Hi Doug
It's only a simple Excel spreadsheet. The formula is T*(1-e^- ^λ ^t )
where T is the total temperature difference (here 10^o C); λis the
inverse of the e-folding time (here 0.01); t is the number of years from
the start.
Regards
Robert
On 27/02/2023 17:18, Douglas Grandt wrote:
Thanks, Robert!
Wouid you mind sharing the software and equation? It’s exactly as I
envisioned.
T = fn (t) = t * (0.063e) * (e^^-(0.01t)) ???
where:
T is temperature °C increase over present
t is number of years from present time
Is that close? My recollection of “ln” decay is a bit rusty. This
equation matches the endpoints at t = 0 and t = 100 years, and
generally has the approximate shape, but I believe the is a more
elegant and absolutely correct equation that this.
Plus, another factor may be required to accommodate the asymptotic
approach to 10°C at the limit t = ♾️
Doug
Sent from my iPhone (audio texting)
On Feb 27, 2023, at 8:22 AM, Robert Chris <robertgch...@gmail.com> wrote:
Doug and Ron
Here's how I arrived at my conclusions.
From the extracts below, I conclude, given that by 2020 (or
thereabouts) we had already doubled atmospheric GHGs from
pre-industrial including non-CO_2 GHGs, that we will eventually warm
the surface by 10^o C with a climate response e-folding time of ~100
years provided the offsetting cooling from anthropogenic aerosols
continues to decline and is eventually largely eliminated.That means
that by 2050 the warming would be ~2.4^o C less the residual aerosol
cooling of, say 0.4^o C, giving their estimate of 2^o C.
·When all feedbacks, including ice sheets, are allowed to respond
to the climate forcing, the equilibrium response is approximately
doubled, i.e., ESS is ~ 10°C.
·Yet the time required for the [improved] model to achieve 63% of
its equilibrium response remains about 100 years.(See Fig 4b –
note log x-axis.)
·With all trace gases included, the increase of GHG effective
forcing between 1750 and 2021 is 4.09W/m^2 , which is equivalent
to increasing the 1750 CO_2 amount (278 ppm) to 561 ppm (formulae
in Supporting Material). We have already reached the GHG climate
forcing level of doubled CO_2 .[Note that they develop a scaling
factor of 2.4^o C per W/m^2 which corresponds to 10^o C for the
4W/m^2 of current GHG forcing.]
·Declining aerosol amount implies acceleration of global warming
above the 1970-2010 rate.
·Global temperature responds reliably to climate forcing on
decadal time scales, with about 50% of the response in the first
decade, with about 15% more in the next 100 years
·we expect some [aerosol] reduction and a forcing increase of at
least +0.1 W/m^2 per decade [between 2010 and 2050].
·we estimate that the global warming rate in 2010-2040 will be at
least 50% greater than in 1970-2010, i.e., at least 0.27°C per
decade.
·The poster child for warming in the pipeline is Fig. 7, showing
that equilibrium warming for today’s GHG level, including slow
feedbacks, is about 10°C. Today’s level of particulate air
pollution reduces equilibrium warming to about 7°C.
·The 7-10°C global warming is the eventual response *if today’s
level of GHGs is fixed and the aerosol amount is somewhere
between its year 2000 amount and preindustrial amount*. (emphasis
added) [Note that the assumptions here are that ‘today’s level of
GHGs is fixed’, which I take to mean that future emissions are
ignored, and aerosols are currently lower than they were in 2000.]
Here's a simple graph showing the realisation of 10^o C of
warming with an e-folding time of 100 years.Assume it starts in
2020 or thereabouts (when atmospheric CO_2 e reached 556ppmv.).
<FHSZ9j4fwfinBYJV.png>
Regards
Robert
On 27/02/2023 03:50, Douglas Grandt wrote:
Ron and Robert,
Visually, the shape of the curve is something like this … more or
less … as best I can fathom.
This is my interpretation of Hansen's assumptions and conclusions,
but I very well could be wrong …
Perhaps somebody has chart generating software that would be more
precise than my eyeball.
Doug
On Feb 26, 2023, at 8:58 PM, Ron Baiman <rpbai...@gmail.com> wrote:
*6.3 C (63% of 10) by 2020*
On Sun, Feb 26, 2023 at 7:56 PM Ron Baiman <rpbai...@gmail.com> wrote:
Robert,
Do you have a page number or an explanation of how you arrived
at your figures? In the paper(https://arxiv.org/abs/2212.04474)
on p. 31 I'm finding: "The 7-10 C global warming is the
eventual response if today's level of GHGs is fixed and the
aerosol amount is somewhere between its year 2000 amount and
preindustrial amount." but the key temp Figure 7 on p. 18
doesn't extend beyond 2025. In the section on Climate response
times (p. 32) the paper states that the in 2020 GISS GCM:
"...the time required for the model to achieve 63% of its
equilibrium response remains about 100 years" which would put
the expected temp based on forcing estimated in the paper at
6.3 C (63% or 10) by 2023. Is this where you're getting your
6.3 C by 2120 from? Unfortunately, I have not had the time (and
probably not the background) to go through the entire paper and
understand it well!
Best,
Ron
On Sun, Feb 26, 2023 at 7:09 PM Ron Baiman <rpbai...@gmail.com>
wrote:
Thanks for the correction Robert!
Sent from my iPhone
On Feb 26, 2023, at 6:41 PM, Robert Chris
<robertgch...@gmail.com> wrote:
Ron
Hansen et al say that the 10degC is based on 'today's GHG
level' and that it has an e-folding time of 100 years.
That implies 6.3degC by 2120 and a bit less by 2100.
Regards
Robert
On 26/02/2023 23:43, Ron Baiman wrote:
Jim Hansen et al (https://arxiv.org/abs/2212.04474 )
believe that existing legacy GHG's have put us in "in
the pipeline" for 10 degrees C warming by 2100!
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