Bódai Tamás, Lucarini Valerio, Lunkeit Frank
Center for Climate Physics, Institute for Basic Science, Busan 46241, South Korea.
Centre for the Mathematics of Planet Earth, University of Reading, Reading RG6 6AX, United Kingdom.
Chaos. 2020 Feb;30(2):023124. doi: 10.1063/1.5122255.
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 [CO] alone. Here, we consider only the cancellation of the expected global mean surface air temperature Δ⟨[T]⟩. 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 f(ω)=(Δ⟨[T]⟩(ω)-χ(ω)f(ω))/χ(ω), where the χ'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 ⟨T⟩, 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⟨[T]⟩ 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 χ. 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⟨[T]⟩ 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.
地球工程只能控制部分气候变量，而无法控制其他变量，从而会产生副作用。我们在一个中等复杂度的气候模型中研究线性响应理论（LRT）在评估一种地球工程方法时的适用性。LRT的这种应用有两个方面。首先，我们的目标（O1）是通过寻找合适的太阳辐射调制来评估仅可能的最佳地球工程方案，这种调制能够抵消或以其他方式调节仅由二氧化碳浓度[CO]上升所导致的气候变化信号。在此，我们仅考虑预期的全球平均地表气温Δ⟨[T]⟩的抵消情况。实际上，对于这种太阳辐射而言，这是一个直接的反问题，并且考虑到无限长的时间段，我们使用LRT在频域中以封闭形式提供解，即f(ω)=(Δ⟨[T]⟩(ω)-χ(ω)f(ω))/χ(ω)，其中χ是线性敏感性。我们提供了适用于有限时间段的数值实现程序。其次，为了能够利用LRT来量化副作用，对于诸如区域平均值⟨T⟩等未控制可观测量的响应必须近似线性。因此，我们这里的目标（O2）是评估响应的线性度。我们发现，在（O1）意义下的地球工程中，即在温室效应和所需太阳辐射共同作用下，渐近响应Δ⟨[T]⟩实际上并不为零。结果表明，这并非是由于地球工程下响应的非线性，而是线性敏感性χ的确定不准确所致。实际上，该误差是由于在通过强迫实验进行系统识别时响应存在显著的二次非线性。这种非线性贡献可以很容易地消除，这会带来对线性敏感性更好的估计，进而在地球工程实践中使Δ⟨[T]⟩降低五倍。这种修正还显著改善了预测的线性响应和真实模型响应的空间模式的一致性。然而，考虑到（O2），这种一致性并不完美，与地表温度情况相比，降水模式下的一致性更差。一些证据表明，这可能是由于降水情况下存在更大程度的非线性。
