A formal analysis of the feedback concept in climate models. Part II: Tangent linear systems in GCMs

Climate analysis is greatly simplified in perturbation analysis when filtered anomalies show linear behavior. In the first part (part I) of this two-part analysis, the formal tangent linear system (TLS) that handles linear behavior was used to demonstrate the strict equivalence between feedback and sensitivity analysis but at the cost of reducing the generality of its application to GCMs. In this second part, the full feedback analysis is introduced from the application of the so-called regression method of Gregory et al. The authors give a complete example of its use in the global analysis of the phase 5 of the Coupled Model Intercomparison Project (CMIP5) abrupt 4×CO₂ and ramp experiments. A simple 1D model with only two ocean layers is shown to be able to explain the slow climate warming of the next century. An extension of the formal results in part I allows a new perturbation method to be designed in GCMs to determine the TLS in models. Aseries of illustrations demonstrates the advantages of implementing such a method in GCMs.