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The representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

The representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

The representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global‐scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (‐14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non‐negligible.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global‐scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (‐14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non‐negligible.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global‐scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (‐14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non‐negligible.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global‐scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (‐14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non‐negligible.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global‐scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (‐14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non‐negligible.

Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global-scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (-14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non-negligible.

The Southern Ocean is central to the global climate and the global carbon cycle, and to the climate's response to increasing levels of atmospheric greenhouse gases, as it ventilates a large fraction of the global ocean volume. Global coupled climate models and earth system models, however, vary widely in their simulations of the Southern Ocean and its role in, and response to, the ongoing anthropogenic trend. Due to the region's complex water-mass structure and dynamics, Southern Ocean carbon and heat uptake depend on a combination of winds, eddies, mixing, buoyancy fluxes, and topography. Observationally based metrics are critical for discerning processes and mechanisms, and for validating and comparing climate and earth system models. New observations and understanding have allowed for progress in the creation of observationally based data/model metrics for the Southern Ocean. Metrics presented here provide a means to assess multiple simulations relative to the best available observations and observational products. Climate models that perform better according to these metrics also better simulate the uptake of heat and carbon by the Southern Ocean. This report is not strictly an intercomparison, but rather a distillation of key metrics that can reliably quantify the "accuracy" of a simulation against observed, or at least observable, quantities. One overall goal is to recommend standardization of observationally based benchmarks that the modeling community should aspire to meet in order to reduce uncertainties in climate projections, and especially uncertainties related to oceanic heat and carbon uptake. Plain Language Summary Observationally based metrics are essential for the standardized evaluation of climate and earth system models, and for reducing the uncertainty associated with future projections by those models.

The Southern Ocean is central to the global climate and the global carbon cycle, and to the climate's response to increasing levels of atmospheric greenhouse gases, as it ventilates a large fraction of the global ocean volume. Global coupled climate models and earth system models, however, vary widely in their simulations of the Southern Ocean and its role in, and response to, the ongoing anthropogenic trend. Due to the region's complex water-mass structure and dynamics, Southern Ocean carbon and heat uptake depend on a combination of winds, eddies, mixing, buoyancy fluxes, and topography. Observationally based metrics are critical for discerning processes and mechanisms, and for validating and comparing climate and earth system models. New observations and understanding have allowed for progress in the creation of observationally based data/model metrics for the Southern Ocean. Metrics presented here provide a means to assess multiple simulations relative to the best available observations and observational products. Climate models that perform better according to these metrics also better simulate the uptake of heat and carbon by the Southern Ocean. This report is not strictly an intercomparison, but rather a distillation of key metrics that can reliably quantify the "accuracy" of a simulation against observed, or at least observable, quantities. One overall goal is to recommend standardization of observationally based benchmarks that the modeling community should aspire to meet in order to reduce uncertainties in climate projections, and especially uncertainties related to oceanic heat and carbon uptake. Plain Language Summary Observationally based metrics are essential for the standardized evaluation of climate and earth system models, and for reducing the uncertainty associated with future projections by those models.

The Southern Ocean is central to the global climate and the global carbon cycle, and to the climate's response to increasing levels of atmospheric greenhouse gases, as it ventilates a large fraction of the global ocean volume. Global coupled climate models and earth system models, however, vary widely in their simulations of the Southern Ocean and its role in, and response to, the ongoing anthropogenic trend. Due to the region's complex water-mass structure and dynamics, Southern Ocean carbon and heat uptake depend on a combination of winds, eddies, mixing, buoyancy fluxes, and topography. Observationally based metrics are critical for discerning processes and mechanisms, and for validating and comparing climate and earth system models. New observations and understanding have allowed for progress in the creation of observationally based data/model metrics for the Southern Ocean. Metrics presented here provide a means to assess multiple simulations relative to the best available observations and observational products. Climate models that perform better according to these metrics also better simulate the uptake of heat and carbon by the Southern Ocean. This report is not strictly an intercomparison, but rather a distillation of key metrics that can reliably quantify the "accuracy" of a simulation against observed, or at least observable, quantities. One overall goal is to recommend standardization of observationally based benchmarks that the modeling community should aspire to meet in order to reduce uncertainties in climate projections, and especially uncertainties related to oceanic heat and carbon uptake. Plain Language Summary Observationally based metrics are essential for the standardized evaluation of climate and earth system models, and for reducing the uncertainty associated with future projections by those models.

The Southern Ocean is central to the global climate and the global carbon cycle, and to the climate's response to increasing levels of atmospheric greenhouse gases, as it ventilates a large fraction of the global ocean volume. Global coupled climate models and earth system models, however, vary widely in their simulations of the Southern Ocean and its role in, and response to, the ongoing anthropogenic trend. Due to the region's complex water-mass structure and dynamics, Southern Ocean carbon and heat uptake depend on a combination of winds, eddies, mixing, buoyancy fluxes, and topography. Observationally based metrics are critical for discerning processes and mechanisms, and for validating and comparing climate and earth system models. New observations and understanding have allowed for progress in the creation of observationally based data/model metrics for the Southern Ocean. Metrics presented here provide a means to assess multiple simulations relative to the best available observations and observational products. Climate models that perform better according to these metrics also better simulate the uptake of heat and carbon by the Southern Ocean. This report is not strictly an intercomparison, but rather a distillation of key metrics that can reliably quantify the "accuracy" of a simulation against observed, or at least observable, quantities. One overall goal is to recommend standardization of observationally based benchmarks that the modeling community should aspire to meet in order to reduce uncertainties in climate projections, and especially uncertainties related to oceanic heat and carbon uptake. Plain Language Summary Observationally based metrics are essential for the standardized evaluation of climate and earth system models, and for reducing the uncertainty associated with future projections by those models.