Can we use linear response theory to assess geoengineering strategies?: Chaos: An Interdisciplinary Journal of Nonlinear Science: Vol 30, No 2

[Andrew Lockley]

https://aip.scitation.org/doi/10.1063/1.5122255

Can we use linear response theory to assess geoengineering strategies?

Chaos 30, 023124 (2020); https://doi.org/10.1063/1.5122255

 Tamás Bódai1,2,a),  Valerio Lucarini3,4,5, and Frank Lunkeit5

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ABSTRACT

Geoengineering can control only some climatic variables but not others, resulting in side-effects. We investigate in an intermediate-complexity climate model the applicability of linear response theory (LRT) to the assessment of a geoengineering method. This application of LRT is twofold. First, our objective (O1) is to assess only the best possible geoengineering scenario by looking for a suitable modulation of solar forcing that can cancel out or otherwise modulate a climate change signal that would result from a rise in carbon dioxide concentration [CO22] alone. Here, we consider only the cancellation of the expected global mean surface air temperature Δ⟨[Ts]⟩Δ⟨[Ts]⟩. It is in fact a straightforward inverse problem for this solar forcing, and, considering an infinite time period, we use LRT to provide the solution in the frequency domain in closed form as fs(ω)=(Δ⟨[Ts]⟩(ω)−χg(ω)fg(ω))/χs(ω)fs(ω)=(Δ⟨[Ts]⟩(ω)−χg(ω)fg(ω))/χs(ω), where the χχ’s are linear susceptibilities. We provide procedures suitable for numerical implementation that apply to finite time periods too. Second, to be able to utilize LRT to quantify side-effects, the response with respect to uncontrolled observables, such as regional averages ⟨Ts⟩⟨Ts⟩, must be approximately linear. Therefore, our objective (O2) here is to assess the linearity of the response. We find that under geoengineering in the sense of (O1), i.e., under combined greenhouse and required solar forcing, the asymptotic response Δ⟨[Ts]⟩Δ⟨[Ts]⟩ is actually not zero. This turns out not to be due to nonlinearity of the response under geoengineering, but rather a consequence of inaccurate determination of the linear susceptibilities χχ. 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 fivefold reduction in Δ⟨[Ts]⟩Δ⟨[Ts]⟩ under geoengineering practice. This correction dramatically improves also the agreement of the spatial patterns of the predicted linear and the true model responses. However, considering (O2), such an agreement is not perfect and is worse in the case of the precipitation patterns as opposed to surface temperature. Some evidence suggests that it could be due to a greater degree of nonlinearity in the case of precipitation.

Geoengineering strategies with the aim of mitigating climate change are receiving increasing attention,1–10 not only because of their potential to solve one of the greatest challenges faced by modern society, but also because of the great risk that such an unprecedented endeavor entails. Here, we would like to advocate that the study of climate change in general, and geoengineering, in particular, would benefit from response theory11,12 and the theory of nonautonomous dynamical systems.13–20 These mathematical tools were introduced into climate science many years ago,21–23 but only recently have they started to really gain traction.24–37 The first application of response theory to the study and efficient assessment of geoengineering, in particular, was by Kravitz and MacMartin.38 They assessed the linearity of the response, but regarding global averages only. However, regional temperature responses to radiative forcing can be nonlinear,32,39–41 and there has been an indication39 that they can be nonlinear in the case of geoengineering too. We show that it is possible to describe in a concise and general way the response of the climate system to two or more forcings with given time-dependent modulations. In particular—and this is the case of interest in geoengineering—if a forcing is given, one can arrange the time modulation of NN other forcings in such a way as to achieve a desired time-dependent change for NN climatic observables of interest. The pitfall of this approach is that (a) the response of any other observable is, in principle, uncontrolled and (b) nonlinearities can become more and more relevant as forcings are added to the system. This indicates that there are some fundamental caveats in the setup of geoengineering strategies.