A Formal Analysis of the Feedback Concept in Climate Models. Part III: Feedback Dynamics and the Seasonal Cycle in a Floquet Analysis

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.