Calculating from accepted figures for the amount of CO2 in the oceans, atmosphere and produced by humans, I think the following scenario seems most likely.
Around 2050 the CO2 concentration in the atmosphere passes the threshold level of 600 ppm, global temperature rises to a level that is over 3 degrees from pre-industrial levels and glaciers melt in a much faster pace. Insolation from the sun will change over the next hundreds of years and it will affect the speed of melting, there may be temporary cooling periods, but if CO2 concentrations keep rising, the two main glaciers in the Greenland and Antarctic will eventually melt. Ocean levels rise significantly and many costal cities will submerge under water, but this will happen over hundreds or thousands of years. Some places will turn dry, there will be storms and all that. When the big glaciers melt cold water from them absorbs the CO2 that humans have produced up to 2050. This cold water sinks to deep ocean waters and in this way distributes CO2 to deep oceans probably somewhat faster than the normal transfer between surface and deep water. When the CO2 concentration in the atmosphere decreases under the threshold of 600 ppm the global temperature decreases and glaciers start to grow again, but this cooling process is rather slow as oceans release some of the buffered CO2. The Earth will finally return to the same equilibrium and the present intergalacial period continues.
If humans continue producing CO2 to the atmosphere over the time 2050-2100, as is likely, the scenario is still more or less the same: the oceans have hundreds of years to mix surface water with deep water and human produced CO2 can mostly be absorbed in oceans. The real problem emerges only if humans keep on producing CO2 also in the next century: glaciers will be lost and the Earth atmosphere will stabilize on another equilibrium point, which may not be so nice for humans.
This scenario does not essentially differ from the “mainstream” scientific view, but the mass media has presented global warming it a more dramatic way, maybe in order to sell electrical cars. I will briefly go through the numbers of the CO2 balance, just to check.
Article [1] gives the average concentration of CO2 in oceans as about 2.3 mmol/kg and the total amount of carbon in the oceans as about 38,000 Pg (Pg=Pentagram=1015 g). Let us calculate the concentration in another way. Oceans contain 1.338*1021 l of water. The density of seawater is 1.025 kg/l, thus there is 1.305*1021 kg of water. 38,000 Pg of C corresponds to 3.665*38,000 Pg of CO2=140*1018 g of CO2. This gives the average concentration (140*1018 g)/(1.305*1021 kg)=107.3 mg/kg. As the molecular mass of CO2 is 44.01 g/mol, the average concentration is (107.3 mg/kg )(44.01 mg/mmol)-1=2.4 mmol/kg. This number is quite close to the estimate 2.3 mmol/kg and we can agree that this number is correct. I prefer the estimate 2.4 mmol/kg as then the numbers in the calculations will not have contradictions.
The carbon content of the pre-anthropogenic atmosphere is given in [1] as about 600 Pg. The addition from human activities is so far 240 Pg. The carbon content of the atmosphere is thus 840 Pg. Let us verify this number by a calculation. In 2017 there was 405 ppm of carbon in the atmosphere. Converting ppm to mg/m3 gives the concentration of CO2 in the atmosphere in 2017 as 785 mg/m3. Earth’s atmosphere weights 1.225 kg/m3. and the total weight of the atmosphere is 5.15*1018 kg. The pressure of the atmosphere is not constant, but we can calculate what the volume would be if the air pressure is everywhere as on the sea level. Then the volume would be (5.15*1018 kg)/(1.225 kg/m3)=4.2*1018 m3 and we can use this volume to calculate the mass of CO2 in the atmosphere: (785 mg/m3)(4.2*1018 m3)=3.3*1015 kg. The carbon content is (3.3*1018 g)/3.665=900 Pg according to this calculation. We can verify it still another way. The Wikipedia [2] gives the information that 33.5*109 tons of CO2 corresponds to 4.3 ppm of atmospheric CO2 and 9.14*109 tons of C. Thus, 405 ppm=94.19*4.3 ppm=94.19*33.5*1012 kg=3.155*1012 kg is the weight of CO2 in the atmosphere. It corresponds to 860 Pg of C. We can conclude that the figures calculated in different ways give about the same result: there is about 850 Pg of carbon in the atmosphere.
Glaciers contain 24.6*1018 l of water. As it is freshwater, it weights 24.6*1018 kg. When this water melts to oceans and becomes saltwater, it can take (2.4 mmol/kg)(24.6*1018 kg)=60*1015 mol of CO2. In kilos it is (44.01 g/mol)( 60*1015 mol)=2640 Pg of CO2. The carbon content is 720 Pg of C. This means that if glaciers melt, they can absorb all human created CO2 from the atmosphere. The Wikipedia [2] gives 600 ppm as the threshold of atmospheric CO2 that started glaciation. It can also be taken as the threshold when glaciers are bound to disappear (after a long time).
The Greenland ice cap melts about 280 km3 per year at the current rate. Antarctic melts even slower: though there is much more ice, it melts only 219 km3 per year. Together these two main glaciers melt about 500*1012 liters. It is so little that it does not matter for CO2. We have to wait for larger amount of melt water before it starts to remove CO2. Now the oceans remove CO2 only by the gas pressure difference in the atmosphere and in the surface water. Oceans remove about 26% of CO2, so the concentration is rising all the time.
The ice cap in Greenland has the volume is 2.9*106 km3. With the current rate the ice will totally melt in 2.9*106/280=10,400 years. The melting speed accelerates when the temperature rises in the Arctic areas. Global temperature has increased 0.9 degrees Celsius since pre-industrial times, but Greenland temperatures have increased 2 degrees Celsius. However, simple calculations, like Pete Stevens did in [4], confirm what climatic scientists well know: the Greenland ice cap will take thousands or hundreds of years to melt if things stay as now.
But things may not stay as now. Look at this figure of the sun’s radiation in the Northern latitudes from the Wikipedia [4]. The Earth’s orbit changes in time and the result is that the radiation from the sun has periods, so called Milankovitch cycles. These cycles are one of the reasons for ice ages in the Earth’s past (but not the only reason: there have been comet impacts, volcano activity, biosphere changes and so on). The calculated insolation is the red curve and we are now at the zero point in the x-axis. Notice that from 160 years to 340 years there are four peaks downward and three peaks upward. It means that in the new 300 years sun’s radiation will decrease and increase in ways that can start an ice age or a warm period. Though humans have caused the present global warming by adding CO2 to the atmosphere, there is no simple way of saying what the result will be in the next hundreds of years and if the ice cap on Greenland finally will melt or not. There could be a volcano eruption that cools the Earth, for instance.
The ice cap on the Antarctic will melt even slower than the ice cap on the Greenland and there are similar issues concerning insolation and other relevant matters. All that can be said is that the two main glaciers will not melt in a very short time (like 30-100 years), unless the Earth is hit by a comet or something else on that scale happens.
In 2010 humans released 33.5*1012 kg of CO2. It is 9.14 GtC (gigatons of carbon). In 1990 humans released only 6.15 GtC, so there has been a major increase. Assuming that this increase continues with the same speed we can calculate how long it takes to reach 600 ppm, which is given in [2] as the threshold which causes the glaciers to melt. Today the CO2 concentration of the atmosphere is at 410 ppm. There remains 190 ppm, which corresponds to 190*9.14/4.3=404 GtC. We will reach this level in 32 years (in the year 2051) and the average yearly production of carbon to the atmosphere will be 5.9 ppm (=12.6 GtC). This figure includes the reductions that absorbing CO2 to the oceans and biosphere causes, but it ignores melting of the glaciers. CO2 absorbs to the oceans because of the pressure difference in the water and in the atmosphere and it is a different mechanism than with glaciers. Water from glaciers is very cold and has no CO2 to start with and for that reason absorbs CO2 more effectively.
The level 600 ppm will be reached around 2050. There is very little chance that humans can decrease the usage of carbon so fast. Global warming from 240 Pg of carbon released by humans has been about 1.5 degrees Celsius. Adding 404 Pg of carbon before 2051 adds 2.5 degrees Celsius. At 600 ppm glaciers will melt faster, but it is still several hundred years. It is good that humans try to stop burning fossil fuels, anyway the best resources have already been used, but all this does not sound so dramatic.
There may be something that has been missed so far and should be better studied. When the Younger Dryas ended glaciers melted very fast in an event that is remembered by many peoples as the deluge of the myths. What happened at that time? There was a comet in 10,800 BC that started the Younger Dryas, but the deluge was at the end of the Younger Dryas. It probably was not a comet, though Hancock speculated so in the Magicians of gods. For sure there were flood lakes kept by ice dams or land barriers and those stoppers broke causing a local flood, but that may not explain the myths. Possibly there is something more, maybe connected with the oscillations of insolation. As my temporary conclusions, the numbers are fine and correct, but it is not explained yet. Something is missing in the global warming story. There very possibly is still some catastrophic flood mechanism that has not been found. The old theory of the Gulf stream shutting on and off is a possible explanation, but I have to look at it. The stream seems to be slowing down.
References:
[1] Richard E. Zeebe and Dieter A. Wolf-Gladrow, “Carbon dioxide, dissolved (ocean)” in
https://www.soest.hawaii.edu/oceanography/faculty/zeebe_files/Publications/ZeebeWolfEnclp07.pdf
[2] Wikipedia: “Carbon dioxide in Earth’s atmosphere”
https://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth%27s_atmosphere
[3] Pete Stevens: “The Greenland ice sheet isn’t melting anywhere near as fast as you think.”
http://www.ex-parrot.com/pete/greenland.html
[4] Wikipedia: “Milankovitch cycles”
https://en.wikipedia.org/wiki/Milankovitch_cycles