Origin and Limits of Invariant Warming Patterns in Climate Models

Abstract Climate models exhibit an approximately invariant surface warming pattern in typical end-of-century projections. This feature has been used extensively in climate impact assessments for fast calculations of local temperature anomalies, with a linear procedure known as pattern scaling . At the same time, emerging research has also shown that time-varying warming patterns are necessary to explain the time evolution of effective climate sensitivity in coupled models, a mechanism that is known as the pattern effect and that seemingly challenges the pattern scaling understanding. Here, we present a simple theory based on local energy balance arguments to reconcile this apparent contradiction. Specifically, we show that the pattern invariance arises from the combination of exponential forcing, linear feedbacks, a constant forcing pattern, and linear changes in heat transport. These conditions are approximately met in typical Coupled Model Intercomparison Project phase 6 (CMIP6) shared socioeconomic pathways (SSPs), except in the Arctic where nonlinear feedbacks are important and in regions where different aerosol projections alter the forcing pattern. In idealized experiments where concentrations of carbon dioxide (CO 2 ) are abruptly increased, such as those used to study the pattern effect, the warming pattern evolves considerably over time because of spatially inhomogeneous ocean heat uptake, even in the absence of nonlinear feedbacks. Our results illustrate why typical future projections are amenable to pattern scaling and provide a plausible explanation of why more complicated approaches, such as nonlinear emulators, have only shown marginal improvements in accuracy over simple linear calculations. Significance Statement In typical end-of-century climate projections from comprehensive models, the ratio between local and global surface temperature anomalies is approximately time and scenario invariant. This feature has enabled fast calculations of local temperature changes by scaling the global average with a constant pattern. At the same time, idealized quadrupling of CO 2 (4xCO 2 ) experiments show a different behavior and a considerable time evolution of the warming pattern. We present a simple theory based on local energy balance to reconcile this apparent contradiction. Specifically, we show that the pattern invariance arises under a set of conditions that are approximately satisfied typical end-of-century scenarios. Our findings clarify why scaling the global average to calculate local temperature anomalies is effective for most future projections.