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Impacts of the Lagrangian Data Assimilation of Surface Drifters on Estimating Ocean Circulation During the Gulf of Mexico Grand Lagrangian Deployment
Monthly Weather Review
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 improves 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.
... Also altimetry can only reconstruct geostrophic velocities. As stressed by simulation and observational studies, the ageostrophic components are however critical features of upper ocean dynamics, for instance regarding vertical mixing properties (Mahadevan & Tandon, 2006) and Lagrangian dynamics at sea surface (Baaklini et al., 2021;Sun et al., 2022). ...
... Regarding the latter aspect, state-of-the-art approaches mostly rely on the one hand on optimal interpolation approaches and on the other hand on data assimilation schemes combined with ocean general circulation models (Baaklini et al., 2021;Benkiran et al., 2021;Fujii et al., 2019). As mentioned above, both approaches still show limitations in the ability to retrieve fine-scale patterns, whereas both observation-driven and theoretical studies evidence the interplay between fine-scale sea surface dynamics and some observed processes such as sea surface tracers (Ciani et al., 2021;Isern-Fontanet et al., 2006) and drifters' trajectories (Sun et al., 2022). ...
... Numerous studies (e.g., (Baaklini et al., 2021;Mahadevan & Tandon, 2006)) have evidenced the key role of ageostrophic dynamics in the mesoscale-to-submesoscale range. This has motivated a large research effort toward the exploitation of other observation sources, alone or combined with satellite altimetry, to retrieve sea surface dynamics, including among others SST (Fablet et al., 2018;Isern-Fontanet et al., 2014;Rio et al., 2016), Ocean Color (Ciani et al., 2021), sea surface drifters (Baaklini et al., 2021;Sun et al., 2022), and SAR observations (Chapron et al., 2005). From a methodological point of view, we may distinguish three main categories of approaches: optimal interpolation schemes (Cressie & Wikle, 2015;Taburet et al., 2019), data-driven approaches Manucharyan et al., 2021), and data assimilation scheme using OGCM (Benkiran et al., 2021;Fujii et al., 2019) or QG dynamical priors (Le Guillou et al., 2020;Ubelmann et al., 2014). ...
Satellite altimetry offers a unique approach for direct sea surface current observation, but it is limited to measuring the surface‐constrained geostrophic component. Ageostrophic dynamics, prevalent at horizontal scales below 100 km and time scales below 10 days, are often underestimated by ocean reanalyzes employing data assimilation schemes. To address this limitation, we introduce a novel deep learning scheme, rooted in a variational data assimilation formulation with trainable observations and a priori terms, that harnesses the synergies between satellite‐derived sea surface observations, namely sea surface height (SSH) and sea surface temperature (SST), to enhance sea surface current reconstruction. Numerical experiments, conducted using realistic simulations, in a case study area of the Gulf Stream, demonstrate the potential of the proposed scheme to capture ageostrophic dynamics at time scales of 2.5–3.0 days and horizontal scales of 0.5°–0.7°. The analysis of diverse observation configurations, encompassing nadir along‐track altimetry, wide‐swath SWOT (Surface Water and Ocean Topography) altimetry, and SST data, highlights the pivotal role of SST features in retrieving a significant portion of the ageostrophic dynamics (approximately 47%). These findings underscore the potential of deep learning and 4DVarNet schemes in improving ocean reanalyzes and enhancing our understanding of ocean dynamics.
... Inversion of sea surface currents from satellite-derived SST-SSH synergies with 4DVarNets A PREPRINT ocean general circulation models [Baaklini et al., 2021, Benkiran et al., 2021, Fujii et al., 2019. As mentionned above, both approaches still show limitations in the ability to retrieve fine-scale patterns, whereas both observation-driven and theoretical studies evidence the interplay between fine-scale sea surface dynamics and some observed processes such as sea surface tracers [Ciani et al., 2021, Isern-Fontanet et al., 2006] and drifters' trajectories [Sun et al., 2022]. ...
... Also altimetry can only reconstruct geostrophic velocities. As stressed by simulation and observational studies, the ageostrophic components are however critical features of upper ocean dynamics regarding for instance vertical mixing properties [Mahadevan and Tandon, 2006], Lagrangian dynamics at sea surface [Baaklini et al., 2021, Sun et al., 2022. ...
... Numerous studies (e.g., [Baaklini et al., 2021, Mahadevan andTandon, 2006]) have evidenced the key role of ageostrophic dynamics in the mesoscale-to-submesoscale range. This has motivated a large research effort towards the exploitation of other observation sources, alone or combined with satellite altimetry, to retrieve sea surface dynamics, including among others SST [Fablet et al., 2018, Isern-Fontanet et al., 2014, Rio et al., 2016, Ocean Colour [Ciani et al., 2021], sea surface drifters [Baaklini et al., 2021, Sun et al., 2022, and SAR observations [Chapron et al., 2005]. From a methodological point of view, we may distinguish three main categories of approaches: optimal interpolation schemes [Cressie andWikle, 2015, Taburet et al., 2019], data-driven approaches , Manucharyan et al., 2021, and data assimilation scheme using OGCM [Benkiran et al., 2021, Fujii et al., 2019 or QG dynamical priors [Le Guillou et al., 2020, Ubelmann et al., 2014. ...
Satellite altimetry is a unique way for direct observations of sea surface dynamics. This is however limited to the surface-constrained geostrophic component of sea surface velocities. Ageostrophic dynamics are however expected to be significant for horizontal scales below 100~km and time scale below 10~days. The assimilation of ocean general circulation models likely reveals only a fraction of this ageostrophic component. Here, we explore a learning-based scheme to better exploit the synergies between the observed sea surface tracers, especially sea surface height (SSH) and sea surface temperature (SST), to better inform sea surface currents. More specifically, we develop a 4DVarNet scheme which exploits a variational data assimilation formulation with trainable observations and {\em a priori} terms. An Observing System Simulation Experiment (OSSE) in a region of the Gulf Stream suggests that SST-SSH synergies could reveal sea surface velocities for time scales of 2.5-3.0 days and horizontal scales of 0.5-0.7, including a significant fraction of the ageostrophic dynamics ( 47\%). The analysis of the contribution of different observation data, namely nadir along-track altimetry, wide-swath SWOT altimetry and SST data, emphasizes the role of SST features for the reconstruction at horizontal spatial scales ranging from \nicefrac{1}{20} to \nicefrac{1}{4}.
... Due to the sparsity of the observation network, ocean surface current velocities are not routinely assimilated in global ocean forecasting systems. There have been some studies on drifter assimilation in regional systems and these largely focus on models of the Mediterranean (Nilsson et al., 2012) and the Gulf of Mexico (Fan et al., 2004, Carrier et al., 2014Sun et al., 2022;Helber et al., 2023;Smith et al., 2023). There are also studies on the assimilation of HF radar data in regional and coastal models (e.g. ...
Accurate prediction of ocean surface currents is important for marine safety, ship routing, tracking of pollutants and in coupled forecasting. Presently, velocity observations are not routinely assimilated in global ocean forecasting systems, largely due to the sparsity of the observation network. Several satellite missions are now being proposed with the capability to measure Total Surface Current Velocities (TSCV). If successful, these would substantially increase the coverage of ocean current observations and could improve accuracy of ocean current forecasts through data assimilation. In this paper, Observing System Simulation Experiments (OSSEs) are used to assess the impact of assimilating TSCV in the Met Office’s global ocean forecasting system. Synthetic observations are generated from a high-resolution model run for all standard observation types (sea surface temperature, profiles of temperature and salinity, sea level anomaly and sea ice concentration) as well as TSCV observations from a Sea surface KInematics Multiscale monitoring (SKIM) like satellite. The assimilation of SKIM like TSCV observations is tested over an 11 month period. Preliminary experiments assimilating idealised single TSCV observations demonstrate that ageostrophic velocity corrections are not well retained in the model. We propose a method for improving ageostrophic currents through TSCV assimilation by initialising Near Inertial Oscillations with a rotated incremental analysis update (IAU) scheme. The OSSEs show that TSCV assimilation has the potential to significantly improve the prediction of velocities, particularly in the Western Boundary Currents, Antarctic Circumpolar Current and in the near surface equatorial currents. For global surface velocity the analysis root-mean-square-errors (RMSEs) are reduced by 23% and there is a 4-day gain in forecast RMSE. There are some degradations to the subsurface in the tropics, generally in regions with complex vertical salinity structures. However, outside of the tropics, improvements are seen to velocities throughout the water column. Globally there are also improvements to temperature and sea surface height when TSCV are assimilated. The TSCV assimilation largely corrects the geostrophic ocean currents, but results using the rotated IAU method show that the energy at inertial frequencies can be improved with this method. Overall, the experiments demonstrate significant potential benefit of assimilating TSCV observations in a global ocean forecasting system.
... The ever-increasing availability of observation data and numerical simulations also greatly contribute to the development and evaluation of learning-based and data-driven approaches as illustrated by the considered experimental setting based on an open data challenge 5 . We could apply and extend the proposed framework to other space-time geophysical products such as ocean colour [51,44], sea surface turbidity [50,42], sea and land surface temperature [5], sea surface currents [11,41]... Future challenges also involve joint calibration and interpolation issues for future satellite missions [22] as well as multimodal synergies between satellite data and other remote sensing and in situ data sources such as drifters [45,4], underwater acoustics data [8], moored buoys [23], argo profilers [13,17]... Especially, the latter might provide new ways to better monitor the interior of the ocean which cannot be directly observed from space. Learnt non-linear SST feature maps Figure 5: Learnt SST features extracted on October 25 th 2012: we depict the maps of the learnt features extracted from the associated input 7-day SST field sequence for the best 4DVarNet schemes with multi-modal observation terms (5) using linear (top) and non-linear (bottom) operators. ...
Due to the irregular space-time sampling of sea surface observations, the reconstruction of sea surface dynamics is a challenging inverse problem. While satellite altimetry provides a direct observation of the sea surface height (SSH), which relates to the divergence-free component of sea surface currents, the associated sampling pattern prevents from retrieving fine-scale sea surface dynamics, typically below a 10-day time scale. By contrast, other satellite sensors provide higher-resolution observations of sea surface tracers such as sea surface temperature (SST). Multimodal inversion schemes then arise as an appealing strategy. Though theoretical evidence supports the existence of an explicit relationship between sea surface temperature and sea surface dynamics under specific dynamical regimes, the generalization to the variety of upper ocean dynamical regimes is complex. Here, we investigate this issue from a physics-informed learning perspective. We introduce a trainable multimodal inversion scheme for the reconstruction of sea surface dynamics from multi-source satellite-derived observations. The proposed 4DVarNet schemes combine a variational formulation involving trainable observation and a priori terms with a trainable gradient-based solver. We report an application to the reconstruction of the divergence-free component of sea surface dynamics from satellite-derived SSH and SST data. An observing system simulation experiment for a Gulf Stream region supports the relevance of our approach compared with state-of-the-art schemes. We report relative improvement greater than 50% compared with the operational altimetry product in terms of root mean square error and resolved space-time scales. We discuss further the application and extension of the proposed approach for the reconstruction and forecasting of geophysical dynamics from irregularly-sampled satellite observations.
Precise measurements of ocean surface flow velocities are essential for refining forecasts in a coupled ocean–atmosphere system. While oceanic data are generally sparse, surface drifters present an opportunity by providing detailed and frequently observed sea surface currents, which are a critical component in the dynamics at air–sea interface. Such observations could potentially address the usual data gaps in a coupled ocean–atmosphere assimilation system. In this study, we investigate the implications of assimilating drifter data within a coupled system with intermediate complexity based on a quasigeostrophic model—Modular Arbitrary-Order Ocean–Atmosphere Model (MAOOAM)—using observing system simulation experiments (OSSEs). Two main strategies for assimilating surface drifter data include the Eulerian approach, which translates Lagrangian positions into Eulerian velocity, and the fully Lagrangian method, which integrates both original fluid states and augmented drifter state variables into the system state vector. We evaluated both Lagrangian and Eulerian drifter assimilation techniques using the ensemble transform Kalman filter (ETKF) across two different coupling intensities within MAOOAM between the atmosphere and the ocean: one featuring strong interaction and the other featuring weak interaction. Our findings indicate a clear advantage of the Lagrangian method over the Eulerian, especially in estimating ocean streamfunctions and temperature. When combined with a large ensemble size and a short data assimilation (DA) window, the Lagrangian ensemble method adeptly manages atmospheric state error propagation. Additionally, as a preliminary demonstration, we evaluated a hybrid particle filter/ensemble Kalman filter (PF/EnKF) approach for Lagrangian DA in the coupled system with long DA windows, which can outperform the EnKF under specific configurations.
This study extends initial work by Sun and Penny et al. (2019, 2022) 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 summer 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, SST, 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 July 20, 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.
The space-time reconstruction of sea surface dynamics from satellite observations is a challenging inverse problem due to the associated irregular sampling. Satellite altimetry provides a direct observation of the sea surface height (SSH), which relates to the divergence-free component of sea surface currents. The associated sampling pattern prevents operational schemes from retrieving fine-scale dynamics, typically below 10 days. By contrast, other satellite sensors provide higher-resolution observations of sea surface tracers such as sea surface temperature (SST). Multimodal inversion schemes then arise as appealing approaches. Though theoretical evidence supports the existence of an explicit relationship between sea surface temperature and sea surface dynamics under specific dynamical regimes, the generalization to the variety of upper ocean dynamical regimes is complex. Here, we investigate this issue from a physics-informed learning perspective. We introduce a trainable multimodal inversion scheme for the reconstruction of sea surface dynamics from multi-source satellite-derived observations, namely satellite-derived SSH and SST data. The proposed multimodal 4DVarNet schemes combine a variational formulation involving trainable observation and
a priori
terms with a trainable gradient-based solver. An observing system simulation experiment for a Gulf Stream region supports the relevance of our approach compared with state-of-the-art schemes. We report a relative improvement greater than 60% compared with the operational altimetry product in terms of root mean square error and resolved space-time scales. We discuss further the potential and the limitations of the proposed approach for the reconstruction and forecasting of geophysical dynamics from irregularly-sampled satellite observations.
The forecast of tropical cyclone (TC) intensity is a significant challenge. In this study, we showcase the impact of strongly coupled data assimilation with hypothetical ocean currents on analyses and forecasts of Typhoon Hato (2017). Several observation simulation system experiments were undertaken with a regional coupled ocean-atmosphere model. We assimilated combinations of (or individually) a hypothetical coastal current HF radar network, a dense array of drifter floats and minimum sea-level pressure. During the assimilation, instant updates of many important atmospheric variables (winds and pressure) are achieved from the assimilation of ocean current observations using the cross-domain error covariance, significantly improving the track and intensity analysis of Typhoon Hato. As compared to a control experiment (with no assimilation), the error of minimum pressure decreased by up to 13 hPa (4 hPa / 57 % on average). The maximum wind speed error decreased by up to 18 knots (5 knots / 41 % on average). By contrast, weakly coupled implementations cannot match these reductions (10% on average). Although traditional atmospheric observations were not assimilated, such improvements indicate there is considerable potential in assimilating ocean currents from coastal HF radar, and surface drifters within a strongly coupled framework for intense landfalling TCs.
Abstract A regional‐scale fully coupled data assimilation (DA) system based on the ensemble Kalman filter is developed for a high‐resolution coupled atmosphere‐ocean model. Through the flow‐dependent covariance both within and across the oceanic and atmospheric domains, the fully coupled DA system is capable of updating both atmospheric and oceanic state variables simultaneously by assimilating either atmospheric and/or oceanic observations. The potential impacts of oceanic observations, including sea‐surface temperature, sea‐surface height anomaly, and sea‐surface current, in addition to the observation of the minimum surface pressure at the storm center (HPI), on tropical cyclone analysis and prediction are examined through observing system simulation experiments of Hurricane Florence (2018). Results show that assimilation of oceanic observations not only resulted in better analysis and forecast of the oceanic variables but also considerably reduced analysis and forecast errors in the atmospheric fields, including the intensity and structure of Florence. Compared to weakly coupled DA in which the analysis update is performed separately for the atmospheric and oceanic domains, fully coupled DA reduces the forecast errors of tropical cyclone track and intensity. Results show promise in potential further improvement in tropical cyclone prediction through assimilation of both atmospheric and oceanic observations using the ensemble‐based fully coupled DA system.
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.
Strongly coupled data assimilation (SCDA) views the Earth as one unified system. This allows observations to have an instantaneous impact across boundaries such as the air‐sea interface when estimating the state of each individual component. Operational prediction centers are moving toward Earth system modeling for all forecast timescales, ranging from days to months. However, there have been few studies that examine fundamental aspects of SCDA and the transition from traditional approaches that apply data assimilation only to a single component, whether forecasts were derived from a coupled model or an uncoupled forced model. The SCDA approach is examined here in detail using numerical experiments with a simple coupled atmosphere‐ocean quasi‐geostrophic model. The impact of coupling is explored with respect to its impact on the Lyapunov spectrum and on data assimilation system stability. Different data assimilation methods are compared within the context of SCDA, including the 3‐D and 4‐D Variational methods, the ensemble Kalman filter, and the hybrid gain method. The impact of observing system coverage is also investigated. We find that SCDA is generally superior to weakly coupled or uncoupled approaches. Dynamically defined background error covariance estimates are essential for SCDA to achieve an accurate coupled state estimate as the observing system becomes sparser. As a clarification of seemingly contradictory findings from previous studies, it is shown that ocean observations can adequately constrain atmospheric state estimates provided that the analysis‐observing frequency is sufficiently high and the ensemble size determining the background error covariance is sufficiently large.
We document the configuration and emergent simulation features from the Geophysical Fluid Dynamics Laboratory (GFDL) OM4.0 ocean/sea ice model. OM4 serves as the ocean/sea ice component for the GFDL climate and Earth system models. It is also used for climate science research and is contributing to the Coupled Model Intercomparison Project version 6 Ocean Model Intercomparison Project. The ocean component of OM4 uses version 6 of the Modular Ocean Model and the sea ice component uses version 2 of the Sea Ice Simulator, which have identical horizontal grid layouts (Arakawa C‐grid). We follow the Coordinated Ocean‐sea ice Reference Experiments protocol to assess simulation quality across a broad suite of climate‐relevant features. We present results from two versions differing by horizontal grid spacing and physical parameterizations: OM4p5 has nominal 0.5° spacing and includes mesoscale eddy parameterizations and OM4p25 has nominal 0.25° spacing with no mesoscale eddy parameterization. Modular Ocean Model version 6 makes use of a vertical Lagrangian‐remap algorithm that enables general vertical coordinates. We show that use of a hybrid depth‐isopycnal coordinate reduces the middepth ocean warming drift commonly found in pure z* vertical coordinate ocean models. To test the need for the mesoscale eddy parameterization used in OM4p5, we examine the results from a simulation that removes the eddy parameterization. The water mass structure and model drift are physically degraded relative to OM4p5, thus supporting the key role for a mesoscale closure at this resolution.
With the increasing number of data produced by numerical ocean models, so increases the need for efficient tools to analyse these data. One of these tools is Lagrangian ocean analysis, where a set of virtual particles is released and their dynamics are integrated in time based on fields defining the ocean state, including the hydrodynamics and biogeochemistry if available. This popular methodology needs to adapt to the large variety of models producing these fields at different formats.
This is precisely the aim of Parcels, a Lagrangian ocean analysis framework designed to combine (1) a wide flexibility to model particles of different natures and (2) an efficient implementation in accordance with modern computing infrastructure. In the new Parcels v2.0, we implement a set of interpolation schemes to read various types of discretized fields, from rectilinear to curvilinear grids in the horizontal direction, from z to s levels in the vertical direction and using grid staggering with the Arakawa A, B and C grids. In particular, we develop a new interpolation scheme for a three-dimensional curvilinear C grid and analyse its properties.
Parcels v2.0 capabilities, including a suite of meta-field objects, are then illustrated in a brief study of the distribution of floating microplastic in the northwest European continental shelf and its sensitivity to various physical processes.
Historical reanalyses that span more than a century are needed for a wide range of studies, from understanding large‐scale climate trends to diagnosing the impacts of individual historical extreme weather events. The Twentieth Century Reanalysis (20CR) Project is an effort to fill this need. It is supported by the National Oceanic and Atmospheric Administration (NOAA), the Cooperative Institute for Research in Environmental Sciences (CIRES), and the U.S. Department of Energy (DOE), and is facilitated by collaboration with the international Atmospheric Circulation Reconstructions over the Earth initiative. 20CR is the first ensemble of sub‐daily global atmospheric conditions spanning over 100 years. This provides a best estimate of the weather at any given place and time as well as an estimate of its confidence and uncertainty. While extremely useful, version 2c of this dataset (20CRv2c) has several significant issues, including inaccurate estimates of confidence and a global sea level pressure bias in the mid‐19th century. These and other issues can reduce its effectiveness for studies at many spatial and temporal scales. Therefore, the 20CR system underwent a series of developments to generate a significant new version of the reanalysis. The version 3 system (NOAA‐CIRES‐DOE 20CRv3) uses upgraded data assimilation methods including an adaptive inflation algorithm; has a newer, higher‐resolution forecast model that specifies dry air mass; and assimilates a larger set of pressure observations. These changes have improved the ensemble‐based estimates of confidence, removed spin‐up effects in the precipitation fields, and diminished the sea‐level pressure bias. Other improvements include more accurate representations of storm intensity, smaller errors, and large‐scale reductions in model bias. The 20CRv3 system is comprehensively reviewed, focusing on the aspects that have ameliorated issues in 20CRv2c. Despite the many improvements, some challenges remain, including a systematic bias in tropical precipitation and time‐varying biases in southern high‐latitude pressure fields.
Instrumented moorings (hereafter referred to as moorings), which are anchored buoys or an anchored configuration of instruments suspended in the water column, are highly valued for their ability to host a variety of interchangeable oceanographic and meteorological sensors. This flexibility makes them a useful technology for meeting end user and science-driven requirements. Overall, societal needs related to human health, safety, national security, and economic prosperity in coastal areas are met through the availability of continuous data from coastal moorings and other complementary observing platforms within the Earth-observing system. These data streams strengthen the quality and accuracy of data products that inform the marine transportation industry, the tourism industry, fisheries, the military, public health officials, coastal and emergency managers, educators, and research scientists, among many others. Therefore, it is critical to sustain existing observing system networks, especially during this time of extreme environmental variability and change. Existing fiscal and operational challenges affecting the sustainability of observing networks will likely continue into the next decade, threatening the quality of downstream data and information products – especially those used for long-term monitoring, planning, and decision-making. This paper describes the utility of coastal moorings as part of an integrated coastal observing system, with an emphasis on stakeholder engagement to inform observing requirements and to ensure data products are tailored to user needs. We provide 10 recommendations for optimizing moorings networks, and thus downstream data products, to guide regional planners, and network operators: 1.Develop strategies to increase investment in coastal mooring networks
2.Collect stakeholder priorities through targeted and continuous stakeholder engagements
3.Include complementary systems and emerging technologies in implementation planning activities
4.Expand and sustain water column ecosystem moorings in coastal locations
5.Coordinate with operators and data managers across geographic scales
6.Standardize and integrate data management best practices
7.Provide open access to data
8.Promote environmental health and operational safety stewardship and regulatory compliance
9.Develop coastal mooring observing network performance metrics
10.Routinely monitor and assess the design of coastal mooring networks
The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean–atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs.
The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan–Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model.
The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere–ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan–Yorke dimension and Kolmogorov–Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs.
This paper highlights the need to investigate the natural variability of the atmosphere–ocean coupled dynamics by associating rate of growth and decay of perturbations with the physical modes described using the formalism of the covariant Lyapunov vectors and considering long integrations in order to disentangle the dynamical processes occurring at all timescales.
This paper describes version 3 of the Simple Ocean Data Assimilation (SODA3) ocean reanalysis with enhancements to model resolution, observation, and forcing datasets, and the addition of active sea ice. SODA3 relies on the ocean component of the NOAA/Geophysical Fluid Dynamics Laboratory CM2.5 coupled model with nominal 1/ 4° resolution.Ascheme has also been implemented to reduce bias in the surface fluxes. A 37-yr-long ocean reanalysis, SODA3.4.2, created using this new SODA3 system is compared to the previous generation of SODA (SODA2.2.4) as well as to the Hadley Centre EN4.1.1 no-model statistical objective analysis. The comparison is carried out in the tropics, the midlatitudes, and the Arctic and includes examinations of the meridional overturning circulation in the Atlantic. The comparison shows that SODA3.4.2 has reduced systematic errors to a level comparable to those of the no-model statistical objective analysis in the upper ocean. The accuracy of variability has been improved particularly poleward of the tropics, with the greatest improvements seen in the Arctic, accompanying a substantial reduction in surface net heat and freshwater flux bias. These improvements justify increasing use of ocean reanalysis for climate studies including the higher latitudes.
Surface heat flux estimates from widely used atmospheric reanalyses differ locally by 10‐30 Wm−2 even in time mean. Here a method is presented to help identify the errors causing these differences and to reduce these errors by exploiting hydrographic observations and the resulting temperature increments produced by an ocean reanalysis. The method is applied to improve the climatological monthly net surface heat fluxes from three atmospheric reanalyses: MERRA‐2, ERA‐Interim, and JRA‐55, during an eight year test period 2007‐2014. The results show that the time mean error, as evaluated by consistency with the ocean heat budget, is reduced to less than ±5 Wm−2 over much of the subtropical and midlatitude ocean. For the global ocean, after all the corrections have been made the eight‐year mean global net surface heat imbalance has been reduced to 3.4 Wm−2. A method is also presented to quantify the uncertainty in the heat flux estimates by repeating the procedure with many different atmospheric reanalyses and then examining the resulting spread in estimates. This reevaluation of net surface flux reveals, among other results, that the Southern Ocean is a source of heat to the atmosphere. Heat exchange between the atmosphere and ocean is the primary way the ocean gains or loses heat, and thus is a key indicator of climate variability and change. Current estimates of surface heat exchange, also known as surface heat flux, are primarily based on meteorological observations and models and are uncertain. This article proposes a method to improve these estimates by exploiting additional information contained in ocean observations in an algorithm known as data assimilation. Tests of this method is shown to reduce the uncertainty of surface heat flux by up to a factor of five. Among the unexpected results is a recognition that the Southern Ocean is gaining heat, rather than losing it to the atmosphere.
Ocean currents play a key role in Earth's climate – they impact almost any process taking place in the ocean and are of major importance for navigation and human activities at sea. Nevertheless, their observation and forecasting are still difficult. First, no observing system is able to provide direct measurements of global ocean currents on synoptic scales. Consequently, it has been necessary to use sea surface height and sea surface temperature measurements and refer to dynamical frameworks to derive the velocity field. Second, the assimilation of the velocity field into numerical models of ocean circulation is difficult mainly due to lack of data. Recent experiments that assimilate coastal-based radar data have shown that ocean currents will contribute to increasing the forecast skill of surface currents, but require application in multidata assimilation approaches to better identify the thermohaline structure of the ocean. In this paper we review the current knowledge in these fields and provide a global and systematic view of the technologies to retrieve ocean velocities in the upper ocean and the available approaches to assimilate this information into ocean models.
A local particle filter (LPF) is introduced that outperforms traditional
ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in
accuracy and computational cost. The standard sampling importance resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each grid point. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights
to smooth the transition between neighboring points. Gaussian noise is
applied with magnitude equal to the local analysis spread to prevent particle
degeneracy while maintaining the estimate of the growing dynamical
instabilities. The approach is validated against the local ensemble transform
Kalman filter (LETKF) using the 40-variable Lorenz-96 (L96) model. The results show that (1) the accuracy of LPF surpasses LETKF as the forecast length
increases (thus increasing the degree of nonlinearity), (2) the cost
of LPF is significantly lower than LETKF as the ensemble size increases, and
(3) LPF prevents filter divergence experienced by LETKF in cases with
non-Gaussian observation error distributions.
A novel method for three-dimensional variational assimilation of Lagrangian data with a primitive-equation ocean model is proposed. The assimilation scheme was implemented in the Mediterranean ocean Forecasting System and evaluated for a 4-month period. Four experiments were designed to assess the impact of trajectory assimilation on the model output, i.e. the sea-surface height, velocity, temperature and salinity fields. It was found from the drifter and Argo trajectory assimilation experiment that the forecast skill of surface-drifter trajectories improved by 15 %, that of intermediate-depth float trajectories by 20 %, and moreover, that the forecasted sea-surface height fields improved locally by 5 % compared to satellite data, while the quality of the temperature and salinity fields remained at previous levels. In conclusion, the addition of Lagrangian trajectory assimilation proved to reduce the uncertainties in the model fields, thus yielding a higher accuracy of the ocean forecasts.
The Lagrangian predictability of general circulation models is limited by the need for high-resolution data streams to constrain small-scale dynamical features. Here velocity observations from Lagrangian drifters deployed in the Gulf of Mexico during the summer 2012 Grand Lagrangian Deployment (GLAD) experiment are assimilated into the Naval Coastal Ocean Model (NCOM) 4D variational (4DVAR) analysis system to examine their impact on Lagrangian predictability. NCOM-4DVAR is a weak-constraint assimilation system using the in-direct representer method. Velocities derived from drifter trajectories, as well as satellite and in-situ observations are assimilated. Lagrangian forecast skill is assessed using separation distance and angular differences between simulated and observed trajectory positions. Results show that assimilating drifter velocities substantially improves the model forecast shape and position of a Loop Current ring. These gains in mesoscale Eulerian forecast skill also improve Lagrangian forecasts, reducing the growth rate of separation distances between observed and simulated drifters by approximately 7.3 km day-1 on average, when compared with forecasts that assimilate only temperature and salinity observations. Trajectory angular differences are also reduced.
Ocean prediction systems rely on an array of assumptions to optimize their data assimilation schemes. Many of these remain untested, especially at smaller scales, because sufficiently dense observations are very rare. A set of 295 drifters deployed in July 2012 in the north-eastern Gulf of Mexico provides a unique opportunity to test these systems down to scales previously unobtainable. In this study, background error covariance assumptions in the 3DVar assimilation process are perturbed to understand the effect on the solution relative to the withheld dense drifter data. Results show that the amplitude of the background error covariance is an important factor as expected, and a proposed new formulation provides added skill. In addition, the background error covariance time correlation is important to allow satellite observations to affect the results over a period longer than one daily assimilation cycle. The results show the new background error covariance formulations provide more accurate placement of frontal positions, directions of currents and velocity magnitudes. These conclusions have implications for the implementation of 3DVar systems as well as the analysis interval of 4DVar systems.
Climate research, monitoring, prediction, and related services rely on accurate observations of the atmosphere, land, and ocean, adequately sampled globally and over sufficiently long time periods. The Global Climate Observing System, set up under the auspices of United Nations organizations and the International Council for Science to help ensure the availability of systematic observations of climate, developed the concept of essential climate variables (ECVs). ECV data records are intended to provide reliable, traceable, observation-based evidence for a range of applications, including monitoring, mitigating, adapting to, and attributing climate changes, as well as the empirical basis required to understand past, current, and possible future climate variability. The ECV concept has been broadly adopted worldwide as the guiding basis for observing climate, including by the United Nations Framework Convention on Climate Change (UNFCCC), WMO, and space agencies operating Earth observation satellites.
This paper describes the rationale for these ECVs and their current selection, based on the principles of feasibility, relevance, and cost effectiveness. It also provides a view of how the ECV concept could evolve as a guide for rational and evidence-based monitoring of climate and environment. Selected examples are discussed to highlight the benefits, limitations, and future evolution of this approach.
The article is intended to assist program managers to set priorities for climate observation, dataset generation and related research: for instance, within the emerging Global Framework for Climate Services (GFCS). It also helps the observation community and individual researchers to contribute to systematic climate observation, by promoting understanding of ECV choices and the opportunities to influence their evolution.
Significance
We report here on results obtained from the largest upper-ocean dispersion field program conducted to date. The observations provided, for the first time to our knowledge, an accurate and nearly simultaneous description of the ocean surface velocity field on spatial scales ranging from 100 m to 100 km. We show conclusively that ocean flows contain significant energy at scales below 10 km and that their fluctuations dictate the initial spread of tracer/pollutant clouds. Neither state-of-the art operational models nor satellite altimeters capture the flows needed for accurately estimating the dispersion of surface particles.
The Radar Altimeter Database System (RADS) has grown to become a mature altimeter data base. Over the last 15 years it is continuously being developed, first at Delft University of Technology, now at the National Oceanic and Atmospheric Administration (NOAA) and Altimetrics.
RADS now serves as a prototype for a fundamental Climate Data Record for sea level. Because of the mul- tiple users involved in vetting the data and the regular updates to the data base, RADS is one of the most accu- rate and complete data bases of satellite altimeter data around.
Eulerian velocity fields are derived from 300 drifters released in the Gulf of Mexico by The Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) during the summer 2012 Grand Lagrangian Deployment (GLAD) experiment. These data are directly assimilated into the Navy Coastal Ocean Model (NCOM) four-dimensional variational data assimilation (4DVAR) analysis system in a series of experiments to investigate their impact on the model circulation. The NCOM-4DVAR is a newly developed tool for data analysis, formulated for weak-constraint data assimilation based on the indirect representer method. The assimilation experiments take advantage of this velocity data along with other available data sources from in situ and satellite measurements of surface and subsurface temperature and salinity. Three different experiments are done: (i) A nonassimilative NCOM free run, (ii) an assimilative NCOM run that utilizes temperature and salinity observations, and (iii) an assimilative NCOM run that uses temperature and salinity observations as well as the GLAD velocity observations. The resulting analyses and subsequent forecasts are compared to assimilated and future GLAD velocity and temperature/salinity observations to determine the performance of each experiment and the impact of the GLAD data on the analysis and the forecast. It is shown that the NCOM-4DVAR is able to fit the observations not only in the analysis step, but also in the subsequent forecast. It is also found that the GLAD velocity data greatly improves the characterization of the circulation, with the forecast showing a better fit to future GLAD observations than those experiments without the velocity data included.
The focus of this paper is on how two main manifestations of
nonlinearity in low-dimensional systems - shear around a center fixed
point (nonlinear center) and the differential divergence of trajectories
passing by a saddle (nonlinear saddle) - strongly affect data
assimilation. The impact is felt through their leading to non-Gaussian
distribution functions. The major factors that control the strength of
these effects is time between observations, and covariance of the prior
relative to covariance of the observational noise. Both these factors -
less frequent observations and larger prior covariance - allow the
nonlinearity to take hold. To expose these nonlinear effects, we use the
comparison between exact posterior distributions conditioned on
observations and the ensemble Kalman filter (EnKF) approximation of
these posteriors. We discuss the serious limitations of the EnKF in
handling these effects.
Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given.
This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.
When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.
A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km x 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deployed in the 1000 km X 1400 km energetic western region. The base reconstruction error, achieved with full observation of the velocity field, ranges from 5% (with 191 basis functions) to 30% (with 65 basis functions). Specific analysis of the relation between spatial coverage and reconstruction error is presented using 180 drifters deployed in 100 different initial configurations that maximize coverage extremes. The simulated drifter data is projected on 107 basis functions for a 50-day period. The base reconstruction error of 15% is achieved when drifters occupy approximately 110 (out of 285) 70-km cells in the western region. Reconstructions from simulated mooring data located at the initial positions of representative good and poor coverage drifter deployments show the effect drifter dispersion has on data voids. The authors conclude that with appropriate coverage, drifter data could provide accurate basin-scale reconstruction of Eulerian velocity fields.
Drifter data from the Gulf of Mexico are used to assess and enhance the output of a primitive equation general circulation model. The analysis is made in a 450km×450km open subdomain encompassing a Loop Current ring. The model velocity field is compared with position data from four drifters at the drogue depth of 50 m using geometrical orthogonal functions (GOF). An Eulerian velocity field is reconstructed from the model velocity field and drifter velocities. This reconstructed velocity improves 8-day numerical trajectories relative to the model field by at least an order of magnitude, as quantified by two Lagrangian error metrics referenced to the real drifter paths. An Eulerian metric that compares the two fields, however, does not exceed 7% for the 20-day assessment period. Thus the drifter data may be reproduced with modest impact on the model velocity. Enhancement of the model velocity field is determined by two tests: the ability of the GOF velocity field to (1) improve the forecast of drifter positions using only a posteriori data and (2) improve the forecast of withheld drifter data. Using a posteriori data, the 20-day temporal mean of the position error is improved for all drifters by 87-89% for 6-hour and 26-38% for 30-hour forecasts. For 6 days, a withheld drifter is 35-40 km from a drifter whose velocity is used in the reconstructed velocity field. The temporal mean of the position error during this period is improved by 20% for 6-hour and 26% for 30-hour forecasts.
Because of the increases in the realism of OGCMs and in the coverage of Lagrangian datasets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications, such as environmental pollutant transport, biological, and naval-related problems.
In this study, a Lagrangian data assimilation method, which was introduced in prior studies in the context of single-layer quasigeostrophic and primitive equation models, is extended for use in multilayer OGCMs using statistical correlation coefficients between velocity fields in order to project the information from the data-containing layer to the other model layers. The efficiency of the assimilation scheme is tested using a set of twin experiments with a three-layer model, as a function of the layer in which the floats are launched and of the assimilation sampling period normalized by the Lagrangian time scale of motion.
It is found that the assimilation scheme is effective provided that the correlation coefficient between the layer that contains the data and the others is high, and the data sampling period Δt is smaller than the Lagrangian time scale TL. When the assimilated data are taken in the first layer, which is the most energetic and is characterized by the fastest time scale, the assimilation is very efficient and gives relatively low errors also in the other layers (≈ 40% in the first 120 days) provided that Δt is small enough, Δt << TL. The assimilation is also efficient for data released in the third layer (errors < 60%), while the dependence on Δt is distinctively less marked for the same range of values, since the time scales of the deeper layer are significantly longer. Results for the intermediate layer show a similar insensitivity to Δt, but the errors are higher (exceeding 70%), because of the lower correlation with the other layers. These results suggest that the assimilation of deep-layer data with low energetics can be very effective, but it is strongly dependent on layer correlation. The methodology also remains quite robust to large deviations from geostrophy.
An experiment design problem–-that of drifter cast strategy–-is discussed. Different optimization techniques used as part of preparations for the Semaphore-93 air-sea experiment, during which drifters were deployed, are examined. The oceanographic experiment objective was to sample a 500-km-square zone cantered at 33°N, 22°W in the Azores current area, using an average of 25 surface drifters for at least one month. We investigate different “orders of merit” for determining the performance of a particular cast strategy, as well as the method of genetic algorithms for optimizing the strategy. Our technique uses dynamic reference knowledge of the area where the simulation takes place. Two reference sets were used: a steady-state field calculated with data collected from the Kiel University April 1982 hydrographic experiment, and data output from a regional quasigeostrophic model assimilating two years of Geosat altimetric data. The strategies obtained via the genetic algorithm method were compared w...
Although satellites do not provide direct measurement of ocean surface currents, these currents can be indirectly inferred from satellite measurements. Such a product is regularly generated with the simultaneous use of three satellite-derived surface variables, namely sea surface height, sea surface winds and sea surface temperature. Ocean surface current has been assimilated in an Indian Ocean circulation model using the nudging technique, which involves extra surface stress acting on the ocean. This stress is the result of a difference between the satellite-derived currents and the model currents. The effect of the assimilation has been judged statistically. The impact has also been quantified in a free run following the assimilation. The assimilation has been found to exhibit a significant positive impact on the model simulation.
We consider the time-sequential state estimation of a flow field given a stream of noisy measurements that are provided by instruments advected by the flow, known as Lagrangian tracers or drifters. Lagrangian drifters collect real-time data as they move through the velocity field and are an important data collection method for atmospheric and oceanic measurements. We quantify the recovery of the Eulerian energy spectra from observations of Lagrangian drifters. This is performed by utilizing special Lagrangian data assimilation algorithms, known as conditionally Gaussian nonlinear filters. We address the following questions: how much of the turbulent Eulerian energy spectra can be recovered from assimilation of Lagrangian trajectory data and how accurately are the various energetic scales recovered relative to the truth. These issues are primarily studied in the perfect model scenario, but we quantify recovery due to model error by reduced order models via spectral truncation of the forecast model. We demonstrate high recovery skill of the two-dimensional turbulent energy spectra for both an exact filter and an imperfect filter, based on extreme localization of the covariance matrix, which is vastly cheaper than the exact filter, for both an inverse cascade spectrum with slope k−5∕3 and a direct cascade spectrum with slope k−3. The dependence of the spectral energy recovery skill on the number of tracers and the spectral truncation grid size is also studied.
A network of High-Frequency radar (HFR) stations runs operationally in the Malta-Sicily Channel (MSC), Central Mediterranean Sea, providing sea surface current maps with high temporal (1 h) and spatial (3 × 3 km) resolutions since August 2012. Comparisons with surface drifter data and near-surface Acoustic Doppler Current Profiler (ADCP) observations, as well as radar site-to-site baseline analyses, provide quantitative assessments of HFR velocities accuracy. Twenty-two drifters were deployed within the HFR domain of coverage between December 2012 and October 2013. Additionally, six ADCP vertical current profiles were collected at selected positions during a dedicated field survey. External radio-frequency interferences lead to significant gaps in the HFR coverage, which were minimized by an interpolation technique applied to the surface current fields. The validation of HFR velocities was first performed for each individual station in the network, using data generated with both the ideal and the measured antenna patterns. The validation was then repeated with pairs of HFR stations using the site-to-site baseline error analysis. The analysis confirms that the baseline error estimations and the full validation metrics for this HFR frequency band are consistent, and in some aspects superior, when compared to results from similar studies in other regions. The validation with drifter tracks suggests that the adopted interpolation procedure does not in general impact on the comparison metrics, but may introduce biases when used to extrapolate currents in regions where radar geometrical constraints are suboptimal. The analysis of the percentage of contribution of individual HFR stations shown that the quality of HFR data is influenced by the network geometry.
There are limitations in approximating Eulerian statistics from surface drifters, due to biases from surface convergences. By contrasting second- and third-order Eulerian and surface drifter structure functions obtained from a model of the Gulf of Mexico, the consequences of the semi-Lagrangian nature of observations during the summer Grand Lagrangian Deployment (GLAD) and winter Lagrangian Submesoscale Experiment (LASER) are estimated. By varying launch pattern and location, the robustness and sensitivity of these statistics are evaluated. Over scales less than 10 km, second-order structure functions of surface drifters consistently have shallower slopes (~r 2/3 ) than Eulerian statistics (~r), suggesting that surface drifter structure functions differ systematically and do not reproduce the scalings of the Eulerian fields. Medians of Eulerian and cluster release second-order statistics are also significantly different across all scales. Synthetic cluster release statistics depend on launch location and weakly on launch pattern. The observations suggest little seasonal difference in the second-order statistics, but the LASER third-order structure function shows a sign change around 1 km, whileGLADand the synthetic cluster releases show a third-order structure function sign change around 10 km. Further, synthetic surface drifter cluster releases (and therefore likely the GLAD observations) show robust biases in the negative third-order structure functions, which may lead to significant overestimation of the spectral energy flux and underestimation of the transition scale to a forward energy cascade. The Helmholtz decomposition, and curl and divergence statistics, of Eulerian and cluster releases differ, particularly on scales less than 10 km, in agreement with observations of drifters preferentially sampling convergences in coherent structures.
The recent article by Li and Toumi (2018, https://doi.org/10.1029/2018GL079677) published in Geophysical Research Letters explored the potential for improving tropical cyclone intensity forecasts by assimilating synthetic coastal surface currents from high-frequency radar observations. Although it is an idealized study using simulated observations, this may signal the beginning of a new frontier in future hurricane prediction through ingesting in situ and remotely sensed observations of oceanic currents into fully coupled systems. Assimilation of oceanic observations can improve not only the state estimation of both oceanic and atmospheric variables but it also has the potential to better estimate uncertain model physics' parameters such as the air-sea exchange coefficients.
High-frequency (HF) radars can provide high-resolution and frequent ocean surface currents observations during tropical cyclone (TC) landfall. We describe the first assimilation of such potential observations using idealized twin experiments with and without these observations. The data assimilation system consists of the Ensemble Adjustment Kalman Filter and a coupled ocean-atmosphere model. In this system, synthetic HF radar-observed coastal currents are assimilated, and the 24-, 48- and 72-hr forecast performances are examined for TCs with various intensities, sizes, and translation speeds. Assimilating coastal surface currents improves the intensity forecast. The errors of the maximum wind speed reduce by 2.7 (33%) and 1.9 m/s (60%) in the 72-hr forecast and 2.8 (40%) and 1.4 m/s (62%) in the 48-hr forecast, for Category 4 and 2 cyclones, respectively. These improvements are similar to the current operational TC forecast errors, so that assimilating HF radar observations could be a substantial benefit.
The ocean current predictability in the data limited Angola Basin was investigated using the Regional Ocean Modelling System (ROMS) with four-dimensional variational data assimilation. Six experiments were undertaken comprising a baseline case of the assimilation of salinity/temperature profiles and satellite sea surface temperature, with the subsequent addition of altimetry, OSCAR (satellite-derived sea surface currents), drifters, altimetry and drifters combined, and OSCAR and drifters combined. The addition of drifters significantly improves Lagrangian predictability in comparison to the baseline case as well as the addition of either altimetry or OSCAR. OSCAR assimilation only improves Lagrangian predictability as much as altimetry assimilation. On average the assimilation of either altimetry or OSCAR with drifter velocities does not significantly improve Lagrangian predictability compared to the drifter assimilation alone, even degrading predictability in some cases. When the forecast current speed is large, it found to be more likely that the combination improves trajectory forecasts. Conversely, when the currents are weaker, it was found to be more likely that the combination degrades the trajectory forecast.
The assimilation of surface velocity observations and their impact on the model sea surface height (SSH) is examined using an operational regional ocean model and its four-dimensional variational data assimilation (4DVAR) analysis component. In this work, drifter-derived surface velocity observations are assimilated into the Navy's Coastal Ocean Model (NCOM) 4DVAR in weak-constraint mode for a Gulf of Mexico (GoM) experiment during August-September 2012. During this period the model is trained by assimilating surface velocity observations (in a series of 96-h assimilation windows), which is followed by a 30-day forecast through the month of October 2012. A free-run model and a model that assimilates along-track SSH observations are also run as baseline experiments to which the other experiments are compared. It is shown here that the assimilation of surface velocity measurements has a substantial impact on improving the model representation of the forecast SSH on par with the experiment that assimilates along-track SSH observations directly. Finally, an assimilation experiment is done where both along-track SSH and velocity observations are utilized in an attempt to determine if the observation types are redundant or complementary. It is found that the combination of observations provides the best SSH forecast, in terms of the fit to observations, when compared to the previous experiments.
This study investigates the results of blending altimetry-based surface currents in the Gulf of Mexico with available drifter observations. Here, subsets of trajectories obtained from the near-simultaneous deployment of about 300 Coastal Ocean Dynamics Experiment (CODE) surface drifters provide both input and control data. The fidelity of surface velocity fields are measured in the Lagrangian frame by a skill score that compares the separation between observed and hindcast trajectories to the observed absolute dispersion. Trajectories estimated from altimetry-based velocities provide satisfactory average results (skill score > 0.4) in large (~100 km) open-ocean structures. However, the distribution of skill score values within these structures is quite variable. In the DeSoto Canyon and on the shelf where smaller-scale structures are present, the overall altimeter skill score is typically reduced to less than 0.2. After 3 days, the dataset-averaged distance between hindcast and drifter trajectories, D(t), is about 45 km-only slightly less than the average dispersion of the observations, D0(t) ≈ 47km. Blending information from a subset of drifters via a variational method leads to significant improvements in all dynamical regimes. Skill scores typically increase to 0.8 with D(t) reduced to less than half of D0(t). Blending available drifter information with altimetry data restores velocity field variability at scales not directly sampled by the altimeter and introduces ageostrophic components that cannot be described by simple Ekman superposition. The proposed method provides a means to improve the fidelity of near-real-time synoptic estimates of ocean surface velocity fields by combining altimetric data with modest numbers of in situ drifter observations.
To develop methodologies to maximize the information content of Lagrangian data subject to position errors, synthetic trajectories produced by both a large-eddy simulation (LES) of an idealized submesoscale flow field and a high-resolution Hybrid Coordinate Ocean Model simulation of the North Atlantic circulation are analyzed. Scale-dependent Lagrangian measures of two-particle dispersion, mainly the finitescale Lyapunov exponent [FSLE; λ(δ)], are used as metrics to determine the effects of position uncertainty on the observed dispersion regimes. It is found that the cumulative effect of position uncertainty on λ(δ) may extend to scales 20-60 times larger than the position uncertainty. The range of separation scales affected by a given level of position uncertainty depends upon the slope of the true FSLE distribution at the scale of the uncertainty. Low-pass filtering or temporal subsampling of the trajectories reduces the effective noise amplitudes at the smallest spatial scales at the expense of limiting the maximum computable value of λ. An adaptive time-filtering approach is proposed as a means of extracting the true FSLE signal from data with uncertain position measurements. Application of this filtering process to the drifters with the Argos positioning system released during the LatMix: Studies of Submesoscale Stirring and Mixing (2011) indicates that the measurement noise dominates the dispersion regime in λ for separation scales δ < 3 km. An expression is provided to estimate position errors that can be afforded depending on the expected maximum λ in the submesoscale regime.
Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean's state (velocity field, salinity field, etc.). However, trajectories from these instruments are often highly nonlinear, leading to difficulties with widely used data assimilation algorithms such as the ensemble Kalman filter (EnKF). Additionally, the velocity field is often modeled as a high-dimensional variable, which precludes the use of more accurate methods such as the particle filter (PF). Here, a hybrid particle-ensemble Kalman filter is developed that applies the EnKF update to the potentially highdimensional velocity variables, and the PF update to the relatively low-dimensional, highly nonlinear drifter position variable. This algorithm is tested with twin experiments on the linear shallow water equations. In experiments with infrequent observations, the hybrid filter consistently outperformed the EnKF, both by better capturing the Bayesian posterior and by better tracking the truth.
In ensemble Kalman filter (EnKF) data assimilation, localization modifies the error covariance matrices to suppress the influence of distant observations, removing spurious long-distance correlations. In addition to allowing efficient parallel implementation, this takes advantage of the atmosphere’s lower dimensionality in local regions. There are two primary methods for localization. In B localization, the background error covariance matrix elements are reduced by a Schur product so that correlations between grid points that are far apart are removed. In R localization, the observation error covariance matrix is multiplied by a distance-dependent function, so that far away observations are considered to have infinite error. Successful numerical weather prediction depends upon well-balanced initial conditions to avoid spurious propagation of inertial-gravity waves. Previous studies note that B localization can disrupt the relationship between the height gradient and the wind speed of the analysis increments, resulting in an analysis that can be significantly ageostrophic.
This study begins with a comparison of the accuracy and geostrophic balance of EnKF analyses using no localization, B localization, and R localization with simple one-dimensional balanced waves derived from the shallow-water equations, indicating that the optimal length scale for R localization is shorter than for B localization, and that for the same length scale R localization is more balanced. The comparison of localization techniques is then expanded to the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) global atmospheric model. Here, natural imbalance of the slow manifold must be contrasted with undesired imbalance introduced by data assimilation. Performance of the two techniques is comparable, also with a shorter optimal localization distance for R localization than for B localization.
A simultaneous assimilation model of drifting buoy and altimetric data is proposed to determine the mean sea surface height (SSH) as well as the temporal evolution of the surface circulation on synoptic scales. To demonstrate the efficiency of our assimilation model, several identical twin experiments for the double-gyre circulation system are performed using a 11/2-layer primitive equation model. An optimal interpolation for the multivariate is used for the assimilation scheme that assumes the geostrophic relationship between the error fields of the velocity and the interface depth. To identify the nature of the assimilation of the buoy-derived velocities into the dynamical ocean model, the authors first conduct the assimilation experiment using the drifting buoy data alone. The result shows that realistic buoy deployment (32 in a 40° square) can effectively constrain the model variables; that is, both the absolute (mean plus time varying) velocity and SSH (interface depth) fields are significantly improved by this buoy data assimilation. Moreover, in the case of denser buoy deployment in the energetic western boundary current regions, where the mean SSH is comparable to the time-varying part and the geoid error is relatively large, the assimilation provides a better determination of the absolute velocity and SSH. This is because significant changes in the mean SSH lead to an improvement along the extensive buoy trajectories associated with the strong current. It is worth noting that the assimilation of drifting buoy data is more effective than that of moored velocity data, thanks to the Lagrangian information content of the drifting buoys. Successive correction of the mean SSH is made with simultaneous assimilation of drifting buoy and altimetric data. Consequently, a better correction of the mean SSH is obtained: The initial error of the mean SSH is reduced by approximately 40% after the 1-year experiment. In contrast, the assimilation experiment of altimetric data alone corrects only the time-varying part, but yields little error reduction for the mean SSH in our model. These results clearly show that the simultaneous assimilation of drifting buoy and altimetric data into the dynamical model is a very useful tool for improving the model's realism.
The nonlinear process of eddy shedding is studied in the context of the Gulf of Mexico. We show that model runs which do not include eddy detachment can reproduce such an event with the assimilation of suitable data obtained from a control run with eddy detachment. This works surprisingly well and with small amounts of data provided the data originates from instruments that are carried by the flow, i.e. Lagrangian. This is compared with analogous assimilation of data from fixed stations which capture the eddy poorly. The remarkable efficacy of Lagrangian data assimilation in this context is explained by considering the structure of the correlation functions and their associated regions of influence.
Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that removes the need for any commonly used approximations. This is accomplished by augmenting the state vector of the prognostic variables with the Lagrangian drifter coordinates at assimilation. It is shown that this method is best formulated using the ensemble Kalman filter, resulting in an algorithm that is essentially transparent for assimilating Lagrangian data. The method is tested using a set of twin experiments on the shallow-water system of equations for an unsteady double-gyre flow configuration. Numerical simulations show that this method is capable of correcting the flow even if the assimilation time interval is of the order of the Lagrangian autocorrelation time scale (TL) of the flow. These results clearly demonstrate the benefits of this method over other techniques that require assimilation times of 20%-50% of TL, a direct consequence of the approximations introduced in assimilating their Lagrangian data. Detailed parametric studies show that this method is particularly effective if the classical ideas of localization developed for the ensemble Kalman filter are extended to the Lagrangian formulation used here. The method that has been developed, there- fore, provides an approach that allows one to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.
Difficulties in the assimilation of Lagrangian data arise because the state of the prognostic model is generally described in terms of Eulerian variables computed on a fixed grid in space, as a result there is no direct connection between the model variables and Lagrangian observations that carry time-integrated information. A method is presented for assimilating Lagrangian tracer positions, observed at discrete times, directly into the model. The idea is to augment the model with tracer advection equations and to track the correlations between the flow and the tracers via the extended Kalman filter. The augmented model state vector includes tracer coordinates and is updated through the correlations to the observed tracers. The technique is tested for point vortex flows: an NF point vortex system with a Gaussian noise term is modeled by its deterministic counterpart. Positions of ND tracer particles are observed at regular time intervals and assimilated into the model. Numerical experiments demonstrate successful system tracking for (NF, ND) 5 (2, 1), (4, 2), provided the observations are reasonably frequent and accurate and the system noise level is not too high. The performance of the filter strongly depends on initial tracer positions (drifter launch locations). Analysis of this dependence shows that the good launch locations are separated from the bad ones by Lagrangian flow structures (separatrices or invariant manifolds of the velocity field). The method is compared to an alternative indirect approach, where the flow velocity, estimated from two (or more) consecutive drifter observations, is assimilated directly into the model.
A new method for directly assimilating Lagrangian tracer observations for flow state estimation is presented. It is developed in the context of point vortex systems. With tracer advection equations augmenting the point vortex model, the correlations between the vortex and tracer positions allow one to use the observed tracer positions to update the non-observed vortex positions. The method works efficiently when the observations are accurate and frequent enough. Low-quality data and large intervals between observations can lead to divergence of the scheme. Nonlinear effects, responsible for the failure of the extended Kalman filter, are triggered by the exponential rate of separation of tracer trajectories in the neighbourhoods of the saddle points of the velocity field.
This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.
In this two-part paper, we present a new nonlinear method for the assimilation of Lagrangian data. In part I, we formulate the method as a generalization of other particle filters. A particularly novel feature of the formulation is the use of a hybrid discretisation of the probability density function (PDF) in physical/phase space. Moreover, we show that, under the assumption that the drifters are uncorrelated, the projection of the Fokker–Planck equation onto the observation space associated with the drifter positions reduces to a set of passive scalar equations. This property allows us to efficiently compute the transitional PDF. To compute the analysis states, we present a grid/particle filter specifically formulated for use with the hybrid representation of our PDF. In common with other particle filters, our filter can suffer from sample impoverishment. To remedy this problem, we extend the Gaussian resampling procedure of Xiong et al. to produce a very efficient filter. This produces a fully functional scheme for Lagrangian data assimilation when combined with our forecasts of the prior. Copyright © 2008 Royal Meteorological Society
Lagrangian data arise from instruments that are carried by the flow in a fluid field. Assimilation of such data into ocean models presents a challenge due to the potential complexity of Lagrangian trajectories in relatively simple flow fields. We adopt a Bayesian perspective on this problem and thereby take account of the fully non-linear features of the underlying model.In the perfect model scenario, the posterior distribution for the initial state of the system contains all the information that can be extracted from a given realization of observations and the model dynamics. We work in the smoothing context in which the posterior on the initial conditions is determined by future observations. This posterior distribution gives the optimal ensemble to be used in data assimilation. The issue then is sampling this distribution. We develop, implement, and test sampling methods, based on Markov-chain Monte Carlo (MCMC), which are particularly well suited to the low-dimensional, but highly non-linear, nature of Lagrangian data. We compare these methods to the well-established ensemble Kalman filter (EnKF) approach. It is seen that the MCMC based methods correctly sample the desired posterior distribution whereas the EnKF may fail due to infrequent observations or non-linear structures in the underlying flow.