# Annual Solar Geoengineering: Mitigating Yearly Global Warming Increases

## Abstract

**:**

## 1. Introduction

^{−2}to reverse most of global warming that has already occurred. For example, Sanchez et al. [4] stated that for L1 space sunshading applications, “Most scenarios for space-based geoengineering target a reduction of solar insolation of 1.7% to offset the effects of a doubling of CO

_{2}concentration”. This is about −5.78 Wm

^{−2}(=340 Wm

^{−2}× 0.017), which does not account for the background climate and can lead to overestimates. Other authors [5,6,7,8,9] have quoted similar goals. A 1 °C global temperature rise equates to about 5.4 Wm

^{−2}(see Section 2.3). However, to achieve this reversal, this paper suggests that a reverse forcing recommendation of only about −1.5 Wm

^{−2}(~0.44% solar isolation) is needed for an albedo SRM target area (see Section 2.3) when the background climate effects are considered (see Section 2.3). This recommendation is extended in this paper for an ASG estimated optimum yearly reverse forcing goal of −0.0293 Wm

^{−2}/Yr. (~0.0086% solar isolation, Section 2.3), a factor of 50 times less than the −1.5 Wm

^{−2}. Well-defined SG goals can help to minimize SRM area requirements.

_{2}concentrations cost-effectively at an acceptable level”. Later, Izrael et al. [12], for example, provided estimates for SAI to stabilize temperature, “investigation of possibilities and conditions to stabilize the global temperature on prescribed acceptable level during the 21st century by SRM…. We demonstrate that climate engineering temperature stabilization during the 21st century is possible within the range of +2 ± 0.11 °C” (see Section 3.3).

_{2}] Yr

^{−1}in 2080 following which it plateaus as global warming in RCP4.5 stabilizes at slightly above 3 K”. This is a cumulative increase from the first year estimate of 0.313 Mt[SO

_{2}]Yr

^{−1}(see Section 3.3) by a factor of 34 over the 60 years, which is a yearly increasing quantity in 2080 and depends on GHG reduction in the RCP4.5 scenario.

**Figure 1.**Global warming’s linear short-term trend (smoothed) assessment [26].

## 2. Methods and Data

#### 2.1. Overview of the ASG Approach

^{−2}) goal is provided. To assist this, the reader is referred to the background work by Feinberg [25]. Also in Section 2.3, Table 2 provide symbol definitions. In Section 2.3.1, motivation is provided by explaining a SG 38% advantage compared to CDR. In addition, the estimated effective GHG reduction that occurs from SRM is given. Next, we translate the ASG goals into the SRM area requirements in Section 2.3.2, where the main equations are presented.

_{3}and SO

_{2}injection examples for ASG. Appendix D provides a method to convert feedback amplification to feedback units. Appendix E details recent 2023 GW trends and how they would affect our estimates.

#### 2.2. ASG Temperature Reversal Estimate

_{R}) up to 2022 requirement for ZGWG per year is (see also Appendix E)

_{R}= −0.0188 °C/year

#### 2.3. Theory

_{R}= −0.0188 °C/year = −0.102 Wm

^{−2}/year

_{1}is taken as the average surface temperature of the Earth of about 14.5 °C and T

_{2}= 14.5 °C + 0.0188 °C = 14.519 °C. Note that Equation (3) is simply a direct conversion from the observed temperature increase per year to energy units. This value contains both feedback and forcing, as indicated in Equations (4)–(6) (see also the SG calculator in Supplementary Materials).

^{−2}consists of forcing and feedback. Feedback typically doubles the forcing. We use a feedback amplification factor of 2.15 {28, 30], as discussed below. Therefore, about 2.4 Wm

^{−2}is due to forcing (i.e., 2.15 × 2.4 Wm

^{−2}= 5.15 Wm

^{−2}). Then, we can write for full global warming mitigation with the background climate parameters considered (from 1950 to 2019), the reversal equates to [25]

- The reverse forcing of the target SRM area required is denoted by $\Delta {P}_{T}$. We note that three things happen in SRM: (1) we increase the albedo reflectivity of a hotspot surface target, causing a reverse forcing of $\Delta {P}_{T}$; (2) this also reduces its associated greenhouse gas re-radiation background climate effect since there are fewer long wavelengths emitted from the SRM area, which means a reduction in re-radiation; and (3) there is also a reduction in water vapor GHG feedback due to the cooling of the hotspot target. Other feedback may also show some reversal.
- In this equation, we assume that feedback, which is dominated by water vapor, will also reverse as part of the background climate cooling effect. That is, SG reverse forcing causes a cooling effect and cooler air holds less water vapor. In Equation (4), the average feedback amplification factor, including water vapor feedback, is estimated in 2019 as ${\overline{A}}_{F}=2.15$ [28,30]—see also Appendix D for the conversion to feedback units. We note that many other authors have anticipated that water vapor feedback likely has a doubling effect [31,32], so a factor of 2.15 is reasonable. Note that this value can be written with temperature dependence, and this is discussed in Appendix A.

^{−2}. To achieve this, we only require an equivalent solar radiance reduction of 0.44% (=1.48 Wm

^{−2}/340 Wm

^{−2}). Taking into consideration the background climate helps minimize estimates. This is compared with other authors [4,5,6,7,8,9], who have used higher estimates. Other updated estimates may be used depending on the reader’s interest. Since, in this paper, we are interested in stabilizing global warming annually, the ASG albedo SRM target goal requirement for a yearly reversal is approximated similarly to Equation (5) as (from Equations (3) and (4))

#### 2.3.1. SG Advantage and the Greenhouse Gas Equivalent Reduction from SRM

^{−2}in Equation (4) requires an estimated SG change of −1.48 Wm

^{−2}, as shown in Equation (5), compared to trying to achieve this with GHG removal, which would require the full −2.4 Wm

^{−2}(Equation (5)). This yields a work saving of 0.92 Wm

^{−2}(=2.4 Wm

^{−2}− 1.48 Wm

^{−2}). This is a 38% (=0.92 Wm

^{−2}/2.4 Wm

^{−2}) advantage for SG [28], yielding much less effort and higher work efficiency compared to CDR. In CDR, two things happen when GHG is removed, whereas in SG, three things happen. This creates the 38% higher efficiency compared to CDR. In CDR, we have (1) a reduction in the GHG effect, and (2) this causes a feedback reduction. In SRM, for example, (1) we cool an area with SRM, (2) this causes an additional reduction in the GHG effect as there are fewer emitted LWs that can be re-radiated, and (3) this causes a reduction in water vapor feedback from the cooling. That is, in SG, fundamentally, we include a 1 + f re-radiation reduction GHG background climate effect in Equation (5) (i.e., increasing the reflectivity of a hotspot surface also reduces its associated greenhouse gas effect).

_{2}and often water vapor feedback re-radiation that can occur in UHIs in the presence of high heat flux using SG [2,33].

_{T}), urbanization heat fluxes from impermeable surfaces can be problematic on both the local and global levels [2,3,33], as discussed in Section 4.1.6.

#### 2.3.2. SRM Area Estimates for Annual Solar Geoengineering

^{−2}reversal, the approach involves using the following updated solar geoengineering equation based on Feinberg [25], given by

- This SG physics-based equation indicates that in SRM, as anticipated, the reversal is proportional to the average solar energy over 24 h and is given by ${S}_{o}/4$.
- The fractional albedo SRM target area change required is denoted as A
_{T}. This change is taken relative to the Earth’s area A_{E}. - The amount of irradiance Xc falling on the target has a global average of ${\overline{X}}_{C}=47\%$ [29] of sunlight passing through the clouds. This can vary depending on the location. This value can be changed in the model depending on the target’s location.
- The amount of outgoing reflected transmission from the target is denoted by ${X}_{O}$. This is primarily used in albedo Earth brightening applications (see Section 3.1). This is just the amount of reflected sunlight from Earth brightening that is anticipated to make it into outer space due to potential issues such as clouds and aerosol particulates. A Bayesian probability estimate for this value is provided in Section 3.1.
- The space irradiance factor denoted by ${X}_{S}$ (see Section 3.2) is typically 1 for non L1 space mirror applications. However, for L1 space mirror applications, the optimal L1 point rotates around the Sun with the same angular speed as the Earth, thus allowing constant sunshading. Then, the sunshading irradiance occurs 24 h a day and the Earth’s curvature is not a factor. This increases S
_{o}/4 to S_{o}. To account for the increase in space irradiance, we can let X_{S}= 4 in Equation (7) for L1 space mirror applications. - The albedo change of the target is denoted as $\Delta {\alpha}_{T}={{\alpha}^{\prime}}_{T}-{\alpha}_{T}$, where the target’s albedo originally has a value of ${\alpha}_{T}$, and when we apply an SRM, its albedo increases to a new value denoted by ${{\alpha}^{\prime}}_{T}$.
- Lastly, included is an UHI de-amplification factor ${H}_{T}$. This is for targets in urban heat island (UHI) areas which can have UHI microclimate de-amplification effects, denoted by H
_{T}[2,33,34]. For example, in UHIs, the solar canyon effect amplifies warming when buildings reflect light onto pavements, increasing the irradiance and amplifying the temperature at the surface. Other amplification issues can include re-radiation due to the increase in local CO_{2}GHGs, local water vapor feedback, temperature inversions, loss of wind and evapotranspiration cooling, increases in the solar heating of impermeable surfaces from building sides, pavements heat fluxes, and so forth [2]. Some of these microclimate amplification effects could reverse and de-amplify in ASG urban applications, increasing cooling, and can be accounted for in Equation (7) with the H_{T}variable. City heat flux amplification is often observed by the UHI’s dome and footprint. The footprint and dome growth are indications of amplified heat flux that is observed to spread beyond the boundaries of the city itself, both horizontally and vertically [2,34,35]. Using ASG, the footprint, dome effects, and city temperatures can be reduced.

## 3. Results

#### 3.1. Earth Brightening Transmission Loss

_{O}factor provides an estimate of the outgoing transmission of reflected short-wave sunlight radiation and is applicable in Earth brightening albedo methods. When taken as unity, the results for Equation (7) in Earth brightening applications yield the minimum required albedo SRM area to achieve a specific ASG reversal goal. In Earth brightening, several eventual losses can occur for the outward reflected short-wavelength transmission through the upper atmosphere. The primary losses are clouds and aerosols that can impede the reflected sunlight [36]. These losses in the upper atmosphere areas can affect the mean lower surface air temperature (MSAT).

_{C}in this paper is taken as 47% due to clouds, as indicated in the IPCC global mean Earth energy budget assessment [29]. However, one might anticipate that the outgoing radiation transmission from an Earth-brightened SRM surface area will have a higher transmissibility probability than the incoming irradiance. For example, given that the incoming sunlight radiation occurred through a clear portion of the sky, we can estimate the probability that there will be loss issues on the outgoing reflective radiation, which should be less. One helpful estimation method is to use a Bayesian approach. Using this prior information that the sunlight makes it to the target, the Bayesian result indicates that the probability of clear transmission is 78%. This is estimated in Appendix B. Therefore, the minimum required albedo SRM area obtained in Equation (7) for Earth brightening is adjusted in this paper using a Bayesian correction by the X

_{O-Bayes’}= 0.78 factor.

_{O-Bayes’}may be close to a value of 1 [36].

#### 3.1.1. Pavement and Roofs

^{2}and is a factor of 160 smaller.

_{2}reductions become significant. This is illustrated for different RCP scenarios in Section 3.5, as ASG projections are also dependent on RCP estimates.

#### 3.2. L1 Space Sunshade Estimates

_{T}area modification requirement for a solar reflective space disc mirror-type sunshade application. In this case, we note that most authors consider the Sun–Earth L1 position as optimal. For the irradiance in space mirror sunshade estimation, we can take X

_{C}as 100% and X

_{S}as 4 (as discussed above). Sunshading can effectively translate to changing the reflectivity of a target on Earth’s to ~100% from the average Earth’s albedo of 30%, so that $\Delta {\alpha}_{T}$ = 0.7. Using these parameters and our ASG goal, Equation (6) is

^{2}(radius 71 km). Section 3.4 summarizes this result. Sánchez et al. (2015) indicated an area-to-mass ratio near 4 × 10

^{3}kg/km

^{2}. Using this, the weight required for an area of 15,686 km

^{2}would roughly be about 63,000 tonnes. We might consider a reflective particle option. However, the injection requirement for SO

_{2}reflective particles assessed in Table 3 is 313,000 tonnes. This is surprisingly higher. However, Appendix C finds lower values of 21,000 tonnes for CaCO

_{3}and 41,000 tonnes for SO

_{2}that may be more applicable for L1 space sunshade applications. Nevertheless, given that these are yearly requirements; this further indicates yearly challenging issues.

_{T}/A

_{E}, this value also yields the required percentage of incident solar radiation that is needed to be reflected away from the Earth to achieve a mitigation goal in Equation (12). Note that Equation (13)’s value is reduced by a factor of 556 (=1.7%/0.003%) compared to the requirements for full mitigation, as estimated by other authors for a reduction in solar insolation of 1.7% to offset the effects of a doubling of CO

_{2}concentration [5,6,7,8]. However, it is only reduced by a factor of 51 compared to the author’s initial paper [25], with a goal of 0.154% reduction required to reverse a 1 °C rise in 2021. Lastly, note that the yearly required increases are estimated in Section 3.5 for different RCP scenarios.

#### 3.3. Annual Stratospheric Injection Estimates

_{2}injected into the stratosphere [37,38,39,40,41,42]. Here, SO

_{2}injected into the stratosphere at the top of the atmosphere (TOA) reduces the Sun’s energy reaching the Earth through solar aerosol reflectivity. As an estimate for annual SAI, we can use the equation given by Niemeier and Timmreck [13], where the reduction in radiation at the top of the atmosphere $\Delta {R}_{TOA}$ is

_{2}]/year—megatonnes of SO

_{2}per year) for full GW reduction according to Equation (6) requires a goal of 1.47 Wm

^{−2}. To provide the first-year annual requirements rather than full mitigation, the injection rate using Equation (14) is 22-fold lower, as shown in Table 3. Here, full climate mitigation requires an injection of 6.9 Mt[SO

_{2}]Yr

^{−1}for a goal of 1.47 Wm

^{−2}, whereas for the first year, the ASG goal is reduced to an injection of 0.313 Mt[SO

_{2}]Yr

^{−1}for a $\Delta {R}_{TOA}$ = 0.0293 Wm

^{−2}goal (Equation (6)). Unfortunately, depending on the SO

_{2}dissipation per year, this would possibly need to be doubled in the second year, tripled in the third year, and so forth to stabilize global warming annually. We note that Izrael et al. [12] estimated an injection rate of 0.25 Mt[SO

_{2}]Yr

^{−1}as the cumulative requirement for global temperature stabilization at +2 °C starting in the year 2050. This injection rate is close to the estimate provided here of 0.313 Mt[SO

_{2}]Yr

^{−1}for a 0.0293 Wm

^{−2}goal. Jones et al. [14] noted that “In GEO4.5, the injection rate increases monotonically to attain a peak value of 10.9 Mt[SO

_{2}]Yr

^{−1}in 2080 following which it plateaus as global warming in RCP4.5 stabilizes at slightly above 3 K”. This is over 60 years and is close to the full reversal estimate in Table 3 of 6.85 Mt[SO

_{2}]Yr

^{−1}.

#### 3.4. Overview of Estimates

_{T}value, as an example, is taken as 3 for UHI areas and conservatively as 2 for Earth mirrors used on urban rooftops, as often implemented by Project MEER [24]. This H

_{T}average estimate can vary depending on the UHI microclimate [2]. In the case of something like sea-type floating mirrors or reflective particles [43], H

_{T}= 1, as shown in Table 4.

^{−2}/0.029 Wm

^{−2}) in energy flux requirements and albedo SRM area (per Equation (7)). For example, desert treatment is reduced from the author’s initial estimate of 1.0% [25] to 0.02% for annual mitigation in Table 4. Therefore, the areas in ASG mitigation are, in general, 50 times smaller, which also minimizes any potential circulation concerns [17,18,19,20,21]. Table 4 suggests several options including multiple combinations that can be considered in annual mitigation, as suggested in Section 4.1.5. In this section, the SRM methods are also rated. For hotspot cooling shown in Table 5, this has the potential to reduce area requirements by a factor of over 150 (per Equation (11)) due to a combination of $\Delta \alpha $ and larger feedback changes in high-humidity areas. The yearly required minimal increases are estimated in the next section for different RCP scenarios.

#### 3.5. RCP ASG Cumulative Area Estimates

_{2}is reached for the thermal equilibrium time period is established, as shown in Table 6. This rough estimate is based on the results of global circulation models that indicate that about 85% of the GHG GW effect occurs in the first 5 to 10 years [2,45]. Near the peak, the CO

_{2}and the GW increases should start to taper-off. This additional reduction should aid in reaching thermal equilibrium in the 10-year allowance period. Further, ASG estimates can be refined as needed.

## 4. Discussion

#### 4.1. Annual Solar Radiation Management

#### 4.1.1. Annual Solar Geoengineering Allocation by Country

- The US’s mitigation = 31% × 120,158 mi
^{2}= 37,249 mi^{2}/Yr or 102 mi^{2}/day - The UK’s mitigation = 3.5% × 120,158 mi
^{2}= 4205 mi^{2}/Yr or 11.5 mi^{2}/day

#### 4.1.2. Implementation Using L1 Space Particle Clusters

_{2,}or moondust [9] in space at L1 may have a long suspension time, reducing the injection rate. Diffusion would likely be slow due to low outer space temperatures (~2.7 K), and studies could be performed to estimate issues.

_{o}= 1360.833 Wm

^{−2}. Then, one finds that 0.167 Wm

^{−2}(=1361 Wm

^{−2}− 1360.833 Wm

^{−2}) is the reduction required for the incoming solar radiation.

#### 4.1.3. Earth Brightening Advances

- The US’s mitigation goal for Earth brightening is 102 mi
^{2}/day - The UK’s mitigation goal for Earth brightening is 11.5 mi
^{2}/day

^{2}/day [50], which includes refills. Then, if we assume that paint drones can be designed with similar capabilities, this may require feasible areas as follows:

- For the US’s mitigation goal, about 102 drones/day
- For the UK’s mitigation goal, about 12 drones/day

_{T}> 1. These reduce the Earth’s annual SG area requirements, as per Equation (7). Alternatively, it may be of interest to use something like sea mirrors or reflective floating particles which would yield a high albedo change, as exemplified in Table 4.

#### 4.1.4. Natural Hotspots

- Flaming Mountains, China
- Bangkok in Thailand (the planet’s hottest city)
- Death Valley, California
- Deserts
- The badlands of Australia
- The tropics and subtropics

#### 4.1.5. ASG Methods Rated with Mixed Planning

#### 4.1.6. Worldwide Negative Solar Geoengineering

_{T}). Currently, it is estimated that roads occupy about 14% of all manmade impermeable surface areas [54] of which impermeable surfaces occupy an estimated 0.26% of the Earth’s surface [55]. Then the estimated area of the Earth occupied by roads is small, at about 0.0364%. This is on a similar scale compared to Equation (9) estimated requirement for area modification and illustrates the negative ASG interference issue. Compared to the estimated total area of impermeable surfaces, it is a factor of 8.5 times higher than the Equation (9) requirement (0.26%/0.0305%). This illustrates the difficult task of annual surface area modification requirements with the worldwide negative SG interference. Feinberg [2] estimated that 1.1% of global warming is likely due to asphalt roads using only an average background climate feedback factor, which, if brightened similar to concrete, with an albedo increase factor of 5, could have reduced global warming by 5.5%. In humid areas this improvement can be 2-fold higher (Appendix A). An MIT pavement study [56] concluded that in all US urban areas, an increased temperature of 1.3 °C occurs in summer months and heatwaves are 41% more intense with 50% more heatwave days due to asphalt pavements. The expansion of cities is increasing rapidly where 55% of the world’s population lives and this is expected to grow to about 70% by 2050 [57].

## 5. Conclusions

_{T}microclimate amplification value in UHIs, as shown in Table 4. The results in general point to challenging but feasible solutions. It is vital for agencies like NASA, Space X, and the Canadian, Chinese, and European space agencies, etc., to help to develop the technologies required for ASG implementation. Much work is needed, especially in the area of L1 space sunshading (see Section 3.2 and Section 4.1.2) and to assist in the development of AI drone paint tools for Earth brightening (see Section 4.1.3 discussion).

## Supplementary Materials

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Symbols | Description of General Terms |

ASG | Annual solar geoengineering: mitigation of yearly global warming increases |

CDR | Carbon dioxide removal |

GCM | Global circulation model |

GHG | Greenhouse gas |

GW | Global warming |

LW | Long wavelength |

MSAT | Mean surface air temperature: Usually at a height of two meters |

RCP | Representative concentration pathway |

Reversal | Total mitigation required (in temperature or Wm^{−2} units) |

Reverse Forcing | Reverse forcing portion of the reversal required to accomplish GW mitigation |

SAI | Stratosphere aerosol injections |

SG | Solar geoengineering: General term can include SRM and/or physics modeling |

SRM | Solar radiation modification: Specific to albedo areas or solar reduction changes |

UHI | Urban heat island |

ZGWG | The observation of zero increases in GW for a period of time (1 Year for ASG) |

## Appendix A. Earth Brightening of Hotspots and Its Influence on Water Vapor Feedback

_{1}and T

_{2}are expressed in degrees K, 2.465E6 J-kg

^{−1}is the latent heat of vaporization, and 462 J-kg

^{−1}K

^{−1}is the specific gas constant for water vapor, and we can denote the Clausius–Clapeyron humidity relationship as CC.

_{F}factor at 27 °C is

_{F}(T) is reasonably greater than the estimated average of ${\overline{A}}_{F}=2.15$.

^{−2}K

^{−1}[33] for cities in humid environments at 15 °C. This is about 2.1 times higher compared to some authors’ estimates for the average feedback in the standard atmosphere [32].

## Appendix B. Bayesian Estimate for Outgoing Transmission Loss in Earth Brightening

_{C}= 0.47 for the incoming sunlight irradiance in Equation (7). Then, to find the Bayesian correction for the outgoing transmission ${X}_{O-Bayes\u2019}$ in Equation (8), we start with the prior information that sunlight falls on a target area. Using Bayes’ theorem, the first quantity of interest is $P({\rm B}|A)\hspace{0.17em}=P(Clear|Cloudy)=0.47$. We then have prior knowledge that the sunlight makes it to the reflective target, so that $P(Clear)=P(B)=1$. We wish to establish the probability of non-transmission of the reflected light due to a cloudy area given that the incoming solar radiation passed through a clear sky area, given by $P(A|{\rm B})=P(Cloudy|Clear)\hspace{0.17em}$. The probability that the sky will be cloudy is $P(A)=P(Cloudy)={X}_{C}=0.47$. The result from Bayes’ theorem yields

_{Clear}= 1–0.22 = 0.78.

## Appendix C. CaCO_{3} and SO_{2} Stratospheric Injections—Area Approach

_{3}and SO

_{2}injection rate are provided for ASG. Here, we can use the area coverage approach using Equation (7) rather than Equation (14) to illustrate stratosphere coverage requirements that may provide some alternative insights.

_{3}example, we assume an increased reflectivity by a factor of 2, with CaCO

_{3}injection bringing an area’s atmospheric albedo to ${{\alpha}^{\prime}}_{T}=0.6$. Then, considering full irradiance, ${X}_{C}=1$, with ${H}_{T}=1$, and using the annual climate mitigation goal to stabilize global warming, Equation (6) yields

^{2}/g) of CaCO

_{3}vary widely depending on the type of CaCO

_{3}, from 5–24 m

^{2}/g [62] to 30–60 m

^{2}/g [63]. If we conservatively use 10 m

^{2}/g, we can calculate the injection rate using Equation (C3) as

_{2}instead of CaCO

_{3}, with particle sizes of about 5 m

^{2}/g [64], which is anticipated to be smaller, then similar to Equations (C4) and (C5), we obtain

_{2}is required. For 70% efficiency, similar to Equation (C5), we obtain

_{3}.

## Appendix D. Feedback Amplification Conversions

^{−2}K

^{−1}to −0.62 Wm

^{−2}K

^{−1}. Therefore, this value is slightly outside the anticipated CMIP6 ESM estimate. However, it provides the estimated value found in the author’s prior research works for the year 2019 [28,30].

## Appendix E. Recent Global Warming 2023 Trend

^{−2}compared to that used in Equation (6) of 0.029 Wm

^{−2}. This is a 45% increase, which would also increase the ASG area requirements proportionately by this amount in Equation (7) and in the results section.

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Objective | Section | Highlighted Results | Other Reference(s) |
---|---|---|---|

ASG temperature reversal | 2.2, Equation (1) | −0.0188 °C/year This is the estimated yearly temperature reversal goal. | NASA [26]; NOAA [27] |

ASG energy reversal | 2.3, Equation (6) | −0.0293 Wm^{−2}/yearThis is the estimated yearly reverse forcing requirement to achieve the temperature reversal. | Findings, Feinberg [25] |

SG savings and greenhouse gas equivalency | 2.3.1 | Results indicate an estimated 38% work saving for climate mitigation using SG compared to CDR. | Feinberg [28], Findings |

SRM area estimate equation | 2.3.2 | $\Delta {P}_{ASG}=-\frac{{S}_{o}}{4}\frac{{A}_{T}}{{A}_{E}}{X}_{C}{X}_{O}{X}_{S}{H}_{T}\left[(\Delta {\alpha}_{T})\right]$ SRM area estimates can be determined using this equation. | Findings, Feinberg [25] |

Earth brightening transmission loss | 3.1 | The probability of clear sky transmission is 78%. This helps to provide estimates since not all of the SRM reflected radiation escapes to outer space. | Findings |

Earth brightening cool pavement example | 3.1.1 | $\frac{{A}_{T}}{{A}_{E}}=\left(\right)open="\{">\begin{array}{l}0.078\%\hspace{0.17em}{per\hspace{0.17em}year}_{Bayes\u2019}\\ 0.0612\%\hspace{0.17em}per\hspace{0.17em}yea{r}_{Minimum}\end{array}$ A _{T} is the area modification relative to the area of the Earth A_{E} | Findings |

L1 Space sunshade estimates | 3.2 | $\frac{{A}_{T}}{{A}_{E}}=0.003\%\hspace{0.17em}per\hspace{0.17em}year\hspace{0.17em}\hspace{0.17em}$ This is the required area for a space disc at L1 | Findings |

Annual stratospheric injection estimates | 3.3 | Table 3, 0.313 Mt[SO_{2}]Yr^{−1}This is the amount of SO _{2} injection per year for ASG | Findings |

Overview of estimates | 3.4 | Table 4 and Table 5 provide a concise summary of the area requirements for different SRM methods | Findings |

RCP ASG cumulative area estimates | 3.5 | ASG cumulative estimates anticipated with different RCP scenarios | Findings |

ASR management—recommendations | 4.1.1, 4.1.2, 4.1.3, 4.1.4, 4.1.5, 4.1.6 | 4.1.1: Allocation by country 4.1.2: L1 Space clusters 4.1.3 Earth brightening 4.1.4: Natural hotspots 4.1.5: Mixed planning and ratings 4.1.6: Negative SG | Findings |

Conclusions | 5 | Findings | |

Earth brightening of hotspots and water vapor feedback | Appendix A | $\Delta {P}_{ASG}=-0.0147{\mathrm{Wm}}^{-2}/\mathrm{Yr}.$ The results find that feedback reductions can be increased in some hotspot areas, further reducing the SRM area. In this example, the SG goal is cut in half. | Findings |

Bayesian estimate for outgoing transmission | Appendix B | Tr_{Clear} = 1 − 0.22 = 0.78This is the Bayes estimate for the probability of the reflected sunlight from an SRM area to reach outer space. | Findings |

CaCO_{3} and SO_{2} stratospheric injections—area approach | Appendix C | $\frac{{A}_{T}}{{A}_{E}}=0.0288\%/\mathrm{eff}$ This is the area coverage estimated for these aerosols and depends on their reflection efficiencies. | Findings |

Feedback conversions | Appendix D | Converts feedback amplification to feedback units. | Estimates |

Recent GW 2023 trends | Appendix E | Recent trends due to a 2023 GW jump | Estimates |

SG calculator | Supplementary Materials | SG helpful calculator is provided for the results. | Findings |

Symbol | Definition |
---|---|

${A}_{T}$ | Target area: This is the area for which an SRM albedo modification is to be applied |

${A}_{E}$ | Earth’s area |

A_{F} | Feedback amplification with average taken as A_{F} = 2.15: A unit less number, to convert to feedback units see Appendix D |

CC | Clausius–Clapeyron relation |

${\alpha}_{T}$, ${{\alpha}^{\prime}}_{T}$ | SG target’s albedo modification: ${\alpha}_{T}$ is before, ${{\alpha}^{\prime}}_{T}$ is after SRM (Equations (7) and (8)) |

f = 62% | Re-radiation factor: Average re-radiation occurring in the atmosphere |

H_{T} | UHI microclimate amplification factor |

${I}_{S{O}_{2}}$ | SO_{2} injection rate |

$\Delta {R}_{TOA}$ | Radiation change at the TOA |

∆P_{ASG} | Annual reversal in Watts/m^{2}: Reverse forcing to mitigate annual yearly increase in GW (this does not include feedback which is assumed to reverse the amount required |

∆P_{Rev} | Reversal change in Watts/m^{2}: Full GW reversal required (includes reverse forcing and feedback) |

$\Delta {P}_{T}$ | Reverse forcing albedo change from a target area T in Watts/m^{2}: This is the reverse forcing required assuming the feedback portion would also reverse |

${S}_{o}/4$ | Average solar radiation ${S}_{o}/4=340.25\hspace{0.17em}{\mathrm{Wm}}^{-2}$ |

T_{R} | Temperature reversal: ASG goal to reverse this temperature rise (Equation (1)) |

TR | Transmissibility: This is applied to a small reduction in the incoming solar radiation from the sun (1361 Wm^{−2}) |

TOA | Top of the atmosphere |

X_{S} | Solar irradiance averaging 47% |

X_{S} | Space irradiance: If at L1 in space, X_{S} = 4, if in other areas, X_{S} = 1 |

Stratosphere Injection | Full Reversal | Annual Reversal |
---|---|---|

ΔR_{TOA} (Wm^{−2}) | 1.47 | 0.0293 |

${I}_{S{O}_{2}}$ (Mt[SO_{2}]Yr^{−1}) | 6.85 | 0.313 |

Savings | 5.7 * | 22 ** |

^{−2}; ** = 6.85/0.313

Earth Brightening | Space | ||||||
---|---|---|---|---|---|---|---|

Parameters | Pavements Roofs | Desert Treatment | UHIs | Earth (Sea) Mirrors ** | L1 Space Sunshading Parameters | Stratosphere Injections | |

∆P_{ASG} (Wm^{−2}) | −0.0293 | −0.0293 | −0.0293 | −0.0293 | ∆P_{ASG} (Wm^{−2}) | −0.0293 | −0.0293 |

X_{S} = 1, X_{O} = 1, X_{C }= | 0.47 | 0.92 | 0.47 | 0.7 (0.85) | X_{C} = 1, X_{S} = | 4 | 1 |

$\Delta {\alpha}_{T}$ | 0.3 | 0.44 | 0.1 | 0.75 | $\Delta {\alpha}_{T}$ | 0.7 | 0.3 |

H_{T} | 1 | 1 | 3 | 2 (1) | H_{T} | 1 | 1 |

${\overline{A}}_{F}$ | 2.15 | 2.15 | 2.15 | 2.15 | ${\overline{A}}_{F}$ | 2.15 | 2.15 |

Earth Brightening Minimal Results | L1 Space Disc Results | SO_{2}, CaCO_{3} Injec. | |||||

A_{T}/A_{E} | 0.061% | 0.0212% | 0.062% | 0.0082% (0.0144%) | A_{T}/A_{E} Earth Shade | 0.00308% | 0.0288%/eff (0.31 Mt[SO _{2}]Yr^{−1}) |

A_{T} (Mi^{2}) | 120,070 | 41,880 | 120,070 | 16,122 (28,350) | Shade A_{T} (Mi^{2}, km^{2}) | 6046, 15,586 | 55,848, 148,644 |

Radius (Mi) | 196 | 115 | 196 | 72 (95) | Shade Radius (Mi, km) | 43, 71 | 133, 218 |

A_{T} (km^{2}) | 3.1 × 10^{5} | 1.08 × 10^{5} | 3.1 × 10^{5} | 4.2 × 10^{4} (7.3 × 10 ^{4}) | Disc Area (Mi^{2}, km^{2}) * | 6046, 15,586 | - |

Radius (km) | 315 | 131 | 315 | 116 (153) | Disc Radius (Mi, km) * | 43, 71 | - |

T2, T1 $\Delta {\alpha}_{T}$X _{C} | 61 °C, 33 °C 0.5, 0.47 |

A_{F} | 4.3 |

ΔP_{ASG} (Wm^{−2}) | −0.0293 |

A_{T}/A_{E} | 0.0184% |

A_{T} (Mi^{2}) | 36,022 |

Radius (Mi) | 107 |

A_{T} (km^{2}) | 0.9 × 10^{5} |

Radius (km) | 169 |

RCP Scenarios | Peak Year, (CO _{2} ppm) | Peak Plus 10-Year Lag for ASG (Starting in 2023) Years | Earth Surface Brightening * A _{T}/A_{E} | L1 Space Disc Size * A _{T}/A_{E} | ${\mathit{I}}_{\mathit{S}{\mathit{O}}_{2}}$ * (Mt[SO _{2}]Yr^{−1}) |
---|---|---|---|---|---|

RCP 2.6 | 2025 (430 ppm) | 12 | 0.061% × 12 = 0.73% | 0.003% × 12 = 0.036% | 0.313 × 12 = 3.8 |

RCP 4.5 | 2045 (475 ppm) | 32 | 0.061% × 32 = 1.95% | 0.003% × 32 = 0.1% | 0.313 × 32 = 10 |

ASG SRM Method | Cost Rating | Political-Governance Rating | Likely Success Rating | Main- Tenance Cost | Average Rating | Key Issues | US Agencies That May Be Involved * |
---|---|---|---|---|---|---|---|

Earth Brightening | 1 | 1–4 (4 for SRM of natural hotspot) | 3 | 3 | 2.0–2.8 | Will require technological advances in AI drones for many paint applications | DOT, NASA, Space-X, city building codes |

SAI | 5 | 9 | 6 | 10 | 7.5 | Highly political | NASA, Space-X |

L1 Space Mirrors | 10 | 3 | 1–3 | 3–5 | 4.3–5.3 | High costs and difficulty | NASA, Space-X |

L1 Moon Dust | 9 | 4 | 2–7 | 10 | 6.3–7.5 | High costs and difficulty | NASA, Space-X |

Mixed Method | 5 | 4.5 | 3 | 5.5 | 4.5 | Same as above | Same as above |

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Feinberg, A.
Annual Solar Geoengineering: Mitigating Yearly Global Warming Increases. *Climate* **2024**, *12*, 26.
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Feinberg A.
Annual Solar Geoengineering: Mitigating Yearly Global Warming Increases. *Climate*. 2024; 12(2):26.
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**Chicago/Turabian Style**

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2024. "Annual Solar Geoengineering: Mitigating Yearly Global Warming Increases" *Climate* 12, no. 2: 26.
https://doi.org/10.3390/cli12020026