Revisiting the Global Energy Budget Dynamics with a Multivariate Earth Energy Balance Model to Account for the Warming Pattern Effect

Climate feedbacks are sensitive to the geographical distribution of sea surface temperature (SST). This sensitivity, called the pattern effect, affects the amplitude of the Earth radiative response to anomalies in global mean surface temperature (GMST) and thus is essential in shaping the global energy budget dynamics. Zero-dimensional energy balance models (EBMs) are the simplest representation of the global energy budget dynamics. Many only depend on GMST anomalies and cannot account for the pattern effect explicitly. In EBMs, the pattern effect leads to apparent variations of the global climate feedback parameter lambda. Assuming a variable lambda in EBMs enables them to more accurately reproduce AOGCM simulations of the GMST anomalies but it leads to variations in lambda of >+15%. These large variations mean lambda is not a constant and the Taylor expansion underpinning EBMs' formulation does not hold, casting doubts on the physical grounding of such EBMs. Here we propose a new EBM based on a multivariate linear Earth radiative response, which depends on both the GMST and the surface warming pattern. The resulting multilinear EBM accurately reproduces AOGCM simulations of anomalies in Earth radiative response and GMST under abrupt 4xCO(2) forcing. When interpreted in terms of variable lambda, the multivariate EBM leads to small variations in lambda that are physically consistent with the underpinning Taylor expansion. We analyze with the multivariate framework the variations of the planetary heat uptake N as a function of the GMST and the pattern of warming through a 3D generalization of the Gregory plot. We show that the apparent nonlinear behavior of the radiative response of the Earth against GMST seen in classical monovariate EBMs (and in classical Gregory plots) can actually be explained by a bilinear dependance of the radiative response of the Earth on the GMST and the pattern of warming. The multivariate EBM further provides an explicit dependence of the global energy budget on the pattern of warming and on the climate state. It has important consequences on the expression of the climate sensitivity.