Proof that cs=36
Climate sensitivity is around 36 and time delay between new CO2 level
and new stabilized temperature is in the range 500-800 years.
Prof. Dr. Reto Knutti, thank you for these encouraging words:
If you make extraordinary claims, you need to provide extraordinary evidence
and disprove five decades of research. I encourage you to do this....
Well, here is the evidence:
( Prof. James Hansen har fått denna härledning och han har godkänt att jag får använda hans
resultat, citat och bilder från hans senaste nyhetsbrev: )
The model for the earth is supposed to be a RC net, where V1(t) is Committed Warming.
Example: If Committed Warming= 2C, then earth will get +2C warmer after
years of time delay if all emissions stop now.
RC forms a time delay and V2(t) is calculated earth temperature anomaly.
V2(t) can then be compared with NASA real earth temperature anomaly.
If CO2 would be constant, it would be easy to compare the calculated graph with NASA real graph.
As climate sensitivity and RC (time delay between new CO2 level and stabilized temperature)
are supposed to be unknown, we use the very shape of the graphs to find maximum
fit with NASA real earth temperature anomaly. Here we will find two important answers:
1. Climate sensitivity
2. RC time delay
That is the most important information in the entire climate crises.
Climate politics will succeed only if we get climate sensitivity right .
Almost every other climate calculation and conclusion depends on this.
As starting point we use the real earth data from the 2022 0922 newsletter from Prof. James Hansen including his qualified estimation that +1.5 C could occur already 2024.
The extracted data is here between 1970 and 2024:
We want to use 1970 as temperature reference . All dots are lifted 0.09 C
to make the first point at 0C.
We can make a model of Earth real temperatur anomaly V2(),
calculated with an ordinary differential equation, and compare with NASA real.
We start the integration in year 1970 and compare with NASA real.
The current i charging the capacitor C = i = C * d V2(t) /dt
The same current is formed by ohms law over R i = V1-V2 / R
C * d V2(t) /dt = V1-V2 / R
Then V2(t) can be solved from the following ordinary differential equation.
Tcommitt_t(t, cs) = V1()
The future development of ppm CO2 can be described with a polynom of first degree:
ppm(t) = -3518.61397849464 + 1.94978494623657*t
The very definition of climate senstitvity cs is
This formula is known for 120 years and it is in daily use by IPCC
to define and use climate sensitivity.
The diagram shows the committed temperature on earth for different
values of cs.
This is the temperature that earth will stabilize on if all emissions are
cut off and the delay time has passed.
Example: At present, with 420 ppm CO2, cs=36, the earth will stabilize at +22C
over 1970 level after 700 years if all emissions are stopped today.
At present, temperature rises with 0.03 C/year.
To reach +22C will take 22/0.03 = 700 years. (Quick estimation )
The committed temperature can be expressed as a funktion
of ppm CO2 and climate sensitivity cs:
Now we can express committed temperature as a function of time and cs
This tells us the additional warming of earth if all emissions are stopped
at a specified year at different climate sensitivities, cs.
Now we can calculate how the earth will warm according to the model V2(t)
and we can compare with NASA real measurements.
The models are plotted here at climate sensitivity=36 with different
time-delays (RC) between CO2 and temperature (400-800 years) and compared
with NASA real measurements.
We have to keep in mind that NASA real measurements has much noice.
Still, there is a clear long term tendency.
The model cs=36 and RC=600 fits well with NASA real.
It is impossible to say if climate sensitivity got higher than 36 after 2010
of if is just noise on the NASA measurement.
It is good enough to conclude that climate sensitivity=36 and
time delay between CO2 release and global temperature
is 600-800 years.
An other view:
If climate sensitivity=cs=3, then it is a forecast.
Every doubeling of ppm CO2 makes earth 3C warmer.
With cs=3, IPCC made a forcast: +2C at 450 ppm year 2100.
This forecast failed miserably.
Also the line in the graph "cs=36 and RC=700 years" is a forecast based on the mathemaics
This forecast makes a perfect fit with Prof James Hansen's "Best linear fit 1970-2015"
in his newsletter 22 sept 2022.
If IPCC had used this input 40 years ago, their forecast would have been
correct. On top of that, cs=36 stands the Test-stick
A number of other indicators speak for cs=36
Test for climate sensitivity=36
The curves show that +2C and 285 ppm have occurred simultaneously 4 times.
At the far right is the year 1895, when CO2 reaches 285 ppm again.
Why is +2C not reached 1895 ? A logical conclusion is, that a new CO2 level needs hundreds of years to reach the corresponding stabilized temperature.
If emissions were stopped 1895, it would take approx. 700 years to reach dangerous +2C,
Test of climate sensitivity=36 with the classical formula:
t=36*ln(225/275) /ln(2)= -10 Ice age may occur OK
t=36*ln(275/275) /ln(2)= 0 Important 0-point OK
t=36*ln(285/275) /ln(2) = +2 Important +2 point OK, see VOSTOK
t=36*ln(10^6/275) /ln(2)=425 Venus point OK
Climate sensitivity=3 fails these tests. Why use a cs=3 that fails all tests
and delivers wrong forecasts ???
It seems that cs=36 should be considered the foundation for
climate calculations and time delay RC= 600-700 years.
This gives climate politics a chance to work.
With this input, it was possible for us to make a correct forecast 2008-2022.
For the same periode, IPCC failed totally (+2C 450 ppm 2100)
The reason is that IPCC relied on climate sensitivity =3
t= cs*ln(ppmCO2/275)/ln(2) cs=3 ppmCO2= 450
t= 3*ln(450/275)/ln(2) = +2 C Yes, that's the way IPCC calculated.
We relied on climate sensitivity =36 and got it exactly right !
Why rely on a climate sensitivity=3 (=IPCC, SMHI) that fails most tests with reality
and brings civilization to collapse ? Is that the reason why Dr Peter Carter calls it
the worst crime ever against humanity ?
At last an example: Swedish government accepted the IPCC summary for policymakers
and Bill and Climate Law are based on the blue line B , +2C at year 2100,
driven by climate sensitivity=3
Nasa real measurements indicate line A and everybody can guess that the red line is driven by a far
higher climate sensitivity than 3. No reaction from climate experts. No discussion in the press.
No reaction at all. Nobody cares about the foundation for the entire climate politics in Sweden.
..... and elsewhere
Another example is the scientific paper
Thorsten Mauritsen and Robert Pincus
Here it is discussed that "Committed Warming" can be as low as +1.1C.
probably seen from 2017, when the report was written.
If all emissions were stopped in 2017, there is only a 13% chance that the Earth
ever exceed +1.5C (Paris Agreement ). Is that correct ?
What's about Prof. James Hansen who says that the
it is quite possible that the Earth will exceed +1.5C as early as 2024.
If climate sensitivity is 36, then committed warming is +22C, not +1.1C
Our survival depends on getting this right.
Hestra, 2022 11 05
(c) Bengt Ovelius
Thanks a lot for all comments !
An other perspective and a different approach is presented here.