Heat engines and heat pumps in a hydrostatic atmosphere: How surface pressure and temperature constrain wind power output and circulation cell size

TL;DR

This paper analytically assesses how surface pressure and temperature differences constrain wind power output and circulation size in Earth's atmosphere, highlighting the dominance of surface pressure gradients in kinetic energy generation.

Contribution

It introduces a relationship between surface pressure and temperature differences that limits circulation cell size and explains the role of heat pumps in atmospheric circulation.

Findings

Kinetic energy generation declines with increasing circulation cell size.

Surface pressure gradients dominate the net kinetic power output.

Heat pumps can reduce overall atmospheric circulation efficiency.

Abstract

The kinetic energy budget of the atmosphere's meridional circulation cells is analytically assessed. In the upper atmosphere kinetic energy generation grows with increasing surface temperature difference \$\Delta T_s\$ between the cold and warm ends of a circulation cell; in the lower atmosphere it declines. A requirement that kinetic energy generation is positive in the lower atmosphere limits the poleward cell extension \$L\$ of Hadley cells via a relationship between \$\Delta T_s\$ and surface pressure difference \$\Delta p_s\$: an upper limit exists when \$\Delta p_s\$ does not grow with increasing \$\Delta T_s\$. This pattern is demonstrated here using monthly data from MERRA re-analysis. Kinetic energy generation along air streamlines in the boundary layer does not exceed \$40\$~J~mol\$^{-1}\$; it declines with growing \$L\$ and reaches zero for the largest observed \$L\$ at 2~km height. The limited meridional cell size necessitates the appearance of heat pumps -- circulation cells with negative work output where the low-level air moves towards colder areas. These cells consume the positive work output of the heat engines -- cells where the low-level air moves towards the warmer areas -- and can in theory drive the global efficiency of atmospheric circulation down to zero. Relative contributions of \$\Delta p_s\$ and \$\Delta T_s\$ to kinetic energy generation are evaluated: \$\Delta T_s\$ dominates in the upper atmosphere, while \$\Delta p_s\$ dominates in the lower. Analysis and empirical evidence indicate that the net kinetic power output on Earth is dominated by surface pressure gradients, with minor net kinetic energy generation in the upper atmosphere. The role of condensation in generating surface pressure gradients is discussed.