Annual Solar Geoengineering: Mitigating Yearly Global Warming Increases

1. Introduction

This paper provides fundamental physics-based annual solar geoengineering (ASG) equations to aid in estimated requirements for yearly solar radiation modification (SRM). Therefore, this paper provides baseline assessments without using computer-aided full climate solutions. Solar geoengineering physics should add a deeper understanding of ASG requirements. Estimates are simplified by focusing on temperature which is the key thermodynamic driver for the climate system and ASG.

Many climatologists have anticipated goals of about -5 Wm^-2 reduction requirements to reverse global warming for an approximate 1°C rise. Depending on their interests, this is likely an overestimate. We illustrate that the goal should be closer to -1.5 Wm^-2. This recommendation can be extended to reverse forcing ASG estimated goal of $-0.0293 W{m}^{-2}/Yr.$, a factor of 50 times less than the -1.5Wm^-2. Overestimates of goals can lead to discouraging reflective area modification requirements in ASG applications for Earth brightening, space mirrors, and SAI.

The IPCC worries about an increase of a 1.5°C rise over the pre-industrial period. This is estimated to possibly occur around 2039-2043 at the current rate of yearly temperature increases. This can be estimated from Figure 1 which shows the short-term GW trends occurring around 2052. However, the graph displays changes since 1975. The IPCC warning is referenced to the pre-industrial period. Translating Figure 1 to the pre-industrial period requires adding about 0.17°C to each data point. Then this would occur around 2043 from the graph. Some authors predict that this could occur 5 to 10 years sooner (Diffenbaugh and Barnes, 2023) showing the importance of implementing an ASG program soon.

ASG will require timely yearly construction rate reflective modified areas both on Earth and possibly in space to reduce some of the Sun’s energy to mitigate yearly global warming increases. Thus, a key purpose of ASG is to maintain the status quo allowing time for future mitigation improvements. Because goals are limited to mitigating yearly warming increases, many controversial SG and governance issues are minimized.

From the graph’s trend analysis equation, the current rate of global warming is an increase in temperature of 0.019°C/year. To maintain the status quo for zero global warming growth, we can divide up the ASG construction task into two parts for simplicity. Half relegated to the stratosphere (Sec. 3.4) or space shading methods. Half relegated to land-based solutions such as that proposed by project MEER (2023) but on a larger scale (see Sec 3.4). Therefore, a reasonable goal is to mitigate a 0.019°C/year global warming increase. This should minimize circulation concerns (Barrett et al., 2014; Jiang et al., 2019; Malik et al., 2020; NASEM, 2021) and many other controversial governance issues. This goal turns out to be about 50 to possibly higher than 150 times less mitigation in Earth brightening area modification requirements compared to prior full mitigation estimates (Feinberg, 2022).

Most of the current SRM literature is focused on stratosphere aerosol injections (SAI). As this is covered by computer-aided models and there are a lot of concerns in this area, this paper focuses more on Earth-brightening and L1 space Sun dimming solutions. However, overviews of physics goals that may be helpful for SAI are presented. There are many reasons that SAI may not be appropriate for ASG. The primary one is yearly maintenance needs (Barrett et al., 2014; Jiang et al., 2019; Malik et al., 2020; NASEM, 2021). This is less of a problem in SRM methods like Earth-brightening.

An additional topic of discussion in this paper is negative solar geoengineering, the increase of black asphalt roads, roofs, and dark buildings. This bad behavior is more of an issue, as it is closer to the scale of effort needed for yearly ASG mitigation. Therefore, it impedes opportunities for positive ASG advances. This is discussed in Sec. 4.5.

2. Method and Data

2.1. Zero global Warming Growth

In this paper, the approach is to provide key physics-based equations and estimates to achieve just enough solar geoengineering to reverse the potential yearly increase in global warming, which we can refer to as annual solar geoengineering. For example, global warming from 1975 to 2022 was 0.9°C (NASA, 2023). If a status quo annual solar geoengineering approach was applied, the ideal result would be a zero temperature increase. The warming level would stay at 0.9°C. According to Figure 1, the current temperature reversal requirement for ZGWG per year is

T_R=-0.0188°C/year

(1)

2.2. Theory

In this section, key physics-based ASG equations and goals are presented. The numbers used in this section and Sec. 3 can be updated for more complex computer-aided models depending on the reader’s interest and the changing climate. As well, mostly averages in approximating estimates are used. The estimated general requirements to offset a temperature increase in energy units is

T_R=-0.0188°C/year=-0.102Wm^-2/year

(2)

This conversion to energy units is obtained (using the Stephan-Boltzmann relation) as

$$\Delta P_{}=P_2-P_1=\sigma (T_2^4-T_1^4)=0.102W{m}^{-2}$$

(3)

Here T₁ is taken as the average surface temperature of the Earth of about 14.5°C and T₂=14.5 ^oC+0.0188°C=14.519°C.

The SG strategy indicates that reversing the global warming that occurred from 1950 to 2019 having a temperature rise of 0.95°C, would require a reversal of $\Delta P_{\mathrm{Re}v}=-5.1W{m}^{-2}$. This is just the global warming rise from 1950 to 2019 of 0.95°C in energy units where $\Delta P_{\mathrm{Re}v}=-\sigma (T_{2021}^4-T_{1950}^4)=-5.1W{m}^{-2}=-\sigma \left({(288.6K)}^4-{(287.65K)}^4\right)$. Here 287.65K=14.5°C is roughly the average temperature of the Earth. Then we can write for full global warming mitigation (from 1950 to 2019), the reversal equates to (Feinberg, 2022)

$$\Delta P_{}=P_2-P_1=\sigma (T_2^4-T_1^4)=0.102W{m}^{-2}$$

(4)

In this equation, the reverse forcing due to an albedo change of the target is denoted by $\Delta P_T$. We note that increasing the reflectivity of a hotspot surface also reduces its associated greenhouse gas effect. This is estimated in Equation (4)with the 1+f term, using an average re-radiation estimate for f of 62% (Feinberg, 2021; Hartmann et al., 2013). In this equation, we assume that feedback, which is dominated by water vapor, will also reverse. That is, SG reverse forcing causes a cooling effect and cooler air holds less water vapor. In Equation (4), the average feedback value is estimated in 2019 as ${\overline{A}}_F=2.15$ (Feinberg, 2021, 2023a). We note that many other authors have anticipated that water vapor feedback likely has a doubling effect (Dessler et al., 2008; Liu et al., 2018). Note that this value can be written with temperature dependence, and this is discussed in Appendix A.

Then inserting ${\overline{A}}_F=2.15$into Equation (4), we can write

$$\Delta P_T=-\frac{2.38W{m}^{-2} }{(1+f)}=-1.47W{m}^{-2}$$

(5)

This is the estimated recommended goal for a total reversal of global warming from 1950 to 2021. Other updated estimates may be used depending on the reader’s interest. Since in this paper, we are interested in zero global warming annual growth, the ASG requirement for a reversal is approximated as (from Equation (3-5))

$$\Delta P_{ASG}=-\frac{1.47W{m}^{-2}}{5.11W{m}^{-2}}x0.102W{m}^{-2}/Yr=-0.0293W{m}^{-2}/Yr.$$

(6)

This is the estimated main reverse forcing ASG recommendation used in this paper.

2.2.1. Greenhouse Gas Equivalent Reduction from SRM

It is helpful to note the SG advantage in Equation (5). To mitigate the 5.1Wm^-2 in Equation (4), requires an estimated SG change of -1.47Wm^-2 compared to trying to do it with GHG removal which would require the full -2.38Wm^-2 (Equation (5)). This yields a work savings of 0.91Wm^-2 (=2.38Wm^-2-1.47Wm^-2). This is a 38% (=0.91Wm^-2 /2.38Wm^-2) SG advantage (Feinberg, 2021) yielding much higher efficiency compared to CR. That is in SG, fundamentally, we can take into account a 1+f re-radiation reduction in Equation (5), (i.e., increasing the reflectivity of a hotspot surface also reduces its associated greenhouse gas effect).

This is a key SG effective advantage that this paper recommends when working on SG mitigation goals. Therefore, 62% of SRM goes into an additional “GHG equivalent reduction’.

This GHG-albedo effect may also in certain areas, decrease the high levels of possible CO₂ and often water vapor feedback re-radiation that can occur in UHIs in the presence of high heat flux (Feinberg, 2022a, 2023).

Alternately, worldwide negative solar geoengineering equivalently increases the GHG effect by this 1+f factor (Sec. 4.5), and its additional associated water vapor feedback increases. When these average effects are considered in addition to the background climate, urbanization heat fluxes from impermeable surfaces can be problematic on both the local and global levels (Feinberg, 2022a; 2023) as discussed in Sec. 4.5.

2.2.1. Area estimates for Annual Solar Geoengineering

To estimate the Equation (6) area modification requirements for a -0.0293Wm^-2 reversal, the approach is to use the following solar geoengineering estimate (Feinberg, 2022) given by

$$\Delta P_T=\Delta P_{ASG}=-\frac{S_o}{4}\frac{A_T}{A_E}{X}_C{X}_O{X}_S{H}_T\left[(\Delta {\alpha }_T)\right]$$

(7)

This SG physics-based equation indicates that in SRM, as anticipated, the reversal is proportional to the average solar energy over 24 hours, $S_o/4$, the fractional target area A_T relative to the Earth’s area A_E, the amount of irradiance Xc falling on the target with global averages of 47% (Hartmann et al., 2013), the amount of outgoing reflected transmission from the target $X_O$(primarily used in Earth brightening application, see Sec. 3.1), a space irradiance factor $X_S$(see Sec. 3.2), and an UHI de-amplification factor $H_T$. These are detailed below. In addition, the albedo change is $\Delta {\alpha }_T={{\alpha }^{\prime }}_T-{\alpha }_T$, where the target’s albedo is given by ${\alpha }_T$, and its increase is denoted by ${{\alpha }^{\prime }}_T$.

The space irradiance factor X_S introduced is generally taken as unity. However, for space mirror application, the optimal L1 point rotates around the Sun with the same angular speed as the Earth, thus allowing constant shading. Then the irradiance shading occurs 24 hours 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)).

This equation also provides provisions for targets in urban heat island (UHI) areas which can have microclimate de-amplification effects denoted by H_T (Feinberg, 2020, 2022a). For example, in UHIs, the solar canyon effect amplifies warming when buildings reflect light onto pavements amplifying heat at the surface. Other amplification issues can include re-radiation due to the increase in local CO₂ GHGs, local water vapor feedback, temperature inversions, loss of wind and evapotranspiration cooling, increases in solar heating of impermeable surfaces from building sides, pavements heat fluxes, and so forth (Feinberg, 2023). Some of these 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 (Zhou et al., 2015; Feinberg, 2020, 2023).

3. Results

3.1. Earth Brightening Transmission Loss

In Equation (7), the X_O factor provides an estimate of the outgoing transmission of reflected short-wave radiation and is applicable in Earth brightening studies. When taken as unity, the results for Equation (7) in Earth brightening applications yields the minimum required area to achieve a specific ASG reversal goal. In Earth brightening, there are several eventual losses that can occur for the outward short wavelength transmission through the upper atmosphere. The primary ones are clouds and aerosols that can impede the reflected sunlight (Smoliak et al., 2022). These losses in the upper atmosphere areas can affect the mean lower surface air temperature (MSAT).

The incoming solar irradiance X_C in this paper is taken as 47% due to clouds as indicated in the IPCC global mean Earth energy budget assessment (Hartmann et al., 2013). However, one might anticipate that the outgoing transmission from an Earth-brightened surface has a higher transmissibility probability than the incoming irradiance. For example, given that the incoming 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 should be less. One helpful estimation method is to use a Bayesian approach. Using this prior information, the Bayesian result indicates that the probability of clear transmission is 78%. This is estimated in Appendix B. Therefore the minimum required area obtained in Equation (7) for Earth brightening, is adjusted in this paper using a Bayes correction X_O-Bayes=0.78 factor.

Readers may wish to model this further for specific areas and adjust this factor using other probability methods and factors (such as aerosols) to improve transmission estimates. One should note that it may not be well-known how transmission loss affects the MSAT. As well there are areas for Earth brightening where SRM is optimal, such as near the equator yielding higher irradiance (Smoliak et al., 2022).

3.1.1. Pavement Example

As an example, consider the required area for worldwide cool pavements. We can consider an average asphalt pavement albedo of about ${\alpha }_T=0.1$, and using cool road methods, estimate an increase for a target pavement area with albedo of ${{\alpha }^{\prime }}_T=0.4$. Then considering an average irradiance of $X_C=0.47$, with $X_S=1$, $H_T=1$, and ${\overline{A}}_F=2.15$, and using a 50% ASG reversal goal, the requirement is

$$\begin{array}{l}\Delta P_{ASG\_50\%}=-\frac{S_o}{4}\frac{A_T}{A_E}{X}_C\left\{\begin{array}{l}{X}_{O-Bayes}\\ X_{O-Minimum}\end{array}\right\}{X}_S{H}_T\left[({{\alpha }^{\prime }}_T-{\alpha }_T)\right]=-340W m^{-2}\frac{A_T}{A_E}0.47\left\{\begin{array}{l}0.78\\ 1\end{array}\right\} \left[0.3\right]=-\frac{0.0293}{2}W{m}^{-2}/Yr\\ =-0.01465W m^{-2}/Yr.\end{array}$$

(8)

Solving we obtain the SG target area percentage for half of ZGWG yielding a minimum and Bayesian estimated requirement of

$$\frac{A_T}{A_E}=\left\{\begin{array}{l}0.039\% per year{ }_{Bayes}\\ 0.0306\% per yea{r}_{Minimum}\end{array}\right.$$

(9)

The pavement modification area that needs to be cooled for a $\Delta {\alpha }_T=0.3$change equates to

$$A_T=\left\{\begin{array}{l}0.00039 per year{ }_{Bayes}\\ 0.000306 per yea{r}_{Minimum}\end{array}\right.x196.6E6m{i}^2=\left\{\begin{array}{l}77,024 m{i}^{2}per year{ }_{Bayes}\\ 60,079 m{i}^{2}per yea{r}_{Minimum}\end{array}\right.$$

(10)

This yields an equivalent minimum radius of 138 miles. This result is summarized in Section 3.4. This example illustrates the SRM area modification requirements for ASG. Other values may be used depending on the reader’s interest.

For pavements that are cooled with $A_F=4.3$ (see Equation (A-4)), the requirement for area modification is much less according to Appendix A. In this case, it is likely that $\Delta {\alpha }_T>0.3$. Letting $\Delta {\alpha }_T=0.5$ for this example, the area modification is reduced from Equation (10) to

$$A_T=\left\{\begin{array}{l}23,091 m{i}^{2}per year{ }_{Bayes}\\ 18,011 m{i}^{2}per yea{r}_{Minimum}\end{array}\right.$$

(11)

This yields a reduced equivalent minimum radius of 76 miles. This result is also summarized in Sec. 3.4. Note that to achieve these results; the goal for 50% mitigation is reduced by more than half.

If we could do full global warming SG mitigation per the equivalent cool pavements in Equation (10) but with $\Delta P=1.47W{m}^{-2}$, $\Delta {\alpha }_T=0.3$, and $A_F=2.15$, the area required would be about 6 million square miles. In comparison, this ASG requirement where $\Delta P_{ASG}=-0.0293W{m}^{-2}/Yr.$, $\Delta {\alpha }_T=0.5$, and hotspot mitigation estimate for $A_F=4.3$ (see Equation (A-4)), the resulting area reduction is 36,000mi². The ASG area factor is reduced by about 160 compared to full SG mitigation.

3.2. L1 Space Shading Estimates

We can translate an A_T area modification requirement to a solar reflective space disc mirror-type shading application. In this case, we note that most authors consider the Sun-Earth L1 position as optimum. For the irradiance in space mirror shading estimation, we can take X_C=100% and X_S=4 (as discussed above). Sun-shading can effectively translate to changing a target on Earth’s reflectivity to ~100% from the average Earth’s albedo of 30%, so that $\Delta {\alpha }_T$=0.7. Using these parameters and our 50% ASG goal, Equation (7) is

$$\Delta P_{ASG-SpaceMirror}=-\frac{X_S{S}_o}{4}\frac{A_T}{A_E}{X}_C\left[({{\alpha }^{\prime }}_T-{\alpha }_T)\right]=-1361W{m}^{-2}\frac{A_T}{A_E}(1)\left[(0.7)\right]=0.01465W{m}^{-2}$$

(12)

Solving we obtain the ASG percentage for half of ZGWG of

$$\frac{A_T}{A_E}=0.0015\% per year (50\% mitigation)$$

(13)

This yields a disc of about 7843 km² (radius 50 km). Results are summarized in Sec. 3.4.

Note when we talk about space mirrors with a value for A_T/A_E, this value becomes the required percent of incident solar radiation that is needed to be reflected away from the Earth to achieve a mitigation goal in Equation (12).

3.3. Annual Stratospheric Injection Estimates

Results appear quite challenging to meet ASG area modification requirements (summarized in Sec. 3.4) for both Earth brightening or space mirror size estimates. Unfortunately, there is no easy solution. Although this paper does not focus on SAI as it is often assessed with computer climate models, it is helpful to overview the ASG goals and estimated differences compared to full GW mitigation. Much has been written about an alternate less expensive Sun-dimming temporarily reflecting particle method such as SO₂ injected into the stratosphere (Keutsch et al., 2020; Keith et al., 2016, Tollefson, 2018; Ferraro et al., 2015; Dykema et al., 2014; Crutzen, 2006). Here SO₂ 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 (2015) where the reduction in radiation at the top of the atmosphere $\Delta R_{TOA}$ is

$$\Delta R_{TOA}=-65W{m}^{-2} \exp -{(2246Mt(S)y{r}^{-1}/I_{S{O}_2})}^{0.23}$$

(14)

The actual injection rate $I_{S{O}_2}$(in units of MT(S)/year - megatonnes of SO₂ per year) for full GW reduction according to Equation (6) requires a goal of 1.47Wm^-2. To provide the first-year annual requirements rather than full mitigation, the injection rate using Equation (14) is 32x less as shown in Table 1. Here full climate mitigation requires an injection of 6.9MT(S)Yr^-1 for a goal of 1.47Wm^-2, whereas, for the first year, the ASG goal is reduced to an injection of 0.216Mt(S)Yr^-1 for a 0.01465 Wm^-2 50% reduction goal. Unfortunately, depending on the SO₂ dissipation per year, this would need to be possibly doubled in the second year, tripled in the third year, and so forth for ZGWG.

The stratosphere area modification required has not been fully established. Initial assessments appear problematic as outlined in Appendix C due mainly to the reflection efficiency. Estimates are often equated to one Pinatubo eruption which may be unreliable.

3.4. Overview of Estim ates

Table 2 provides an overview of the needed estimates based on the suggested inputs to mitigate the annual global warming growth trend of 0.019°C/year for ASG. The results in Table 2 are divided, with Earth brightening area modification of surface land and half to space-type application. The objective for each is to reduce the incoming solar energy by -0.01465Wm^-2 per year for 50% annual GW mitigation. Therefore, any two combinations would ideally meet the ASG requirements. Note that in Table 2, the H_T value, as an example, is taken as 3 for UHI areas and conservatively 2 for Earth mirrors used on urban rooftops as often implemented by project MEER (2023). This H_T average estimate can vary depending on the UHI microclimate (Feinberg, 2023). In the case of something like sea-type floating mirrors, H_T=1, also is shown in Table 2.

Note the ASG requirement (Equation (6) compared to full mitigation (Equation (5) is ~50 times (=1.47Wm^-2/0.029Wm^-2) reduced in energy flux requirements and area modification (per Equation (7)). For example, desert treatment is reduced from the author’s initial estimate of 1.0% (Feinberg, 2022) to 0.010% for 50% annual mitigation in Table 2. Therefore the areas in ASG mitigation are in general a factor of 50 times smaller which also minimizes any potential circulation concerns (Barrett et al., 2014; Jiang et al., 2019; Malik et al., 2020; NASEM, 2021). Table 2 suggests several options including multiple combinations that can be considered in annual mitigation. For hotspot cooling shown in Table 3, this has the potential to reduce area requirements by a factor of over 150 (per Equation (11).

4. Discussion

4.1. Annual Solar Radiation Management

4.1.1. Annual Solar Geoengineering Allocation by Country Area

To aid solar radiation management, we can allocate goals amongst countries by their wealth. For example, using the total household wealth by county the United States and England’s requirements would be 31% and 3.5% (Wikipedia, 2022) respectively. Then the area allocations, for example, with surface albedo change $\Delta {\alpha }_T=0.3$ in Equation (10) would be:

• U.S. mitigation =31% x 60,000 mi²=18,600mi²/Yr or 51mi²/day
• England mitigation =3.5% x 60,000 mi²=2100mi²/Yr or 5.75mi²/day

Such goals may be obtainable with mixed technology (see Sec. 4.2).

Costs associated with solar geoengineering in space shading can similarly be divided.

4.1.2. L1 Space Particle Clusters

Another similar idea that may merit investigation is to use space particle clusters instead of space mirrors, at or near the L1 Sun-Earth region. This idea has been suggested in the past (Mautner , 1991). A cluster of particles such as calcium carbonate, SO_2, or moondust (Bromley et al., 2023) 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 (~2.7K) and studies could be done to estimate issues.

We can estimate the requirement for solar reduction for an ASG value using a transmissibility method (Feinberg, 2022). For example, considering the Earth’s solar absorbed radiation estimate as $\frac{S_o}{4}(1-.3)=238.175W m^{-2}$ a required absorption reduction estimate can be found for Equation (6) from

$$\frac{S_o}{4}(1-.3)=238.175W m^{-2}-0.0293W m^{-2}=238.1457W m^{-2}$$

(15)

Solving yields S_o=1360.833Wm^-2. Then one finds 0.167Wm^-2 (=1361 Wm^-2 -1360.833Wm^-2) is the reduction required for the incoming solar radiation.

If we measure the transmission of the incoming solar radiation above and below the particle treatment, the transmissibility (TR) from sun-dimming should be (Feinberg, 2022)

$$TR=1360.833W m^{-2}/1361W m^{-2}=99.9877\%$$

(16)

Measuring the transmissibility is likely a helpful method to assess the injection amount. Note, that we can also use similar measurement methods for SAI.

4.2. Earth Brightening Advances

Earth brightening SG’s state-of-the-art potential is a lot higher today. Drone technology, for example, has had major advances in painting buildings (Maghazel and Netland, 2019) and agriculture spray methods (Klauser and Paushinger, 2021). For example, consider the US and England’s goals for Earth brightening in Sec. 3.4 in terms of area per day

• U.S. Mitigation Goal Earth Brightening is 51 mi²/day
• England Mitigation Goal Earth Brightening is 5.75 mi²/day

A typical two-gallon per acre agriculture drone can spray about 1 mi²/day (Agri Spray Drones, 2023) which includes refills. Then if we assume paint drones can be designed with similar capabilities, this requires the

• U.S. Mitigation Goal of about 51 drones/day
• England Mitigation Goal of about 6 drones/day

Although paint drones are not equivalent and rated similar to agriculture drones, technology improvements likely should be able to provide this type of capability for paint drones. Given AI technological advances, improvement in Earth-brightening drones, while difficult, is likely more feasible than one might think. However, paint areas have to be made available. Nevertheless, this technology should be part of the solution. The full solution will likely require a mixture of ASG Earth brightening technologies (Sec. 4.4).

New ultra-thin bright white paint surface treatments (98.1% reflective and half as thick) have been developed to help cool the Earth (Li et al., 2021; Felicelli et al., 2022). Possibly other technologies could be developed specifically for the Earth-brightening of buildings, streets, desert areas, mountain tops, and UHI areas. Possibly an agency like SpaceX or NASA could vastly improve AI drone use for SG implementation. AI technology could allow for 24-hour-a-day drone ASG work with automatic target brightening, refilling, and target recognition. Furthermore, studies could help assess the best strategies to try and improve coverage areas including mountain ranges since mountains cover about 24% of the Earth. Brightening mountain areas could also increase condensation and snowfall as was done on the Peruvian Andes mountain tops (Grossman, 2012) which can increase snowfall and spring runoff to reservoirs in drought-prone areas.

Annual mitigation using Earth mirrors, as suggested by project MEER (2023), has several advantages. Mirrors can be placed in areas of high irradiance, yielding a likely large albedo change, and when used in city areas on roofs, H_T>1. These reduce the Earth’s annual SG area requirements per Equation (7). Alternately, it may be of interest to use something like floating sea mirrors or particles which would yield a high albedo change as exemplified in Table 2.

One might question the practice of painting the Earth a light color. Yet, we continue to accept negative solar geoengineering (Sec. 4.5). Unfortunately, we may already be at the point where we are faced with these types of difficult decisions.

4.3. Natural Hotspots

Natural hotspots like deserts and mountain areas are likely good ASG targets to consider to find ways to cool them to help reduce global warming. They may cover a significant area and are relatively free from urbanized regions. Similar to pavements and UHIs, natural hotspot cooling would likely help reduce atmospheric water vapor feedback. As well certain regions are optimal such as the tropics and subtropics (Smoliak, 2022). Certainly, natural hotspots would be highly controversial geoengineering targets. Nevertheless, their amplification of heat and its effect on the Earth’s temperature will likely be related to their area and temperature differences compared to the global ambient. Some examples of such hotspots include:

• Flaming Mountains, China
• Bangkok Areas in Thailand (with planet’s hottest city)
• Deserts
• Badlands of Australia
• Tropics and Subtropics

4.4. Mixed Planning for Annual Global Warming Mitigation

A mixed plan for annual global warming mitigation (AGWM) of -0.02°C/year can reduce the burden of relying on any one method which would reduce governance issues and technological unforeseen problems. In addition to ASG, the author has estimated that half of the annual warming increase is due to population growth (Feinberg, 2023a). That is under zero population growth, we would anticipate a reduction to a 0.01°C/year increase. A mixed plan should include ASG with ocean reflective particles/floating mirrors, AI drone painting, space mirrors or clusters as well as the traditional ideas of stratospheric aerosol injection, marine cloud brightening, and cirrus cloud thinning. Non-SG efforts in the area of population development supported by multi-actor governance would be extremely helpful according to this recent study (Feinberg, 2023a). The importance of ASG and AGWM is key to the success and our ability to address the immediate GW yearly trend increases occurring. This effort should also include a strong effort to reduce negative solar geoengineering as well.

4.5. Worldwide negative solar geoengineering

ZGWG is challenging enough. However, the problem of yearly increases in black asphalt roads, rooftops, and even dark-colored cars worldwide makes the task harder. Although many issues like black electric vehicles and gas cars do not contribute significantly to global warming, it encourages bad behavior for poor solar color choices. This illustrates the lack of SG awareness which is highly problematic for an increasing population (Feinberg, 2022a). As a suggestion, restricting cars to light colors would go a long way in greatly increasing such awareness.

In terms of global warming, these issues are a form of ‘negative solar geoengineering’. Currently, it is estimated that roads occupy about 14% of all manmade impermeable surface areas (Huang et al., 2022) of which impermeable surfaces occupy an estimated 0.26% of the Earth (Sun et al., 2022). Then the estimated area of the Earth occupied by roads is small, about 0.0364%. This is a bit higher compared to Equation (9) estimated requirement for area modification but illustrates the negative ASG interference issue. By comparison to the estimated total 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 worldwide negative solar geoengineering. Feinberg (2023) estimated that 1.1% of global warming is likely due to asphalt roads using only the average feedback factor which if brightened similar to concrete with an albedo increase of 5, could have reduced global warming by 5.5%. An MIT pavement study (MIT, 2020) concluded that in all U.S. 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. 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 (Wikipedia, 2021).

Feinberg (2022) estimated that heat from asphalt roads and roofs can produce 7.5 times more energy in heat pollution per acre than a solar power plant where studies have found they average about 0.33GWh per acre per year (Ong, 2013). Furthermore, a gallon of gas equates to 33.6 kWh (Wikipedia, 2021). Then this heat pollution equates to 74,200 gallons of gasoline energy per year per acre.

This illustrates the enormous energy in an acre of asphalt heat pollution and how black roads and roofs make significant incremental warming contributions.

Negative solar geoengineering also has the potential to increase local and global water vapor feedback as it creates increases in warm air which can hold more water vapor. Hotspots can increase water vapor feedback dramatically as illustrated in the assessment in Appendix A and 3.1. As discussed previously, Zhao et al. (2014) observed that UHI temperatures increase in the daytime (ΔT) by 3.3K more in humid compared to dry climates. A primary issue in humid UHI areas is the use of black asphalt which, given the worldwide urban heatwave problems, this author feels should be banned in most cases. The warming consequences of black asphalt are not fully understood, but it is bad for the local environment and is well-documented for many problems, especially in concentrated urban areas where heatwaves cause related health issues (MIT, 2020; EPA, 2005).

5. Conclusion

In this paper, estimates are provided for annual solar geoengineering requirements. The results illustrate many challenges. However, results show higher feasibility for annual solar geoengineering modification to help mitigate global warming. This is due to reductions in goals that lead to a factor of 50 to possibly over 150 times less area modification requirements compared to full SG mitigation. This minimizes circulation concerns and many other controversial issues.

Many recommendations are made in this paper. These include the use of ASG and the calculations, the use of mixed technology (Sec. 4.4) for ASG Earth brightening modification, the suggested method of using space clusters that may be highly useful, and UHI use of the H_T value in Table 2. Results in general point to challenging but feasible solutions. Suggestions are provided for solar radiation management using wealth allocations by country for Earth brightening to improve feasibility (Sec 4.1).

It is pointed out that for ASG to be effective; it is helpful to address many global warming issues including the ongoing negative solar geoengineering especially the practice of black asphalt use. We should not condone the bad behavior of dark color choices whether it be in automotive or the construction practices of roads, houses, and buildings. It also impedes the efforts of positive solar geoengineering. Such issues should be addressed in worldwide climate meetings.

It is likely important to have a mixed plan that should include AGWM that could include in addition to ASG the likely need for population development supported by multi-actor governance to reduce warming due to anthropogenic effects.

There is little time left to meet the IPCC suggested 1.5°C goal as shown in Figure 1. The longer we delay in implementing an ASG program, the more unacceptable our status quo will be due to increases in global warming reducing our options. This paper provides improved solar geoengineering feasibility with annual mitigation goals that can greatly supplement carbon removal and reduction efforts.