Global and Regional Temperature Projections Using the Fractional Energy Balance Equation

Abstract

We present the Fractional Energy Balance Equation (FEBE): a generalization of the standard EBE. The key FEBE novelty is the assumption of a hierarchy of energy storage mechanisms: scaling energy storage. Mathematically the storage term is of fractional rather than integer order. The special half-order case (HEBE) can be classically derived from the continuum mechanics heat equation used by Budyko and Sellers simply by introducing a vertical coordinate and using the correct conductive-radiative surface boundary conditions (the FEBE is a mild extension).