Rising geopotential height under global warming

Geopotential height (H) is a widely used metric for atmospheric circulation. H has been reported to rise under global warming, but the amplitude and mechanism of this rise are not clear. Based on reanalysis datasets and climate models participating in CMIP6, this study quantitatively evaluates the sensitivity of H to global mean surface air temperature (Ts), i.e., dH/dTs. Reanalysis datasets and model simulations consistently show that dH/dTs increases monotonically with altitude in the troposphere, with a global averaged value of about 24.5 gpm/K at 500 hPa, which overwhelms the interannual H variability. Diagnosis based on the hypsometric equation shows that the rise in global H is dominated by expansion of the air column due to warming-induced reduction in air density, and the magnitude of dH/dTs is determined largely by a vertical integration of the warming profile below the pressure level. Since the anthropogenic forced rise in H is rather horizontally uniform and proportional to Ts change, past and projected future changes in the global H field at each pressure level can be reproduced by change in Ts multiplied by a constant historical dH/dTs value. Spatially uniform rise in H reproduces the past and projected future expansion of the widely used H = 5880 gpm contour at 500 hPa, suggesting that it does not indicate enhancement of the subtropical high but is simply caused by thermal expansion of the atmosphere. This work uncovers the physical mechanism for rising H and offers a simple way to estimate H anomaly based on Ts anomaly.