There are at least 3 very obvious “lags” to any significant change to climate forcing, and we see these throughout the paleoclimate record when looking at past climate change, such as coming and going to and from glacial periods.. But before discussing these lags, let’s called them something a bit more scientific and that would be both slow-feedback responses to forcing and the ocean’s heat capacity and thermal inertia..
First, let’s discuss the ocean itself. The ocean, as the prime reservoir of energy on the planet also has the greatest thermal inertia. We’ve been getting better and better at measuring the energy going into the ocean, and have seen that by far most of the warming the planet has seen has gone to the oceans. Somewhere around 23 x 10^22 Joules of energy over the past 40 years has gone into the top 2000m of the ocean due to the Earth’s energy imbalance This energy is still there, and growing, and will effect the clmate for centuries as it eventually comes back into the atmosphere.
But the next “lags” or slow-feedbacks to climate change are the cryosphere and biosphere. Both of these take many decades to fully respond to any given forcing, and thus, they are currently still responding to 392 ppm of CO2. The cryosphere has annual cycles, but ressponds over decades to changes in forcing. We see this in the paleoclimate record as glaciers grow or contract over thousands, recacting to small changes in solar insolation brough about through Milankovitch cycles and the resultant positive feedback creating by the outgassing of CO2 from the oceans. In the future, as CO2 continues to increase, we will never actually see the planet’s equilibrium response to CO2 to 392 ppm, and (assuming we stop at 450 or 560 ppm), our future generations may get the opportunity to see what the final equilibrium response to that future CO2 level, albeit many decades after that level is reached and has stabilized. Equally, the biosphere can take many decades to respond to warming as species slowly migrate to new areas, changing the landscape and eventually eventually even planetary albedo. The paleoclimate record shows the biosphere response is especially strong in polar regions, which makes sense as that’s where warming is the strongest as well..