Two Flavours of Ocean Temperature Change and the Implication for Reconstructing the History of Ocean Warming

Introducing Excess and Redistributed Temperatures. 

By: Quran Wu

Monitoring and understanding ocean heat content change is an essential task of climate science because the ocean stores over 90% of extra heat that is trapped in the Earth system. Ocean warming results in sea-level rise which is one of the most severe consequences of anthropogenic climate change.

Ocean warming under greenhouse gas forcing is often thought of as extra heat being added to the ocean surface by greenhouse warming and then carried to depths by ocean circulation. This one-way heat transport diagram assumes that all subsurface temperature changes are due to the propagation of surface temperature changes, and is widely used to construct conceptual models of ocean heat uptake (for example, the two-layer model in Gregory 2000).

Recent studies, however, have found that ocean temperature change under greenhouse warming is also affected by a redistribution of the original temperature field (Gregory et al. 2016). The ocean temperature change due to the redistribution is referred to as redistributed temperature change, while that due to propagation of surface warming is referred to as excess temperature change.

A Dye Analogy

To help explain the separation of excess and redistributed temperature, let us consider a dye analogy. Heating the ocean from the surface is like adding a drop of dye into a glass of water that already has a non-uniform distribution of the same dye. After the dye injection, two things happen simultaneously. First, the newly-added dye gradually spreads into the water in the glass (excess temperature). Second, the dye injection disturbs the water and causes water motion that rearranges the original dye (redistributed temperature). Both processes contribute to changes in dye concentrations.

Climate Model Simulation

Figure 1: Time evolution of global-mean ocean temperature change (in Kelvin) under increasing greenhouse gas emission in a climate model simulation (a). Change in (a) is decomposed into excess temperature change (b) and redistributed temperature change (c).

Excess and redistributed temperatures are both derived from thought experiments; neither of them can be directly observed in the real world. Here, we demonstrate their behaviours using a climate model simulation under increasing greenhouse gas emission. The simulation shows that ocean warming starts from the surface, and propagates into depths gradually, reaching 500 m after 50 years (Figure 1a). The ocean warming is mostly driven by excess temperature change (compare Figures 1a with 1b) but strongly disrupted by a downward heat redistribution near the surface (cooling at the surface and warming underneath) (Figure 1c). The downward heat redistribution is caused by a reduction of ocean convection (which pumps heat upward), because surface warming stabilises water columns.


Distinguishing excess from redistributed temperature change is important because they behave in different ways. While one can reconstruct excess temperature at depths by propagating its surface change using ocean transports, the same cannot be done with redistributed temperature. This is because temperature redistribution can potentially happen anywhere in the ocean, unlike extra heat, which can only enter the ocean from the surface (under greenhouse warming). Such a distinction has important implications for estimating the history of ocean warming from surface observations.

Ocean warming is traditionally estimated by interpolating in-situ temperature measurements, which were gathered in discrete locations and times, to the global ocean. This in-situ method suffers a large uncertainty because the ocean remains poorly sampled until the global deployment of Argo floats (a fleet of robotic instruments) in 2005.

A new approach to estimate ocean warming is to propagate its surface signature, that is sea surface temperature change, downward using information of ocean transports (Zanna et al. 2019). This transport method is useful because it relies on surface observations, which have a longer historical coverage than subsurface observations. However, this method ignores the fact that part of surface temperature change is due to temperature redistribution, which does not correspond to subsurface temperature change. In a computer simulation of the historical ocean, we found that propagating sea surface temperature change results in an underestimate of simulated ocean warming due to redistributive cooling at the surface (as shown in Figure 1c) (Wu and Gregory 2022). This result highlights the need for isolating excess temperature change from surface observations when applying the transport method to reconstruct ocean warming.


Thanks to Jonathan Gregory for reading an early version of this article and providing useful comments and suggestions.


Gregory, J. M., 2000: Vertical heat transports in the ocean and their effect on time-dependent climate change. Climate Dynamics, 16, 501–515,

Gregory, J. M., and Coauthors, 2016: The Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) contribution to CMIP6: investigation of sea-level and ocean climate change in response to CO2 forcing. Geoscientific Model Development, 9, 3993–4017,

Wu, Q., and J. M. Gregory, 2022: Estimating ocean heat uptake using boundary Green’s functions: A perfect‐model test of the method. Journal of Advances in Modeling Earth Systems, 14,

Zanna, L., S. Khatiwala, J. M. Gregory, J. Ison, and P. Heimbach, 2019: Global reconstruction of historical ocean heat storage and transport. Proceedings of the National Academy of Sciences, 116, 1126–1131,


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