The varying Earth’s radiative feedback connected to the ocean energy
uptake: a theoretical perspective from conceptual frameworks
Abstract
When quadrupling the atmospheric CO$_{2}$ concentration in relation
to pre-industrial levels, most global climate models show an initially
strong net radiative feedback that significantly reduces the energy
imbalance during the first two decades after the quadrupling.
Afterwards, the net radiative feedback weakens, needing more surface
warming than before to reduce the remaining energy imbalance. Such
weakening radiative feedback has its origin in the tropical oceanic
stratiform cloud cover, linked to an evolving spatial warming pattern.
In the classical linearized energy balance framework, such variation is
represented by an additional term in the planetary budget equation. This
additional term is usually interpreted as an ad-hoc emulation of the
cloud feedback change, leaving unexplained the relationship between this
term and the spatial warming pattern. I use a simple non-linearized
energy balance framework to justify that there is a physical
interpretation of this term: the evolution of the spatial pattern of
warming is explained by changes in the ocean’s circulation and energy
uptake. Therefore, the global effective thermal capacity of the system
also changes, leading to the additional term. In reality, the clouds
respond to what occurs in the ocean, changing their radiative effect. In
the equation, the term is now a concrete representation of the ocean’s
role. Additionally, I derive for the first time an explicit mathematical
expression of the net radiative feedback and its temporal evolution in
the linearized energy balance framework. This mathematical expression
supports the new proposed interpretation. As a corollary, it justifies
the twenty-year time scale used to study the variation of the net
radiative feedback.