We know that Global Warming can be reduced during the years of the century ahead of us if we — our civilization — steadily reduces its emissions of carbon dioxide gas (CO2) into the atmosphere.
Given a specific rate for the reduction of anthropogenic (our CO2) emissions:
+ how long will it take to return Earth’s average temperature to its unperturbed pre-industrial level?, and
+ how much higher will Global Warming (Earth’s temperature) become before it begins to decrease?
Answering these questions is the subject of my recent study. This work is based on a Carbon Balance Model, which I described in an earlier report. 
That model has been further refined in order to address these questions, and the details of that refinement are described in a technical report. 
Prior to the buildup of anthropogenic CO2 emissions in the air, the fluxes of CO2 released by the respiration of Life-on-Earth; and the fluxes of CO2 absorbed from the air by photosynthesis, the surface waters of the oceans, and rock weathering chemical reactions; were in balance. That balance is known as the Carbon Cycle.
As the rate and buildup of anthropogenic emissions increased (after ~1750, but particularly from the mid-20th century), the Carbon Cycle was perturbed out of balance, and the magnitude of that imbalance is determined by the difference between two effects: Anthropogenic Sources, and Stimulated Sinks.
The Anthropogenic Sources are:
+ the CO2 emissions by the human activities of fossil-fueled energy generation and industry, and
+ the CO2 emissions from land use changes (deforestation and its attendant increase of wildfires).
The Stimulated Sinks are the additional absorption of CO2 by photosynthesis and the surface waters of the oceans, because of higher atmospheric concentrations of CO2. At a sufficiently high level of atmospheric CO2 concentration, both these sinks will saturate — stop absorbing CO2. What that “sufficiently high level” is remains uncertain.
The work summarized here includes more realistic (more complicated) models of these source and sink terms in the rate equation for the change of the Carbon Balance over time.
Now I am able to quantitatively link specific rates of the reduction of anthropogenic CO2 emissions, to consequent projected histories of the slowing and then reversal of Global Warming.
Such quantitative linkages have long been featured in the super-computer models of CO2 accumulation in the atmosphere, by the major Climate Science institutes; but now I have my own quantitative version of this correlation, which is analytical (expressed as math formulas, and enumerated with a hand calculator and basic home computer).
Anthropogenic CO2 emissions in year 2020 are 42.2GtCO2/y (42.2 giga-metric-tons of CO2 per year = 42.2*10+12 kilograms/year). This magnitude of total anthropogenic emissions, E, is the addition of our fossil-fueled and land use emissions.
I considered three cases of the intentional steady reduction of annual human-caused CO2 emissions, which are defined to decrease exponentially. The characteristic decay time of each case is: 40 years (CASE 1, a 2.5% annual reduction), 100 years (CASE 2, a 1% annual reduction), and 200 years (CASE 3, a 0.5% annual reduction).
Emissions would be reduced to half their initial rate in 28 years for CASE 1; in 69 years for CASE 2; and in 139 years for CASE 3.
If each of these reduction plans were alternatively initiated in the year 2020, then:
CASE #1, ∆t=40y:
This trend reaches a peak of 449ppm and +1.32°C in year 2048 (in 28 years); it remains above 440ppm and +1.25°C over the years 2032 to 2064 (between 12 to 44 years from now); then descends to 350ppm and +0.56°C in year 2120 (in 100 years); and 300ppm and +0.18°C in year 2140 (in 120 years).
CASE #2, ∆t=100y:
This trend reaches a peak plateau of 485ppm and +1.6°C over the years 2078 to 2088 (between 58 and 68 years from now); it remains above 480ppm and +1.56°C during years 2066 to 2100 (between 46 and 80 years from now); it descends to 350ppm and +0.56°C in year 2202 (in 182 years); and 300ppm and +0.18°C in year 2225 (in 205 years).
CASE #3, ∆t=200y:
This trend reaches a peak plateau of 524ppm and +1.9°C over the years 2125 to 2135 (between 105 and 115 years from now); it remains above 500ppm and +1.72°C between years 2075 and 2190 (between 55 and 170 years from now); and descends down to 360ppm and +0.64°C in year 2300 (in 280 years).
Message to the Humans
The singular challenge for the progressive political and social elements of our civilization is to awaken the rest of the world — and particularly the “developed” and “developing” high-emissions nations — to a full commitment (demonstrated by action) to steadily and significantly reduce anthropogenic CO2 emissions for the rest of human history.
The sooner such reduction programs are initiated, and the greater the vigor with which they are implemented, the sooner we will begin slowing the advance of Global Warming and its continuing erosion of the habitability of Planet Earth, which humans have enjoyed for over 2 million years, and particularly since the end of the Ice Ages (~11,000 year ago).
With decades to a century of discipline applied to this purpose, we can even reverse Global Warming. The longer we wait to do this, the worse the consequences we will have to suffer through, and the longer it would take to extricate our species — and so many other wonderful forms of Life-on-Earth — from the Hell-on-Earth we are creating by our willful and destructive ignorance.
I can only imagine such major programs of CO2 emissions reductions being synonymous with the economic, political and social uplift of the vast majority of people, because Global Warming is directly caused by the unbounded economic, political and social exploitation of the many by the few.
The fact is that we all live on the same planet, and whatever happens to it — whether worsening conflagration and flooding in the now, or eventual cooling and restoration by human commitment — will affect everybody. There is no guaranteed escape.
The CO2 accumulation model that I have described here is just this old scientist’s way of saying: We can do so much better for ourselves, and our children deserve that we try.
 A Carbon Balance Model of Atmospheric CO2
11 September 2020, [PDF file]
 Trends for Reducing Global Warming
15 September 2020, [PDF file]