Unravelling the mechanism of the Pattern Effect with a Two-box Model of the Tropical Atmospheric Circulation

The pattern effect describes how the spatial structure of surface warming modulates Earth’s top-of-atmosphere (TOA) radiative imbalance, such that identical increases in global-mean surface temperature can produce distinct global radiative responses and distinct effective climate sensitivities. GCM studies consistently point to the tropical Pacific through changes in deep convection and low-cloud feedbacks as a dominant contributor to this sensitivity. Yet isolating the causal chain from regional SST perturbations to the global radiative response remains challenging in comprehensive GCMs.

To address this, we develop a minimal two-box model of the tropical Pacific atmosphere, partitioning it into a warm, convective box and a cooler, inversion-capped subsident box, representative of an idealized Hadley–Walker circulation. The framework retains a strict Weak Temperature Gradient (WTG) constraint in the free troposphere, quasi-equilibrium structure functions for temperature and humidity, and low-cloud radiative effects in the subsident region scale with lower-tropospheric stability (EIS), on top of a clear-sky radiative code. For a given SST and greenhouse-gas forcing, the model state is described by only six scalar variables and closed by six coupled sensible-heat and moisture conservation equations, with fixed convective/subsident fractional areas and no explicit dynamical closure.

This formulation which is purely thermodynamic (no representation of the dynamics beyond the WTG) aims to include only the processes thought to be essential for the tropical pattern effect.

This minimal set of processes is sufficient to reproduce the sign asymmetry of the pattern effect, via WTG-mediated tropospheric temperature adjustment and low-cloud sensitivity to EIS in subsident regions, but it underestimates the amplitude of local radiative sensitivities, suggesting a missing mechanism linked to the fixed-area, no-dynamics assumption.

We therefore introduce a dynamical formulation based on a linear, stationary 2D momentum balance without Coriolis and with Rayleigh damping, yielding a momentum-budget closure that links the overturning circulation strength to the boundary-layer temperature contrast. This additional constraint allows us to relax the fixed fractional-area assumption and introduces a fractional area feedback: surface warming in convective regions tends to expand the subsident fraction, whereas subsident warming contracts it weaklier. Because subsident regions radiate more effectively to space due to their dryness and high low-cloud cover, these area shifts amplify radiative sensitivities and move the model closer to GCM-inferred sensitivities.

We confirm the relevance of this mechanism in idealized atmospheric GCM experiments forced by SST fields with identical tropical-mean SST but different spatial patterns. We show that changes in convective/subsident fractional areas, account for a surprising substantial share (order 20–40%) of the resulting TOA radiative imbalance in these configurations and this contribution is asymmetric with the SST pattern.  These results show that changes in the dynamics should be accounted for to explain the pattern effect.