We propose a new perspective on the hierarchy of climate models which goes beyond the "classical" climate modeling pyramid that is restricted mainly to atmospheric processes. Most notably, we introduce a new indicator, called "integration", which characterizes the number of interacting components of the climate system being explicitly described in a model. The location of several model types, from conceptual to comprehensive, is presented in a new spectrum of climate system models. In particular, the location of the Earth system Models of Intermediate Complexity (EMICs) in this spectrum is discussed in some detail and examples are given, which indicate that there is currently a broad range of EMICs in use. In some EMICs, the number of processes and/or the detail of description is reduced for the sake of simulating the feedbacks between as many components of the climate system as feasible. Others, with a lesser degree of interaction, or "integration", are used for long-term ensemble simulations to study specific aspects of climate variability. EMICs appear to be closer to comprehensive coupled models of atmospheric and oceanic circulation (CGCMs) than to "conceptual" or "box" models. We advocate that EMICs be considered as complementary to CGCMs and conceptual models, because we believe that there is an advantage of having a spectrum of climate system models which are designed to tackle specific aspects of climate and which together provide the proper tool for climate system modeling.

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