Brief Communication: Assessing theoretical frameworks for thermodynamic and dynamic responses to atmospheric warming: application to shallow cumulus clouds over the tropics and in the Polar regions

Abstract. Clouds exert a major influence on Earth’s radiative balance, yet the net radiative feedback from different cloud types remains one of the largest uncertainties in climate science. Tropical shallow cumulus and stratocumulus clouds are particularly influential for Earth’s mean climate state and are expected to contribute a positive feedback to future warming, with stratocumulus clouds playing the dominant role. The key objectives of this study are (i) to analyze how shallow cumulus clouds in the subtropics and polar regions change in a warming climate using high-resolution CM1 simulations, and (ii) to identify suitable theoretical approaches to disentangle thermodynamic and dynamic contributions to climate variability and change. We introduce novel thermodynamic and dynamic variants of the Dynamic State Index (DSI) that are defined via energy and vorticity quantities and indicate deviations from thermodynamic or dynamic equilibrium conditions. Therefore, these DSI variants provide a suitable framework to investigate cloud processes.

Shallow cumulus clouds are simulated with the high-resolution Cloud Model 1, and DSI variants are subsequently calculated to address three key research questions: (1) How do shallow clouds in the subtropics and polar regions respond to warming?, (2) Can the DSI identify shallow cumulus clouds?, (3) How do their thermodynamic and dynamic states change with temperature increase? The simulations reveal clear regional contrasts. In the subtropics, a warming of up to +4 K at the surface causes a slight reduction in the vertical and horizontal extent of shallow clouds, whereas in the polar region, significant cloud deepening and densification occur. All DSI variants successfully detect shallow cumulus clouds, confirming their suitability for further analysis of long-term changes in thermodynamic and dynamic processes and for advancing process‑based understanding of cloud responses to climate warming.