Time series of sea-level rise are fitted by a sinusoid of period ~ 60 years, confirming the cycle reported for the global mean temperature of the earth. This cycle appears in phase with the Atlantic Multidecadal Oscillation (AMO). The last maximum of the sinusoid coincides with the temperature plateau observed since the end of the 20th century. The onset of declining phase of AMO, the recent excess of the global sea ice area anomaly and the negative slope of global mean temperature measured by satellite from 2002 to 2015, all these indicators sign for the onset of the declining phase of the 60-year cycle. Once this cycle is subtracted from observations, the transient climate response is revised downwards consistent with latest observations, with latest evaluations based on atmospheric infrared absorption and with a general tendency of published climate sensitivity. The enhancement of the amplitude of the CO2 seasonal oscillations which is found up to 71% faster than the atmospheric CO2 increase, focus on earth greening and benefit for crops yields of the supplementary photosynthesis, further minimizing the consequences of the tiny anthropogenic contribution to warming.