Ensemble Kalman Filter Experiments Research Articles

Review article: Towards strongly coupled ensemble data assimilation with additional improvements from machine learning

Abstract. We assessed different coupled data assimilation strategies with a hierarchy of coupled models, ranging from a simple coupled Lorenz model to the state-of-the-art coupled general circulation model CFSv2 (Climate Forecast System version 2). With the coupled Lorenz model, we assessed the analysis accuracy by strongly coupled ensemble Kalman filter (EnKF) and 4D-Variational (4D-Var) methods with varying assimilation window lengths. The analysis accuracy of the strongly coupled EnKF with a short assimilation window is comparable to that of 4D-Var with a long assimilation window. For 4D-Var, the strongly coupled approach with the coupled model produces more accurate ocean analysis than the Estimating the Circulation and Climate of the Ocean (ECCO)-like approach using the uncoupled ocean model. Experiments with the coupled quasi-geostrophic model conclude that the strongly coupled approach outperforms the weakly coupled and uncoupled approaches for both the full-rank EnKF and 4D-Var, with the strongly coupled EnKF and 4D-Var showing a similar level of accuracy higher than other coupled data assimilation approaches such as outer-loop coupling. A strongly coupled EnKF software framework is developed and applied to the intermediate-complexity coupled model SPEEDY-NEMO and the state-of-the-art operational coupled model CFSv2. Experiments assimilating synthetic or real atmospheric observations into the ocean through strongly coupled EnKF show that the strongly coupled approach improves the analysis of the atmosphere and upper ocean but degrades observation fits in the deep ocean, probably due to the unreliable error correlation estimated by a small ensemble. The correlation-cutoff method is developed to reduce the unreliable error correlations between physically irrelevant model states and observations. Experiments with the coupled Lorenz model demonstrate that strongly coupled EnKF informed by the correlation-cutoff method produces more accurate coupled analyses than the weakly coupled and plain strongly coupled EnKF regardless of the ensemble size. To extend the correlation-cutoff method to operational coupled models, a neural network approach is proposed to systematically acquire the observation localization functions for all pairs between the model state and observation types. The following strongly coupled EnKF experiments with an intermediate-complexity coupled model show promising results with this method.

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.

Generating Observation-Based Snow Depletion Curves for Use in Snow Cover Data Assimilation

Snow depletion curves (SDC) are functions that are used to show the relationship between snow covered area and snow depth or water equivalent. Previous snow cover data assimilation (DA) studies have used theoretical SDC models as observation operators to map snow depth to snow cover fraction (SCF). In this study, a new approach is introduced that uses snow water equivalent (SWE) observations and satellite-based SCF retrievals to derive SDC relationships for use in an Ensemble Kalman filter (EnKF) to assimilate snow cover estimates. A histogram analysis is used to bin the SWE observations, which the corresponding SCF observations are then averaged within, helping to constrain the amount of data dispersion across different temporal and regional conditions. Logarithmic functions are linearly regressed with the binned average values, for two U.S. mountainous states: Colorado and Washington. The SDC-based logarithmic functions are used as EnKF observation operators, and the satellite-based SCF estimates are assimilated into a land surface model. Assimilating satellite-based SCF estimates with the observation-based SDC shows a reduction in SWE-related RMSE values compared to the model-based SDC functions. In addition, observation-based SDC functions were derived for different intra-annual and physiographic conditions, and landcover and elevation bands. Lower SWE-based RMSE values are also found with many of these categorical observation-based SDC EnKF experiments. All assimilation experiments perform better than the open-loop runs, except for the Washington region’s 2004–2005 snow season, which was a major drought year that was difficult to capture with the ensembles and observations.

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.

On the Impact of Additive Noise in Storm-Scale EnKF Experiments

Abstract Storm-scale ensemble Kalman filter (EnKF) studies routinely use methods to accelerate the spinup of convective structures when assimilating convective-scale radar observations. This typically involves adding coherent perturbations into analyses at regular intervals in regions where radar observations indicate convection is ongoing. Significant uncertainty remains as to the most effective use of these perturbations, including appropriate perturbation magnitudes, spatial scales, fields, and smoothing kernels, as well as flexible strategies that can be applied across a spectrum of convective events with negligible a priori tuning. Here, several idealized experiments were performed to elucidate the impact and sensitivity of adding coherent perturbations into storm-scale analyses of convection. Through the use of toy experiments, it is demonstrated that various factors exhibit substantial influence on the postsmoothed perturbation magnitudes, making tuning challenging. Several OSSEs were performed to document the impact of these perturbations on the analyses, particularly thermodynamic analyses within convection. The repeated addition of coherent perturbations produced temperature and moisture biases that are most pronounced in analyses of the surface cold pool and aloft near the tropopause, and eventually lead to biases in the dynamic fields. In an attempt to reduce these biases and make the noise procedure more adaptive, reflectivity innovations were used to restrict the addition of noise to areas where these innovations are large. This produced analyses with reduced thermodynamic biases and RMSE values comparable to the best-performing experiment where the noise magnitudes were manually adjusted. The impact of these findings on previous and future convective-scale EnKF analyses and forecasts are discussed.

Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

Abstract. The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetary-scale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both, over a 10-day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and stream function and velocity potential (EnKF-ψχ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone only assimilation improves winds (WEP = 46% for EnKF-uv, and 58% for EnKF-ψχ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84%) and EnKF-ψχ (81%). Assimilation of only height observations also improved the winds (WEP = 60% for EnKF-uv, and 69% for EnKF-ψχ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ~87% (~90% with NMI) for both EnKF-uv and EnKF-ψχ, demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

An Investigation of the Goshen County, Wyoming, Tornadic Supercell of 5 June 2009 Using EnKF Assimilation of Mobile Mesonet and Radar Observations Collected during VORTEX2. Part I: Experiment Design and Verification of the EnKF Analyses

Abstract High-resolution Doppler radar velocities and in situ surface observations collected in a tornadic supercell on 5 June 2009 during the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2) are assimilated into a simulated convective storm using an ensemble Kalman filter (EnKF). A series of EnKF experiments using a 1-km horizontal model grid spacing demonstrates the sensitivity of the cold pool and kinematic structure of the storm to the assimilation of these observations and to different model microphysics parameterizations. An experiment is performed using a finer grid spacing (500 m) and the most optimal data assimilation and model configurations from the sensitivity tests to produce a realistically evolving storm. Analyses from this experiment are verified against dual-Doppler and in situ observations and are evaluated for their potential to confidently evaluate mesocyclone-scale processes in the storm using trajectory analysis and calculations of Lagrangian vorticity budgets. In Part II of this study, these analyses will be further evaluated to learn the roles that mesocyclone-scale processes play in tornado formation, maintenance, and decay. The coldness of the simulated low-level outflow is generally insensitive to the choice of certain microphysical parameterizations, likely owing to the vast quantity of kinematic and in situ thermodynamic observations assimilated. The three-dimensional EnKF wind fields and parcel trajectories resemble those retrieved from dual-Doppler observations within the storm, suggesting that realistic four-dimensional mesocyclone-scale processes are captured. However, potential errors are found in trajectories and Lagrangian three-dimensional vorticity budget calculations performed within the mesocyclone that may be due to the coarse (2 min) temporal resolution of the analyses. Therefore, caution must be exercised when interpreting trajectories in this area of the storm.

The Impact of Covariance Localization for Radar Data on EnKF Analyses of a Developing MCS: Observing System Simulation Experiments

Abstract Several observing system simulation experiments (OSSEs) were performed to assess the impact of covariance localization of radar data on ensemble Kalman filter (EnKF) analyses of a developing convective system. Simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) observations were extracted from a truth simulation and assimilated into experiments with localization cutoff choices of 6, 12, and 18 km in the horizontal and 3, 6, and 12 km in the vertical. Overall, increasing the horizontal localization and decreasing the vertical localization produced analyses with the smallest RMSE for most of the state variables. The convective mode of the analyzed system had an impact on the localization results. During cell mergers, larger horizontal localization improved the results. Prior state correlations between the observations and state variables were used to construct reverse cumulative density functions (RCDFs) to identify the correlation length scales for various observation-state pairs. The OSSE with the smallest RMSE employed localization cutoff values that were similar to the horizontal and vertical length scales of the prior state correlations, especially for observation-state correlations above 0.6. Vertical correlations were restricted to state points closer to the observations than in the horizontal, as determined by the RCDFs. Further, the microphysical state variables were correlated with the reflectivity observations on smaller scales than the three-dimensional wind field and radial velocity observations. The ramifications of these findings on localization choices in convective-scale EnKF experiments that assimilate radar data are discussed.

Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

The Impact of Assimilating Surface Pressure Observations on Severe Weather Events in a WRF Mesoscale Ensemble System

Abstract Surface pressure observations are assimilated into a Weather Research and Forecast ensemble using an ensemble Kalman filter (EnKF) approach and the results are compared with observations for two severe weather events. Several EnKF experiments are performed to evaluate the relative impacts of two very different pressure observations: altimeter setting (a total pressure field) and 1-h surface pressure tendency. The primary objective of this study is to determine the surface pressure observation that is most successful in producing realistic mesoscale features, such as convectively driven cold pools, which often play an important role in future convective development. Results show that ensemble-mean pressure analyses produced from the assimilation of surface temperature, moisture, and winds possess significant errors in regard to mesohigh strength and location. The addition of surface pressure tendency observations within the assimilation yields limited ability to constrain such errors, while the assimilation of altimeter setting yields accurate depictions of the mesoscale pressure patterns associated with mesoscale convective systems. The mesoscale temperature patterns produced by all the ensembles are quite similar and tend to reproduce the observed features. Results suggest that even though surface pressure observations can have large cross covariances with temperature and the wind components, the resulting analyses fail to improve upon the EnKF temperature and wind analyses that exclude the surface pressure observations. Ensemble forecasts following the assimilation period show the potential to improve short-range forecasting of surface pressure.

4-D-Var or ensemble Kalman filter?

We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation.With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4-D-Var. For infrequent observations, when ensemble perturbations grow non-linearly and become non-Gaussian, 4-D-Var attains lower errors than EnKF. If the model is imperfect, the 4-D-Var with long windows requires weak constraint. Similar results are obtained with a quasi-geostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3-D-Var and guidance on model error and ‘observation localization’. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4-D-Var, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.

Ensemble‐based data assimilation for thermally forced circulations

The effectiveness of the ensemble Kalman filter (EnKF) for thermally forced circulations is investigated with simulated observations. A two‐dimensional, nonlinear, hydrostatic, non‐rotating, and incompressible sea breeze model is developed for this purpose with buoyancy and vorticity as the prognostic variables. Model resolution is 4 km horizontally and 50 m vertically. Forcing is maintained through an explicit heating function with additive stochastic noise. Pure forecast experiments reveal that the model exhibits moderate nonlinearity. The strongest nonlinearity occurs along the sea breeze front at the time of peak sea breeze phase. Considerable small‐scale error growth occurs at this phase for vorticity, while buoyancy is dominated by large‐scale error as the direct result of the initial condition uncertainty. In the EnKF experiments, simulated buoyancy observations (with assumed error of 10−3 ms−2) on land surface with 40‐km spacing are assimilated every 3 hours. As a result of their resolution, the observations naturally sample the larger‐scale flow structure. At the first analysis step, the filter is found to remove most of the large‐scale error resulting from the initial conditions and the domain‐averaged error of buoyancy and vorticity is reduced by about 83% and 42%, respectively. Subsequent analyses continue to remove error at a progressively slower rate and the error ultimately stabilizes within about 24 hours for both variables. At later model times, while mostly large‐scale buoyancy errors due to the stochastic heating uncertainty are effectively removed, the filter also performs well at reducing smaller‐scale vorticity errors associated with the sea breeze front. This is an indication that observations also contain useful small‐scale information relevant at the scales of frontal convergence.

Wind and Temperature Retrievals in the 17 May 1981 Arcadia, Oklahoma, Supercell: Ensemble Kalman Filter Experiments

The feasibility of using an ensemble Kalman filter (EnKF) to retrieve the wind and temperature fields in an isolated convective storm has been tested by applying the technique to observations of the 17 May 1981 Arcadia, Oklahoma, tornadic supercell. Radial-velocity and reflectivity observations from a single radar were assimilated into a nonhydrostatic, anelastic numerical model initialized with an idealized (horizontally homogeneous) base state. The assimilation results were compared to observations from another Doppler radar, the results of dual-Doppler wind syntheses, and in situ measurements from an instrumented tower. Observation errors make it more difficult to assess EnKF performance than in previous storm-scale EnKF experiments that employed synthetic observations and a perfect model; nevertheless, the comparisons in this case indicate that the locations of the main updraft and mesocyclone in the Arcadia storm were determined rather accurately, especially at midlevels. The magnitudes of vertical velocity and vertical vorticity in these features are similar to those in the dual-Doppler analyses, except that the low-level updraft is stronger in the EnKF analyses than in the dual-Doppler analyses. Several assimilation-scheme parameters are adjustable, including the method of initializing the ensemble, the inflation factor applied to perturbations, the magnitude of the assumed observation-error variance, and the degree of localization of the filter. In the Arcadia storm experiments, in which observations of a mature storm were assimilated over a relatively short (47 min) period, the results depended most on the ensemble-initialization method. In the data assimilation experiments, too much northerly storm-relative outflow along the south side of the low-level cold pool eventually developed during the assimilation period. Assimilation of Doppler observations did little to correct temperature errors near the surface in the cold pool. Both observational limitations (poor spatial resolution in the radar data near the ground) and model errors (coarse resolution and uncertainties in the parameterizations of moist processes) probably contributed to poor low-level temperature analyses in these experiments.