Ensemble Kalman Filter System Research Articles

Representing uncertainty in limited-area data assimilating ocean models

A limited-area ocean prediction system is developed to acquire forecast error covariances related to uncertainty in atmospheric forcing and turbulent mixing using perturbed model parameters within an Ensemble Kalman Filter (EnKF). The system performs sequential data assimilation delivering realistic ocean state estimation and forecasts. It is initialised to observations using the EnKF, the hybrid-EnKF and Ensemble Optimal Interpolation (EnOI). It has higher resolution than the parent global model, includes tides and assimilates altimetric sea level anomaly to constrain the offshore mesoscale circulation. Dynamic ensemble spread introduced by parameter uncertainty shows agreement with error estimates obtained from forecast innovation statistics. Hybrid EnKF offers improvements to both EnKF and EnOI, having smaller analysis increments and forecast errors. The ensemble mean of the hybrid-EnKF is more accurate than any member due to the introduction of parameterised error which behaves as additive inflation in the hybrid EnKF system. This indicates the parameterisation acts as a non-linear filter for model forecast error growth. To demonstrate consistency, experiments are carried out for various regions that differ in their oceanographic situations. The hybrid EnKF data assimilation system enables practical use of dynamic ensembles that capture the flow dependent errors which are mixed with static or climatological covariances for situations where model error is systematically under-estimated.

Improving the predictability of the Qendresa Medicane by the assimilation of conventional and atmospheric motion vector observations. Storm-scale analysis and short-range forecast

Abstract. The coastal population in the western Mediterranean Basin is frequently affected by high-impact weather events that produce huge economic and human losses. Among the wide spectrum of maritime severe weather events, tropical-like Mediterranean cyclones (a.k.a. medicanes) draw particular attention, specially due to their poor predictability. The accurate prediction of this kind of event still remains a key challenge to the weather forecast community, mainly because of (i) errors in the initial conditions, (ii) lack of accuracy of modeling micro-scale physics processes and (iii) chaotic behavior inherent to numerical weather prediction models. The 7 November 2014 Qendresa Medicane, that took place over the Sicilian channel affecting the islands of Lampedusa, Pantelleria and Malta, was selected for this study because of its extremely low predictability behavior in terms of its track and intensity. To enhance the prediction of Qendresa, a high-resolution (4 km) ensemble-based data assimilation technique, known as ensemble Kalman filter (EnKF), is used. In this study, both in situ conventional and satellite-derived observations are assimilated with the main objective of improving Qendresa's model initial conditions and thus its subsequent forecast. The performance of the EnKF system and its impact on the Qendresa forecast are quantitatively assessed using different deterministic and probabilistic verification methods. A discussion in terms of the relevant physical mechanisms adjusted by the EnKF is also provided. Results reveal that the assimilation of both conventional and satellite-derived observations improves the short-range forecasts of the trajectory and intensity of Qendresa. In this context, the relevance of assimilating satellite-derived observations to improve the pre-convective estimation of Qendresa's upper-level dynamics is shown, which is key to obtain a realistic track and intensity forecast of this event.

An ensemble Kalman filter system with the Stony Brook Parallel Ocean Model v1.0

Abstract. This study develops an ensemble Kalman filter (EnKF)-based regional ocean data assimilation system in which the local ensemble transform Kalman filter (LETKF) is implemented with version 1.0 of the Stony Brook Parallel Ocean Model (sbPOM) to assimilate satellite and in situ observations at a daily frequency. A series of sensitivity experiments are performed with various settings of the incremental analysis update (IAU) and covariance inflation methods, for which the relaxation-to-prior perturbations and spread (RTPP and RTPS, respectively) and multiplicative inflation (MULT) are considered. We evaluate the geostrophic balance and the analysis accuracy compared with the control experiment in which the IAU and covariance inflation are not applied. The results show that the IAU improves the geostrophic balance, degrades the accuracy, and reduces the ensemble spread, and that the RTPP and RTPS have the opposite effect. The experiment using a combination of the IAU and RTPP results in a significant improvement for both balance and analysis accuracy when the RTPP parameter is 0.8–0.9. The combination of the IAU and RTPS improves the balance when the RTPS parameter is ≤0.8 and increases the analysis accuracy for parameter values between 1.0 and 1.1, but the balance and analysis accuracy are not improved significantly at the same time. The experiments with MULT inflating the forecast ensemble spread by 5 % do not demonstrate sufficient skill in maintaining the balance and reproducing the surface flow field regardless of whether the IAU is applied or not. The 11 d ensemble forecast experiments show consistent results. Therefore, the combination of the IAU and RTPP with a parameter value of 0.8–0.9 is found to be the best setting for the EnKF-based ocean data assimilation system.

An Observing System Simulation Experiment (OSSE) to Study the Impact of Ocean Surface Observation from the Micro Unmanned Robot Observation Network (MURON) on Tropical Cyclone Forecast

The Micro Unmanned Robot Observation Network (MURON) is a planned in-situ observation network over the surface of West Pacific Ocean, and it is designed to sample high spatial and temporal resolution observations of wind and mass fields over the ocean surface. The impacts of MURON observations for Tropical Cyclone (TC) intensity forecast are investigated using Observation System Simulation Experiments. The regional Ensemble Kalman Filter (EnKF) system of Gridpoint Statistical Interpolation is used with the Advanced Research version of the Weather Research and Forecasting model to conduct OSSEs for typhoon Haiyan (2013) while Haiyan goes through rapid intensification. Assimilating MURON observations improves the TC structure and intensity analysis and forecast. The intensity forecast is improved largely due to the correction of initial vorticity and vertical transport of mass flux. The improvement of intensity forecast is attributed largely to the assimilated MURON wind observations when Haiyan is at the tropical disturbance stage, and then by the MURON mass observations when Haiyan enters the tropical storm stage. In addition, our results show that the quality of moisture analysis is sensitive to the choice of the moisture control variable (CV) in the EnKF system. Using the default pseudo relative humidity (PRH) as the moisture CV degrades the accuracy of the moisture analysis. This is likely due to the neglect of updated temperature field during the nonlinear conversion from the PRH CV to the mixing ratio variable and due to the larger deviation of the PRH from Gaussian distribution. The use of mixing ratio moisture CV mitigates these problems.

Integrated Hybrid Data Assimilation for an Ensemble Kalman Filter

Abstract Hybrid ensemble–variational assimilation methods that combine static and flow-dependent background error covariances have been widely applied for numerical weather predictions. The commonly used hybrid assimilation methods compute the analysis increment using a variational framework and update the ensemble perturbations by an ensemble Kalman filter (EnKF). To avoid the inconsistencies that result from performing separate variational and EnKF systems, two integrated hybrid EnKFs that update both the ensemble mean and ensemble perturbations by a hybrid background error covariance in the framework of EnKF are proposed here. The integrated hybrid EnKFs approximate the static background error covariance by use of climatological perturbations through augmentation or additive approaches. The integrated hybrid EnKFs are tested in the Lorenz05 model given different magnitudes of model errors. Results show that the static background error covariance can be sufficiently estimated by climatological perturbations with an order of hundreds. The integrated hybrid EnKFs are superior to the traditional hybrid assimilation methods, which demonstrates the benefit to update ensemble perturbations by the hybrid background error covariance. Sensitivity results reveal that the advantages of the integrated hybrid EnKFs over traditional hybrid assimilation methods are maintained with varying ensemble sizes, inflation values, and localization length scales. Significance Statement Data assimilation is critical for providing the best possible initial condition for forecast and improving the numerical weather predictions. The hybrid ensemble–variational data assimilation method has been widely adopted and developed by many operational centers. The hybrid ensemble–variational assimilation method combines the advantages of ensemble and variational methods and minimizes the weaknesses of the two methods, and thus it outperforms the stand-alone variational and ensemble assimilation methods. The hybrid ensemble–variational assimilation method often computes the control analysis using a variational solver with hybrid background error covariances, but generates the ensemble perturbations by an ensemble Kalman filter (EnKF) system with pure flow-dependent background error covariances. The inconsistencies that result from performing separate variational and EnKF systems can lead to suboptimality in the hybrid ensemble–variational assimilation method. Therefore, integrated hybrid EnKF methods that utilize the framework of an EnKF to update both the ensemble mean and ensemble perturbations by the hybrid background error covariance, are proposed. The integrated hybrid EnKFs use climatological ensemble perturbations to approximate the static background error covariance. The integrated hybrid EnKFs are superior to the traditional hybrid ensemble–variational assimilation methods by producing smaller errors, and the advantages are persistent with varying assimilation parameters.

Assimilation of X‐Band Phased‐Array Radar Data With EnKF for the Analysis and Warning Forecast of a Tornadic Storm

AbstractThe impact of assimilating China's operational X‐band Phased‐Array radar's (X‐PAR) data on the analysis and warning forecast of the vortex structure and intensity of the June 8, 2018 Foshan, Guangdong province, tornadic storm was investigated for the first time using an Ensemble Kalman Filter (EnKF) data assimilation system. Both radar radial velocity (Vr) and reflectivity (Z) from two S‐band operational radars and one X‐PAR were assimilated. Deterministic forecasts were launched every 6 min from 05:42 UTC (20 min before the tornado touched down) to 06:00 UTC from the EnKF mean analysis field. Five experiments were conducted to examine the added capability of Z assimilation of the EnKF system, and to investigate the impact of assimilating X‐PAR data on the analysis and prediction of the tornadic storm. Compared to the experiment without Z assimilation, the assimilation of Z reduced the analysis error and greatly reduced the forecast error of Z. The assimilation of X‐PAR data greatly improved the vortex structure of the tornadic storm at low levels, and improved the intensity of the rear inflow of the tornadic storm, especially with a higher assimilation frequency. Compared to the experiments without X‐PAR data assimilation, assimilating X‐PAR data improved the predictability of tornadic storm.

Evaluation of soil state representation in the NCAR ensemble analysis system

Accurate characterization of soil state is imperative for weather and climate research, hydrological modeling, agriculture, water resources management, and drought monitoring. Limited-area data assimilation (DA) systems can provide high-resolution real-time soil state analyses. However, soil state representations from regional continuously cycling DA systems have not been examined. This study evaluates soil moisture and temperature estimates and spread characteristics from a real-time, limited-area, continuously-cycling ensemble Kalman filter (EnKF) data assimilation (DA) system run at the National Center for Atmospheric Research (NCAR) for 2.7 years over the conterminous United States (CONUS). Soil moisture and temperature data from both the EnKF and operational Global Forecast System (GFS) analysis are compared against the North American Land Data Assimilation System (NLDAS-2) soil state estimates. Results demonstrate the continuously-cycling EnKF was generally able to represent the spatial and temporal characteristics of soil moisture and temperature across the CONUS, demonstrating the feasibility of using limited-area continuously cycling EnKFs as a method to improve simulations of soil moisture and temperature. Soil state estimates from the NCAR ensemble exhibited lower Bias and RMSE compared to GFS analyses over west and southeast CONUS. Additionally, the ensemble spread characteristics suggest that future limited-area continuously cycling EnKF systems could successfully assimilate both in situ and remotely-sensed soil moisture and temperature observations to further improve soil state analyses.

Use of a Genetic Algorithm to Optimize a Numerical Weather Prediction System

AbstractAn important step in an ensemble Kalman filter (EnKF) algorithm is the integration of an ensemble of short-range forecasts with a numerical weather prediction (NWP) model. A multiphysics approach is used in the Canadian global EnKF system. This paper explores whether the many integrations with different versions of the model physics can be used to obtain more accurate and more reliable probability distributions for the model parameters. Some model parameters have a continuous range of possible values. Other parameters are categorical and act as switches between different parameterizations. In an evolutionary algorithm, the member configurations that contribute most to the quality of the ensemble are duplicated, while adding a small perturbation, at the expense of configurations that perform poorly. The evolutionary algorithm is being used in the migration of the EnKF to a new version of the Canadian NWP model with upgraded physics. The quality of configurations is measured with both a deterministic and an ensemble score, using the observations assimilated in the EnKF system. When using the ensemble score in the evaluation, the algorithm is shown to be able to converge to non-Gaussian distributions. However, for several model parameters, there is not enough information to arrive at improved distributions. The optimized system features slight reductions in biases for radiance measurements that are sensitive to humidity. Modest improvements are also seen in medium-range ensemble forecasts.

Adaptive Localization for Tropical Cyclones With Satellite Radiances in an Ensemble Kalman Filter

One important aspect of successfully implementing an ensemble Kalman filter (EnKF) in a high dimensional geophysical application is covariance localization. But for satellite radiances whose vertical locations are not well defined, covariance localization is not straightforward. The global group filter (GGF) is an adaptive localization algorithm, which can provide adaptively estimated localization parameters including the localization width and vertical location of observations for each channel and every satellite platform of radiance data, and for different regions and times. This adaptive method is based on sample correlations between ensemble priors of observations and state variables, aiming to minimize sampling errors of estimated sample correlations. The adaptively estimated localization parameters are examined here for typhoon Yutu (2018), using the regional model WRF and a cycling EnKF system. The benefits of differentiating the localization parameters for tropical cyclone (TC) and non-TC regions and varying the localization parameters with time are investigated. Results from the 6-h priors verified relative to the conventional and radiance observations show that the adaptively estimated localization parameters generally produce smaller errors than the default Gaspari and Cohn (GC) localization. The adaptively estimated localization parameters better capture the onset of rapid intensification and yield improved intensity and structure forecasts for typhoon Yutu (2018) compared to the default GC localization. The time-varying localization parameters have slightly advantages over the time-constant localization parameters. Further improvements are achieved by differentiating the localization parameters for TC and non-TC regions.

Comparison of 4DVAR and EnKF state estimates and forecasts in the Gulf of Mexico

An experiment is conducted to compare four‐dimensional variational (4DVAR) and ensemble Kalman filter (EnKF) assimilation systems and their predictability in the Gulf of Mexico (GoM) using the Massachusetts Institute of Technology general circulation model (MITgcm). The quality of the ocean‐state estimates, forecasts, and the contribution of ensemble prediction are evaluated. The MITgcm–Estimating the Circulation and Climate of the Ocean (ECCO) 4DVAR (MITgcm–ECCO) and the MITgcm–Data Assimilation Research Testbed (DART) EnKF (MITgcm–DART) systems were used to compute two‐month hindcasts (March–April, 2010) by assimilating satellite‐derived along‐track sea‐surface height (SSH) and gridded sea‐surface temperature (SST) observations. The estimates from both methods at the end of the hindcast period were then used to initialize forecasts for two months (May–June, 2010). This period was selected because a loop current (LC) eddy (Eddy Franklin: Eddy‐F) detachment event occurred at the end of May 2010, immediately after the Deepwater Horizon (DwH) oil spill. Despite some differences between the setups, both systems produce analyses and forecasts of comparable quality and both solutions significantly outperformed model persistence. A reference forecast initialized from the 1/12° Hybrid Coordinate Ocean Model (HYCOM)/NCODA global analysis also performed well. The EnKF experiments for sensitivity to filter parameters showed enhanced predictability when using more ensemble members and stronger covariance localization, but not for larger inflation. The EnKF experiments varying the number of assimilation cycles showed enhanced short‐term (long‐term) predictability with fewer (more) assimilation cycles. Additional hindcast and forecast experiments at other times of significant LC evolution showed mixed performance of both systems, which depends strongly on the background state of the GoM circulation. The present work demonstrates a practical application of both assimilation methods for the GoM and compares them in a limited number of realizations. The overall conclusion showing improved short‐term (long‐term) predictability for EnKF (4DVAR) carries an important caveat that the results from this study are specific to a few 4DVAR and EnKF LC eddy separation experiments in the GoM and cannot be generalized to conclude the relative performance of both methods, especially in other applications. However, some of the concepts and methods should carry over to other applications.

Impact of surface data assimilation using an ensemble Kalman filter technique on the improvement of weather prediction

Initial condition data is known to be an important factor, which contributes to the accuracy of a weather prediction. One of an attempt to improve the initial condition is by applying data assimilation method. Ensemble Kalman Filter (EnKF) is a sophisticated data assimilation method that has shown great promise for atmospheric data assimilation in a way that the method uses flow-dependent error statistics estimated from relatively short period of prediction. Data assimilation of surface observations using an EnKF technique is evaluated for the potential improvement of a regional nonhydrostatic model. We use Weather Research and Forecasting - Advanced Research WRF (WRF-ARW) model to implement the EnKF data assimilation system.The EnKF system combined with the WRF-ARW model on a 1-km horizontal grid spacing over Karimunjawa Island is cycled over a field course period from 14-18 August 2015. The analysis ensemble is generated every 6 h by assimilating surface observations from three different locations of automatic weather stations (AWSs). By assimilating the surface observation data, the models produce colder temperature over the sea near Karimunjawa Island compare to those without assimilation process. Thus, the assimilation data give a stronger and more defined sea breeze circulation because the circulation generated by temperature difference between the sea and land.

Using the hybrid gain algorithm to sample data assimilation uncertainty

At the Canadian Meteorological Centre (CMC), an ensemble variational (EnVar) data assimilation system is used for the global deterministic prediction system and an ensemble Kalman filter (EnKF) is used for the global ensemble prediction system. These two systems are co‐developed and co‐evolving at the CMC and in this study we explore how to maximize the impact of having two algorithms.Following earlier work at the European Centre for Medium‐Range Weather Forecasts (ECMWF), we perform experiments with a pure EnKF and an EnKF system that is recentered on the EnVar solution, as well as with a hybrid gain configuration, in which the EnKF system is recentered on the mean of the EnKF and EnVar analyses. Encouraged by the results of the hybrid gain algorithm, we modify it to leave half of the members unchanged and to recenter the other half on the EnVar analysis. With this multi‐analysis approach, we sample the different design decisions made for the EnKF and EnVar and see corresponding improvements, notably for the stratospheric analysis.An evaluation using humidity‐sensitive radiance channels shows more mixed results of the hybrid gain and multi‐analysis approaches. An investigation of the spread–skill relation showed that the background ensembles were overdispersive for humidity and this issue was resolved by a reduction of the additive error for humidity. This highlights the fact that diagnostic information from two analysis systems can be used to identify where those systems have room for improvement. Finally, for various aspects of data assimilation systems, we weigh the benefits of algorithmic diversity against the corresponding additional development cost.

The impact of covariance localization on the performance of an ocean EnKF system assimilating glider data in the Ligurian Sea

Abstract Data assimilation through an ensemble Kalman filter (EnKF) is not exempt from deficiencies, including the generation of long-range unphysical correlations that degrade its performance. The covariance localization technique has been proposed and used in previous research to mitigate this effect. However, an evaluation of its performance is usually hindered by the sparseness and unsustained collection of independent observations. This article assesses the performance of an ocean prediction system composed of a multivariate EnKF coupled with a regional configuration of the Regional Ocean Model System (ROMS) with a covariance localization solution and data assimilation from an ocean glider that operated over a limited region of the Ligurian Sea. Simultaneous with the operation of the forecast system, a high-quality data set was repeatedly collected with a CTD sensor, i.e., every day during the period from 5 to 20 August 2013 (approximately 4 to 5 times the synoptic time scale of the area), located on board the NR/V Alliance for model validation. Comparisons between the validation data set and the forecasts provide evidence that the performance of the prediction system with covariance localization is superior to that observed using only EnKF assimilation without localization or using a free run ensemble. Furthermore, it is shown that covariance localization also increases the robustness of the model to the location of the assimilated data. Our analysis reveals that improvements are detected with regard to not only preventing the occurrence of spurious correlations but also preserving the spatial coherence in the updated covariance matrix. Covariance localization has been shown to be relevant in operational frameworks where short-term forecasts (on the order of days) are required.

Assimilation of Hourly Surface Observations with the Canadian High-Resolution Ensemble Kalman Filter

ABSTRACTAn hourly-cycling ensemble Kalman filter (EnKF) working at 2.5 km horizontal grid spacing is implemented over southern Ontario (Canada) to assimilate Meteorological Terminal Aviation Routine Weather Reports (METARs) in addition to the observations assimilated operationally at the Canadian Meteorological Centre. This high-resolution EnKF (HREnKF) system employs ensemble land analyses and perturbed roughness length to prevent an ensemble spread that is too small near the surface. The HREnKF then performs continuously for a four-day period, from which twelve-hour ensemble forecasts are launched every six hours. The impact on analyses and short-term forecasts of assimilating METAR data is given special attention.It is shown that using ensemble land surface analyses increases near-surface ensemble spreads for temperature and specific humidity. Perturbing roughness length enlarges the spread for surface wind. Given sufficient ensemble spread, the four-day case study shows that the near-surface model state is brought closer to surface observations during the cycling process. The impact of assimilating surface data can also be seen at higher levels by using aircraft reports for verification. The ensemble forecast verification suggests that METAR data assimilation improves ensemble forecasts of air temperature and dewpoint near the surface up to a lead time of six hours or even longer. However, only minor improvement is found in surface wind forecasts.

Examining dynamic interactions among experimental factors influencing hydrologic data assimilation with the ensemble Kalman filter

The ensemble Kalman filter (EnKF) is recognized as a powerful data assimilation technique that generates an ensemble of model variables through stochastic perturbations of forcing data and observations. However, relatively little guidance exists with regard to the proper specification of the magnitude of the perturbation and the ensemble size, posing a significant challenge in optimally implementing the EnKF. This paper presents a robust data assimilation system (RDAS), in which a multi-factorial design of the EnKF experiments is first proposed for hydrologic ensemble predictions. A multi-way analysis of variance is then used to examine potential interactions among factors affecting the EnKF experiments, achieving optimality of the RDAS with maximized performance of hydrologic predictions. The RDAS is applied to the Xiangxi River watershed which is the most representative watershed in China’s Three Gorges Reservoir region to demonstrate its validity and applicability. Results reveal that the pairwise interaction between perturbed precipitation and streamflow observations has the most significant impact on the performance of the EnKF system, and their interactions vary dynamically across different settings of the ensemble size and the evapotranspiration perturbation. In addition, the interactions among experimental factors vary greatly in magnitude and direction depending on different statistical metrics for model evaluation including the Nash–Sutcliffe efficiency and the Box–Cox transformed root-mean-square error. It is thus necessary to test various evaluation metrics in order to enhance the robustness of hydrologic prediction systems.

Verification of 24-h Quantitative Precipitation Forecasts over the Pacific Northwest from a High-Resolution Ensemble Kalman Filter System

Abstract Environment and Climate Change Canada (ECCC) has recently developed an experimental high-resolution EnKF (HREnKF) regional ensemble prediction system, which it tested over the Pacific Northwest of North America for the first half of February 2011. The HREnKF has 2.5-km horizontal grid spacing and assimilates surface and upper-air observations every hour. To determine the benefits of the HREnKF over less expensive alternatives, its 24-h quantitative precipitation forecasts are compared with those from a lower-resolution (15 km) regional ensemble Kalman filter (REnKF) system and to ensembles directly downscaled from the REnKF using the same grid as the HREnKF but with no additional data assimilation (DS). The forecasts are verified against rain gauge observations and gridded precipitation analyses, the latter of which are characterized by uncertainties of comparable magnitude to the model forecast errors. Nonetheless, both deterministic and probabilistic verification indicates robust improvements in forecast skill owing to the finer grids of the HREnKF and DS. The HREnKF exhibits a further improvement in performance over the DS in the first few forecast hours, suggesting a modest positive impact of data assimilation. However, this improvement is not statistically significant and may be attributable to other factors.

Developing a Convective-Scale EnKF Data Assimilation System for the Canadian MEOPAR Project

Abstract This study discusses the construction of a high-resolution ensemble Kalman filter system (the HREnKF) developed for the Marine Environmental Observation Prediction and Response (MEOPAR) network. The HREnKF runs at a horizontal resolution of 2.5 km and is intended to provide forecasts at lead times up to 12 h. This system was adapted from the global EnKF system in operation at Environment and Climate Change Canada. As a first development step, only the most necessary modifications have been implemented. The changes include an hourly cycling frequency, smaller localization radii, and the explicit representation of microphysical processes. To assess its performance and orient future developments, the HREnKF was continuously cycled for a period of 12 days. Verification against surface observations reveals that the skill of the forecasts initialized from the HREnKF is comparable to that of control forecasts also integrated at a resolution of 2.5 km. A key component of this study is the comparison of correlation estimated from ensembles at resolutions of 2.5, 15, and 50 km. At 2.5 km, correlation lengths are smaller than those found at 15 and 50 km. These short correlation lengths demand a high observational density, which is not available over the west coast domain where the HREnKF was tested. The spatial and temporal variability of the correlations is also assessed for the HREnKF system. It is found that correlation patterns are complex and do not generally decrease monotonically away from the reference point around which they are estimated. This result is important as it indicates that separation distance may not be the ideal parameter to use as a basis for localization strategies.

Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation

AbstractThis paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research.ContentsIntroduction...4490Popular flavors of the EnKF algorithm...4491General description...4491Stochastic and deterministic filters...4492The stochastic filter...4492The deterministic filter...4492Sequential or local filters...4493Sequential ensemble Kalman filters...4493The local ensemble transform Kalman filter...4494Extended state vector...4494Issues for the development of algorithms...4495Use of small ensembles...4495Monte Carlo methods...4495Validation of reliability...4497Use of group filters with no inbreeding...4498Sampling error due to limited ensemble size: The rank problem...4498Covariance localization...4499Localization in the sequential filter...4499Localization in the LETKF...4499Issues with localization...4500Summary...4501Methods to increase ensemble spread...4501Covariance inflation...4501Additive inflation...4501Multiplicative inflation...4502Relaxation to prior ensemble information...4502Issues with inflation...4503Diffusion and truncation...4503Error in physical parameterizations...4504Physical tendency perturbations...4504Multimodel, multiphysics, and multiparameter approaches...4505Future directions...4505Realism of error sources...4506Balance and length of the assimilation window...4506The need for balancing methods...4506Time-filtering methods...4506Toward shorter assimilation windows...4507Reduction of sources of imbalance...4507Regional data assimilation...4508Boundary conditions and consistency across multiple domains...4509Initialization of the starting ensemble...4510Preprocessing steps for radar observations...4510Use of radar observations for convective-scale analyses...4511Use of radar observations for tropical cyclone analyses...4511Other issues with respect to LAM data assimilation...4511The assimilation of satellite observations...4512Covariance localization...4512Data density...4513Bias-correction procedures...4513Impact of covariance cycling...4514Assumptions regarding observational error...4514Recommendations regarding satellite observations...4515Computational aspects...4515Parameters with an impact on quality...4515Overview of current parallel algorithms...4516Evolution of computer architecture...4516Practical issues...4517Approaching the gray zone...4518Summary...4518Hybrids with variational and EnKF components...4519Hybrid background error covariances...4519E4DVar with the α control variable...4519Not using linearized models with 4DEnVar...4520The hybrid gain algorithm...4521Open issues and recommendations...4521Summary and discussion...4521Stochastic or deterministic filters...4522The nature of system error...4522Going beyond the synoptic scales...4522Satellite observations...4523Hybrid systems...4523Future of the EnKF...4523APPENDIX A...4524Types of Filter Divergence...4524Classical filter divergence...4524Catastrophic filter divergence...4524APPENDIX B...4524Systems Available for Download...4524References...4525

Potential of sequential EnKF for the short-range prediction of a maritime severe weather event

The Western Mediterranean coastlands are persistently affected by severe phenomena related to maritime convective systems. Areas with low density of observations around highly populated regions pose serious forecasting challenges due to the risk of misrepresenting crucial structures. This forecast problem is exemplified by the squall line that affected Mallorca (Spain) on 4th October 2007. Ensemble Kalman Filter (EnKF) assimilation algorithms exploit the statistical information conveyed by ensembles and are specially suited for regions with poor knowledge about climatological error statistics and covariances. We investigate the potential for predictability improvement from the assimilation of standard observations in the squall line event. Ensemble forecasts are assessed in terms of probabilistic products which clearly bring out the differences between assimilation and control experiments. Results show the large improvements rendered by the EnKF system in terms of severe weather threat. The attribution of these improvements is discussed in terms of the environmental ingredients linked to squall line formation. Experiments reveal that forecast improvements are fully attributable to the ability of EnKF to accurately represent the convergent flow over the Alboran Sea responsible for the thunderstorm initiation. Additional sensitivity experiments are performed to confirm the hypothesised primary role of the terrestrial observations in the accurate representation of the low-level convergent flow. These experiments confirm the ability of the sequential assimilation system in conveying crucial observational information from terrestrial to marine areas, and thus bestowing the EnKF a central role in future upgrades of high impact weather prediction systems in the Western Mediterranean region.

Estimates of European uptake of CO<sub>2</sub> inferred from GOSAT X<sub>CO<sub>2</sub></sub> retrievals: sensitivity to measurement bias inside and outside Europe

Abstract. Estimates of the natural CO2 flux over Europe inferred from in situ measurements of atmospheric CO2 mole fraction have been used previously to check top-down flux estimates inferred from space-borne dry-air CO2 column (XCO2) retrievals. Several recent studies have shown that CO2 fluxes inferred from XCO2 data from the Japanese Greenhouse gases Observing SATellite (GOSAT) and the Scanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) have larger seasonal amplitudes and a more negative annual net CO2 balance than those inferred from the in situ data. The cause of this elevated European uptake of CO2 is still unclear, but some recent studies have suggested that this is a genuine scientific phenomenon. Here, we put forward an alternative hypothesis and show that realistic levels of bias in GOSAT data can result in an erroneous estimate of elevated uptake over Europe. We use a global flux inversion system to examine the relationship between measurement biases and estimates of CO2 uptake from Europe. We establish a reference in situ inversion that uses an Ensemble Kalman Filter (EnKF) to assimilate conventional surface mole fraction observations and XCO2 retrievals from the surface-based Total Carbon Column Observing Network (TCCON). We use the same EnKF system to assimilate two independent versions of GOSAT XCO2 data. We find that the GOSAT-inferred European terrestrial biosphere uptake peaks during the summer, similar to the reference inversion, but the net annual flux is 1.40 ± 0.19 GtC a−1 compared to a value of 0.58 ± 0.14 GtC a−1 for our control inversion that uses only in situ data. To reconcile these two estimates, we perform a series of numerical experiments that assimilate observations with added biases or assimilate synthetic observations for which part or all of the GOSAT XCO2 data are replaced with model data. We find that for our global flux inversions, a large portion (60–90 %) of the elevated European uptake inferred from GOSAT data in 2010 is due to retrievals outside the immediate European region, while the remainder can largely be explained by a sub-ppm retrieval bias over Europe. We use a data assimilation approach to estimate monthly GOSAT XCO2 biases from the joint assimilation of in situ observations and GOSAT XCO2 retrievals. The inferred biases represent an estimate of systematic differences between GOSAT XCO2 retrievals and the inversion system at regional or sub-regional scales. We find that a monthly varying bias of up to 0.5 ppm can explain an overestimate of the annual sink of up to 0.20 GtC a−1. Our results highlight the sensitivity of CO2 flux estimates to regional observation biases, which have not been fully characterized by the current observation network. Without further dedicated measurements we cannot prove or disprove that European ecosystems are taking up a larger-than-expected amount of CO2. More robust inversion systems are also needed to infer consistent fluxes from multiple observation types.