Evaluating the Dimension of the Design Space for Stratospheric Aerosol Geoengineering

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INTRODUCTION
Stratospheric aerosol injection (SAI) can provide global cooling by adding aerosols to the lower stratosphere, and thus is considered as a possible supplement to emission reduction.Previous studies have shown that injecting aerosols at different latitude(s) and season(s) can lead todifferences in regional surface climate, and there are at least three independent degrees of freedom (DOF) that can be used to simultaneously manage three different climate goals.To understand the fundamental limits of how well SAI might compensate for anthropogenic climate change, we need to know the possible surface climate responses to SAI by evaluating the SAI design space.This research work quantifies the number of meaningfully-independent DOF of the SAI design space.
This number of meaningfully-independent DOF depends on both the climate metrics that we care about and the amount of cooling.From the available simulation data ofdifferent SAI strategies, we observe that between surface air temperature and precipitation, surface air temperature dominates the change of surface climate.The number of injection choices that produce detectably different surface temperature is more than the number of injection choices that produce detectably different precipitation.At low levels of cooling, only a small set of injection choices yield detectably different surface climate responses.As more cooling is needed, more injection choices produce detectably different surface climate.For a cooling level of 1-1.5°C, we find that there are likely between 6 and 8 DOFs.

MODEL AND SIMULATIONS
All simulations in this study were conducted using the Community Earth System Model version 1 with the Whole Atmosphere Community Climate Model as the atmospheric component, CESM1(WACCM).CESM1(WACCM) includes atmosphere, ocean, land, and sea ice components, with a horizontal resolution of 0.95° latitude and 1.25° longitude.The model has 70 vertical levels that extend from the earth surface to 140 km in altitude.
We sampled 29 possible choices in the aerosol optical depth (AOD) design space, which are highlighted in lighter color in Figure 1.We also used existing simulations for 5 different stratospheric injection strategies to relate how similar or dissimilar AOD patterns are to how similar or dissimilar the resulting surface climate responses are.
Table 1.Injection design of the 5 existing SAI simulations analyzed in this study.

AOD DESIGN SPACE
In this section, we quantify how well the overall design space of possible AOD patterns can be approximated by a subset.
We first verify that our set of 29 injection choices sufficiently describes other possible AOD patterns that we have not simulated, and then quantify how well the sample set can be approximated by each possible subset of injection choices.
For each possible value of , we identify the "best" set of injection choices that best approximates any possible pattern of AOD.We estimate the maximum error in approximating any possible pattern of AOD by the maximum AOD angle between the simulated AOD pattern and the pattern approximated by the subset of .As we increase the number of DOF, the maximum error decreases, but with diminishing returns.The maximum angles for different values of are plotted in Figure 2.

AOD AND SURFACE CLIMATE
In this section, we evaluate the relationship between how similar or dissimilar two AOD patterns are and how similar or dissimilar the corresponding surface climate responses are.To estimate this relationship, we consider the different strategies described in Table 1.Each of injection strategies described in

RESEARCH OUTCOMES
Research to date has concluded that there are at least 3 degrees of freedom (DOF).A key observation from this study is that the number of DOF effectively depends on the amount of global cooling provided by SAI.
The number of meaningfully-independent DOF increases as the amount of global cooling increases.From this study, we found that, for a cooling level of 1-1.5°C, there are likely between 6 and 8 meaningfullyindependent DOF.That is, for these levels of cooling, 6-8 independent climate goals can be simultaneously met.This expands the manageable number of climate metrics relative to what has been considered in previous studies, which reveals new opportunities for exploring alternate designs with different distributions of climate impacts.Further research should be conducted to explore alternate SAI designs and to compare the resulting climate responses and associated trade-offs.
Table 2.The minimum number of DOF of the SAI design space for four targeted levels of cooling.At each level of cooling, is the maximum angle that can be formed between two AOD patterns that yield undetectably different temperature responses.
is the maximum angle between any possible AOD pattern and the design space of DOFs, and must be smaller than .
Figure 4.The minimum number of DOF corresponding to the worst-case error in approximating AOD patterns.corresponds to the minimum AOD angle btween two detectable SAI strategies, at a cooling level of 1°C.
corresponds to the minimum AOD angle btween two detectable SAI strategies, at a cooling level of 1.5°C.
https://agu2021fallmeeting-agu.ipostersessions.com/Default.aspx?s=22-9B-FD-06-97-63-B8-E9-87-41-A5-77-B2-7C-C8-C7&pdfprint=true&guestview=true 9/9 ABSTRACT Stratospheric aerosol injection (SAI) can provide global cooling by adding aerosols to the lower stratosphere, and thus is considered as a possible supplement to emission reduction.Previous studies have shown that injecting aerosols at different latitude(s) and season(s) can lead to differences in regional surface climate, and there are at least three independent degrees of freedom (DOF) that can be used to simultaneously manage three different climate goals.To understand the fundamental limits of how well SAI might compensate for anthropogenic climate change, we need to know the possible surface climate responses to SAI by evaluating the SAI design space.This research work quantifies the number of meaningfully-independent DOFs of the SAI design space.This number of meaningfully-independent DOF depends on both the climate metrics that we care about and the amount of cooling.From the available simulation data of different SAI strategies, we observe that between surface air temperature and precipitation, surface air temperature dominates the change of surface climate.The number of injection choices that produce detectably different surface temperature is more than the number of injection choices that produce detectably different precipitation.At low levels of cooling, only a small set of injection choices yield detectably different surface climate responses.As more cooling is needed, more injection choices produce detectably different surface climate.For a cooling level of 1-2°C, we find that there are likely between 6 and 12 DOFs.This reveals new opportunities for exploring alternate SAI designs with different distributions of climate impacts and evaluating the underlying trade-offs between different climate goals.
Table 2.The minimum number of DOF of the SAI design space for four targeted levels of cooling.At each level of cooling,

Figure 1 .
Figure 1.The 29 injection choices included in the sample set.

Figure 2 .
Figure 2. The maximum angle between the best set of DOF and any other injection choices in the sample set.Diminishing returns are generally observed as increases.