Can heatwave temperatures go up indefinitely?

In recent summers, the world has witnessed one extreme heatwave after another, raising concerns related to climate change. Such events prompt the pressing question: what limits the maximum surface temperature?

Traditionally, researchers have focused on processes that elevate surface temperatures, such as blocking anticyclones, dry soil, intense solar radiation, and the advection of warm air. These processes accumulate heat within the atmospheric boundary layer, the layer that extends a few kilometers above the Earth’s surface.

However, this study takes a different angle. We explore the mechanisms that halt any further rise in surface temperatures. Essentially, if the surface temperature climbs too high, the nearby air mass becomes buoyant, leading to convective instability. This results in vigorous upward motion, effectively exporting the accumulated heat out of the boundary layer. Under conditions of a blocking anticyclone, this mechanism enables us to deduce an upper limit for the surface temperature, $T_s$. This theoretical upper bound solely depends on the temperature at the middle troposphere, $T_{500}$, which is considered externally given by the anticyclone and remains relatively stable throughout a heatwave’s development.

\begin{equation} T_{s} \leq T_{\rm 500}+\frac{L_v}{c_p}q_{\rm sat}(T_{\rm 500})+\frac{g\overline{z_{\rm 500}}}{c_p\overline{T_{\rm 500}}}T_{\rm 500}-\frac{g}{c_p}z_s. \end{equation}

example image — Theoretical upper bound of surface temperature divides the phase space into unstable and stable parts, with observations lying in the stable part.

This upper bound is nonlinearly dependent on $T_{500}$ due to the property of warmer air holding more water vapor, a relationship governed by the Clausius-Clapeyron equation. As a result, with each increment in $T_{500}$ warming, the change in the upper bound accelerates. In our current climate, the hottest days of the year correspond to a $T_{500}$ value that yields a slope of approximately 2 for the upper bound shown in the Figure. This partially explains why annual maximum temperatures over land have been increasing at roughly double the rate of the global mean surface temperature.

By highlighting the role of convective instability in heatwaves and presenting a theoretical upper bound, this work offers a fresh perspective on the dynamics of extreme temperature events.

Cover image source: NY Times

Heatwaves damage societies worldwide and are intensifying with global warming. Several mechanistic drivers of heatwaves, such as atmospheric blocking and soil moisture-atmosphere feedback, are well-known for their ability to raise surface air temperature. However, what limits the maximum surface air temperature in heatwaves remains unclear; this became evident during recent Northern Hemisphere heatwaves which achieved temperatures far beyond the upper tail of the observed statistical distribution. Here, we present evidence for the hypothesis that convective instability limits annual maximum surface air temperatures (TXx) over midlatitude land. We provide a theory for the corresponding upper bound of midlatitude temperatures, which accurately describes the observed relationship between temperatures at the surface and in the midtroposphere. We show that known heatwave drivers shift the position of the atmospheric state in the phase space described by the theory, changing its proximity to the upper bound. This theory suggests that the upper bound for midlatitude TXx should increase 1.9 times as fast as 500-hPa temperatures at the time and location of TXx occurrences. Using empirical 500-hPa warming, we project that the upper bound of TXx over Northern Hemisphere midlatitude land (40°N to 65°N) will increase about twice as fast as global mean surface air temperature, and TXx will increase faster than this bound over regions that dry on the hottest days.

Can heatwave temperatures go up indefinitely?

References

2023