Observations

Observation operators

In previous applications of ROMS 4D-Var, the misfit between prior forecast and newly acquired observations, i.e. the "innovations" in DA parlance, that force the right-hand-side of the Adjoint equation appear as Dirac delta functions. That is to say, the 4D-Var observation operator merely interpolates the forecast ocean state to the position and time of the observation. This is appropriate for observations that are essentially instantaneous, such as Argo profiling floats or high-resolution (2-km scale) infrared satellite sea surface temperature.

However, many ocean observing platforms return data that have a spatial resolution much lower than the ECCOFS grid, or are effectively an average over some time interval much longer that the high frequencies that ECCOFS time stepping resolves. For such data, the model ocean state should similarly averaged so that the innovations more appropriately represent the true misfit between predicted and observed ocean conditions.

Examples of observations with explicit space and/or time averaging are:

• Satellite passive microwave radiometers (e.g. AMSR2) that observe sea surface temperature averaged over a spatial footprint with a radius of tens of kilometers

• Microwave sea surface salinity (SSS) sensors (e.g. SMAP) for which the observation is effectively an average at a spatial scale of ~40 km and are commonly further averaged in time to reduce noise.

• Land-based HF-radar ocean surface current products are compiled from radial component velocity observations made in coordinates locally centered on individual radar sites. To present vector data on a regular spatial grid, the radial data are merged by weighted least squares or optimal interpolation methods that are effectively both space and time filters.

In the case of gridded sea surface height anomaly (SSHA) products, such as the popular SSALTO/Duacs "all satellites merged” product (Copernicus Marine Service ID SEALEVEL_GLO_PHY_L4_NRT_008_046 https://doi.org/10.48670/moi-00149), combine along-track data from several altimeter satellites using optimal interpolation with explicit filtering on scales exceeding 100 km in space and 10 days in time. Furthermore, there is an implicit time filter in conventional preprocessing of the along-track data that removes variability due to tides and the high frequency barotropic ocean response to winds and air pressure (the so-called Dynamic Atmosphere Correction, or DAC). The resulting product is effectively an estimate of the slowly evolving ocean mesoscale absent tides, the inverted barometer effect, and high frequency coastal trapped waves - all dynamics that ECCOFS physics explicitly models.

To better utilize these observation types we have developed space and time averaging observations operators for ROMS 4D-Var. The change effectively appears in the forcing of the Adjoint model, wherein innovations influence the adjoint variables within a spatial radius centered on the nominal observation position, and/or over a time duration matched to the notional averaging interval of the observation.

For some data types, such as microwave SST and hourly or daily-average HF-radar vector currents, the definition of space and time averaging scales is straightforward. For others, especially SSHA, this is much less clear and demands experimention. Questions as to the appropriate choice of observation error also arise, which will in turn require further experimentation.

Observations assimilated

Table 1 shows the observations presently being assimilated in the prototype ECCOFS system. Satellite SST data are from (i) the constellation of Low Earth Orbit (LEO) infrared imagers processed into AM and PM satellite aggregations by NOAA STAR using the Advanced Clear Sky Processor for Oceans (ASCPO), (ii) the geostationary GOES ABI infrared sensor, and (ii) the AMSR2 microwave imager. Along-track satellite altimeter SSHA data is obtained from Sentinel-3b and 3b, Sentinel-6/MF, and CryoSat. In situ observations (Argo, gliders, buoys) of temperature and salinity are drawn from the Copernicus Marine Service aggregation, augmented by bottom temperatures from the northeast U.S. fishing fleet through the eMOLT program.

Observation type and platform	Source	Sampling frequency  and resolution
Infrared SST: ACSPO v2.80 L3S Dataset LEO (NOAA  JPSS/VIIRS  & METOP AVHRR)	NASA PO.DAAC DataSet IDs:  L3S_LEO_AM/PM-STAR-v2.80  ABI_G16-STAR-L3C-v2.70	0.02o (2-km); 4 per day (AM/PM  ascending and descending)
Infrared SST: GOES-16 ABI L3C SST v2.70	0.02o (2-km); hourly
Microwave SST: AMSR2 L3U v8.2	AMSR2-REMSS-L3U-v8.2	0.25o daily
SSHA: Satellite altimeters: Sentinel-3a/b, S-6/MF with coastal corrections, [Jason-3, AltiKa, CryoSat], SWOT	Radar Altimeter Database  System rads.tudelft.nl	~numerous passes per cycle;  7 km along-track
In situ T,S: Coriolis Ocean Dataset for Reanalysis (CORA) Argo, gliders, XBT, drifters, vessel CTD DataSet ID; INSITU_GLO_PHY_TS_DISCRETE_MY_013_001	Copernicus EU
eMOLT Fishing Fleet and fixed gear bottom temperatures	Comm. Fisheries Res. Found.	~ 300 obs. per week

Until evaluation and experimentation with the new observation operators is concluded, along-track altimeter SSHA data is being assimilated as instantaneous observations using the standard ROMS 4D-Var observation operator, but with repetition of the data at 30-min intervals in the 2 hours prior to and following the nominal observation time, which is a crude approximation to the correctly formulated time-average operator. The assimilation of satellite SSS data also awaits evaluation of the joint space and time averaging operators.

Prior experience with assimilation of hourly HF-radar vectors currents has shown relatively little impact of these observations on analysis skill. We have attributed this to the signal at high frequencies being dominated by tides and the immediate response to winds, which ROMS captures well already due to the careful configuration of grid, coastline and bathymetry, and the accurate high-resolution meteorological forcing from NWS products. Where we anticipate HF-radar currents can offer new information to the 4D-Var state estimate is in the subinertial frequency weather band with timescales longer than 1 day out to 3 days, which are unconstrained by altimetry. The plan for ECCOFS HR-radar DA is to preprocess the hourly HRFnet total currents into 24-hour or 36-hour averages at their native 6-km resolution and assimilate with the time-average operator. This is a topic of active experimentation by the ECCOFS team.

The typical number of observations available for assimilation is shown in Figure 7. The left panel shows satellite altimeter tracks and in situ observations locations (principally Argo profiling floats) during a 3-day interval centered on July 6, 2025. The center panel is the number of observations per day in the entire ECCOFS domain for satellite SSHA and SST, and in situ temperature and salinity. The right panel indicates the number of in situ observations per month aggregated by depth. These are dominated by Argo profiles to 2000 m, but augmented by a substantial volume of glider data in the upper water column (note the log scale for observation count).