Ensemble of Data Assimilations in the ocean for better exploitation of surface observations

Marcin Chrust, Magdalena A. Balmaseda, Philip Browne (all ECMWF), Matthew Martin (Met Office, UK), Andrea Storto (CMRE, Italy), Arthur Vidard (INRIA, France), Anthony Weaver (CERFACS, France), Hao Zuo (ECMWF)


Since February 2019, experts from Member State institutes have been working alongside ECMWF scientists to improve ocean model initialisation for the EU-funded Copernicus Climate Change Service (C3S). The Ensemble of data assimilations (EDA) for the Reanalysis of the Global Ocean (ERGO) project, ending in July 2021, has brought a step improvement to the ocean data assimilation capabilities at ECMWF. The EDA was originally developed by Météo-France and ECMWF for the atmospheric data assimilation system. It is used to supply information about the statistics of background errors for the initialisation of the operational ensemble and for reanalysis. Introducing the same technology for the ocean helps the assimilation of surface observations, aids reanalysis in dealing with changes in observing networks and paves the way for the development of a coupled EDA system in the future.​

Work performed. Schematic diagram of the work carried out under the C3S ERGO contract.

The ERGO project had three distinct components (see the figure showing the schematic diagram of the work performed): advancing data ​assimilation methodology by developing efficient ensemble-based background error covariance models; improving the assimilation of sea-surface height (SSH) and sea-surface temperature (SST) observations; and overarching system developments focusing on ensemble generation, statistics and diagnostics. The developments have been continuously integrated into the ECMWF repository.

Flow-dependent background error covariance modelling​

Scientists from the Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS, France) and their ECMWF colleagues have developed two different approaches for extracting information from ensembles to capture 'errors of the day' in the specification of the background error covariances.

Climatological background error covariance. A significant reduction in the standard deviation of the background temperature fit to observations is obtained when using the new seasonal climatology of background errors computed from the ORAS5 ensemble. The plots concern the period of 1 January 2010 to 31 December 2013. Similar improvements were obtained for salinity and sea-surface height (not shown).

In the first approach, an innovative estimation and filtering methodology has been developed to derive background error variances and correlation length scales from ensembles. This methodology was first applied to compute a seasonal climatology of background error statistics which, after appropriate tuning, resulted in a significant improvement of the performance of the system even without errors of the day (see the figure on climatological background error covariance). Work is ongoing to combine errors of the day with the seasonal climatology (see the figure on the EDA temperature spread) to provide more robust estimates.

A new method has been developed to compute normalisation factors to ensure that the correlation operator within the background error model has an amplitude approximately equal to one. The new method is affordable and sufficiently accurate to allow the vertical correlation length scales to be varied from cycle to cycle. This development is particularly important for the assimilation of sea-surface observations, such as SST, explored in the project.

A second approach was to use the ensemble perturbations to construct a localised sampled background error covariance matrix to account for more complex covariance structures than can be achieved with existing methods. Localisation is essential to remove spurious long-distance correlations resulting from sampling errors, but it is a costly operation. Experts from the National Institute for Research in Digital Science and Technology (Inria, France) have developed a capability to use multiple grid resolutions, allowing the localisation operator to be applied on a coarser grid and thus at a much lower cost. While the second approach still needs to mature, at some point it will complement the modelled covariance matrix with climatological parameters to provide a rich and robust representation of the background error covariances. The multi-grid capabilities are also crucial for implementation of future high-resolution EDA configurations by allowing, similarly to our atmospheric system, the minimisation to be performed at a reduced resolution compared to the forecast model.

Sea-surface observations

Researchers from the Met Office (UK) have developed a capability to assimilate level 2 SST observations in the ECMWF system, which will allow us to progressively move away from our current nudging approach. The work included implementation of a variational bias correction scheme and explored issues related to the vertical projection of the SST information into the mixed layer. Assimilation of altimeter SSH observations has also been revisited.

EDA temperature spread. Ocean temperature spread at the surface from an Ensemble of Ocean Data Assimilations. The highest background errors are in western boundary current and Antarctic Circumpolar Current regions. This shows more details than without errors of the day, including a more detailed structure of sub-mesoscale eddies with much sharper fronts, and a hint of tropical instability waves in the tropical Pacific Ocean.

A variational bias correction approach has been implemented for the online estimation of the mean-dynamic topography (MDT), which is needed as part of the observation operator for the assimilation of SSH. Such an approach has an advantage over current methodology in that it relies on an error-free prescribed MDT.

Ensemble generation

The quality of the estimates of the background error statistics from the ensemble crucially depends on its reliability. Our current ocean ensemble is generated by sampling the uncertainties in the observations and surface forcing fields according to their assumed error characteristics.

Stochastic physics. The new ocean stochastic physics schemes enhance the eddy kinetic energy at mid-latitudes in the NEMO simulations at 1/4° spatial resolution, due to the inclusion of stochastic kinetic energy backscatter. The experiments concern the period of 2010 to 2015.

To improve the reliability of the ensemble, the crucial sources of ​uncertainty arising from ocean model inaccuracies, approximations and limited spatial resolution need to be accounted for. This was achieved thanks to the work of scientists from the Centre for Maritime Research and Experimentation (CMRE, Italy) who have implemented stochastic physics parametrization schemes in the NEMO ocean model: SPP (stochastically perturbed parameters), SPPT (stochastically perturbed parametrization tendencies) and SKEB (stochastic kinetic energy backscatter). The three schemes work together to provide a larger and more realistic ensemble spread in global ocean ensemble simulations and to enhance mesoscale activity at mid-latitudes (see the figure on stochastic physics). They are now embedded in EDA experiments.

Contribution to service evolution

The developments carried out in the ERGO project will enhance the quality of service of C3S products and ECMWF operations. They will be the basis for the ocean data assimilation used in OCEAN6 and ERA6, the next generation of ocean and coupled reanalysis. OCEAN6 will be used to initialise the operational ECMWF seamless forecasts, including the future SEAS6 seasonal system, the ECMWF contribution to the C3S seasonal multi-model.

Contributions from Anass El Aouni, Gabriel Jonville, Daniel Lea, Benjamin Ménétrier, Andrea Piacentini and James While were crucial to the success of the ERGO project and are kindly acknowledged.