Abstract

Hybrid data assimilation methods combine elements of ensemble Kalman filters (EnKF) and variational methods. While most approaches have focused on augmenting an operational variational system with dynamic error covariance information from an ensemble, this study takes the opposite perspective of augmenting an operational EnKF with information from a simple 3D variational data assimilation (3D-Var) method. A class of hybrid methods is introduced that combines the gain matrices of the ensemble and variational methods, rather than linearly combining the respective background error covariances. A hybrid local ensemble transform Kalman filter (Hybrid-LETKF) is presented in two forms: 1) a traditionally motivated Hybrid/Covariance-LETKF that combines the background error covariance matrices of LETKF and 3D-Var, and 2) a simple-to-implement algorithm called the Hybrid/Mean-LETKF that falls into the new class of hybrid gain methods. Both forms improve analysis errors when using small ensemble sizes and low observation coverage versus either LETKF or 3D-Var used alone. The results imply that for small ensemble sizes, allowing a solution to be found outside of the space spanned by ensemble members provides robustness in both hybrid methods compared to LETKF alone. Finally, the simplicity of the Hybrid/Mean-LETKF design implies that this algorithm can be applied operationally while requiring only minor modifications to an existing operational 3D-Var system.

Abstract

Four-dimensional variational (4D-Var) data assimilation (DA) is developed for a coupled atmosphere–ocean quasigeostrophic application. Complications arise in coupled data assimilation (CDA) systems due to the presence of multiple spatiotemporal scales. Various formulations of the background error covariance matrix ( $\mathsf{B}$ ), using different localization strategies, are explored to evaluate their impact on 4D-Var performance in a CDA setting. 4D-Var requires access to tangent linear and adjoint models (TLM/AM) to propagate information about the misfit between the forecast and observations within an optimization window. In practice, particularly for coupled models, the TLM and adjoint are often difficult to produce, and for some models are nonexistent in analytic form. Accordingly, a statistical data-driven alternative is also employed and evaluated to determine its feasibility for a 4D-Var CDA system. Using experiments conducted with a coupled atmosphere–ocean quasigeostrophic model, it is found that ensemble generation of flow-dependent error covariance statistics can increase the accuracy of 4D-Var CDA. When observing all variables, the hybrid climatological/flow-dependent $\mathsf{B}$ constructions outperform either independently. The use of a hybrid $\mathsf{B}$ matrix combined with a rapid updating ensemble transform Kalman filter (RU-ETKF) using either strongly or weakly CDA resulted in lower overall RMSE. The ocean component achieved its lowest RMSE when using a fully flow-dependent $\mathsf{B}$ matrix generated using 4D-ETKF and using weakly CDA. These results show the importance of time scales and analysis update frequencies. The use of a statistically derived TLM/AM generated from the ETKF ensemble perturbations produces results similar to cases using the analytical coupled TLM/AM in 4D-Var.

Abstract

The assimilation of position data from Lagrangian observing platforms is underdeveloped in operational applications because of two main challenges: 1) nonlinear growth of model and observation error in the Lagrangian trajectories, and 2) the high dimensionality of realistic models. In this study, we propose a localized Lagrangian data assimilation (LaDA) method that is based on the local ensemble transform Kalman filter (LETKF). The algorithm is tested with an “identical twin” approach in observing system simulation experiments (OSSEs) using a simple double-gyre configuration of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model. Results from the OSSEs show that with a proper choice of localization radius, the LaDA can outperform conventional assimilation of surface in situ temperature and salinity measurements. The improvements are seen not only in the surface state estimate, but also throughout the ocean column to 1000 m depth. The impacts of localization radius and model error in estimating accuracy of both fluid and drifter states are further investigated.

Abstract

Satellite-tracked in situ surface drifters, providing measurements of near-surface ocean quantities, have become increasingly prevalent in the global ocean observation system. However, the position data from these instruments are typically not leveraged in operational ocean data assimilation (DA) systems. In this work, the impact of an augmented-state Lagrangian data assimilation (LaDA) method using the local ensemble Kalman transform filter is investigated within a realistic regional ocean DA system. Direct positioning data of surface drifters released by the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment during the summer 2012 Grand Lagrangian Deployment Experiment are assimilated using a Gulf of Mexico (GoM) configuration of the Modular Ocean Model, version 6, of the Geophysical Fluid Dynamics Laboratory. Multiple cases are tested using both 1/4° eddy-permitting and 1/12° eddy-resolving model resolutions: 1) a free running model simulation, 2) a conventional assimilation of temperature and salinity profile observations, 3) an assimilation of profiles and Lagrangian surface drifter positions, and 4) an assimilation of the profiles and derived Eulerian velocities. LaDA generally produces more accurate estimates of all fields compared to the assimilation of derived Eulerian velocities, with estimates of surface currents notably improving, when transitioning to 1/12° model resolution. In particular, LaDA produces the most accurate estimates of sea surface velocities under tropical cyclone conditions when Hurricane Isaac (2012) impacted the GoM. Further experiments applying a vertical localization while assimilating surface drifter positions improve the estimates of temperature and salinity below the mixed layer depth. Cases including the surface drifter positions in the DA show better Lagrangian predictability than the conventional DA.

Abstract

This study extends recent ocean reanalysis comparisons to explore improvements to several next-generation products, the Simple Ocean Data Assimilation, version 3 (SODA3); the Estimating the Circulation and Climate of the Ocean, version 4, release 3 (ECCO4r3); and the Ocean Reanalysis System 5 (ORAS5), during their 23-yr period of overlap (1993–2015). The three reanalyses share similar historical hydrographic data, but the forcings, forward models, estimation algorithms, and bias correction methods are different. The study begins by comparing the reanalyses to independent analyses of historical SST, heat, and salt content, as well as examining the analysis-minus-observation misfits. While the misfits are generally small, they still reveal some systematic biases that are not present in the reference Hadley Center EN4 objective analysis. We next explore global trends in temperature averaged into three depth intervals: 0–300, 300–1000, and 1000–2000 m. We find considerable similarity in the spatial structure of the trends and their distribution among different ocean basins; however, the trends in global averages do differ by 30%–40%, which implies an equivalent level of disagreement in net surface heating rates. ECCO4r3 is distinct in having quite weak warming trends while ORAS5 has stronger trends that are noticeable in the deeper layers. To examine the performance of the reanalyses in the Arctic we explore representation of Atlantic Water variability on the Atlantic side of the Arctic and upper-halocline freshwater storage on the Pacific side of the Arctic. These comparisons are encouraging for the application of ocean reanalyses to track ocean climate variability and change at high northern latitudes.

Abstract

This study extends initial work by Sun and Penny and Sun et al. to explore the inclusion of path information from surface drifters using an augmented-state Lagrangian data assimilation based on the local ensemble transform Kalman filter (LETKF-LaDA) with vertical localization to improve analysis of the ocean. The region of interest is the Gulf of Mexico during the passage of Hurricane Isaac in the summer of 2012. Results from experiments with a regional ocean model at eddy-permitting and eddy-resolving model resolutions are used to quantify improvements to the analysis of sea surface velocity, sea surface temperature, and sea surface height in a data assimilation system. The data assimilation system assimilates surface drifter positions, as well as vertical profiles of temperature and salinity. Data were used from drifters deployed as a part of the Grand Lagrangian Deployment beginning 20 July 2012. Comparison of experiment results shows that at both eddy-permitting and eddy-resolving horizontal resolutions Lagrangian assimilation of drifter positions significantly improves analysis of the ocean state responding to hurricane conditions. These results, which should be applicable to other tropical oceans such as the Bay of Bengal, open new avenues for estimating ocean initial conditions to improve tropical cyclone forecasting.

Abstract

The viability of a parameterless hybrid data assimilation algorithm is investigated. As an alternative to the traditional hybrid covariance scheme, hybrid gain data assimilation (HGDA) was proposed to blend the gain matrix derived from the variational method and the ensemble-based Kalman filter (EnKF). A previously proposed HGDA algorithm uses a two-step process applying the EnKF with a variational update. The algorithm is modified here to limit the variational correction to the subspace orthogonal to the ensemble perturbation subspace without the use of a hybrid weighting parameter, as the optimization of such a parameter is nontrivial. The modified HGDA algorithm is investigated with a quasigeostrophic (QG) model. Results indicate that when the climatological background error covariance matrix $\mathsf{B}$ and the observation error covariance $\mathsf{R}$ are well estimated, state estimates from the parameterless HGDA are more accurate than the parameter-dependent HGDA. The parameterless HGDA not only has potential advantages over the standard HGDA as an online data assimilation algorithm but can also serve as a valuable diagnostic tool for tuning the $\mathsf{B}$ and $\mathsf{R}$ matrices. It is also found that in this QG model, the empirically best static $\mathsf{B}$ matrix for the stand-alone 3DVAR has high variance at larger spatial scales, which degrades the accuracy of the HGDA systems and may not be the best choice for hybrid methods in general. A comparison of defining the orthogonal subspace globally or locally demonstrates that global orthogonality is more advantageous for stabilizing the hybrid system and maintains large-scale balances.

Abstract

Artificial neural networks (ANNs) applied to nonlinear wave ensemble averaging are developed and studied for Gulf of Mexico simulations. It is an approach that expands the conservative arithmetic ensemble mean (EM) from the NCEP Global Wave Ensemble Forecast System (GWES) to a nonlinear mapping that better captures the differences among the ensemble members and reduces the systematic and scatter errors of the forecasts. The ANNs have the 20 members of the GWES as input, and outputs are trained using observations from six buoys. The variables selected for the study are the 10-m wind speed (U10), significant wave height (Hs), and peak period (Tp) for the year of 2016. ANNs were built with one hidden layer using a hyperbolic tangent basis function. Several architectures with 12 different combinations of neurons, eight different filtering windows (time domain), and 100 seeds for the random initialization were studied and constructed for specific forecast days from 0 to 10. The results show that a small number of neurons are sufficient to reduce the bias, while 35–50 neurons produce the greatest reduction in both the scatter and systematic errors. The main advantage of the methodology using ANNs is not on short-range forecasts but at longer forecast ranges beyond 4 days. The nonlinear ensemble averaging using ANNs was able to improve the correlation coefficient on forecast day 10 from 0.39 to 0.61 for U10, from 0.50 to 0.76 for Hs, and from 0.38 to 0.63 for Tp, representing a gain of five forecast days when compared to the EM currently implemented.

Abstract

The error characteristics of surface waves and winds produced by ensemble forecasts issued by the National Centers for Environmental Prediction are analyzed as a function of forecast range and severity. Eight error metrics are compared, separating the scatter component of the error from the systematic bias. Ensemble forecasts of extreme winds and extreme waves are compared to deterministic forecasts for long lead times, up to 10 days. A total of 29 metocean buoys is used to assess 1 year of forecasts (2016). The Global Wave Ensemble Forecast System (GWES) performs 10-day forecasts four times per day, with a spatial resolution of 0.5° and a temporal resolution of 3 h, using a 20-member ensemble plus a control member (deterministic) forecast. The largest errors in GWES, beyond forecast day 3, are found to be associated with winds above 14 m s⁻¹ and waves above 5 m. Extreme percentiles after the day-8 forecast reach 30% of underestimation for both 10-m-height wind (U10) and significant wave height (Hs). The comparison of probabilistic wave forecasts with deterministic runs shows an impressive improvement of predictability on the scatter component of the errors. The error for surface winds drops from 5 m s⁻¹ in the deterministic runs, associated with extreme events at longer forecast ranges, to values around 3 m s⁻¹ using the ensemble approach. As a result, GWES waves are better predicted, with a reduction in error from 2 m to less than 1.5 m for Hs. Nevertheless, under extreme conditions, critical systematic and scatter errors are identified beyond the day-6 and day-3 forecasts, respectively.

Abstract

Seasonal forecasting with a coupled model requires accurate initial conditions for the ocean. A hybrid data assimilation has been implemented within the National Centers for Environmental Prediction (NCEP) Global Ocean Data Assimilation System (GODAS) as a future replacement of the operational three-dimensional variational data assimilation (3DVar) method. This Hybrid-GODAS provides improved representation of model uncertainties by using a combination of dynamic and static background error covariances, and by using an ensemble forced by different realizations of atmospheric surface conditions. An observing system simulation experiment (OSSE) is presented spanning January 1991 to January 1999, with a bias imposed on the surface forcing conditions to emulate an imperfect model. The OSSE compares the 3DVar used by the NCEP Climate Forecast System (CFSv2) with the new hybrid, using simulated in situ ocean observations corresponding to those used for the NCEP Climate Forecast System Reanalysis (CFSR).

The Hybrid-GODAS reduces errors for all prognostic model variables over the majority of the experiment duration, both globally and regionally. Compared to an ensemble Kalman filter (EnKF) used alone, the hybrid further reduces errors in the tropical Pacific. The hybrid eliminates growth in biases of temperature and salinity present in the EnKF and 3DVar, respectively. A preliminary reanalysis using real data shows that reductions in errors and biases are qualitatively similar to the results from the OSSE. The Hybrid-GODAS is currently being implemented as the ocean component in a prototype next-generation CFSv3, and will be used in studies by the Climate Prediction Center to evaluate impacts on ENSO prediction.