Operational ocean forecasting systems such as those coordinated through the OceanPredict program (OceanPredict, 2024) rely on observations. These observations are routinely combined with model information using data assimilation techniques to produce realistic initial conditions from which to launch forecasts, and to produce historical reanalyses. Ocean forecasts and reanalyses are used by many downstream users, for instance to provide information for safe and efficient marine navigation, improved search and rescue operations, modelling of oil spills, renewable energy operations and defence applications. They are also used in the context of coupled weather forecasting at short and seasonal timescales.

Since operational forecasts are reliant on accurate and timely observations (Davidson et al., 2019), it is important that the OceanPredict community demonstrates the impact of those observations to the observing community and its funders. It is also important that the OceanPredict community feeds its requirements into the design of enhancements to the ocean observing system. For these reasons, the Observing System Evaluation Task Team (OSEval-TT) was set up as part of OceanPredict (and its predecessors). The OSEval-TT has produced regular summaries of the impact of observations, for example Oke et al. (2015a); Fujii et al. (2019) and Oke et al. (2015b). As well as these overview summaries of impacts of observations, the OSEval-TT has produced Observation Impact Statements (OISs) which aim to summarise the impact of a particular observing system on operational forecasting systems. It is important that these OISs be based on evidence from multiple (at least two) forecasting systems since the impact is usually dependent on the details of the model, data assimilation and other aspects of the forecasting systems. A recent example by Martin et al. (2020) described the impact of satellite sea surface salinity data, relying largely on results from Observing System Experiments (OSEs) using the Met Office (MetO) and Mercator Ocean International (MOI) operational ocean forecasting systems. The present paper aims to provide an OIS for Total Surface Current Velocity (TSCV) data.

Ocean currents are an area of particular interest for many users. Accurate ocean currents at global scales can benefit ship routing and offshore operations, marine safety, modelling advection of nutrients and pollutants and our understanding of large-scale ocean circulation. Despite their importance, there are currently no direct observations of ocean surface currents with global coverage and the present network is inadequate for constraining the global TSCVs. Several satellites with the capability to measure TSCVs have been proposed to plug this gap in the ocean observation network, these include SKIM (Ardhuin et al., 2019), SEASTAR (Gommenginger et al., 2019), WaCM (Rodríguez et al., 2019) and ODYSEA (Torres et al., 2023). The European Space Agency Assimilation of TSCV (ESA A-TSCV¹) project has performed Observing System Simulation Experiments (OSSEs) using the MetO and MOI ocean forecasting systems to demonstrate the potential impact of assimilating satellite measurements of TSCV from a SKIM like satellite. A detailed description of those forecasting systems, the OSSEs carried out and the results showing the impact of assimilating TSCV data is provided in Waters et al. (2024) and Mirouze et al. (2024). The aim of this paper is to provide a comparison of those results and an overall summary of the likely impact satellite TSCV observations would have on operational ocean forecasts. We also provide a set of requirements for satellite TSCV observations from future missions for use within global ocean prediction systems.

The methodology and design of the experiments used in this study are described in section 2. In section 3 we will demonstrate the impact of TSCV assimilation on the surface and subsurface currents and on the temperature, salinity and sea surface height fields. We outline a set of requirements for satellite TSCV observations for global ocean prediction systems in section 4 and in section 5 we provide some overall conclusions.

The OSSEs used in the A-TSCV project assimilate synthetic observations generated from a high-resolution model run, referred to as the Nature Run (NR). Synthetic observations were generated for the standard observing systems assimilated operationally: in situ profiles of temperature and salinity, satellite along-track altimeter sea surface height (SSH) data from various platforms, satellite sea-ice concentration (SIC) data and satellite sea surface temperature (SST) data. These were generated from a 1/12^th degree NEMO 3.1 free model run with a temperature and salinity bias correction, forced using operational ECMWF atmospheric fields (Gasparin et al., 2018). The pseudo-observations have realistic sampling and error characteristics (Gasparin et al., 2019). In addition, synthetic observations of TSCV were generated from the NR using the SKIMulator tool (Gaultier and Ubelmann, 2024). The TSCV observations used in this study have a 270km wide swath and 5 km resolution in the along and across track directions. An example of the SKIM coverage for the Atlantic during a 24-hour period is shown in Figure 1 . Two versions were assimilated here: one set with only the mapping error (~3 cm/s) associated with the conversion from radial velocities to currents in the north and east directions (A-TSCV_No_err in Table 1 ); and one set which also included some of the errors associated with the SKIM instrument design (A-TSCV_Instr_err in Table 1 ). Figure 1 shows an example of the SKIM instrument errors in the Eastward and Northward direction on one day. Note that the instrument error is largest close to the nadir in the Eastward component and at the edge of swath in the Northward component, and the instrument errors are overall larger in the Eastward direction. Both the A-TSCV_No_err and A-TSCV_Instr_err experiments assimilate the standard observing systems as well as the TSCV data. The experiments performed are summarised in Table 1 and include a control experiment which assimilated the standard observing systems but no velocity observations. These were carried out for the period January to December 2009 with the assessment carried out between the 25^th of February and 30^th of December to allow the impact of TSCV assimilation to spin-up. Full details of the spin ups and other details for the various experiments are provided in Waters et al. (2024) and Mirouze et al. (2024).

A summary of the characteristics of the MetO and MOI forecasting systems used in the A-TSCV OSSEs is given in Table 2 . Both the MetO and MOI ocean forecasting systems use the NEMO 3.6 model (Madec et al., 2022) and the OSSEs carried out here were at 1/4° horizontal resolution, with a top model level representative of the upper 1 m of the ocean and were forced with ERA5 atmospheric data. The data assimilation schemes are different. The MetO system uses a multivariate incremental 3DVar-FGAT (first-guess-at-appropriate-time) scheme based on the NEMOVAR code with a one-day time window (Waters et al., 2015). Waters et al. (2024) provide a detailed description of the velocity background error covariances used in the MetO system. The background error covariances are specified by defining a field of background error standard deviations and background error correlation length-scales, where the vertical correlation scales at the surface are dependent on the locally defined mixed layer depth for that day. The MOI system uses a SEEK filter with a fixed basis (the background error covariances are estimated from the mesoscale variability in a historical model run) and has a 7-day time window (Lellouche et al., 2018). A key difference in the two systems is the representation of the multivariate balance in the background error covariances. The multivariate balances are important because they control how information from the velocities is propagated to other model variables. The MetO system uses linearized physical balances to represent the multivariate balance in the background error covariance (Weaver et al., 2005). The balanced relationships are linearized around the daily background model state (meaning they are flow dependent). Water mass conservation is used for temperature-salinity balance, hydrostatic balance is used for SSH balance and geostrophy is used for velocity balance. Meanwhile the MOI system uses multivariate balances derived from the statistics of anomalies from a historical model run. The approach used in the MOI system has the potential benefit of being able to capture multivariate correlations which are not represented by the balanced relationships used in the MetO system, for example ageostrophic velocity balances. However, they have the disadvantage of being climatological estimates and they may include spurious noise if not localized carefully. Idealised experiments where single TSCV innovations are assimilated at locations in the Gulf Stream and Equatorial Atlantic show quite different behaviours in the MetO and MOI system (see Supplementary Figures 1, 2 ). The vertical propagation of the velocity increments tends to be deeper in the MOI system and in the Equatorial Atlantic the MOI velocity increment reverses sign below 50m depth. The horizontal spread is similar in the Gulf Stream for both systems but we see larger horizontal spread in the Equatorial Atlantic for the MetO system. The magnitude of the velocity increments is larger in the MOI system mainly due to the time window differences. The differences in the structure of the velocity increments reflects differences in the background error covariances used in the two systems. As described in Table 2 , the MOI and MetO experiments used different observation thinning for the synthetic SKIM TSCV observations. The MetO system retained one in four of the observations in the along-track and across-track directions (resulting in a 20 km resolution for the thinned data), whereas the MOI system retained one in two in the across-track direction with no thinning in the along-track direction. The MOI system therefore assimilates more of the data (which are at a higher resolution than the model grid).

The OSSEs are designed to differ from the NR in order to realistically represent the differences between operational forecasting systems and the true ocean state. These differences are introduced through the different resolution, model version, forcings and initial conditions used in the OSSEs compared to the NR. Table 3 shows some summary global analysis root mean squared error (RMSE) statistics from the MetO and MOI control. These are calculated by taking the daily mean difference of the experiment to the Nature Run, calculating the spatial RMS of the differences, and averaging these throughout the assessment period. The surface and subsurface velocity errors are larger in the MetO control relative to the MOI control. This is partly related to the differences in the model set-up and in particular the wind-current coupling. Using relative winds (equivalent to a wind/current coupling coefficient of 100%) is known to dampen the mean circulation and mesoscale features, while using absolute winds (equivalent to a wind/current coupling coefficient of 0%) over-estimates the mean circulation and mesoscale features (Renault et al., 2020). The MetO system uses relative winds, while the NR uses a 50% wind/current coupling coefficient so it is likely that the MetO system will underestimate current intensity relative to the NR. The MOI system uses the parametrisation proposed by Renault et al. (2017) based on a linearization of the wind/current coupling coefficient which depends on the mean surface wind. This scheme was shown to improve the representation of the ocean - atmosphere energy transfer especially in eddy-rich regions. It is likely to simulate currents and eddies that are more similar to the NR than the MetO system. Differences in the assimilation systems, such as the assimilation time windows and treatment of multivariate balances, are also expected to produce different results in the two control experiments. This impact is seen in all variables, with the MetO control having a lower RMSE for SSH, SST and SSS relative to the MOI control, but larger RMSE for subsurface temperature. It is worth mentioning that the higher SSS RMSE in the MOI system is also partly due to a setting error that strongly decreases the precipitation flux (Mirouze et al., 2024). SST and SSH RMSE are consequently affected through their relationships with SSS. From Barbosa Aguiar et al. (2024) in the standard MetO system global SSH RMSE is 6-7 cm, SST RMSE is ~0.35°C, SSS RMSE is ~0.25 PSU. From Lellouche et al. (2023) the MOI systems global SSH RMSE is 5 cm, SST RMSE is 0.4°C and the salinity at 5 m depth is 0.36 PSU. The global 15m velocity RMSE varies between 13 cm/s and 16 cm/s for MetO and 13 cm/s and 14 cm/s for MOI (Aijaz et al., 2023). These RMSEs are all calculated relative to observations and therefore depend on the sampling of the observation network (unlike the results in Table 3 ). The impact of sampling is likely to have the largest impact on more sparsely observed quantities such as the currents and salinity, however, the RMSEs in the “real” systems are broadly consistent with the OSSE control errors. This supports the realism of the OSSE experiment design.

In this section we assess the impact of the TSCV assimilation in the two systems. Assessment is performed against the NR which is assumed to be the truth in an OSSE framework. Daily mean fields from the OSSEs and NR are used to calculate the statistics presented in this section.

In this section we provide a set of requirements for satellite TSCV observations for use with global ocean prediction systems. These are summarized in Table 6 and are based on recommendations and results from literature, input from the international community obtained at a workshop, the authors’ experiences of running operational ocean forecasting systems and the results provided from the ESA A-TSCV OSSEs.

A sampling strategy which provides observations for at least 80% of the global ocean in less than 4 to 5 days is recommended, this is equivalent to a temporal resolution of 4-5 days for most of the ocean. The MetO forced global ocean system uses a 1-day data assimilation window (see Table 2 ) while the Met Office’s coupled global ocean-atmosphere system uses an even shorter assimilation window of 6 hours (Lea et al., 2015). Systems with daily or sub-daily time windows are likely to benefit from observations with high temporal resolution. Wang et al. (2023) showed that the NIOs can be recovered from satellite TSCVs using a wide swath of at least 1800km which allows temporal sampling of less than 12 hours in the midlatitude. Improved data assimilation techniques would be required to make effective use of this high temporal information. Overall, the results from our OSSEs have demonstrated that the impact of TSCV assimilation is well retained in the forecasts. This means that longer observation revisiting time, of the order of days, can provide valuable improvements to our systems.

The recommended horizontal resolution of the satellite TSCV observations is 20 to 50 km to allow mesoscale processes to be resolved over much of the globe. The lower scale is consistent with the baseline horizontal resolution recommended for observing of the surface Ekman and geostrophic currents provided in the 2022 Global Climate Observing System essential climate variable recommendation document (GCOS, 2022).

A measurement accuracy of 10 cm/s in the along and across track direction is recommended for the TSCV observations. Villas Bôas et al. (2019) suggested that surface currents with 10 cm/s accuracy at 30 km spatial resolution and 10 day temporal resolution would significantly improve air-sea flux residuals and surface transport pathway prediction. Our recommendations are slightly more stringent, we recommend this accuracy at higher spatial/temporal resolutions. These are baseline requirements based on today’s accuracy of ocean prediction systems for the scales proposed. From our OSSE controls the accuracy of predicted surface currents varies between 10 and 13 cm/s (see Table 3 ) while Aijaz et al. (2023) showed that operational ocean forecasting systems produce global daily mean near surface (15 m) currents with an accuracy of 13 -16 cm/s when verified against drifter observation. The authors also showed that the veering angle between the model and observations is mainly within +/-15°. A 10 cm/s accuracy should ensure that TSCV observations provide valuable information when assimilated into global ocean prediction systems. The measurement accuracy is associated with a daily mean estimate, but it can also be refined regionally with larger errors associated with stronger current intensity, as found in western boundary currents and in the ACC. For comparison, the upcoming Harmony mission (Harmony, 2023) has a target accuracy of 25 cm/s at 10 km spatial resolution.

Any satellite TSCV observations should be provided within one day of measurement time in order for them to be used effectively in operational global ocean and coupled forecasting systems.

We recommend that satellite TSCV data is provided at L2b and L2c level (see Table 6 for definitions). The OSSEs performed in this study assimilated L2c TSCV data. This simplified the observation operators used in the MetO and MOI systems, but it also introduces the additional mapping error association with transforming radial velocity to North/East currents. This error is relatively small (~3 cm/s) but it does include some spatial correlations. It may be better to assimilate the lower-level L2b product, which is closer to the “raw” observations, and subsequently have less processing and less complex error characteristics compared to the L2c products. Finally, it is recommended that observation uncertainty estimates are provided with the TSCV data to allow us to accurately represent realistic observation errors within our data assimilation schemes.

The expected benefits to operational ocean forecasting of observing TSCV data from space are:

1. Improved accuracy of surface current forecasts through their assimilation, and associated improvements to the currents at depth and other model variables.

2. Improved representation of surface currents through ocean model improvements based on model-observation comparisons.

3. Improved coupled models through better representation of momentum exchanges between ocean, waves, sea-ice and atmosphere.

In the ESA A-TSCV project we have used OSSEs to assess the first of these benefits. In this paper we have summarised the results from the OSSEs performed using the MetO and MOI systems. We have shown that there is the potential to significantly improve global surface currents with TSCV assimilation. This should help to better meet the requirements of users of operational ocean forecasts, for example, search and rescue, oil spill modelling, ship navigation, offshore industry operations and better ocean, waves and sea-ice forecasts in coupled numerical weather prediction (NWP) and seasonal forecasting. In addition, we have seen improvements to the global subsurface currents down to at least 1500 m in the MetO system and 400 m in the MOI system. In the MetO system we also saw substantial improvements to global SSH, temperature and salinity prediction through TSCV assimilation.

It should be highlighted that the impacts summarised above are from idealised experiments. The 1/12^th degree NR used to simulate the observations does not contain all the processes represented by real TSCVs. Tides, Stokes drift and sub-mesoscale processes are not represented in the NR. In addition, we have attempted to represent some of the main sources of error in the model, surface forcing and observations, but it is difficult to represent all of the sources of errors in the real operational systems. The observations of TSCV from real satellite missions would be expected to have larger errors with more complex error characteristics than those used in these experiments. We have not included errors here which have significant spatial correlations since the data assimilation systems cannot currently deal properly with these types of errors, though work is underway to implement methods to represent such errors (e.g. Guillet et al., 2019).

There are some areas where improvements to the assimilation of velocity data could lead to more significant and consistent improvements in the accuracy of the operational forecasting systems if TSCV data were available. Improvements to the velocities in the MetO system away from the equator are predominantly due to corrections to the geostrophic velocities. Some preliminary work on initialising inertial oscillations has taken place (Waters et al., 2024) and further work on this could lead to improved forecasts of these high frequency ageostrophic processes. Additionally, regions such as the middle of the gyres (where we see some degradations to zonal velocity in the MetO system) could be improved by further tuning of the background and observation error covariances. Improvements in the way information from velocity is propagated to other model variables could also lead to further reductions in errors, particularly in the MOI system which saw some degradations in sub-surface temperature, salinity and velocities, even though the surface velocities were improved. The use of different control variables in the assimilation system for velocities could also lead to better control of the divergence and rotational properties of the resulting analyses which could be beneficial in terms of the impact of TSCV assimilation on vertical motions.

Finally, we have outlined a set of requirements for satellite TSCV data for use in global ocean prediction systems which should be considered in the development of future satellite missions.

The datasets presented in this article are not readily available because the data volumes prevent them being made easily available. Requests to access the datasets should be directed to jennifer.waters@metoffice.gov.uk and eremy@mercator-ocean.fr.

JW: Methodology, Validation, Writing – original draft. MM: Conceptualization, Project administration, Writing – original draft. IM: Methodology, Validation, Writing – original draft. ER: Conceptualization, Writing – original draft. RK: Data curation, Writing – review & editing. LG: Data curation, Writing – review & editing. CU: Validation, Visualization, Writing – review & editing. CD: Conceptualization, Writing – review & editing. SG: Validation, Visualization, Writing – review & editing.