This book will introduce and develop the energy balance climate models for the scientific community. These models are the simplest among the hierarchy of ocean-atmosphere climate models. The EBCMs have been around for many decades and predate the introduction of large general circulation models. The models are phenomenological in the sense that they employ a few empirical parameters that are adjusted to agree with real data. Their origin lies in the balance of incoming and outgoing radiative energy at the top of the atmosphere. This book begins with the global average models and explores them from their elementary forms yielding the global average temperature to the incorporation of feedback mechanisms and some analytical properties of interest, such as temperature dependent albedo. The effect of stochastic forcing will be used to introduce natural variability in the models. The global average models are then used to introduce the concept of stability theory. Also other one dimensional or zonally averaged models will be introduced before presenting some applications. These include chapters on: Paleoclimatology, especially the inception of continental glaciations; detection of signals in the climate system, and optimal estimation of large scale quantities from point scale data. Throughout the book the authors will work at two mathematical levels: 1) Qualitative physical expositions of the material, and 2) Optional mathematical sections that include derivations and treatments of the equations along with some proofs of stability theorems, etc. COURSE CODES: ATMS 559 "Climate modeling", ATMS 571 "Advanced physical climatology", ATMS 587 "Climate dynamics", ATMS 589 "Paleoclimate modeling.

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