Does extrapolating current CO2 trends indicate 7632 PPM CO2 and 14C temperature anomaly within 200 years?

Question

Does extrapolating current CO2 trends indicate 7632 PPM CO2 and 14C temperature anomaly within 200 years?

It looks like simply extrapolating the current trends of increasing atmospheric CO2 would show that totally unmitigated green house gas emissions (for the next 200 years) would result in more drastic climate change than ever seen in the last 600 million years. This period included several very extreme extinction events.

3.32 PPM annual CO2 increase compounded at the 1.9% annual growth rate derives 7632 PPM from the current 410 PPM.

This CO2 increase over preindustrial CO2 levels of 280 PPM derives a 3 * log2(7632 / 280) = 14.3C temperature anomaly over the 14C base temperature. 14C + 14C = 28C hotter than any time in the last 600 million years.

This derivation uses the current standard logarithmic casual relationship between increases in CO2 and global temperature: 3C ± 1.5C per CO2 doubling. https://en.wikipedia.org/wiki/Climate_sensitivity#Intergovernmental_Panel_on_Climate_Change

Below shows the basis of the extrapolated 7632 PPM CO2 calculations and a full table of each annual increment to global CO2 for the next 200 years.

https://www.co2.earth/co2-acceleration#

Oct  31  2019: 409.64 ppm<br>
Oct  31  2018: 406.32 ppm<br>
3.32 CO2 Growth<br>

2014 2.11 ppm<br>
1959 0.73 ppm<br>
  55 2.89 growth factor<br>
1.019 ^ 55 = 2.81 growth factor<br>

Thus a 1.9% annual acceleration to the current 3.32 PPM CO2 growth rate

Applying accelarating CO2 growth rate to current CO2 levels for 200 years: in 2219 we would have 7632 ppm of CO2. (See table).

3C ± 1.5C per CO2 doubling we derive:
3 * log2(7632 / 280) = 14.3C tempeature anomaly from 14C base.

28C is hotter than any time in the last 600 million years, thus the next 200 years of utterly unmitigated green house gas emissions would cause the most drastic climate change in 600 million years if we merely extrapolate the current trends.

If I got my {facts, climate science, math} correctly and CO2 continues to increase at its current accelerating rate for 200 years then the world will experience greater climate change than at anytime in the prior 600 million years.

Apparently we are already emitting much more than the 28GT RPC8.5 levels
https://judithcurry.com/2018/11/24/is-rcp8-5-an-impossible-scenario/

My year 2100 emission projection of 1008 PPM matches RCP8.5

CO2_growth over 200 years at currently accelerating rate

  1       3.32   409.64
  2       3.38   412.96
  3       3.45   416.34
  4       3.51   419.79
  5       3.58   423.30
  6       3.65   426.88
  7       3.72   430.53
  8       3.79   434.25
  9       3.86   438.03
 10       3.93   441.89
 11       4.01   445.83
 12       4.08   449.83
 13       4.16   453.92
 14       4.24   458.08
 15       4.32   462.32
 16       4.40   466.64
 17       4.49   471.04
 18       4.57   475.53
 19       4.66   480.10
 20       4.75   484.76
 21       4.84   489.51
 22       4.93   494.35
 23       5.02   499.28
 24       5.12   504.30
 25       5.22   509.42
 26       5.31   514.63
 27       5.42   519.95
 28       5.52   525.36
 29       5.62   530.88
 30       5.73   536.51
 31       5.84   542.24
 32       5.95   548.08
 33       6.06   554.03
 34       6.18   560.09
 35       6.30   566.27
 36       6.42   572.56
 37       6.54   578.98
 38       6.66   585.52
 39       6.79   592.18
 40       6.92   598.97
 41       7.05   605.88
 42       7.18   612.93
 43       7.32   620.12
 44       7.46   627.43
 45       7.60   634.89
 46       7.74   642.49
 47       7.89   650.24
 48       8.04   658.13
 49       8.19   666.17
 50       8.35   674.36
 51       8.51   682.71
 52       8.67   691.22
 53       8.83   699.89
 54       9.00   708.73
 55       9.17   717.73
 56       9.35   726.90
 57       9.53   736.25
 58       9.71   745.78
 59       9.89   755.48
 60      10.08   765.37
 61      10.27   775.45
 62      10.47   785.72
 63      10.66   796.19
 64      10.87   806.85
 65      11.07   817.72
 66      11.28   828.79
 67      11.50   840.08
 68      11.72   851.58
 69      11.94   863.29
 70      12.17   875.23
 71      12.40   887.40
 72      12.63   899.80
 73      12.87   912.43
 74      13.12   925.30
 75      13.37   938.42
 76      13.62   951.79
 77      13.88   965.41
 78      14.14   979.29
 79      14.41   993.43
 80      14.69   1007.84
 81      14.96   1022.53
 82      15.25   1037.49
 83      15.54   1052.74
 84      15.83   1068.28
 85      16.14   1084.11
 86      16.44   1100.25
 87      16.75   1116.69
 88      17.07   1133.45
 89      17.40   1150.52
 90      17.73   1167.91
 91      18.06   1185.64
 92      18.41   1203.71
 93      18.76   1222.11
 94      19.11   1240.87
 95      19.48   1259.98
 96      19.85   1279.46
 97      20.22   1299.31
 98      20.61   1319.53
 99      21.00   1340.14
100      21.40   1361.14
101      21.81   1382.54
102      22.22   1404.34
103      22.64   1426.56
104      23.07   1449.20
105      23.51   1472.27
106      23.96   1495.78
107      24.41   1519.74
108      24.88   1544.15
109      25.35   1569.03
110      25.83   1594.38
111      26.32   1620.21
112      26.82   1646.53
113      27.33   1673.35
114      27.85   1700.68
115      28.38   1728.53
116      28.92   1756.91
117      29.47   1785.82
118      30.03   1815.29
119      30.60   1845.32
120      31.18   1875.92
121      31.77   1907.10
122      32.38   1938.87
123      32.99   1971.24
124      33.62   2004.23
125      34.26   2037.85
126      34.91   2072.11
127      35.57   2107.01
128      36.25   2142.58
129      36.93   2178.83
130      37.64   2215.77
131      38.35   2253.40
132      39.08   2291.75
133      39.82   2330.83
134      40.58   2370.66
135      41.35   2411.24
136      42.14   2452.59
137      42.94   2494.72
138      43.75   2537.66
139      44.58   2581.41
140      45.43   2625.99
141      46.29   2671.42
142      47.17   2717.72
143      48.07   2764.89
144      48.98   2812.96
145      49.91   2861.94
146      50.86   2911.86
147      51.83   2962.72
148      52.81   3014.55
149      53.82   3067.36
150      54.84   3121.18
151      55.88   3176.02
152      56.94   3231.90
153      58.02   3288.84
154      59.13   3346.87
155      60.25   3405.99
156      61.40   3466.25
157      62.56   3527.64
158      63.75   3590.20
159      64.96   3653.95
160      66.20   3718.92
161      67.45   3785.11
162      68.74   3852.57
163      70.04   3921.30
164      71.37   3991.34
165      72.73   4062.72
166      74.11   4135.44
167      75.52   4209.55
168      76.95   4285.07
169      78.42   4362.03
170      79.91   4440.44
171      81.42   4520.35
172      82.97   4601.77
173      84.55   4684.74
174      86.15   4769.29
175      87.79   4855.44
176      89.46   4943.23
177      91.16   5032.69
178      92.89   5123.85
179      94.65   5216.74
180      96.45   5311.39
181      98.29   5407.85
182     100.15   5506.13
183     102.06   5606.28
184     104.00   5708.34
185     105.97   5812.34
186     107.98   5918.31
187     110.04   6026.29
188     112.13   6136.33
189     114.26   6248.46
190     116.43   6362.71
191     118.64   6479.14
192     120.89   6597.78
193     123.19   6718.68
194     125.53   6841.87
195     127.92   6967.40
196     130.35   7095.32
197     132.82   7225.67
198     135.35   7358.49
199     137.92   7493.84
200     140.54   7631.76

Answer 1

It looks as if you are assuming a constant percentage increase, compounded annually. There are many reasons why this is not so. It reminds me of many decades ago when I routinely weighed my baby son. On the basis of his rate of growth I calculated that he would weigh 2660 kg by the age of 3! So much for simple extrapolation. Humans are already using vastly more than the renewable rate of resource consumption, so it is obvious that our population cannot continue to grow at anything like the historic rates. In particular, the rate of carbon emissions is slowing; not by anything like fast enough, but slowing nevertheless. Then there are the climate change feedback processes that will kick in sooner or later. Some are probably beginning already. By my estimation there are at least 16 feedback processes, a mix of positive and negative, but mostly positive. None of them are adequately calibrated. In short, future atmospheric $\small\mathsf{CO_2}$ levels will be the product of a host of non-linear processes. It would be rash of anyone to try and predict far into the next century. That said, if I was absolutely forced to project so far into the future, I would try to adapt the graph of the last few thousand years of atmospheric $\small\mathsf{CO_2}$ to an error function curve. But then you would be forced into an extrapolation in which the error bounds far exceed the final quasi-equilibrium $\small\mathsf{CO_2}$ concentration. In other words, it would be a meaningless exercise. We will all be in deep trouble if the $\small\mathsf{CO_2}$ reaches even 760 ppm, let alone 7600+ of your estimate! I find it scary enough that we are still on an RCP trajectory that is closer to 8.5 than any of the other 'standard scenarios'. Present reality is alarming enough without speculating on fantastic projections.

Answer 2

As a thought experiment it may tell us something about why simplistic extrapolation is inadequate for climate change prediction. Climate modelling of extreme scenarios might be compared and contrasted with simple extrapolation, but is more likely to show deficits in such extrapolation than in the modelling. It cannot work as prediction because there are very significant real world factors and constraints - physical, economic, societal - at work that are not included, that mean simple extrapolation will almost certainly be wrong.

Answer 3

A linear correlation can not be done as the atmosphere have not a linear progression. Take a look to this interested link to these Chicago University Climate Models Webpage. The first one you should check is this.

First of all, $\small\mathsf{CO_2}$ is acting as a Greenhouse Effect Gas because it is absorbing some of the infrared radiation that it is trying to leave the Earth. $\small\mathsf{CO_2}$ it is just absorving this radiation and bringing back to the surface (as well as $\small\mathsf{H_2O}$, $\small\mathsf{CH_4}$...).

So the natural cooling system of our planet is disturbed by all this gases. But there is a limit for all of them. The gas is not acquiring all the energy, just a range (Band Saturation). So it can absorb just some of the energy.

Let´s see one example: Considering no $\small\mathsf{CH_4}$ collaboration or $\small\mathsf{H_2O}$... Same point on different latitudes...

| CO2 CONCENTRATION   |        |         |         |        |        |        |        |        |        |        |        |
|---------------------|--------|---------|---------|--------|--------|--------|--------|--------|--------|--------|--------|
| (Energy in W/m2)    | 0      | 10      | 50      | 100    | 200    | 400    | 800    | 1600   | 3200   | 6400   | 12800  |
|---------------------|--------|---------|---------|--------|--------|--------|--------|--------|--------|--------|--------|
| Tropical Atmosphere | 339.12 | 325.62  | 317.45  | 313.84 | 310.39 | 306.97 | 303.51 | 299.93 | 296.10 | 291.93 | 287.15 |
| MidLattitude Summer | 328.13 | 315.57  | 307.908 | 304.77 | 301.69 | 298.61 | 295.44 | 292.21 | 288.82 | 285.21 | 281.16 |
| MidLattitude Winter | 264.36 | 254.59  | 248.97  | 246.62 | 244.23 | 241.81 | 239.33 | 236.79 | 234.28 | 231.73 | 229.00 |
| Subartic Summer     | 303.29 | 292.271 | 286.12  | 283.61 | 281.12 | 278.61 | 276.04 | 273.46 | 270.89 | 268.19 | 265.14 |
| Subartic Winter     | 222.38 | 215.53  | 211.48  | 209.82 | 208.15 | 206.39 | 204.57 | 202.75 | 201.02 | 199.36 | 197.69 |

With this figures, we can see that it is a linear regression:

But as soon as we are absorbing energy, we need more $\small\mathsf{CO_2}$ to increase the amount. For example, the preindustrial readings were 280 ppm until the actual 400 ppm, with this amount of energy retained, you have the actual temperature increasing. In order to collect the same amount of energy (so in order to increase the temperature) we need to reach 608 ppm:

| CO2 Increasing      | 200-400 | 400-800 |   | 400-608 |       |
|---------------------|---------|---------|---|---------|-------|
| Tropical Atmosphere | 3,42    | 3,46    |   | 1,76    | 51,0% |
| MidLattitude Summer | 3,08    | 3,17    |   | 1,57    | 50,4% |
| MidLattitude Winter | 2,42    | 2,48    |   | 1,26    | 51,3% |
| Subartic Summer     | 2,51    | 2,57    |   | 1,32    | 52,0% |
| Subartic Winter     | 1,76    | 1,82    |   | 0,91    | 51,0% |
| Average             | 2,77    | 2,83    |   | 1,43    | 51,1% |

So the concentration is growing linearly, but that is not the case of energy and temperature.

You can not make a simple correlation because the temperature depends of: $\small\mathsf{CO_2}$, $\small\mathsf{H_2O}$, $\small\mathsf{CH_4}$, Ozone, Aerosols, Sun Energy Emission, Clouds, Latitude, Ground colour... So it is not just a number.

The main uncertainty on the Greenhouse Effect are clouds. Check the different models and you will see that a 2X concentration growing can increase the energy on 3-4 $\small\mathsf{W/m^2}$, clouds can reduce/increase from -17 W to +5 W. Considering your figures, with a 3.32 ppm/year growing, in order to get the temperature increasing from preindustrial area until now, you will reach 2079. If we reduce the growing, this period will be extended.

There are some more problems that just $\small\mathsf{CO_2}$: $\small\mathsf{CH_4}$, Permafrost areas, high altitude clouds...

I recommend you this reading from David Archer.

Hope it helps