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The concept of feedback has been used by several authors in the field of climate science to describe the behavior of models and to assess the importance of the different mechanisms at stake. Here, a simple 1D model of climate has been built to analyze the water vapor feedback. Beyond a static quantification of the water feedback, a more general formal definition of feedback gain based on the tangent linear system is introduced. This definition reintroduces the dynamical aspect of the system response to perturbation from Bode's original concept. In the model here, it is found that, even though the water vapor static gain proves consistent with results from GCMs, it turns out to be negative for time scales below 4 yr and positive only for longer time scales. These results suggest two conclusions: (i) that the water vapor feedback may be fully active only in response to long-lived perturbations; and (ii) that the water vapor feedback could reduce the natural variability due to tropospheric temperature perturbations over short time scales, while enhancing it over longer time scales. This second conclusion would be consistent with studies investigating the influence of air-sea coupling on variability on different time scales.

This article introduces a new decomposition of climate feedback mechanisms based on their characteristic times. As the last of a series of three, it complements the first two parts by Lahellec and Dufresne to give a comprehensive review of climate feedbacks that will help to ensure consistency between practice and theory. In Parts I and II, analysis of the climate response to perturbations at the large spatial scales and time scales necessary to obtain linearity restricted the characterization to the slow components of the response. This part incorporates the fast mechanisms' impact on the climate feedbacks, bringing the seasonal cycle into the analysis. Thanks to the Floquet theory, the authors could extend the formal framework of Parts I and II to incorporate the fast mechanisms. An illustration of the formal results with a simple 1D model highlights a clear distinction between the role of fast (intraseasonal) and slow (decadal) feedbacks, with an application to the water-cycle feedback of Part II. The same implementation of the Gâteaux difference in LMDZ, the GCM of LMD, as in Part II is used for comparing results with the authors' toy model. This comparison essentially validates the Floquet decomposition obtained with the toy model: the fast component linked to precipitation is contributing negatively to the water-cycle feedback while the slow component is building up the positive feedback. The comparison also provides further insight on the sensitivity of models' precipitation to climate warming. [ABSTRACT FROM AUTHOR]

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. A series of illustrations demonstrates the advantages of implementing such a method in GCMs. [ABSTRACT FROM AUTHOR]

Climate sensitivity and feedback are key concepts if the complex behavior of climate response to perturbation is to be interpreted in a simple way. They have also become an essential tool for comparing global circulation models and assessing the reason for the spread in their results. The authors introduce a formal basic model to analyze the practical methods used to infer climate feedbacks and sensitivity from GCMs. The tangent linear model is used first to critically review the standard methods of feedback analyses that have been used in the GCM community for 40 years now. This leads the authors to distinguish between exclusive feedback analyses as in the partial radiative perturbation approach and inclusive analyses as in the 'feedback suppression' methods. This review explains the hypotheses needed to apply these methods with confidence. Attention is paid to the more recent regression technique applied to the abrupt 2×CO2 experiment. A numerical evaluation of it is given, related to the Lyapunov analysis of the dynamical feature of the regression. It is applied to the Planck response, determined in its most strict definition within the GCM. In this approach, the Planck feedback becomes a dynamical feedback among others and, as such, also has a fast response differing from its steady-state profile. [ABSTRACT FROM AUTHOR]