The simple model was not applied to geoengineering at that time, however mentioned negative emissions already in 2008. Of course, like all physical equations fitting a complex system, it depends on the model parameters (here B, beta, sigma, mu, alpha, C_1). These can be treated as approximately constant only within a certain range.

If this range is left (as you suggest with the various geoengineering measures), these parameters need to be adjusted accordingly as a function of the variables G, F, C and T (and other variables), taking higher orders into consideration. Nonetheless, the principle logic of the first-order model and the solutions still remain.

This also applies to more complex climate models that use some "constants" which are not really constant for large system modifications. Here we have the limits of modelling for problems for which have no experience and data.

Jürgen Scheffran


On 14.09.2019 13:05, Aaron Franklin wrote:
Yes, but does this paper include margins of error wide enough to include the [conservatively speaking] permafrost and clathrate C of polar and deep ocean regions of over 100 thousand gigatons C not to mention burning tropical and Boreal forests, peat, CO2/methane/black carbon soot, nitrous oxides, water vapor feedbacks... Which could inject CO2e of some 500 thousand gigatons + into our planetary greenhouse budget in the next 50-1000 years? 🧐🤔🤯🙄

Arawyn Lloyd Tudor Franklin

On Sat, 14 Sep 2019, 10:47 PM Juergen Scheffran, <juergen.scheff...@uni-hamburg.de <mailto:juergen.scheff...@uni-hamburg.de>> wrote:

    The fundamental relationships discussed here were analysed in an
    early paper, using equations of a basic climate model often
    applied in integrated assessment of climate change. It determines
    mathematical conditions for zero and negative emissions (shown in
    Figure 3 as a function of climate sensitivity and climate
    targets). The integral mentioned by Klaus Lackner is used on page
    266. The paper also determines economic conditions for energy
    transitions to meet climate targets but can also be used to
    determine conditions for climate engineering (which 2008 was a
    rather new topic):

    Scheffran J (2008) Adaptive management of energy transitions in
    long-term climate change. Computational Management Science 5(3):
    259-286. https://link.springer.com/article/10.1007/s10287-007-0044-1

    Access:
    
https://www.researchgate.net/publication/24053927_Adaptive_management_of_energy_transitions_in_long-term_climate_change


    On 14.09.2019 12:15, Klaus Lackner wrote:

    For climate change the integral over the emissions matter.   If
    the integral is to remain constant, we have to drive the
    emissions to zero, i.e., they have to come down.  For that we
    need a negative time derivative of emissions, but so far we have
    kept even derivative positive as well.  We are still on the
    accelerator not on the brake.

    If we want to have the integral to come down, we need negative
    emission. (And yes the ocean helps a little, but the ocean is
    good at it, because the rising CO2 levels in the atmosphere
    maintain a gradient.  If the CO2 does not go up anymore, the
    gradient into the ocean will gradually go away and with it the
    rate at which the ocean picks up CO2.

    Uptake will slow down right away and not wait until the entire
    ocean filled up.

    Klaus

    *From: *"Hawkins, David" <dhawk...@nrdc.org>
    <mailto:dhawk...@nrdc.org>
    *Date: *Saturday, September 14, 2019 at 12:03 PM
    *To: *Klaus Lackner <klaus.lack...@asu.edu>
    <mailto:klaus.lack...@asu.edu>
    *Cc: *Andrew Revkin <rev...@gmail.com> <mailto:rev...@gmail.com>,
    "durb...@gmail.com" <mailto:durb...@gmail.com>
    <durb...@gmail.com> <mailto:durb...@gmail.com>,
    "geoengineering@googlegroups.com"
    <mailto:geoengineering@googlegroups.com>
    <geoengineering@googlegroups.com>
    <mailto:geoengineering@googlegroups.com>
    *Subject: *Re: [geo] No fossil fuels = global warming stops “soon”

    And, we are not stopping emissions yet.  Even under the most
    ambitious scenario (the LED scenario by Grübler, et al),
    cumulative additional  CO2 emissions to 2100 from fossil energy
    use are over 630 Gt.  Coupled with about 250 Gt of enhanced
    “nature-based” removals, the result is more than a 40% increase
    in the temperature anomaly we are suffering today—an increase
    that persists into the 22nd century.

    When one considers the pain that is being inflicted today from
    extreme events (to which climate disruption is already adding),
    that is a lot of additional suffering.

    We have crossed into the realm of dangerous anthropogenic
    interference with the climate system.  We must not trespass
    further but we will. The job is to move back toward the climate
    we enjoyed earlier as fast as we can.

    David

    Sent from my iPad


    On Sep 14, 2019, at 10:45 AM, Klaus Lackner
    <klaus.lack...@asu.edu <mailto:klaus.lack...@asu.edu>> wrote:

        Yes, the oceans are taking on heat.   But the energy
        imbalance remains until the CO2 is gone.  The oceans will
        take up both the CO2 and the heat, but it is a slow (and
        slowing) process.

        *From: *Andrew Revkin <rev...@gmail.com
        <mailto:rev...@gmail.com>>
        *Date: *Friday, September 13, 2019 at 7:42 PM
        *To: *Klaus Lackner <klaus.lack...@asu.edu
        <mailto:klaus.lack...@asu.edu>>
        *Cc: *"durb...@gmail.com <mailto:durb...@gmail.com>"
        <durb...@gmail.com <mailto:durb...@gmail.com>>,
        "geoengineering@googlegroups.com
        <mailto:geoengineering@googlegroups.com>"
        <geoengineering@googlegroups.com
        <mailto:geoengineering@googlegroups.com>>
        *Subject: *Re: [geo] No fossil fuels = global warming stops
        “soon”

        If we stop the energy imbalance, oceans can also go a long
        way toward spreading that existing heat burden over time, as
        per this Rosenthal, Linsley, Oppo work:

        https://science.sciencemag.org/content/342/6158/617
        
<https://urldefense.proofpoint.com/v2/url?u=https-3A__science.sciencemag.org_content_342_6158_617&d=DwMFaQ&c=l45AxH-kUV29SRQusp9vYR0n1GycN4_2jInuKy6zbqQ&r=hFjA8A8KwwhQx5qilpfIleTL0XYVr_fckT8DnwIEWlQ&m=c5WkKQm80oGtr-ik0DfPBRt8G9lGzOp9Rc3aUa_j94M&s=GysUrJWxBv1OzAzhlNJZ5RtjBqxRsmk9ibIxV3U2Ik4&e=>

        
https://dotearth.blogs.nytimes.com/2013/10/31/10000-year-study-finds-oceans-warming-fast-but-from-a-cool-baseline/
        
<https://urldefense.proofpoint.com/v2/url?u=https-3A__dotearth.blogs.nytimes.com_2013_10_31_10000-2Dyear-2Dstudy-2Dfinds-2Doceans-2Dwarming-2Dfast-2Dbut-2Dfrom-2Da-2Dcool-2Dbaseline_&d=DwMFaQ&c=l45AxH-kUV29SRQusp9vYR0n1GycN4_2jInuKy6zbqQ&r=hFjA8A8KwwhQx5qilpfIleTL0XYVr_fckT8DnwIEWlQ&m=c5WkKQm80oGtr-ik0DfPBRt8G9lGzOp9Rc3aUa_j94M&s=v9pklsd2w8YcGIIivLMYXTHahJdT_7PyynBwqc7wvAE&e=>

        On Fri, Sep 13, 2019 at 8:16 AM Klaus Lackner
        <klaus.lack...@asu.edu <mailto:klaus.lack...@asu.edu>> wrote:

            If by warming you mean an increase in the temperature,
            then warming will stop soon.  If by warming you mean that
            it is warmer than without excess Greenhouse gases, then
            this excess temperature will be with us a long time. 
            Solomon et al claimed it is 1000 years.

            Klaus

            *From: *<geoengineering@googlegroups.com
            <mailto:geoengineering@googlegroups.com>> on behalf of E
            Durbrow <durb...@gmail.com <mailto:durb...@gmail.com>>
            *Reply-To: *"durb...@gmail.com
            <mailto:durb...@gmail.com>" <durb...@gmail.com
            <mailto:durb...@gmail.com>>
            *Date: *Friday, September 13, 2019 at 5:09 PM
            *To: *"geoengineering@googlegroups.com
            <mailto:geoengineering@googlegroups.com>"
            <geoengineering@googlegroups.com
            <mailto:geoengineering@googlegroups.com>>
            *Subject: *[geo] No fossil fuels = global warming stops
            “soon”

            Alan Robock wrote: "Certainly if we stop burning fossil
            fuels, global warming will not stop immediately, but it
            will stop soon. “

            As a layperson, my understanding is that even if fossil
            fuels burning stops tomorrow, warming and acidification
            will continue for decades rather than years. This is
            because of 2 centuries of greenhouse gas build-up (and
            greenhouse contributions from agriculture).

            Would some kind soul tell me that I’m wrong here?

            Thanks!

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