Dear Andrew,
Many thanks for promoting my manuscript, and also for inviting me to edit the wiki article. I will do this shortly. As i see, the article now only considers linear systems, i.e., when f(x) in my eq. (1) is linear. However, nonlinear chaotic systems can also have a linear response, as my paper claims. Please see my references (Risken, 1996; Abramov and Majda, 2008; Ruelle, 2009). This is what i would like to add to the wiki article in a hopefully accessible form. Please note that it is not control theory but response theory that we applied. Please see more about this distinction in my answer to Douglas below. Dear Ken, Many thanks for calling our attention to your paper. I will make sure to cite it in an appropriate way, should my manuscript emerge successfully from the discussion. Dear Douglas, Having read some parts of your paper (doi: 10.1007/s00382-013-1822-9 <http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00382-013-1822-9> ) that i thought relevant, and reading the context of every occurrence of the word (fragment) “linear”, I don’t understand how the paper would answer the question in my paper’s title and what the actual answer is. Would you please point to the particular statements and findings of your paper for the benefit of everyone who you addresses in this thread? I would like to recap — as i also wrote in the response to the referee comments — that the new title refers to point (II) of the abstract, namely, whether e.g. the local response under geoengineering (or the response wrt. other variables that are not controlled in the sense of point (I) of the abstract) is linear to a good approximation. My new analysis in the process of revising the paper sheds light on that in the examined model the local surface temperature response is not so linear, and that of the precipitation is even less so. Therefore, linear response theory cannot provide accurate prediction of this response; and it should be examined in Earth system models whether this situation is any different. The latter has not been done. Please say so if I’m wrong about this and you have a reference. I would also like to point to another argument in the response to the referee report and already in the submitted manuscript that the control method that is presented in your paper (doi: 10.1007/s00382-013-1822-9 <http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00382-013-1822-9> ) is not suitable to an _efficient_ assessment like what response theory could provide. Using response theory it is envisaged to be able to predict the response for any emission scenario and geoengineering scenario combined, without having to rerun an expensive simulation for each scenario. Please notice also that i cited a number of your papers on the control approach. I can certainly add your paper (doi: 10.1007/s00382-013-1822-9 <http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00382-013-1822-9> ) to this list. However, on the matter of linearity that my title refers to it doesn’t appear to be relevant. The latter is something that the referee claimed to be settled by yourself and Kravitz (https://doi.org/10.5194/acp-16-15789-2016), and many other — unspecified — papers, however, in my response I contested this to be the case regarding (https://doi.org/10.5194/acp-16-15789-2016), and asked the referee to provide other references what he/she had in mind. However, so far we have not got a response from the referee. Perhaps we will get a response now as the discussion has been extended. Best wishes, Tamas On Sunday, August 26, 2018 at 12:20:54 AM UTC+1, Douglas MacMartin wrote: > > “Relatively recent” as in at least 4 years ago... the question posed in > the title seems straightforward to answer, since it’s been done already a > number of times! > > > > MacMartin, D. G., Kravitz, B., Keith, D. W., and Jarvis, A., “Dynamics of > the coupled human-climate system resulting from closed-loop control of > solar geoengineering”, *Climate Dynamics, **43*(1-2): 243-258, 2014*. *(doi: > 10.1007/s00382-013-1822-9 > <http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00382-013-1822-9> > ) > > And about a dozen other papers. > > > > (I should read the posted paper, though, before commenting on anything > other than the inappropriateness of the title.) > > > > *From:* [email protected] <javascript:> [mailto: > [email protected] <javascript:>] *On Behalf Of *Andrew Lockley > *Sent:* Saturday, August 25, 2018 5:48 PM > *To:* geoengineering <[email protected] <javascript:>> > *Cc:* [email protected] <javascript:> > *Subject:* [geo] Can We Use Linear Response Theory to Assess > Geoengineering Strategies? > > > > Poster's note: a primer on linear response theory is available at > https://en.m.wikipedia.org/wiki/Linear_response_function - I hope that > the corresponding author will be available to join the group and post a > plain English summary. The application of control theory to geoengineering > is IMO an important advance, and apparently a relatively recent one. > > > > > http://scholar.google.com/scholar_url?url=https://www.earth-syst-dynam-discuss.net/esd-2018-30/esd-2018-30-AC1-supplement.pdf&hl=en&sa=X&d=8709275723963611654&scisig=AAGBfm1hG13oxCRJ0QzTgJdX4Jg-35qpxg&nossl=1&oi=scholaralrt&hist=tDjNe6QAAAAJ:15126857386591841230:AAGBfm3hgOHpwz-gQp1d_Wc583FiI4qafA > > > > Can We Use Linear Response Theory to Assess Geoengineering > > Strategies? > > > > Tamás Bódai1,2, Valerio Lucarini1,2,3, and Frank Lunkeit3 > > 1Centre for the Mathematics of Planet Earth, University of Reading, UK > > 2Department of Mathematics and Statistics, University of Reading, UK > > 3CEN, Meteorological Institute, University of Hamburg, Germany > > Correspondence: T. Bódai ([email protected] <javascript:>) > > > > Abstract. Geoengineering can control only some variables but not others, > resulting in side-effects. We investigate in an > > intermediate-complexity climate model the applicability of linear response > theory to assessing a geoengineering method. The > > application of response theory for the assessment methodology that we are > proposing is two-fold. First, as a new ap- > > proach, (I) we wish to assess only the best possible geoengineering > scenario for any given circumstances. This requires > > 5 solving the following inverse problem. A given rise in carbon dioxide > concentration [CO2] would result in a global climate > > change with respect to an appropriate ensemble average of the surface air > temperature ∆h[Ts]i. We are looking for a suit- > > able modulation of solar forcing which can cancel out the said global > change – the only case that we will analyse here – > > or modulate it in some other desired fashion. It is rather straightforward > to predict this solar forcing, considering an infinite > > time period, by linear response theory in frequency-domain as: fs(ω) = > (∆h[Ts]i(ω)−χg(ω)fg(ω))/χs(ω), where the χ’s are > > 10 linear susceptibilities; and we will spell out an iterative procedure > suitable for numerical implementation that applies to finite > > time periods too. Second, (II) to quantify side-effects using response > theory, the response with respect to uncontreolled > > observables, such as regional averages hTsi, must of course be > approximately linear. > > We find that under geoengineering in the sense of (I), i.e. the combined > greenhouse and required solar forcing, the response > > ∆h[Ts]i asymptotically is actually not zero. This turns out to be not due > to nonlinearity of the response under geoengi- > > 15 neering, but that the linear susceptibilities χ are not determined > correctly. The error is in fact due to a significant quadratic > > nonlinearity of the response under system identification achieved by a > forced experiment. This nonlinear contribution can be > > easily removed, which results in much better estimates of the linear > susceptibility, and, in turn, in a five-fold reduction in > > ∆h[Ts]i under geoengineering. This correction improves dramatically the > agreement of the spatial patterns of the pre- > > dicted linear and true model responses (that are actually consistent with > the findings of previous studies). However, (II) > > 20 due to the nonlinearity of the response with respect to local > quantities, e.g. hTsi, even under goengineering, the linear > > prediction is still erroneous. We find that in the examined model > nonlinearities are stronger for precipitation compared > > to surface air temperature. > > -- > You received this message because you are subscribed to the Google Groups > "geoengineering" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/geoengineering. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "geoengineering" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/geoengineering. For more options, visit https://groups.google.com/d/optout.
