If by warming you mean an increase in the temperature, then warming will stop soon. If by warming you mean that it is warmer than without excess Greenhouse gases, then this excess temperature will be with us a long time. Solomon et al claimed it is 1000 years.
Klaus
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Yes, the oceans are taking on heat. But the energy imbalance remains until the CO2 is gone. The oceans will take up both the CO2 and the heat, but it is a slow (and slowing) process.
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For climate change the integral over the emissions matter. If the integral is to remain constant, we have to drive the emissions to zero, i.e., they have to come down. For that we need a negative time derivative of emissions, but so far we have kept even derivative positive as well. We are still on the accelerator not on the brake.
If we want to have the integral to come down, we need negative emission. (And yes the ocean helps a little, but the ocean is good at it, because the rising CO2 levels in the atmosphere maintain a gradient. If the CO2 does not go up anymore, the gradient into the ocean will gradually go away and with it the rate at which the ocean picks up CO2.
Uptake will slow down right away and not wait until the entire ocean filled up.
Klaus
The fundamental relationships discussed here were analysed in an
early paper, using equations of a basic climate model often
applied in integrated assessment of climate change. It determines
mathematical conditions for zero and negative emissions (shown in
Figure 3 as a function of climate sensitivity and climate
targets). The integral mentioned by Klaus Lackner is used on page
266. The paper also determines economic conditions for energy
transitions to meet climate targets but can also be used to
determine conditions for climate engineering (which 2008 was a
rather new topic):
Scheffran J (2008) Adaptive management of energy transitions in
long-term climate change. Computational Management Science 5(3):
259-286.
https://link.springer.com/article/10.1007/s10287-007-0044-1
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The simple model was not applied to geoengineering at that time,
however mentioned negative emissions already in 2008. Of course,
like all physical equations fitting a complex system, it depends
on the model parameters (here B, beta, sigma, mu, alpha, C_1).
These can be treated as approximately constant only within a
certain range.
If this range is left (as you suggest with the various
geoengineering measures), these parameters need to be adjusted
accordingly as a function of the variables G, F, C and T (and
other variables), taking higher orders into consideration.
Nonetheless, the principle logic of the first-order model and the
solutions still remain.
This also applies to more complex climate models that use some "constants" which are not really constant for large system modifications. Here we have the limits of modelling for problems for which have no experience and data.
Jürgen Scheffran
Yes, but does this paper include margins of error wide enough to include the [conservatively speaking] permafrost and clathrate C of polar and deep ocean regions of over 100 thousand gigatons C not to mention burning tropical and Boreal forests, peat, CO2/methane/black carbon soot, nitrous oxides, water vapor feedbacks...Which could inject CO2e of some 500 thousand gigatons + into our planetary greenhouse budget in the next 50-1000 years? 🧐🤔🤯🙄
Arawyn Lloyd Tudor Franklin
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