Total Energy Singular Vectors Research Articles

Physical Mechanisms Underlying Selected Adaptive Sampling Techniques for Tropical Cyclones

Abstract To efficiently and effectively prioritize resources, adaptive observations can be targeted by using some objective criteria to estimate the potential impact an initial condition perturbation (or analysis increment) in a specific region would have on the future forecast. Several objective targeting guidance techniques have been developed, including total-energy singular vectors (TESV), adjoint-derived sensitivity steering vectors (ADSSV), and the ensemble transform Kalman filter (ETKF), all of which were tested during the 2008 The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T-PARC) and the Office of Naval Research Tropical Cyclone Structure-2008 (TCS-08) field experiments. An intercomparison between these techniques is performed in order to find underlying physical mechanisms in the respective guidance products, based on four tropical cyclone (TC) cases from the T-PARC/TCS-08 field campaigns. It is found that the TESV energy norm and the ADSSV response function are largely indirect measures of the TC track divergence that can be produced by an initial condition perturbation, explaining the strong correlation between these products. The downstream targets routinely chosen by the ETKF guidance system are often not found in the TESV and ADSSV guidance products, and it is found that downstream perturbations can affect the steering of a TC through the development of a Rossby wave in the subtropics that modulates the strength of the nearby subtropical ridge. It is hypothesized that the ubiquitousness of these downstream targets in the ETKF is largely due to the existence of large uncertainties downstream of the TC that are not taken into consideration by either the TESV or ADSSV techniques.

Statistical distributions of singular vectors for tropical cyclones affecting Korea over a 10-year period

To investigate the statistical sensitivity distributions of tropical cyclone (TC) forecasts over the Korean Peninsula, total energy (TE) singular vectors (SVs) were calculated and evaluated over a 10-year period. TESVs were calculated using the fifth-generation Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model (MM5) and its tangent linear and adjoint models with a Lanczos algorithm over a 48-h period. Chosen cases were 21 TCs that affected the Korean Peninsula among 230 TCs that were generated in the western North Pacific from 2001 to 2010. Sensitive regions indicated by TESVs were mainly located near mid-latitude troughs and TC centers but varied depending on TC track and environmental conditions such as subtropical high and mid-latitude trough. The cases were classified into three groups by clustering TC tracks based on the finite mixture model. The two groups that passed through the western and southern sea of the Korean Peninsula had maximally sensitive regions in the mid-latitude trough and largely sensitive regions around the TC center, while the other group that passed straight through the eastern sea of the Korean Peninsula had maximally sensitive regions near the northeastern region of the TC center. Vertically, the former two clustered groups had the westerly tilted TESVs and potential vorticity structures under the mid-latitude troughs at the initial time, indicating the TCs were in a baroclinic environment. Conversely, the straight-moving TCs were not in a baroclinic environment. Based on the results in the present study, the TCs moving toward a fixed verification region over the Korean Peninsula have different sensitivity regions and structures according to their moving tracks and characteristic environmental conditions, which may provide guidance for targeted observations of TCs affecting the Korean Peninsula.

Real-Time Adaptive Observation Guidance Using Singular Vectors for Typhoon Jangmi (200815) in T-PARC 2008

Abstract In this study, structures of real-time adaptive observation guidance provided by Yonsei University (YSU) in South Korea during The Observing System Research and Predictability Experiment (THORPEX)-Pacific Asian Regional Campaign (T-PARC) are presented and compared with those of no-lead-time adaptive observation guidance recalculated as well as other adaptive observation guidance for a tropical cyclone (Jangmi 200815). During the T-PARC period, real-time dry total energy (TE) singular vectors (SVs) based on the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the corresponding tangent linear and adjoint models with a Lanczos algorithm are provided by YSU to help determine sensitive regions for targeted observations. While YSU provided the real-time TESV guidance based on a mesoscale model, other institutes provided real-time TESV guidance based on global models. The overall features of the real-time MM5 TESVs were similar to those generated from global models, showing influences from tropical cyclones, midlatitude troughs, and subtropical ridges. TESV structures are very sensitive to verification region and forecast lead time. If a more accurate basic-state trajectory with no lead time is used, more accurate TESVs, which yield more accurate determinations of sensitive regions for targeted observations, may be calculated. The results of this study may imply that reducing forecast lead time is an important component to obtaining better sensitivity guidance for real-time targeted observation operations.

An Observing System Experiment for Tropical Cyclone Targeting Techniques Using the Global Forecast System

Abstract In 1997, the National Oceanic and Atmospheric Administration’s National Hurricane Center and the Hurricane Research Division began operational synoptic surveillance missions with the Gulfstream IV-SP jet aircraft to improve the numerical guidance for hurricanes that threaten the continental United States, Puerto Rico, the U.S. Virgin Islands, and Hawaii. The dropwindsonde observations from these missions were processed and formatted aboard the aircraft and sent to the National Centers for Environmental Prediction and the Global Telecommunications System to be ingested into the Global Forecasting System, which serves as initial and boundary conditions for regional numerical models that also forecast tropical cyclone track and intensity. As a result of limited aircraft resources, optimal observing strategies for these missions are investigated. An Observing System Experiment in which different configurations of the dropwindsonde data based on three targeting techniques (ensemble variance, ensemble transform Kalman filter, and total energy singular vectors) are assimilated into the model system was conducted. All three techniques show some promise in obtaining maximal forecast improvements while limiting flight time and expendables. The data taken within and around the regions specified by the total energy singular vectors provide the largest forecast improvements, though the sample size is too small to make any operational recommendations. Case studies show that the impact of dropwindsonde data obtained either outside of fully sampled, or within nonfully sampled target regions is generally, though not always, small; this suggests that the techniques are able to discern in which regions extra observations will impact the particular forecast.

The impact of targeted observations made during the Greenland Flow Distortion Experiment

AbstractThe impact of targeted sonde observations on the 1‐3 day forecasts for northern Europe is evaluated using the Met Office four‐dimensional variational data assimilation scheme and a 24 km gridlength limited‐area version of the Unified Model (MetUM). The targeted observations were carried out during February and March 2007 as part of the Greenland Flow Distortion Experiment, using a research aircraft based in Iceland. Sensitive area predictions using either total energy singular vectors or an ensemble transform Kalman filter were used to predict where additional observations should be made to reduce errors in the initial conditions of forecasts for northern Europe. Targeted sonde data was assimilated operationally into the MetUM. Hindcasts show that the impact of the sondes was mixed. Only two out of the five cases showed clear forecast improvement; the maximum forecast improvement seen over the verifying region was approximately 5% of the forecast error 24 hours into the forecast. These two cases are presented in more detail: in the first the improvement propagates into the verification region with a developing polar low; and in the second the improvement is associated with an upper‐level trough. The impact of cycling targeted data in the background of the forecast (including the memory of previous targeted observations) is investigated. This is shown to cause a greater forecast impact, but does not necessarily lead to a greater forecast improvement. Finally, the robustness of the results is assessed using a small ensemble of forecasts. Copyright © 2009 Royal Meteorological Society and Crown Copyright

Intercomparison of Targeted Observation Guidance for Tropical Cyclones in the Northwestern Pacific

Abstract This study compares six different guidance products for targeted observations over the northwest Pacific Ocean for 84 cases of 2-day forecasts in 2006 and highlights the unique dynamical features affecting the tropical cyclone (TC) tracks in this basin. The six products include three types of guidance based on total-energy singular vectors (TESVs) from different global models, the ensemble transform Kalman filter (ETKF) based on a multimodel ensemble, the deep-layer mean (DLM) wind variance, and the adjoint-derived sensitivity steering vector (ADSSV). The similarities among the six products are evaluated using two objective statistical techniques to show the diversity of the sensitivity regions in large, synoptic-scale domains and in smaller domains local to the TC. It is shown that the three TESVs are relatively similar to one another in both the large and the small domains while the comparisons of the DLM wind variance with other methods show rather low similarities. The ETKF and the ADSSV usually show high similarity because their optimal sensitivity usually lies close to the TC. The ADSSV, relative to the ETKF, reveals more similar sensitivity patterns to those associated with TESVs. Three special cases are also selected to highlight the similarities and differences among the six guidance products and to interpret the dynamical systems affecting the TC motion in the northwestern Pacific. Among the three storms studied, Typhoon Chanchu was associated with the subtropical high, Typhoon Shanshan was associated with the midlatitude trough, and Typhoon Durian was associated with the subtropical jet. The adjoint methods are found to be more capable of capturing the signal of the dynamic system that may affect the TC movement or evolution than are the ensemble methods.

The characteristics of Hessian singular vectors using an advanced data assimilation scheme

Initial condition uncertainty is a significant source of forecast error in numerical weather prediction. Singular vectors of the tangent linear propagator can identify directions in phase-space where initial errors are likely to make the largest contribution to forecast-error variance. The physical characteristics of these singular vectors depend on the choice of initial-time metric used to represent analysis-error covariances: the total-energy norm serves as a proxy to the analysis-error covariance matrix, whereas the Hessian of the cost function of a 4D-Var assimilation scheme represents a more sophisticated estimate of the analysis-error covariances, consistent with observation and background-error covariances used in the 4D-Var scheme. This study examines and compares the structure of singular vectors computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System using these two types of initial metrics. Unlike earlier studies that use background errors derived from lagged forecast differences (the NMC method), the background-error covariance matrix in the Hessian metric is based on statistics from an ensemble of 4D-Vars using perturbed observations, which produces tighter correlations of background-error statistics than in previous formulations. In light of these new background-error statistics, this article re-examines the properties of Hessian singular vectors (and their relationship to total-energy singular vectors) using cases from different periods between 2003 and 2005. Energy profiles and wavenumber spectra reveal that the total-energy singular vectors are similar to Hessian singular vectors that use all observation types in the operational 4D-Var assimilation. This is in contrast to the structure of Hessian singular vectors without observations. Increasing the observation density tends to reduce the spatial scale of the Hessian singular vectors. Copyright © 2009 Royal Meteorological Society

Singular Vector Structure and Evolution of a Recurving Tropical Cyclone

Abstract In this study, the structure and evolution of total energy singular vectors (SVs) of Typhoon Usagi (2007) are evaluated using the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) and its tangent linear and adjoint models with a Lanczos algorithm. Horizontal structures of the initial SVs following the tropical cyclone (TC) evolution suggest that, relatively far from the region of TC recurvature, SVs near the TC center have larger magnitudes than those in the midlatitude trough. The SVs in the midlatitude trough region become dominant as the TC passes by the region of recurvature. Increasing magnitude of the SVs over the midlatitude trough regions is associated with the extratropical transition of the TC. While the SV sensitivities near the TC center are mostly associated with warming in the midtroposphere and inflow toward the TC along the edge of the subtropical high, the SV sensitivities in the midlatitude are located under the upper trough with upshear-tilted structures and associated with strong baroclinicity and frontogenesis in the lower troposphere. Given the results in this study, sensitive regions for adaptive observations of TCs may be different following the TC development stage. Far from the TC recurvature, sensitive regions near TC center may be important. Closer to the TC recurvature, effects of the midlatitude trough become dominant and the vertical structures of the SVs in the midlatitude are basically similar to those of extratropical cyclones.

Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones

Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

A Comparison of Adaptive Observing Guidance for Atlantic Tropical Cyclones

Abstract Airborne adaptive observations have been collected for more than two decades in the neighborhood of tropical cyclones, to attempt to improve short-range forecasts of cyclone track. However, only simple subjective strategies for adaptive observations have been used, and the utility of objective strategies to improve tropical cyclone forecasts remains unexplored. Two objective techniques that have been used extensively for midlatitude adaptive observing programs, and the current strategy based on the ensemble deep-layer mean (DLM) wind variance, are compared quantitatively using two metrics. The ensemble transform Kalman filter (ETKF) uses ensembles from NCEP and the ECMWF. Total-energy singular vectors (TESVs) are computed by the ECMWF and the Naval Research Laboratory, using their respective global models. Comparisons of 78 guidance products for 2-day forecasts during the 2004 Atlantic hurricane season are made, on both continental and localized scales relevant to synoptic surveillance missions. The ECMWF and NRL TESV guidance identifies similar large-scale target regions in 90% of the cases, but are less similar to each other in the local tropical cyclone environment (56% of the cases) with a more stringent criterion for similarity. For major hurricanes, all techniques usually indicate targets close to the storm center. For weaker tropical cyclones, the TESV guidance selects similar targets to those from the ETKF (DLM wind variance) in only 30% (20%) of the cases. ETKF guidance using the ECMWF ensemble is more like that provided by the NCEP ensemble (and DLM wind variance) for major hurricanes than for weaker tropical cyclones. Minor differences in these results occur when a different metric based on the ranking of fixed storm-relative regions is used.

A comparison of variance and total‐energy singular‐vectors

AbstractThe analysis‐error variance estimates produced by the Naval Research Laboratory Atmospheric Variational Data Assimilation System are used to constrain singular vectors (SVs) at initial time (the final‐time metric is total energy). These ‘VAR SVs’ are compared to SVs for which total energy is both the initial‐ and final‐time metrics (TE SVs). The spatial distributions and structures of the VAR SVs and TE SVs are examined and their effectiveness in explaining forecast error is compared. Consistent with previous results, the VAR SVs have relatively larger amplitude than TE SVs in regions where analysis errors are larger (such as over oceans and polar regions). In contrast to previous results, the initial‐time VAR SV energy peaks at lower altitudes than the TE SV energy, reflecting the influence of the data‐assimilation‐error variance estimates. Despite these significant differences, the TE and VAR SVs explain comparable amounts of forecast error in both linear and nonlinear contexts. By projecting the VAR SV pseudo‐inverse perturbation onto the TE SVs, it is found that the component inside the TE‐SV subspace accounts for most of the forecast‐error reduction. The component outside the TE‐SV subspace has very little impact on error reduction. It is noteworthy that for both the TE and VAR SVs, nonlinear pseudo‐inverse forecast‐corrections are better than the expected linear corrections. Both sets of SVs exhibit a relationship between singular‐vector growth and forecast‐error total energy, when averaged over many cases. This indicates that the SVs have some utility in predicting forecast‐error variance. Copyright © 2005 Royal Meteorological Society.

Ensemble Forecasts and the Properties of Flow-Dependent Analysis-Error Covariance Singular Vectors

Abstract Approximations to flow-dependent analysis-error covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitive-equation global model. Sets of 400-member ensembles of analyses were generated by an ensemble-based data assimilation system. A sparse network of simulated rawinsonde observations were assimilated, and a perfect model was assumed. Ensembles of 48-h forecasts were also generated from these analyses. The structure of evolved singular vectors was determined by finding the linear combination of the forecast ensemble members that resulted in the largest forecast-error variance, here measured in a total-energy norm north of 20°N latitude. The same linear combination of analyses specifies the initial-time structure that should evolve to the forecast singular vector under assumptions of linearity of error growth. The structures of these AEC SVs are important because they represent the analysis-error structures associated with the largest forecast errors. If singular vectors using other initial norms have very different structures, this indicates that these structures may be statistically unlikely to occur. The European Centre for Medium-Range Weather Forecasts currently uses singular vectors using an initial total-energy norm [“total-energy singular vectors” or (TE SVs)] to generate perturbations to initialize their ensemble forecasts. Approximate TE SVs were also calculated by drawing an initial random ensemble with perturbations that were white in total energy and applying the same approach as for AEC SVs. Comparing AEC SVs and approximate TE SVs, the AEC SVs had maximum amplitude in midlatitudes near the tropopause, both at the initial and evolved times. The AEC SVs were synoptic in scale, deep, and did not appear to be geographically localized nor tilted dramatically upshear. This contrasts with TE SVs, which started off relatively smaller in scale, were tilted upshear, and had amplitudes typically largest in the lower to midtroposphere. The difference between AEC SVs and TE SVs suggests that operational ensemble forecasts based on TE SVs could be improved by changing the type of singular vector used to generate initial perturbations. This is particularly true for short-range ensemble forecasts, where the structure of the forecast ensemble is more closely tied to the analysis ensemble.

Adaptive observations in the context of 4D-Var data assimilation

The design of adaptive observations strategies must account for the particular properties of the data assimilation method. A new adjoint sensitivity approach to the targeted observations problem is proposed in the context of four-dimensional variational data assimilation (4D-Var). The method is based on a periodic update of the adjoint sensitivity field that takes into account the interaction between time distributed adaptive and routine observations. Information provided by all previously located observations is used to identify best locations for new targeted observations. Adaptive observations at distinct instants in time are selected in a sequential manner such that the method is only suboptimal. The selection algorithm proceeds backward in time and requires only one additional adjoint model integration in the assimilation window. Therefore, the method is very efficient and is suitable for practical applications. A comparative performance analysis is presented using the traditional adjoint sensitivity method as well as the total energy singular vectors technique as alternative adaptive strategies. Numerical experiments are performed in the twin experiments framework using a two-dimensional global shallow water model in spherical coordinates and an explicit Turkel-Zwas discretization scheme. Data from a NASA 500 mb analysis valid for 00Z 16 Mar 2001 6 h obtained with the GEOS-3 model was used to specify the geopotential height at the initial time and the initial velocities were obtained from a geostrophic balance. Numerical results show that the new adaptive observations approach is a promising method for targeted observations and its implementation is feasible for large scale atmospheric models.

A comparison of ensemble‐transform Kalman‐filter targeting guidance with ECMWF and NRL total‐energy singular‐vector guidance

AbstractOngoing adaptive observing programmes strive to improve short‐ and medium‐range forecasts of winter weather over populated areas. Aircraft equipped with Global Positioning System (GPS) dropwindsondes are directed over ordinarily data‐sparse regions (oceans) to collect observations to enhance the subsequent operational analysis–forecast cycle. Two objective techniques that have been used to identify optimal ‘target regions’ are the ensemble‐transform Kalman filter (ET KF) and the singular‐vector technique. The similarities and differences between targeting guidance based on the ET KF and total‐energy singular vectors (TESVs) are assessed for ten cases during the North Pacific Experiment (NORPEX). TESVs are computed at the European Centre for Medium‐Range Weather Forecasts (ECMWF) and the Naval Research Laboratory (NRL) using their respective global models, and the ET KF uses 25 ECMWF ensemble perturbations.Using measures based on (i) rankings of aircraft flight tracks and (ii) spatial similarities between targeting guidance maps, the main finding is that (a) the ET KF guidance is reasonably correlated with TESV guidance for at least seven of the ten NORPEX cases. Other findings include: (b) the ECMWF and NRL TESV targets sometimes differ significantly, (c) the ET KF and TESV guidance maps often display different optimal locations for targeting on smaller scales, but larger‐scale aspects are usually similar, (d) the ET KF generally identifies larger regions over which useful observations can be taken compared with the SV technique, and (e) regions that are deemed effective for targeting by both techniques often correspond to baroclinic zones.The ET KF and SV techniques may identify similar regions for targeting if locations of large ensemble‐based analysis‐error variance coincide with areas where rapid perturbation growth occurs. On the other hand, they may identify different targeting locations for the following two reasons. First, the ET KF implicitly accounts for error correlation length‐scales in its predictions of forecast‐error variance reduction produced by any set of targeted observations. Hence, it can identify locations for targeted observations that are distant from the regions of high analysis sensitivity that are selected for targeting by the SV technique. Second, ET KF estimates of analysis‐error variance are constrained to a subspace of evolved ensemble perturbations and are, therefore, rank deficient. Copyright © 2002 Royal Meteorological Society

Potential improvement to forecasts of two severe storms using targeted observations

AbstractThe potential to improve short‐range forecasts of two extratropical storms by using supplementary observations in regions lacking accurate observations is investigated. In the idealized framework used here, a control and a truth experiment are selected from a set of forecasts initialized with analyses from different numerical weatherprediction centres. Synthetic soundings of wind and temperature are created from the truth experiment and are assimilated with four‐dimensional variational analysis using the operational observation‐error estimates for radiosondes and the initial condition of the control experiment as background. Through multiple analysis/forecast experiments we obtain a nonlinear estimate of the optimal zone for observing (OZO); that is the zone in which the use of a given number of supplementary observations leads to the largest reduction in forecast error. We evaluate targeting techniques based on either total‐energy singular vectors (TESVs) or on Hessian singular vectors (HSVs) by comparison with the OZO and by comparison with experiments in which the same amount of supplementary observations are distributed in an untargeted manner, namely with a random distribution scheme (RDS).Overall, the HSV targeting is superior to the TESV targeting in the two cases. In one case there is a significant difference between the target regions determined with TESVs and HSVs. The HSV‐based observing strategy resembles the OZO in terms of the observing region and the achieved forecast‐error reduction. With the RDS, the forecast error is variable and likely to be larger than the forecast error obtained with singular‐vector targeting. Experiments with target regions of different sizes show that supplementary observations in an area of about 3×106 km2 are required to achieve a significant forecast improvement. A two‐dimensional sampling pattern with soundings spaced at a distance of about 1–2 times the horizontal correlation length‐scale of the backgrounderror estimate appears very efficient. In additional impact experiments for one case, observations were perturbed with noise to represent observational error. The perturbations are almost as likely to improve the forecast as to worsen it compared with the forecast using unperturbed observations. Copyright © 2002 Royal Meteorological Society.

3D-Var Hessian singular vectors and their potential use in the ECMWF Ensemble Prediction System

Singular vectors are computed which are consistent with 3D-Var (three-dimensional variational) estimates of analysis error statistics. This is achieved by defining the norm at initial time in terms of the full Hessian of the 3D-Var cost function. At final time the total energy norm is used. the properties of these Hessian singular vectors (HSVs) differ considerably from total energy singular vectors (TESVs) in such aspects as energy spectrum and growth rate. Despite these differences, the leading 25 TESVs and HSVs explain nearly the same part of the 2-day forecast error. Two experimental ensemble configurations are studied. One configuration uses perturbations based on HSVs in the computation of initial perturbation, the other uses TESVs and 2-day linearly evolved singular vectors (ESVs) of two days before. the latter approach provides a way to include more stable and large-scale structures in the perturbations. Ten pairs of ensembles are compared to the operational European Centre for Medium-Range Weather Forecasts Ensemble Prediction System. the ensembles using ESVs perform slightly better. the ensembles based on HSVs show a slightly worse performance and are lacking some spread in the medium range. Possible directions to improve the computation of HSVs are discussed.

3D‐Var Hessian singular vectors and their potential use in the ECMWF ensemble prediction system

AbstractSingular vectors are computed which are consistent with 3D‐Var (three‐dimensional variational) estimates of analysis error statistics. This is achieved by defining the norm at initial time in terms of the full Hessian of the 3D‐Var cost function. At final time the total energy norm is used. the properties of these Hessian singular vectors (HSVs) differ considerably from total energy singular vectors (TESVs) in such aspects as energy spectrum and growth rate. Despite these differences, the leading 25 TESVs and HSVs explain nearly the same part of the 2‐day forecast error.Two experimental ensemble configurations are studied. One configuration uses perturbations based on HSVs in the computation of initial perturbation, the other uses TESVs and 2‐day linearly evolved singular vectors (ESVs) of two days before. the latter approach provides a way to include more stable and large‐scale structures in the perturbations. Ten pairs of ensembles are compared to the operational European Centre for Medium‐Range Weather Forecasts Ensemble Prediction System. the ensembles using ESVs perform slightly better. the ensembles based on HSVs show a slightly worse performance and are lacking some spread in the medium range. Possible directions to improve the computation of HSVs are discussed.