Meyssignac et al. Measuring OHC to Estimate the EEI efficient approach to estimate EEI. In this community paper we review the current four state-of-the-art methods to estimate global OHC changes and evaluate their relevance to derive EEI estimates on different time scales. These four methods make use of: (1) direct observations of in situ temperature; (2) satellite-based measurements of the ocean surface net heat fluxes; (3) satellite-based estimates of the thermal expansion of the ocean and (4) ocean reanalyses that assimilate observations from both satellite and in situ instruments. For each method we review the potential and the uncertainty of the method to estimate global OHC changes. We also analyze gaps in the current capability of each method and identify ways of progress for the future to fulfill the requirements of EEI monitoring. Achieving the observation of EEI with sufficient accuracy will depend on merging the remote sensing techniques with in situ measurements of key variables as an integral part of the Ocean Observing System.

Abstract. The Earth climate system is out of energy balance, and heat has accumulated continuously over the past decades, warming the ocean, the land, the cryosphere, and the atmosphere. According to the Sixth Assessment Report by Working Group I of the Intergovernmental Panel on Climate Change, this planetary warming over multiple decades is human-driven and results in unprecedented and committed changes to the Earth system, with adverse impacts for ecosystems and human systems. The Earth heat inventory provides a measure of the Earth energy imbalance (EEI) and allows for quantifying how much heat has accumulated in the Earth system, as well as where the heat is stored. Here we show that the Earth system has continued to accumulate heat, with 381±61 ZJ accumulated from 1971 to 2020. This is equivalent to a heating rate (i.e., the EEI) of 0.48±0.1 W m−2. The majority, about 89 %, of this heat is stored in the ocean, followed by about 6 % on land, 1 % in the atmosphere, and about 4 % available for melting the cryosphere. Over the most recent period (2006–2020), the EEI amounts to 0.76±0.2 W m−2. The Earth energy imbalance is the most fundamental global climate indicator that the scientific community and the public can use as the measure of how well the world is doing in the task of bringing anthropogenic climate change under control. Moreover, this indicator is highly complementary to other established ones like global mean surface temperature as it represents a robust measure of the rate of climate change and its future commitment. We call for an implementation of the Earth energy imbalance into the Paris Agreement's Global Stocktake based on best available science. The Earth heat inventory in this study, updated from von Schuckmann et al. (2020), is underpinned by worldwide multidisciplinary collaboration and demonstrates the critical importance of concerted international efforts for climate change monitoring and community-based recommendations and we also call for urgently needed actions for enabling continuity, archiving, rescuing, and calibrating efforts to assure improved and long-term monitoring capacity of the global climate observing system. The data for the Earth heat inventory are publicly available, and more details are provided in Table 4.

Analysis of Argo temperature and salinity profiles (gridded at 0.5° × 0.5° resolution for 2005–12) shows a strong North Pacific Subtropical Mode Water (NPSTMW) volume and density decrease during 2006–09. In this time period, upper-ocean temperature, stratification, and potential vorticity (PV) all increased within the region in and around the NPSTMW low-PV pool, contributing to the NPSTMW volume decrease in two ways: (i) the volume of water satisfying the low-PV constraint that is part of the “mode water” definition decreased, and (ii) some water that was initially in the NPSTMW density range σθ = 25.0–25.5 kg m−3 was transformed into lighter water. Both changes in density and in PV in the NPSTMW region were a manifestation of basinwide changes. A positive PV anomaly started to propagate westward from the central Pacific in 2005, followed by a negative density anomaly in 2007, which caused a dramatic NPSTMW volume and density decrease. A Walin estimate of surface formation in the NPSTMW density range accounted better (although not entirely) for the interannual variability of the volume of water in the NPSTMW density range without imposing the PV < 2 × 10−10 m−1 s−1 constraint than did the same estimate with the PV constraint imposed. This underlines the importance of the PV constraint in identifying the mode water. The mode water evolution cannot be fully described from a density budget alone; rather, the PV budget must be considered simultaneously.

South Atlantic Ocean middepth water property (temperature, salinity, oxygen, nutrients, etc.) distributions are set by salty, well‐ventilated, and relatively nutrient‐poor North Atlantic Deep Water (NADW) spreading southward toward the Southern Ocean underneath fresher, well‐ventilated, and relatively nutrient‐poor northward spreading Antarctic Intermediate Water (AAIW). The layer between the NADW and AAIW is oxygen‐poor and nutrient‐rich, with small vertical temperature gradients. Salinity stratification dominates the vertical density gradient, hence the layer is referred to as Salinity Stratified Layer (SSL). Decadal warming (0.044 ∘C decade−1) and freshening (0.006 g kg−1 decade−1) of this layer are analyzed using Argo data, a climatology, and repeat hydrographic sections. Warming within the SSL accumulates heat at a rate of ∼20 TW, is unlikely to be caused by vertical heave, and is consistent with anomalous southward advection of order 102 km decade−1 in the Atlantic Meridional Overturning Circulation. Salinity changes within the SSL are consistent with a downward velocity anomaly of order 10 m decade−1.