Ocean heat content estimation from altimetry and in-situ fusion
Sea-surface height anomaly from radar altimetry, fused with Argo float temperature profiles, constrains depth-integrated ocean heat content through the steric sea-level relationship. The method underpins Earth energy imbalance assessments but carries real uncertainty below 2000 m and in mesoscale-active boundary currents.
Sensors
- Jason-3 / Sentinel-6 Michael Freilich: Dual-frequency Ku/C-band radar altimeters measuring sea-surface height to roughly 2–3 cm single-pass precision along 1-Hz ground tracks (~7 km along-track). Jason-3 and Sentinel-6 fly in a coordinated tandem, together providing a 10-day exact-repeat cycle on the reference ground track, the backbone of the continuous sea-level anomaly record since 1992.
- SWOT (NASA/CNES, launched 2022): Ka-band radar interferometer resolving two-dimensional sea-surface height at roughly 1 km spatial resolution and a 21-day repeat. SWOT's wide-swath coverage (120 km, excluding a 20 km nadir gap) resolves mesoscale and sub-mesoscale eddies that classic nadir altimeters alias, improving steric decomposition in boundary-current regions.
- CryoSat-2 (ESA): Ku-band SAR/interferometric radar altimeter with a 369-day exact-repeat and a 30-day sub-cycle. Its drifting ground track provides denser spatial sampling than the Jason reference track, helping constrain the mesoscale covariance structure used in optimal interpolation of altimetric anomalies.
- Argo float network (in-situ reference): Approximately 4000 active profiling floats globally, each cycling to 2000 m every 10 days and transmitting temperature and salinity profiles via satellite. Core Argo covers 0–2000 m; Deep Argo floats, numbering in the hundreds, extend profiles to 6000 m. Spatial density is roughly one float per 3° × 3° cell, with sparser coverage in the Southern Ocean and marginal seas.
What a floating roof gives away
Water expands when it warms. That expansion lifts the sea surface by a measurable amount, and radar altimeters have been reading that signal continuously since TOPEX/Poseidon in 1992. The thermosteric contribution to sea-level change is the dominant signal at interannual to decadal timescales: a 1 °C warming of the upper 700 m across a 100 m layer raises the surface by roughly 1–2 mm, depending on the background temperature. Halosteric effects, driven by salinity change, are smaller globally but locally significant, particularly in the Arctic and in regions affected by ice-melt runoff.
The steric sea-level anomaly is not the whole story. Total sea-level change also includes mass addition from ice sheets and glaciers, and from terrestrial water storage. Separating steric from mass contributions requires either a gravimetric satellite (GRACE-FO covers that ground, handled on a sibling page) or a statistical model. The altimetry-plus-Argo approach avoids that ambiguity by using the Argo profiles to anchor the steric signal directly, treating altimetry as a spatially dense constraint on the covariance structure between surface height and subsurface heat.
The statistical machinery behind sparse profiles
Argo's 10-day, 3° × 3° sampling is adequate for basin-scale heat budgets but misses mesoscale eddies with length scales of 50–300 km. Altimetry provides the spatial detail; Argo provides the vertical structure. The fusion works through optimal interpolation (or its Bayesian equivalents): the altimetric sea-level anomaly field, which is observed nearly everywhere, is used as a covariate to extrapolate the sparse Argo profiles to unsampled locations. The covariance between surface height and subsurface temperature at each depth is estimated empirically from collocated altimeter-Argo pairs, then applied globally.
The method has a well-documented name in the literature: regression-based or EOF-based synthetic profiles, sometimes called altimetry-constrained Argo mapping. Published implementations include the ISAS (In Situ Analysis System) from Ifremer and the EN4 dataset from the UK Met Office. The skill of the approach degrades in two situations: boundary currents such as the Gulf Stream and Kuroshio, where the height-temperature covariance is non-stationary and eddy-induced heave dominates; and in the deep ocean below 2000 m, where Argo coverage is sparse and the steric signal is small but not negligible over decadal timescales.
From sea-level anomaly to a heat budget number
Depth-integrated ocean heat content, expressed in joules per square metre, is calculated from the temperature profiles by integrating the product of seawater density, specific heat capacity, and temperature anomaly from a reference climatology (typically WOA, the World Ocean Atlas). The 0–700 m layer is the best-constrained; the 0–2000 m layer is standard for climate reporting. SWOT's improved resolution of mesoscale features is expected to reduce the aliasing error that affects basin-mean OHC estimates, though the mission is still accumulating its calibration record.
The resulting OHC time series feeds directly into Earth energy imbalance (EEI) assessments. The ocean absorbs roughly 90 percent of the excess energy trapped by greenhouse gases, so OHC change rate is the most direct observational proxy for EEI. Published estimates of the current imbalance cluster around 0.87 W m⁻² (von Schuckmann et al., 2023, published in Earth System Science Data), with an uncertainty of roughly ±0.12 W m⁻². That uncertainty is dominated by the deep-ocean gap and by the difficulty of sampling boundary currents adequately, not by altimeter precision.
Where the method honestly struggles
Below 2000 m, Deep Argo is still being deployed. The abyssal ocean holds a significant fraction of the long-term heat uptake, particularly in the Southern Ocean, but the observational constraint is thin. Studies using repeat hydrographic sections (the GO-SHIP programme) suggest the 2000–6000 m layer may contribute 10–20 percent of total OHC change over multi-decadal periods, a number that altimetry-Argo fusion cannot yet resolve reliably.
Boundary currents are a different problem. The Gulf Stream and Kuroshio carry enormous heat poleward, and their meandering generates sea-level anomalies of 30–50 cm that are dominated by dynamic height rather than steric expansion. The covariance between surface height and subsurface temperature breaks down here. SWOT's two-dimensional coverage helps characterise the eddy field, but the vertical projection from surface to depth remains uncertain. Regional OHC estimates in these zones carry error bars two to three times larger than open-ocean estimates.
What an operational analytics programme looks like
A government or research client typically wants three things: a calibrated OHC time series for a defined region, an uncertainty envelope that is honest about the sources of error, and a cadence fast enough to detect anomalies before they propagate into downstream forecasts. The altimetry record is near-real-time: Sentinel-6 data reach operational users within three hours of acquisition in the NRT stream, and within two days in the more precise STC (short time-critical) product. Argo profiles are transmitted within 24 hours of surfacing. The fusion step, running optimal interpolation on a regular grid, typically adds one to two days of processing latency.
Satellize runs this class of analysis on open constellation data, combining Sentinel-6 and Jason-3 sea-level anomaly fields with the publicly distributed Argo dataset, and applies regional covariance models tuned to the client's area of interest. The Tonga crop-estimation programme is a different domain, but the underlying workflow, ingesting open-access geophysical data and producing calibrated, uncertainty-quantified outputs for a sovereign client, is the same pattern. For ocean heat content, the deliverable is a gridded OHC anomaly layer updated on each Argo reporting cycle, with a separate uncertainty layer that flags boundary-current and deep-ocean zones explicitly.
Typical figures
| Along-track spatial resolution (Jason-3 / Sentinel-6) | ~7 km at 1 Hz; ~350 m at 20 Hz (smoothed to ~1 km operationally) |
| Sea-surface height precision (single pass) | 2–3 cm RMS for Jason-3 / Sentinel-6; ~1 cm for gridded multi-mission products |
| Altimeter repeat cycle | 10-day exact repeat (Jason-3 / Sentinel-6 tandem); 21-day (SWOT); 369-day exact / ~30-day sub-cycle (CryoSat-2) |
| SWOT swath width and resolution | 120 km (20 km nadir gap); ~1 km SSH resolution in ocean science mode |
| Argo profile depth and cadence | 0–2000 m (core); 0–6000 m (Deep Argo); one profile per float per 10 days |
| Argo spatial density | Approximately one float per 3° × 3° cell (~300 km) globally; sparser in Southern Ocean and marginal seas |
| NRT data latency (Sentinel-6) | ~3 hours (NRT stream); ~2 days (STC, higher accuracy) |
| OHC uncertainty (0–2000 m, open ocean) | ±0.5–1.5 × 10²² J per basin-scale estimate; larger in boundary-current regions |
| Altimetry archive depth | Continuous record from TOPEX/Poseidon, 1992 to present |
| Standard OHC output grid | 1° × 1° monthly (e.g. ISAS, EN4); 0.25° × 0.25° for altimetry-only SSH anomaly maps |
Analytics Satellize can run
| Regional OHC anomaly time series (0–700 m and 0–2000 m) | Optimal interpolation of Argo profiles constrained by multi-mission altimetric SSH anomaly covariance fields | Monthly gridded NetCDF layers with per-cell uncertainty estimates; summary statistics report |
| Thermosteric vs. halosteric decomposition | Separate integration of temperature and salinity anomaly profiles from Argo, referenced to WOA climatology | Stacked bar time series showing thermosteric and halosteric contributions to regional sea-level change; GIS-compatible raster layers |
| Mesoscale eddy heat anomaly mapping | SSH-based eddy detection (closed contour method) applied to SWOT and multi-mission gridded products, with Argo-derived temperature anomaly composited by eddy polarity | Eddy census GIS layer with associated heat content anomaly per eddy; updated on each SWOT repeat cycle |
| Earth energy imbalance proxy for defined ocean basin | Time-differenced OHC integrated over full water column (0–2000 m core Argo + Deep Argo where available), expressed as W m⁻² | Annual EEI estimate with uncertainty breakdown by depth layer and region; PDF report suitable for climate inventory submissions |
| Boundary-current heat transport anomaly flag | Elevated SSH variance mask derived from CryoSat-2 drifting ground tracks, applied to flag cells where steric decomposition uncertainty exceeds a defined threshold | Uncertainty flag layer overlaid on OHC product; narrative section in monthly report quantifying affected area |
| Long-term OHC trend and acceleration assessment | Linear and quadratic trend fitting to the 1992-to-present altimetry record, cross-validated against Argo-era (post-2004) in-situ OHC estimates | Trend coefficient table with confidence intervals; time-series chart formatted for IPCC-style climate assessment use |
Who does the work
We can get this done for you. Satellize runs its own analyst desk and a strong science team. You do not buy a data feed and work out what it means; our people source the imagery, run the analysis described on this page, and hand you the answer with its confidence limits stated. Discuss this requirement.