This paper presents a new statistical method to map ocean heat content and its uncertainty. The authors use temperature profiles from Argo floats collected from 2004 to 2022. By modeling the upper and mid depths together, they account for the vertical connection between layers. That connection reduces uncertainty in global ocean heat anomaly estimates by as much as 15 percent compared with mapping the two layers separately.

Ocean heat content (OHC) matters because the ocean stores more than 90 percent of the extra energy entering the climate system from Earth’s energy imbalance. The study uses Argo profiling floats, which sample the upper roughly 2,000 meters of the ocean about every 10 days. There are about 4,100 active floats and, after quality control, the authors use about 1.54 million profiles for the upper layer (15–975 dbar) and 1.13 million for the mid layer (975–1850 dbar). Many floats do not sample the full depth range and coverage gets sparser with depth. Those sampling gaps make uncertainty estimation difficult.

At a high level the authors replace the previous practice of mapping each depth layer separately with a joint approach. They use a bivariate locally stationary Gaussian process — a statistical model that represents how heat anomalies vary in space and time in both layers and how the two layers are correlated. They then draw conditional simulations, which are many realistic maps consistent with the data and the model. Those simulated maps let the researchers estimate uncertainty in sums across depth (the total OHC) in a statistically rigorous and computationally feasible way.

The joint model improves predictive performance in cross-validation and reduces mapped predictive variance by more than 10 percent, most clearly in the mid-ocean layer where observations are fewer. When the two mapped layers are combined, modeling their vertical dependence cuts uncertainties in global OHC anomalies by up to 15 percent compared to treating the layers independently. The authors illustrate the practical effect of those smaller uncertainties in three climate analyses: the total OHC trend, the total ocean heat uptake and its comparison with top-of-atmosphere radiative flux, and the correlation between total OHC anomaly and the Oceanic Niño Index. They note that obtaining a rigorous uncertainty for the latter would not have been possible without accounting for vertical dependence.