Albedo Solution to Global Warming In the Control of CO 2 , Hotspots, & Hydro-Hotspots Forcing and Their Albedo-GHG Interactions

Although global warming (GW) albedo solutions are currently not being used worldwide, they are anticipated to be vital as a significant supplement to CO 2 reduction efforts. Conservatively, albedo surface controls are seriously lacking. Furthermore, without albedo solutions there is a reasonable probability, as many authors have suggested, for a 1.5 o C-3 o C GW increase, which is expected to be enough for a tipping point to occur. An important aspect to bring to the attention of policymakers is the albedo-greenhouse gas (GHG) interactions. We model this interaction which has a major influence in assessing climate change. For example, modeling is used to help exemplify the amount of albedo surface area modification required to mitigate CO 2 GW effects. Additionally, albedo controls are the only way to mitigate impermeable hotspots and hydro-hotspots surfaces that have increased at an alarming rate. We illustrate their growth rate; discuss their historical recognized significance and known correlations to climate change. Our results are directed toward influencing policymakers on the unique practical aspects of albedo solutions and their imminent need.


Introduction
Although albedo solutions have been recommended in helping to mitigate climate change [1-12] and likely a vital supplement to CO 2 efforts, little work is being done in this area. There have been a number of proposed albedo solutions, both surface and atmospheric methods [1, 4-10] to reduce climate change. Such techniques have not been widely adopted by governments [9], typically given little funding consideration, and were not part of the Paris Climate Accord [13].
In this paper, we describe the albedo-GHG interactions that applies to three observed forcing issues and using historical information, model its strength and discuss its unique role for potential albedo solutions in climate controls. This provides guidance to policymakers on the increase strength of albedo solutions that are optimum as the only controls in mitigating all three types of forcing. Thus, this interaction strength is important for both solar surface and atmospheric geoengineering in assessing such climate controls and directing climate policy. The cumulative effect of widespread select [11] albedo-GHG mitigation surface areas is anticipated to have significant influence both to the Earth's solar surface heat absorption and associated GHG re-radiation power. The albedo solution has also been projected as vital in preventing a 1.5 o C-3 o C rise and preventing a tipping point [1][2][3][4][5][6][7][8]. We are hopeful this work will help contribute to influencing climate policy and related funding.

Method
It is helpful to describe the albedo-GHG interactions and associated historical information for three types of observed GW forcing issues: • CO 2 (ignoring other GHGs) • Hotspots (such as Urban Heat Islands (UHIs) and Roads) • Hydro-hotspots We term a hydro-hotspot [14] as a solar hot impermeable surface common in cities and roads that creates atmospheric moisture in the presence of precipitation. This moisture increase can act as a local greenhouse gas. A possible mechanism includes warmer expanded air-surface temperatures due to the initial hotspot, and then during precipitation, evaporation increases the local atmosphere humidity GHG (as warm air holds more water vapor). The level of hydro-hotspot significance in climate change is currently unknown.
However observations of this effect are reasonably well established. For example, Zhao et al. [15] observed that UHI temperatures increase in daytime ΔT by 3.0 o C in humid climates but decrease ΔT by 1.5 o C in dry climates. They found a strong correlation between T increase and daytime precipitation. Their results concluded that albedo management would be a viable means of reducing T on large scales.
A major benefit of the albedo solution often overlooked is the interaction strength with the greenhouse gas mechanism which arises from the simple fact that • Increasing the reflectivity of a hotspot surface reduces its greenhouse gas effect • Decreasing the reflectivity of a hotspot surface increases its greenhouse gas effect • The Global Warming (GW) change associated with a reflectivity hotspot modification is given by the albedo-GHG radiation factor having an approximate inherent value of 1.6 (Sec. 2.2).
This additional benefit means that albedo solutions [1-12] are proficient, and the only climate control having strong distinct mitigation interactions with all three forcing mechanisms. Such simple knowledge could be helpful in educating policy makers on realizing the value of the albedo solution.
• In Section 2.2, we detail this 1.6 average albedo-GHG interaction strength for solar geoengineering and provide estimates of this additional GHG effect in two different time periods, 1950 and 2019. • In Section 4, we specifically show how practical the albedo surface solution is for even mitigating increases in CO 2 levels (see also Eq. 23).
It is important to note that the albedo-GHG heat exchange is often dominated with water vapor and clouds GHG, 36-72% compared with CO 2 GHG 9-26% [16]. This provides a possible breakdown of the GHG power, but not the forcing strengths [17,18]. Due to this interaction, albedo solutions would decrease risks of GHG effects, hydro-hotspot forcing as well as the possible significance of hotspots. Since hydro-hotspots create higher warming impact in humid climates, these select widespread urban surface areas generally have higher GW impact and mitigating albedo surface solutions in these regions would be desirable.
The significance of hotspot forcing has been highly controversial in global warming as it relates to UHIs. Measurements and their assessments have been described by a number of authors [19][20][21][22][23][24][25][26][27][28][29] and more recently in modeling [11,30]. One key work, often referred to is by McKitrick and Michaels [19,20] concluded that about half the reported warming trend in global-average land surface air temperature in 1980-2002 resulted from local land-surface changes (i.e. urbanization and other manmade surface changes). . Although this study has been severely criticized especially by Schmidt [31] and defended successfully by Mckitrick [20] over many years, the research still remains apparently difficult to accept. Some acceptance finally appeared in a later IPCC report [32] but still disputed (without peer review) the extent of influence reported. Nevertheless, these results [19][20][21][22][23][24][25][26][27][28][29], completed over 10 years ago, still have not been influential for implementing worldwide "surface" albedo controls and solutions. For example, such solutions were not part of the Paris Climate Accord [13]. Therefore, valuable time has been lost as many authors feel [1-12] that supplementary worldwide albedo controls and solutions should be added to the accord as a more conservative approach.
In modeling recently, by the author [11,30], UHI amplification factors were estimated (for solar area, heat capacity, surface albedo, canyon effect, etc.) with the help of UHI footprint and dome estimates that extended the UHI effect beyond its own area and applied to albedo modeling. Results showed feasible support for these authors' findings [19][20][21][22][23][24][25][26][27][28][29] that UHIs can significantly contribute to GW with one model showing 4.5%-38% [30] and a second model showing 6%-82% [11] of GW could be due to UHIs. These large variations are due to uncertainties in UHI amplification factors and estimates of how much of the Earth is urbanized.
More importantly, whether or not hotspots are a significant source in climate change is independent of the fact that surface and atmospheric albedo controls can provide strong aid in reducing climate change and the practicality of surface solutions has been demonstrated by the author [11] and also described in Sec. 4. Therefore, implementation of surface and/or atmospheric albedo controls and methods should be an added focus in obtaining appropriate policy.

 Policymakers can recommend surface and atmospheric albedo controls conservatively for serving two purposes: 1) In the event that hotspots and hydro-hotspots are truly significant and by 2) Offset CO 2 GW effects through enhanced albedo (high reflectivity) solutions (See Sec. 4 for a CO 2 albedo mitigation example)
Little is understood about hydro-hotspot GW forcing significance. However, since the industrial revolution, impermeable surfaces have increased at a high rate (like CO 2 ) correlated to population growth and thus, GW increases [30]. This is illustrated in Figure 1 that shows correlations to both GW and population growth to natural aggregates that are used to build cities and roads. Although no definitive conclusion can be made on GW significance, it is important to point out the growth rate of impermeable surfaces, as they have a high level of concern by many authors in numerous issues related to climate change [33][34][35][36][37][38][39]. In terms of amplification effects, hydro-hotspots would likely have both local water-vapor GHG interactions and the additional 1.6 warming influence on GW (with UHI heat capacity also playing an important role).

 Policymakers should recommend world-wide surface albedo hotspot controls in the construction of UHIs, rooftops, roads, parking lots, car colors, and so forth. Methods and studies are needed to provide implementing optimum solutions [1-11].
Lastly, one can justify the need for albedo controls due to the:  slow progress reported in CO 2 reduction  yearly increases in reports on large desertification and deforestation occurring [43]  lack of hotspot and hydro-hotspot surface albedo controls that are continually increasing  threat of the tipping point occurring as we are running out of time Regarding the interactive strength, it is helpful to determine the geoengineering albedo-GHG re-radiation inherent 1.6 factor [11] and its change since the pre-industrial revolution. Such values relate to the effective emissivity constant of the planetary system. Results will also help to demonstrate how albedo solution can offset CO 2 forcing (see Sec. 4) for policymakers. Therefore, assessment helps to strengthen interests in the albedo solution.

Albedo-GHG Radiation Factor
In geoengineering the albedo-GHG interaction requires a different approach compared to CO 2 doubling theory. When initial solar absorption occurs, part of the long wavelength radiation given off is re-radiated back to Earth. In the absence of forcing we denote this fraction as f 1 . This presents a simplistic but effective model and T s is the surface temperature, P pre-industrial , P  , and P GHG are the total pre-industrial warming, albedo warming and GHG warming in W/m 2 , respectively. As one might suspect, f 1 turns out to be exactly  4 in the absence of forcing, so that f 1 is a redefined variable taken from the effective emissivity constant of the planetary system. We identify 1+f 1 =1.618034 (see Section 2.2) as the pre-industrial albedo-GHG radiation factor (Table 1).
We identify the re-radiation 2019 having a value of 1+f 2 =1.6276 (Table 1). That is, in 2019, due to increases in GHGs, an increase in the re-radiation fraction occurs In this way f 2019 =f 2 is a function of f 1 . The RHS of Eq. 2 indicates that   ≈  (see verification results in Eq. 18 and 19). We find that f=0.0096 is relatively small compared to (1+f 1 ) which we show can fairly accurately be assessed in geoengineering.

Estimating the Pre-industrial Albedo-GHG Interaction Strength
In geoengineering, we are working with absorption and re-radiation, we define Note that when  4 =1, there are no GHG contributions. We note that f, the re-radiation parameter equals 4 in the absence of forcing.
We can also define the blackbody re-radiated by GHGs given by some fraction f 1 such that Consider f=f 1 , in this case according to Equations 5 and 6, it requires This dependence leads us to the solution of the quadratic expression This is very close to the common value estimated for  and this has been obtained through energy balance in the planetary system providing a self-determining assessment. In geoengineering we can view the re-radiation as part of the albedo effect. Consistency with the Planck parameter is shown in Section 3.1. We note that the assumption f=f 1 only works if planetary energy is in balance without forcing. In the next section, we double check this model in another way by balancing energy in and out of our global system.

Balancing Pout and Pin in 1950
In equilibrium the radiation that leaves must balance P  , the energy absorbed, so that   This is consistent, so that in 1950, Eq. 9 requires the same quadratic solution as Eq. 8. It is also apparent that The RHS of Eq. 11 is Eq. 8. This illustrates f 1 from another perspective as the fractional amount of total radiation in equilibrium. As a final check, the application in the Section 3, in Table 1, illustrates that f 1 provides reasonable results.

Re-radiation Model Applied to 2019
In 2019 due to global warming trends, to apply the model we assume that feedback can be applied as a separate term and we make use of some IPCC estimates for GHG forcing as a way to calibrate our model. In the traditional sense of forcing, we assume some small change to the albedo and most of the forcing due to IPCC/NOAA estimates for GHGs where Here, we assume a small change in the albedo denoted as P  ' and f 2 is adjusted to the IPCC GHG forcing value estimated between 1950 and 2019 of 2.38W/m 2 [18]. Although this value does not include hydrohotspot forcing assessment described in the introduction, it possibly may be effectively included since forcing estimates also relate to accurate GW temperature changes. Then the feedback amplification factor, is calibrated so that T S =T 2019 (see Table 1) yielding A F =2.022 [also see ref. 44]. The main difference in our model is that the forcing is about 6% higher than the IPCC for this period. Here, we take into account a small albedo decline of 0.15% that the author has estimated in another study due to likely issues from UHIs [30] and their coverage. We note that unlike f 1 , f 2 is not a strict measure of the emissivity due to the increase in GHGs.

Results Applied to 1950 and 2019 with an Estimate for f 2
In 1950 we will simplify estimates by assuming the re-radiation parameter is fixed and reasonable close to the pre-industrial level of f 1 =0.618034. Then, to obtain the average surface temperature T 1950 =13.89 o C (287.04 o K), the only adjustable parameter left in our basic model is the global albedo (see also Eq. 1). This requires an albedo value of 0.3008 (see Table 1) to obtain the T 1950 .=287.04 o K. This albedo number is reasonable and similar to values cited in the literature [45].
In 2019, the average temperature of the Earth is T 2019 =14.84 o C (287.99 o K) given in Eq. 15. We have assumed a small change in the Earth's albedo due to UHIs [30]. The f 2 parameter is adjusted to 0.6276 to obtain the GHG forcing shown in Column 7 of 2.38W/m 2 [18]. Therefore the next to last row in Table 1 is a summary without feedback, and the last row incorporates the A F =2.022 feedback amplification factor.
as modeled. We also note an estimate has now been obtained in Table 1 for f 2 =0.6276, A F =2.022, and P Total_Feedback_amp =5.12W/m 2 .

Model Consistency with the Planck Parameter
As a measure of model consistency, the forcing change with feedback, and resulting temperatures T 1950 Here R OLW is the outgoing long wave radiation change. We note these are very close in value showing miner error and consistency with Planck parameter value, often taken as 3.3W/m 2 / o K.
Also note the Betas are very consistent with Eq. 8 for the two different time periods since from

Hotspot Versus GHG Forcing Equivalency
From Equation 1 and 12 we can estimate the effect in a change in hotspot forcing as  

Discussion
From Table 1 we used two key forcing changes that are responsible for climate change since 1950 • f and  We know that  can only be mitigated by albedo controls. In Table 1, the albedo effect used was fairly minimal, contributing only a 0.15 W/m 2 (6%) to the warming. However, if we were to implement a worldwide albedo surface solution of select areas, for example, Table 2 lists the albedo amplification factors that can potentially be realized. Here, selecting surfaces with high heat storage capacity, such as buildings (or possibly mountains) are likely good strategic targets. These areas are a function of heat capacity, surface albedo, mass, temperature storage, solar irradiance and humid environments, which can yield amplification factors between 3.1-8.4 (averaging 6) [11,30]. These estimates are not unreasonable for UHIs [11]. As well there are atmospheric albedo solutions [1-6].
Consider how this applies to Table 1 GHGs. In Table 1, f is controlled by GHGs assumed to be dominated by CO 2 forcing (recall that part of this may actually intrinsically include hydro-hotspots which are mitigated only by albedo methods). The reverse forcing albedo reduction to mitigate f when considering these albedo amplification factors applied to Table 2 The amount of Earth that would have to be modify with reflectivity albedo increase between 4-7.5 has been assessed by the author [11] for this particular problem, yielding a  Modification area of about 0.2% to 1% of the Earth, depending on the selected target types Therefore, we note by employing albedo solutions, reverse cooling results would help compensate for CO 2 forcing, and conservatively include hotspots and hydro-hotspots mitigation. In the event that hotspots and hydro-hotspots are truly significant, this would be the optimum approach. This helps in clarifying the benefit and need for including albedo controls and solutions in climate change policies.

Summary
In this paper we have focused on the albedo-GHG interaction to show how the albedo solution, could be a vital method to help mitigate global warming when three types of forcing issues are considered. Such implementation would greatly supplement CO 2 solutions. Results can improve the speed in helping to prevent a tipping point from occurring (especially with desertification and deforestation occurring). Furthermore, analysis showed that the surface albedo solution can effectively compensate for CO 2 forcing without having to modify an unreasonable area of the Earth. As well, atmospheric albedo solutions are available.
The GHG-albedo interaction strength due to the re-radiation factor has been fully described in application to two time periods. Results show that the re-radiation factor for 1950 when taken as a pre-industrial value is 1.6181 which is directly given by  4 (the emissivity constant of the planetary system). However in present day, this factor has increase to 1.6276 due to the increase in GHGs. In order to make the present day assessment, we assumed a small planetary albedo decrease from 1950 of 0.15% and GHG forcing of about 2.38 W/m 2 (in accordance with IPCC estimates). In terms of geoengineering albedo modification estimates, the interactive value of 1.62 should to be a good approximation.
Below we provide suggestions and corrective actions for policymakers to consider:  Modification of the Paris Climate Agreement to include albedo controls and solutions  Albedo guidelines for both UHIs and roads similar to on-going CO 2 efforts  Guidelines for future albedo design considerations of cities  Government money allocation for geoengineering and implement albedo solutions  Recommend an agency like NASA to be tasked with finding applicable albedo solutions and implementing them  Recommendation for cars to be more reflective. Although world-wide vehicles likely do not embody much of the Earth's area, recommending that all new manufactured cars be higher in reflectivity (e.g., silver or white) would help raise awareness of this issue similar to electric automobiles that help improve CO 2 emissions.