5 km). The new time quotient function temporally changes the mixture of differences from each season, to make up the seasonal component. The daily component is an 11 km moving 2.5 days average changing in real‐time. Subsequent B‐matrix computation sees the ingestion of forecast differences from both components, with a fixed split of 80%–20% seasonal‐daily, every 2 days. The sourcing of these forecast differences from both seasonal and daily sources is in continuous temporal flux therefore. We consider a case study to illustrate the potential of estimating weather regime change using CERRA‐EDA with varying proportions of seasonal‐daily mixing, while including settings used for CERRA production. Our case study shows that the most influential factors are differences in observation networks between the given years, their spatial distribution across the CERRA domain, and the proportion of seasonal‐daily split. It is shown that our method provides improvement over a static B‐matrix.

On the addition of microwave sounders and numerical weather prediction skill

AbstractThe utility of microwave sounding for numerical weather prediction (NWP) is well established. However, the volume of sounder data assimilated in NWP systems may change substantially in upcoming years, as there is an ageing constellation of satellites but also the prospect of proliferating small satellite constellations. This study examines the addition of temperature and humidity sounders from a baseline that includes no microwave sounders at all, aiming to elucidate the incremental benefit gained from adding sounders to the assimilation system. Framed as a series of observing‐system experiments (OSEs), large improvements in forecast skill and background fits to independent observations are gained from the first sounders added. Significant further benefit is observed from additional sounders, with the impacts largest at higher latitudes and no saturation evident in the maximal setup. In the second part of this study, the relative importance of updating background errors for OSEs is investigated to give greater context to the sounder addition results. The ensemble of data assimilations (EDA) underlying the background‐error specification is rerun for this purpose to be consistent with the observation usage in the OSE. Comparing experiments with updated and unchanged background errors shows that the effect of updating background errors is secondary to that caused by the observing‐system change itself. Rerunning the EDA can reduce some of the forecast skill apparently lost in a data‐denial experiment or gained when assessing data addition, but this is roughly 10% of the overall change and should not alter conclusions resulting from typical OSEs, in which background errors are not tailor‐made.

Accounting for land model error in numerical weather prediction ensemble systems: toward ensemble-based coupled land/atmosphere data assimilation

AbstractThe ensembles used in the NOAA National Centers for Environmental Prediction (NCEP) global data assimilation and numerical weather prediction (NWP) system are under-dispersed at and near the land surface, preventing their use in ensemble-based land data assimilation. Comparison to offline (land-only) data assimilation ensemble systems suggests that while the relevant atmospheric fields are under-dispersed in NCEP’s system, this alone cannot explain the under-dispersed land component, and an additional scheme is required to explicitly account for land model error. This study then investigates several schemes for perturbing the soil (moisture and temperature) states in NCEP’s system, qualitatively comparing the induced ensemble spread to independent estimates of the forecast error standard deviation in soil moisture, soil temperature, 2m temperature, and 2m humidity. Directly adding perturbations to the soil states, as is commonly done in offline systems, generated unrealistic spatial patterns in the soil moisture ensemble spread. Application of a Stochastically Perturbed Physics Tendencies scheme to the soil states is inherently limited in the amount of soil moisture spread that it can induce. Perturbing the land model parameters, in this case vegetation fraction, generated a realistic distribution in the ensemble spread, while also inducing perturbations in the land (soil states) and atmosphere (2m states) that are consistent with errors in the land/atmosphere fluxes. The parameter perturbation method is then recommended for NCEP’s ensemble system, and it is currently being refined within the development of an ensemble-based coupled land/atmosphere data assimilation for NCEP’s NWP system.

Lagrangian matches between observations from aircraft, lidar and radar in a warm conveyor belt crossing orography

Abstract. Warm conveyor belts (WCBs) are important airstreams in extratropical cyclones, often leading to the formation of intense precipitation and the amplification of upper-level ridges. This study presents a case study that involves aircraft, lidar and radar observations in a WCB ascending from western Europe towards the Baltic Sea during the Hydrological Cycle in the Mediterranean Experiment (HyMeX) and T-NAWDEX-Falcon in October 2012, a preparatory campaign for the THORPEX North Atlantic Waveguide and Downstream Impact Experiment (T-NAWDEX). Trajectories were used to link different observations along the WCB, that is, to establish so-called Lagrangian matches between observations. To this aim, an ensemble of wind fields from the global analyses produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble of Data Assimilations (EDA) system were used, which allowed for a probabilistic quantification of the WCB occurrence and the Lagrangian matches. Despite severe air traffic limitations for performing research flights over Europe, the German Aerospace Center (DLR) Falcon successfully sampled WCB air masses during different phases of the WCB ascent. The WCB trajectories revealed measurements in two distinct WCB branches: one branch ascended from the eastern North Atlantic over southwestern France, while the other had its inflow in the western Mediterranean. Both branches passed across the Alps, and for both branches Lagrangian matches coincidentally occurred between lidar water vapour measurements in the inflow of the WCB south of the Alps, radar measurements during the ascent at the Alps and in situ aircraft measurements by Falcon in the WCB outflow north of the Alps. An airborne release experiment with an inert tracer could confirm the long pathway of the WCB from the inflow in the Mediterranean boundary layer to the outflow in the upper troposphere near the Baltic Sea several hours later. The comparison of observations and ensemble analyses reveals a moist bias in the analyses in parts of the WCB inflow but a good agreement of cloud water species in the WCB during ascent. In between these two observations, a precipitation radar measured strongly precipitating WCB air located directly above the melting layer while ascending at the southern slopes of the Alps. The trajectories illustrate the complexity of a continental and orographically influenced WCB, which leads to (i) WCB moisture sources from both the Atlantic and Mediterranean, (ii) different pathways of WCB ascent affected by orography, and (iii) locally steep WCB ascent with high radar reflectivity values that might result in enhanced precipitation where the WCB flows over the Alps. The linkage of observational data by ensemble-based WCB trajectory calculations, the confirmation of the WCB transport by an inert tracer and the model evaluation using the multi-platform observations are the central elements of this study and reveal important aspects of orographically modified WCBs.

Ensemble hindcasting of wind and wave conditions with WRF and WAVEWATCH III® driven by ERA5

Abstract. When hindcasting wave fields of storm events with state-of-the-art wave models, the quality of the results strongly depends on the meteorological forcing dataset. The wave model will inherit the uncertainty of the atmospheric data, and additional discretization errors will be introduced due to a limited spatial and temporal resolution of the forcing data. In this study, we apply an atmospheric downscaling to (i) add regional details to the wind field, (ii) increase the temporal resolution of the wind fields, (iii) provide a more detailed representation of transient events such as storms and (iv) generate ensembles with perturbed atmospheric conditions, which allows for a flow-dependent and spatio-temporally variable uncertainty estimation. We test different strategies to generate an ensemble hindcast of a relatively strong storm event in February 2002 in the Baltic Sea. The Weather Research and Forecasting (WRF) model used for this purpose is driven by the ECMWF ERA5 reanalysis, and wind fields are passed to the third-generation wave model WAVEWATCH III®. A combination of initial conditions from the ERA5 ensemble of data assimilations and stochastic perturbations during runtime is identified as the most promising strategy. The final aim of the ensemble approach is to quantify the hindcast error, but this approach can also be used to generate alternative representations of historical extreme events to sample the recent climate and to increase the sample size for statistical studies, such as for civil engineering applications for coastal protection studies.

Treatment of model uncertainty from radiation by the Stochastically Perturbed Parametrization Tendencies (SPPT) scheme and associated revisions in the ECMWF ensembles

The Stochastically Perturbed Parametrization Tendencies (SPPT) scheme is used in ensemble forecast systems to represent uncertainties due to the atmospheric physics parametrizations. The scheme works by introducing random perturbations to the tendencies from the physics schemes. The size of the perturbations is modulated by the size of the net tendencies from the full physics suite. Recent work has identified an inconsistency in this approach to attributing model uncertainty: greater uncertainty is attributed to the night‐time sky than to the daytime sky in clear‐sky conditions, which is not deemed physically realistic. This paper documents the details of a revised configuration of SPPT, which became active in the recent operational version of the ensemble forecast system (“CY45R1”) at the European Centre for Medium‐Range Weather Forecasts (ECMWF) — released in June 2018. In this work, a modification to SPPT is outlined such that the clear‐sky contribution from the radiation scheme is subtracted from the physics tendencies that are acted on by SPPT. Inspection of individual vertical profiles of physics tendencies provides a greater understanding of the interactions between processes, and helps demonstrate that the revision gives a more realistic description of the associated uncertainties. Forecast experiments with the revised version of SPPT demonstrate neutral to positive impacts on the skill of the ensemble forecasts in the medium‐range; and in the extended‐range, a significantly improved match between the spread and error of the principal components describing the Madden–Julian Oscillation. In addition, it is shown that including the revisions in the ensemble of data assimilations leads to increases in spread in the boundary layer.

Generating atmospheric forcing perturbations for an ocean data assimilation ensemble

Running ensemble of reanalyses or forecasts has proved successful at improving their performances, despite the cost. Generating ensemble simulations requires generating perturbations within the models, and for the assimilated observations and subsidiary conditions. This paper proposes a statistical model to generate atmospheric forcing random perturbations in a flexible and cheap way, for all the variables required to calculate bulk formulae. The training data are a ten-year set of differences between ERA-INTERIM (from ECMWF) and MERRA (from NASA) atmospheric forcing fields, unbiased with a high-pass filter. The model is designed to generate global spatially-varying multi-variate and unbiased perturbations with consistent spatial structures. Based on linear regressions, the model allows for regression coefficients and residual standard deviations to vary with the time of the year. Once defined, the model does not rely on any other external data to generate the perturbations, and can hence be used on- or off-line in the goal of seeding the ensemble more appropriately. Once designed, the model has been validated by comparing three years of generated perturbations to three years of differences between the reanalyses out of the training period. Statistical tests show that the distributions of the sets comply reasonably well, except for precipitation and snow. The major issues come from regions with high kurtosis or where no clear patterns can be established. In terms of structure, the perturbation standard deviation of both sets show similar patterns for all variables.

Block Krylov methods for accelerating ensembles of variational data assimilations

We consider the problem of efficiently solving ensembles of variational data assimilations in the context of numerical weather prediction. Running several assimilations notably allows us to initialize ensemble prediction systems and to more accurately represent background‐error statistics, but is computationally expensive, limiting ensemble size. We propose a new class of algorithms for speeding up the minimization of the ensemble of data assimilations. It consists of using block Krylov methods to simultaneously perform the minimization for all members of the ensemble, instead of performing each minimization separately.We develop preconditioned block Krylov versions of the Full Orthogonal Method and of the Lanczos algorithm in both primal and dual space. The latter works in observation space that is usually of smaller dimension than the state space, thus giving an advantage in terms of memory requirements and computational cost. We describe and compare several parallelization strategies for speeding up the minimization and limiting the communications.These methods have been tested on a quasi‐geostrophic system, consisting of a simplified atmospheric circulation model equipped with an ensemble of 3D‐Var schemes tuned to mimic some features of a limited‐area numerical weather prediction system. Experimentation shows that the number of iterations needed to converge is drastically reduced by the block Krylov approaches. We indicate that, while working in primal space does not save significant computational time, working in the dual space may reduce the computational time by a factor of 2 to 5 (depending on ensemble size) compared to standard Krylov methods, making our approach attractive for operational use.

Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case

Abstract. Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called here ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is studied in this two-part paper on the non-linear low-dimensional Lorenz-96 chaotic system, with the assimilation being performed by the standard variational procedure. In this first part, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered either as a probabilistic or a deterministic estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for the ensemble Kalman filter (EnKF) and particle filter (PF), although at a higher cost. Globally similar results are obtained with the Kuramoto–Sivashinsky (K–S) equation.

Analysis of iterative ensemble smoothers for solving inverse problems

This paper examines the properties of the Iterated Ensemble Smoother (IES) and the Multiple Data Assimilation Ensemble Smoother (ES–MDA) for solving the history matching problem. The iterative methods are compared with the standard Ensemble Smoother (ES) to improve the understanding of the similarities and differences between them. We derive the three smoothers from Bayes’ theorem for a scalar case which allows us to compare the equations solved by the three methods, and we can better understand which assumptions are applied and their consequences. When working with a scalar model, it is possible to use a vast ensemble size, and we can construct the sample distributions for both priors and posteriors, as well as intermediate iterates. For a linear model, all three methods give the same result. For a nonlinear model, the iterative methods improve on the ES result, but the two iterative methods converge to different solutions, and it is not clear which should be the preferred choice. It is clear that the ensemble of cost functions used to define the IES solution does not represent an exact sampling of the posterior-Bayes’ probability density function. Also, the use of an ensemble representation for the gradient in IES introduces an additional approximation compared to using an exact analytic gradient. For ES–MDA, the convergence, as a function of increasing number of uniform update steps, is studied for a huge ensemble size. We illustrate that ES–MDA converges to a solution that differs from the Bayesian posterior. The convergence is also examined using a realistic sample size to study the impact of the number of realizations relative to the number of update steps. We have run multiple ES–MDA experiments to examine the impact of using different schemes for choosing the lengths of the update steps, and we have tried to understand which properties of the inverse problem imply that a non-uniform update step length is beneficial. Finally, we have examined the smoother methods with a highly nonlinear model to examine their properties and limitations in more extreme situations.

MATLAB algorithm to implement soil water data assimilation with the Ensemble Kalman Filter using HYDRUS

Data assimilation is becoming a promising technique in hydrologic modelling to update not only model states but also to infer model parameters, specifically to infer soil hydraulic properties in Richard-equation-based soil water models. The Ensemble Kalman Filter method is one of the most widely employed method among the different data assimilation alternatives. In this study the complete Matlab© code used to study soil data assimilation efficiency under different soil and climatic conditions is shown. The code shows the method how data assimilation through EnKF was implemented. Richards equation was solved by the used of Hydrus-1D software which was run from Matlab.•MATLAB routines are released to be used/modified without restrictions for other researchers•Data assimilation Ensemble Kalman Filter method code.•Soil water Richard equation flow solved by Hydrus-1D.

Inflation and localization tests in the development of an ensemble of 4D‐ensemble variational assimilations

A new method for generating ensemble predictions based on an ensemble of data assimilations has been developed. Using an ensemble of four‐dimensional ensemble‐variational minimizations provides an approach which is close to the Met Office's operational data assimilation system and less computationally expensive than other alternatives. In developing this system, several inflation schemes have been compared. One form of additive inflation, based on analysis increments, was developed and found to be very effective at increasing the overall ensemble spread and correcting systematic biases in the model. However, the analysis increments are not flow‐dependent since they are randomly drawn from a long archive. It was decided to scale back their amplitude to avoid them dominating the overall performance. Of the other inflation schemes considered, it was found that relaxation‐to‐prior‐perturbations was the most effective at maintaining the ensemble spread. However, this scheme also produced perturbations which are too large‐scale and too balanced. The relaxation‐to‐prior‐spread scheme performed well in many respects, but required a relaxation factor greater than one to produce an acceptable spread. Therefore these two schemes were combined in order to mitigate the drawbacks of each. This combination proved successful and was used in final testing of the ensemble against the currently operational ensemble transform Kalman filter (ETKF). The ETKF has its perturbations centred around a high‐resolution ‘deterministic’ analysis. This was seen to be an important benefit, and the new ensemble system also benefited from being recentred around the high‐resolution analysis. This recentred system has slightly lower forecast skill than the ETKF over a variety of variables, due to the fact that the spread of this ensemble is less than the spread of the ETKF ensemble. The deficiency of the spread of the new ensemble system will be addressed in ongoing work.

Diagnosing non-Gaussianity of forecast and analysis errors in a convective-scale model

Abstract. In numerical weather prediction, the problem of estimating initial conditions with a variational approach is usually based on a Bayesian framework associated with a Gaussianity assumption of the probability density functions of both observations and background errors. In practice, Gaussianity of errors is tied to linearity, in the sense that a nonlinear model will yield non-Gaussian probability density functions. In this context, standard methods relying on Gaussian assumption may perform poorly. This study aims to describe some aspects of non-Gaussianity of forecast and analysis errors in a convective-scale model using a Monte Carlo approach based on an ensemble of data assimilations. For this purpose, an ensemble of 90 members of cycled perturbed assimilations has been run over a highly precipitating case of interest. Non-Gaussianity is measured using the K2 statistics from the D'Agostino test, which is related to the sum of the squares of univariate skewness and kurtosis. Results confirm that specific humidity is the least Gaussian variable according to that measure and also that non-Gaussianity is generally more pronounced in the boundary layer and in cloudy areas. The dynamical control variables used in our data assimilation, namely vorticity and divergence, also show distinct non-Gaussian behaviour. It is shown that while non-Gaussianity increases with forecast lead time, it is efficiently reduced by the data assimilation step especially in areas well covered by observations. Our findings may have implication for the choice of the control variables.

Reliability in ensemble data assimilation

A key attribute of a probabilistic forecast system is its reliability: the degree to which forecast probabilities agree with outcome frequencies. Here, we focus on short‐lead‐time (12 h) reliability in the nonlinear background forecasts of the Ensemble of Data Assimilations (EDA) from the European Centre for Medium‐Range Weather Forecasts (ECMWF). A ‘reliability budget’, derived from consistency arguments, is used to separate the mean‐squared departures of the ensemble mean (relative to observations) into bias, ensemble variance and observation‐error contributions, along with a residual that indicates a deficiency in reliability. At these short lead times, the residual is found to be sensitive, in a local manner, to the assignment of observation errors and to the parametrization of ‘stochastic physics’, which accounts for the deficit in a model's error growth rate. In particular, the results highlight the importance of the stochastic physics parametrization to represent error growth rates fully in convective regions and suggest that current stochastic physics may be too active in subtropical anticyclones, where the mid‐tropospheric meteorology is largely characterized by time‐mean descent and radiative cooling. Other results demonstrate how the reliability budget can be used to tune observation errors, which leads to an improvement in diagnosed background reliability. Although there remains some ambiguity in the attribution of deficiencies, the budget represents a useful additional tool that can help stimulate improvements in model stochastic error representation and observation‐error estimates. Such improvements should help facilitate the development of more reliable ensemble forecasts in future.

The evolution of the ECMWF hybrid data assimilation system

The trend towards using flow‐dependent, ensemble‐based estimates of background‐error covariances has been one of the main themes of atmospheric data assimilation research and development in recent years. In this work it is documented how flow‐dependent ensemble information from the ECMWF ensemble of data assimilations (EDA) has gradually been incorporated into the B model which describes the background‐error covariance matrix at the start of the ECMWF 4D‐Var assimilation window. Starting with background‐error variances for the balanced part of the control vector and observation quality control, the current article extends the flow‐dependency to background‐error variances for the unbalanced part of the control vector and for background‐error correlation structures. The correlations are determined either online from previous days or from a hybrid of climatological and current cycle estimates. Each of these changes is shown to improve both the realism of the modelled B and the accuracy of the analysis and forecast fields produced by the 4D‐Var assimilation cycle which makes use of the improved B. Finally, increasing the resolution at which the EDA 4D‐Vars are run is shown to reduce the underestimation of the EDA‐based error estimates.

On the impact of re‐centring initial conditions for ensemble forecasts

Many weather forecasting centres generate the initial conditions for their ensemble prediction system by adding a set of perturbations to a single analysis. At the European Centre for Medium‐Range Weather Forecasts (ECMWF), initial conditions from an ensemble of data assimilations (EDA) are re‐centred on the deterministic high‐resolution analysis. This study assesses how the re‐centring step affects the ensemble forecasts and what benefits starting directly from the perturbed EDA members may bring. Numerical experiments are based on suitably modified configurations of the ECMWF medium‐range ensemble.Re‐centring leads to an artificial increase of the climatological variance of the initial conditions for variables and spatial scales that are not well constrained in the analysis. For those variables and spatial scales, the EDA variance can reach a similar magnitude as the climatological variance. Re‐centring on the unperturbed member of the EDA leads to a degradation of the ensemble skill in comparison to starting directly from the perturbed EDA members. Depending on the amplitude of the EDA spread and which scales are less constrained, different lead times are affected. Furthermore, the re‐centring step increases the jumpiness of the ensemble forecasts in general and alters the precipitation frequency during the first 12 h of the forecasts.It also becomes apparent from our results that the benefit for the ECMWF ensemble of starting directly from EDA initial conditions is sensitive to several factors: the difference in analysis accuracy between the unperturbed EDA control and the high‐resolution analysis, the number of EDA members, and the EDA spread. At present, the forecast skill still benefits from centring the ensemble initial conditions on the high‐resolution analysis, but future changes to the EDA may change the balance.

Linearity aspects of the ensemble of data assimilations technique

AbstractWe examine the linearity of the Ensemble of Data Assimilations (EDA) technique with respect to the amplitude of the applied observation perturbations. We provide explicit examples to assess the linear relationship between such modifications of the observing system and the resulting changes in the EDA ensemble spread. The results demonstrate that, for a state‐of‐the‐art numerical weather prediction (NWP) system, such linearity between the applied observation perturbations and the EDA ensemble spread holds well for temporal and spatial regimes relevant to global medium‐range weather prediction: specifically, for forecast lead‐times of up to approximately 5 days, in the vertical throughout the troposphere up to the lower and middle stratosphere and for broad horizontal scales.