Quantifying the non-conservative production of potential temperature over the past 22000 years

The energy budgets of the ocean play a crucial role in the analysis of climate change. Potential temperature is traditionally used as a conservative quantity to express variations associated with “heat” in oceanography, such as the heat content and heat transport. However, potential temperature is usually not conserved during turbulent mixing, so the use of conservative temperature is more accurate. Based on climatological simulations under the modern and Last Glacial Maximum (LGM;~21 ka;ka=thousand years ago), as well as a transient climate simulation of the past 22 000 years, we quantify the errors induced by the neglect of the non-conservation of potential temperature in paleo-climate research for the first time. The temperature error reaches 0.9℃ near the coasts aff ected by river discharges but is much smaller in the open oceans, typically 0.03°C above the main thermocline and less than 0.01℃ elsewhere. The error of the ocean heat content (OHC) is roughly 3×10^22 J and is relatively steady over the past 22 000 years. However, the OHC increases to six times the original value during the last glacial termination from 20 ka to 7 ka. As a result, the relative OHC error decreases from 1.2% in the LGM climate to 0.14% in the modern climate. The error of the ocean meridional heat transport (OMHT) is generally smaller than 0.005 PW (1 PW=10 15 W), with very small temporal variations (typically 0.000 4 PW), and induces a relative OMHT error of typically 0.3% over the past 22 000 years. Therefore, the neglect of the non-conservation of potential temperature induces a relative error of generally less than 1% in the analyses of basin-scale climate variations.

The energy budgets of the ocean play a crucial role in the analysis of climate change. Potential temperature is traditionally used as a conservative quantity to express variations associated with "heat"in oceanography, such as the heat content and heat transport. However, potential temperature is usually not conserved during turbulent mixing, so the use of conservative temperature is more accurate. Based on climatological simulations under the modern and Last Glacial Maximum(LGM; ～21 ka; ka=thousand years ago), as well as a transient climate simulation of the past 22 000 years, we quantify the errors induced by the neglect of the non-conservation of potential temperature in paleo-climate research for the first time. The temperature error reaches 0.9°C near the coasts af fected by river discharges but is much smaller in the open oceans, typically 0.03°C above the main thermocline and less than 0.01°C elsewhere. The error of the ocean heat content(OHC) is roughly 3×10 22 J and is relatively steady over the past 22 000 years. However, the OHC increases to six times the original value during the last glacial termination from 20 ka to 7 ka. As a result, the relative OHC error decreases from 1.2% in the LGM climate to 0.14% in the modern climate. The error of the ocean meridional heat transport(OMHT) is generally smaller than 0.005 PW(1 PW=10 15 W),with very small temporal variations(typically 0.000 4 PW), and induces a relative OMHT error of typically0.3% over the past 22 000 years. Therefore, the neglect of the non-conservation of potential temperature induces a relative error of generally less than 1% in the analyses of basin-scale climate variations.